From 566e869467928baf8c5ae119552864cdbbfbf9d9 Mon Sep 17 00:00:00 2001 From: AlejGarcia Date: Tue, 20 Dec 2016 15:37:56 -0800 Subject: [PATCH] Numerical Methods for Physics - Program Programs from the textbook "Numerical Methods for Physics" by Alejandro Garcia. --- Cpp/Matrix.h | 93 ++++ Cpp/NumMeth.h | 8 + Cpp/SampList.h | 53 +++ Cpp/SortList.h | 47 ++ Cpp/advect.cpp | 109 +++++ Cpp/balle.cpp | 100 ++++ Cpp/bess.cpp | 29 ++ Cpp/cinv.cpp | 114 +++++ Cpp/colider.cpp | 84 ++++ Cpp/contents.txt | 57 +++ Cpp/dftcs.cpp | 83 ++++ Cpp/dsmceq.cpp | 104 +++++ Cpp/dsmcne.cpp | 173 +++++++ Cpp/errintg.cpp | 12 + Cpp/fft.cpp | 68 +++ Cpp/fft2.cpp | 48 ++ Cpp/fftpoi.cpp | 95 ++++ Cpp/fnewt.cpp | 27 ++ Cpp/ftdemo.cpp | 83 ++++ Cpp/ge.cpp | 75 +++ Cpp/gravrk.cpp | 23 + Cpp/ifft.cpp | 27 ++ Cpp/ifft2.cpp | 50 ++ Cpp/interp.cpp | 56 +++ Cpp/intrpf.cpp | 16 + Cpp/inv.cpp | 84 ++++ Cpp/legndr.cpp | 19 + Cpp/linreg.cpp | 45 ++ Cpp/lorenz.cpp | 104 +++++ Cpp/lorzrk.cpp | 21 + Cpp/lsfdemo.cpp | 66 +++ Cpp/mover.cpp | 69 +++ Cpp/neutrn.cpp | 90 ++++ Cpp/newtn.cpp | 86 ++++ Cpp/orbit.cpp | 122 +++++ Cpp/orthog.cpp | 34 ++ Cpp/pendul.cpp | 102 ++++ Cpp/pollsf.cpp | 61 +++ Cpp/rand.cpp | 16 + Cpp/randn.cpp | 15 + Cpp/relax.cpp | 126 +++++ Cpp/rk4.cpp | 51 ++ Cpp/rka.cpp | 76 +++ Cpp/rombf.cpp | 43 ++ Cpp/sampler.cpp | 61 +++ Cpp/schro.cpp | 142 ++++++ Cpp/sorter.cpp | 54 +++ Cpp/sprfft.cpp | 107 +++++ Cpp/sprrk.cpp | 18 + Cpp/traffic.cpp | 123 +++++ Cpp/trige.cpp | 45 ++ Cpp/zeroj.cpp | 30 ++ Fortran/Barrow.txt | 230 +++++++++ Fortran/Mauna.txt | 230 +++++++++ Fortran/advect.f | 130 ++++++ Fortran/balle.f | 111 +++++ Fortran/bess.f | 40 ++ Fortran/cinv.f | 90 ++++ Fortran/colider.f | 90 ++++ Fortran/contents.txt | 53 +++ Fortran/dftcs.f | 97 ++++ Fortran/dsmceq.f | 113 +++++ Fortran/dsmcne.f | 187 ++++++++ Fortran/errintg.f | 12 + Fortran/fft.f | 66 +++ Fortran/fft2.f | 46 ++ Fortran/fftpoi.f | 108 +++++ Fortran/fnewt.f | 30 ++ Fortran/ftdemo.f | 88 ++++ Fortran/ge.f | 96 ++++ Fortran/gravrk.f | 28 ++ Fortran/ifft.f | 27 ++ Fortran/ifft2.f | 50 ++ Fortran/interp.f | 54 +++ Fortran/intrpf.f | 18 + Fortran/inv.f | 109 +++++ Fortran/legndr.f | 21 + Fortran/linreg.f | 52 +++ Fortran/lorenz.f | 118 +++++ Fortran/lorzrk.f | 26 ++ Fortran/lsfdemo.f | 65 +++ Fortran/mover.f | 79 ++++ Fortran/neutrn.f | 107 +++++ Fortran/newtn.f | 94 ++++ Fortran/orbit.f | 122 +++++ Fortran/orthog.f | 34 ++ Fortran/pendul.f | 102 ++++ Fortran/pollsf.f | 69 +++ Fortran/rand.f | 18 + Fortran/randn.f | 14 + Fortran/relax.f | 150 ++++++ Fortran/rk4.f | 53 +++ Fortran/rka.f | 87 ++++ Fortran/rombf.f | 47 ++ Fortran/sampler.f | 68 +++ Fortran/schro.f | 158 +++++++ Fortran/sorter.f | 54 +++ Fortran/sprfft.f | 110 +++++ Fortran/sprrk.f | 22 + Fortran/traffic.f | 142 ++++++ Fortran/trige.f | 47 ++ Fortran/zeroj.f | 33 ++ Matlab/Barrow.txt | 230 +++++++++ Matlab/Mauna.txt | 230 +++++++++ Matlab/advect.m | 70 +++ Matlab/balle.m | 67 +++ Matlab/bess.m | 25 + Matlab/colider.m | 69 +++ Matlab/contents.txt | 44 ++ Matlab/dftcs.m | 56 +++ Matlab/dsmceq.m | 78 ++++ Matlab/dsmcne.m | 120 +++++ Matlab/errintg.m | 9 + Matlab/fftpoi.m | 57 +++ Matlab/fnewt.m | 25 + Matlab/ftdemo.m | 44 ++ Matlab/gravrk.m | 17 + Matlab/interp.m | 25 + Matlab/intrpf.m | 15 + Matlab/legndr.m | 16 + Matlab/linreg.m | 33 ++ Matlab/lorenz.m | 53 +++ Matlab/lorzrk.m | 18 + Matlab/lsfdemo.m | 38 ++ Matlab/mover.m | 55 +++ Matlab/neutrn.m | 63 +++ Matlab/newtn.m | 57 +++ Matlab/orbit.m | 66 +++ Matlab/orthog.m | 18 + Matlab/pendul.m | 69 +++ Matlab/pollsf.m | 40 ++ Matlab/relax.m | 97 ++++ Matlab/rk4.m | 24 + Matlab/rka.m | 53 +++ Matlab/rombf.m | 39 ++ Matlab/sampler.m | 41 ++ Matlab/schro.m | 77 +++ Matlab/sorter.m | 40 ++ Matlab/sprfft.m | 60 +++ Matlab/sprrk.m | 17 + Matlab/traffic.m | 90 ++++ Matlab/tri_ge.m | 35 ++ Matlab/zeroj.m | 21 + MatlabRevised/BalleEnergy.asv | 84 ++++ MatlabRevised/Barrow.txt | 230 +++++++++ MatlabRevised/Mauna.txt | 230 +++++++++ MatlabRevised/advect.m | 70 +++ MatlabRevised/balle.asv | 67 +++ MatlabRevised/balle.m | 67 +++ MatlabRevised/bess.m | 25 + MatlabRevised/colider.m | 68 +++ MatlabRevised/contents.txt | 44 ++ MatlabRevised/dftcs.m | 56 +++ MatlabRevised/dsmceq.m | 78 ++++ MatlabRevised/dsmcne.m | 120 +++++ MatlabRevised/errintg.m | 9 + MatlabRevised/fftpoi.m | 56 +++ MatlabRevised/fnewt.m | 25 + MatlabRevised/ftdemo.asv | 45 ++ MatlabRevised/ftdemo.m | 45 ++ MatlabRevised/gravrk.m | 17 + MatlabRevised/interp.m | 25 + MatlabRevised/intrpf.m | 15 + MatlabRevised/legndr.m | 16 + MatlabRevised/linreg.m | 33 ++ MatlabRevised/lorenz.m | 53 +++ MatlabRevised/lorzrk.m | 18 + MatlabRevised/lsfdemo.asv | 38 ++ MatlabRevised/lsfdemo.m | 38 ++ MatlabRevised/mover.m | 55 +++ MatlabRevised/neutrn.m | 63 +++ MatlabRevised/newtn.asv | 57 +++ MatlabRevised/newtn.m | 59 +++ MatlabRevised/orbit.m | 66 +++ MatlabRevised/orthog.m | 18 + MatlabRevised/pendul.m | 70 +++ MatlabRevised/pollsf.m | 40 ++ MatlabRevised/relax.asv | 106 +++++ MatlabRevised/relax.m | 98 ++++ MatlabRevised/rk4.asv | 24 + MatlabRevised/rk4.m | 24 + MatlabRevised/rka.m | 53 +++ MatlabRevised/rombf.asv | 40 ++ MatlabRevised/rombf.m | 40 ++ MatlabRevised/sampler.m | 41 ++ MatlabRevised/schro.m | 77 +++ MatlabRevised/sorter.m | 40 ++ MatlabRevised/sprfft.asv | 60 +++ MatlabRevised/sprfft.m | 60 +++ MatlabRevised/sprrk.m | 17 + MatlabRevised/traffic.asv | 90 ++++ MatlabRevised/traffic.m | 90 ++++ MatlabRevised/tri_ge.m | 35 ++ MatlabRevised/zeroj.m | 21 + Misc/Barrow.txt | 230 +++++++++ Misc/Mauna.txt | 230 +++++++++ Misc/readme.txt | 33 ++ .../Advect-checkpoint.ipynb | 171 +++++++ .../.ipynb_checkpoints/Balle-checkpoint.ipynb | 137 ++++++ .../.ipynb_checkpoints/Bess-checkpoint.ipynb | 169 +++++++ .../.ipynb_checkpoints/Dftcs-checkpoint.ipynb | 159 +++++++ .../Dsmceq-checkpoint.ipynb | 422 +++++++++++++++++ .../Fftpoi-checkpoint.ipynb | 223 +++++++++ .../Ftdemo-checkpoint.ipynb | 147 ++++++ .../Interp-checkpoint.ipynb | 132 ++++++ .../Legndr-checkpoint.ipynb | 117 +++++ .../Lorenz-checkpoint.ipynb | 272 +++++++++++ .../Lsfdemo-checkpoint.ipynb | 264 +++++++++++ .../Neutrn-checkpoint.ipynb | 154 ++++++ .../.ipynb_checkpoints/Newtn-checkpoint.ipynb | 141 ++++++ .../.ipynb_checkpoints/Orbit-checkpoint.ipynb | 273 +++++++++++ .../Orthog-checkpoint.ipynb | 84 ++++ .../Pendul-checkpoint.ipynb | 134 ++++++ .../.ipynb_checkpoints/Relax-checkpoint.ipynb | 280 +++++++++++ .../.ipynb_checkpoints/Rk4-checkpoint.ipynb | 60 +++ .../.ipynb_checkpoints/Rombf-checkpoint.ipynb | 155 ++++++ .../.ipynb_checkpoints/Schro-checkpoint.ipynb | 441 ++++++++++++++++++ .../Schro_T-checkpoint.ipynb | 299 ++++++++++++ .../Sprfft-checkpoint.ipynb | 222 +++++++++ .../Test_bess-checkpoint.ipynb | 115 +++++ .../Test_legndr-checkpoint.ipynb | 115 +++++ .../Traffic-checkpoint.ipynb | 228 +++++++++ .../Untitled-checkpoint.ipynb | 6 + .../.ipynb_checkpoints/Zeroj-checkpoint.ipynb | 6 + Python/Advect.ipynb | 171 +++++++ Python/Balle.ipynb | 137 ++++++ Python/Bess.ipynb | 169 +++++++ Python/Dftcs.ipynb | 159 +++++++ Python/Dsmceq.ipynb | 422 +++++++++++++++++ Python/Fftpoi.ipynb | 223 +++++++++ Python/Ftdemo.ipynb | 147 ++++++ Python/Interp.ipynb | 132 ++++++ Python/Legndr.ipynb | 109 +++++ Python/Lorenz.ipynb | 272 +++++++++++ Python/Lsfdemo.ipynb | 215 +++++++++ Python/Neutrn.ipynb | 154 ++++++ Python/Newtn.ipynb | 141 ++++++ Python/Orbit.ipynb | 324 +++++++++++++ Python/Orthog.ipynb | 84 ++++ Python/Pendul.ipynb | 134 ++++++ Python/Relax.ipynb | 280 +++++++++++ Python/Rk4.ipynb | 60 +++ Python/Rombf.ipynb | 155 ++++++ Python/Schro.ipynb | 441 ++++++++++++++++++ Python/Schro_T.ipynb | 299 ++++++++++++ Python/Sprfft.ipynb | 222 +++++++++ Python/Test_bess.ipynb | 133 ++++++ Python/Test_legndr.ipynb | 115 +++++ Python/Traffic.ipynb | 228 +++++++++ Python/Untitled.ipynb | 141 ++++++ 250 files changed, 23142 insertions(+) create mode 100644 Cpp/Matrix.h create mode 100644 Cpp/NumMeth.h create mode 100644 Cpp/SampList.h create mode 100644 Cpp/SortList.h create mode 100644 Cpp/advect.cpp create mode 100644 Cpp/balle.cpp create mode 100644 Cpp/bess.cpp create mode 100644 Cpp/cinv.cpp create mode 100644 Cpp/colider.cpp create mode 100644 Cpp/contents.txt create mode 100644 Cpp/dftcs.cpp create mode 100644 Cpp/dsmceq.cpp create mode 100644 Cpp/dsmcne.cpp create mode 100644 Cpp/errintg.cpp create mode 100644 Cpp/fft.cpp create mode 100644 Cpp/fft2.cpp create mode 100644 Cpp/fftpoi.cpp create mode 100644 Cpp/fnewt.cpp create mode 100644 Cpp/ftdemo.cpp create mode 100644 Cpp/ge.cpp create mode 100644 Cpp/gravrk.cpp create mode 100644 Cpp/ifft.cpp create mode 100644 Cpp/ifft2.cpp create mode 100644 Cpp/interp.cpp create mode 100644 Cpp/intrpf.cpp create mode 100644 Cpp/inv.cpp create mode 100644 Cpp/legndr.cpp create mode 100644 Cpp/linreg.cpp create mode 100644 Cpp/lorenz.cpp create mode 100644 Cpp/lorzrk.cpp create mode 100644 Cpp/lsfdemo.cpp create mode 100644 Cpp/mover.cpp create mode 100644 Cpp/neutrn.cpp create mode 100644 Cpp/newtn.cpp create mode 100644 Cpp/orbit.cpp create mode 100644 Cpp/orthog.cpp create mode 100644 Cpp/pendul.cpp create mode 100644 Cpp/pollsf.cpp create mode 100644 Cpp/rand.cpp create mode 100644 Cpp/randn.cpp create mode 100644 Cpp/relax.cpp create mode 100644 Cpp/rk4.cpp create mode 100644 Cpp/rka.cpp create mode 100644 Cpp/rombf.cpp create mode 100644 Cpp/sampler.cpp create mode 100644 Cpp/schro.cpp create mode 100644 Cpp/sorter.cpp create mode 100644 Cpp/sprfft.cpp create mode 100644 Cpp/sprrk.cpp create mode 100644 Cpp/traffic.cpp create mode 100644 Cpp/trige.cpp create mode 100644 Cpp/zeroj.cpp create mode 100644 Fortran/Barrow.txt create mode 100644 Fortran/Mauna.txt create mode 100644 Fortran/advect.f create mode 100644 Fortran/balle.f create mode 100644 Fortran/bess.f create mode 100644 Fortran/cinv.f create mode 100644 Fortran/colider.f create mode 100644 Fortran/contents.txt create mode 100644 Fortran/dftcs.f create mode 100644 Fortran/dsmceq.f create mode 100644 Fortran/dsmcne.f create mode 100644 Fortran/errintg.f create mode 100644 Fortran/fft.f create mode 100644 Fortran/fft2.f create mode 100644 Fortran/fftpoi.f create mode 100644 Fortran/fnewt.f create mode 100644 Fortran/ftdemo.f create mode 100644 Fortran/ge.f create mode 100644 Fortran/gravrk.f create mode 100644 Fortran/ifft.f create mode 100644 Fortran/ifft2.f create mode 100644 Fortran/interp.f create mode 100644 Fortran/intrpf.f create mode 100644 Fortran/inv.f create mode 100644 Fortran/legndr.f create mode 100644 Fortran/linreg.f create mode 100644 Fortran/lorenz.f create mode 100644 Fortran/lorzrk.f create mode 100644 Fortran/lsfdemo.f create mode 100644 Fortran/mover.f create mode 100644 Fortran/neutrn.f create mode 100644 Fortran/newtn.f create mode 100644 Fortran/orbit.f create mode 100644 Fortran/orthog.f create mode 100644 Fortran/pendul.f create mode 100644 Fortran/pollsf.f create mode 100644 Fortran/rand.f create mode 100644 Fortran/randn.f create mode 100644 Fortran/relax.f create mode 100644 Fortran/rk4.f create mode 100644 Fortran/rka.f create mode 100644 Fortran/rombf.f create mode 100644 Fortran/sampler.f create mode 100644 Fortran/schro.f create mode 100644 Fortran/sorter.f create mode 100644 Fortran/sprfft.f create mode 100644 Fortran/sprrk.f create mode 100644 Fortran/traffic.f create mode 100644 Fortran/trige.f create mode 100644 Fortran/zeroj.f create mode 100644 Matlab/Barrow.txt create mode 100644 Matlab/Mauna.txt create mode 100644 Matlab/advect.m create mode 100644 Matlab/balle.m create mode 100644 Matlab/bess.m create mode 100644 Matlab/colider.m create mode 100644 Matlab/contents.txt create mode 100644 Matlab/dftcs.m create mode 100644 Matlab/dsmceq.m create mode 100644 Matlab/dsmcne.m create mode 100644 Matlab/errintg.m create mode 100644 Matlab/fftpoi.m create mode 100644 Matlab/fnewt.m create mode 100644 Matlab/ftdemo.m create mode 100644 Matlab/gravrk.m create mode 100644 Matlab/interp.m create mode 100644 Matlab/intrpf.m create mode 100644 Matlab/legndr.m create mode 100644 Matlab/linreg.m create mode 100644 Matlab/lorenz.m create mode 100644 Matlab/lorzrk.m create mode 100644 Matlab/lsfdemo.m create mode 100644 Matlab/mover.m create mode 100644 Matlab/neutrn.m create mode 100644 Matlab/newtn.m create mode 100644 Matlab/orbit.m create mode 100644 Matlab/orthog.m create mode 100644 Matlab/pendul.m create mode 100644 Matlab/pollsf.m create mode 100644 Matlab/relax.m create mode 100644 Matlab/rk4.m create mode 100644 Matlab/rka.m create mode 100644 Matlab/rombf.m create mode 100644 Matlab/sampler.m create mode 100644 Matlab/schro.m create mode 100644 Matlab/sorter.m create mode 100644 Matlab/sprfft.m create mode 100644 Matlab/sprrk.m create mode 100644 Matlab/traffic.m create mode 100644 Matlab/tri_ge.m create mode 100644 Matlab/zeroj.m create mode 100644 MatlabRevised/BalleEnergy.asv create mode 100644 MatlabRevised/Barrow.txt create mode 100644 MatlabRevised/Mauna.txt create mode 100644 MatlabRevised/advect.m create mode 100644 MatlabRevised/balle.asv create mode 100644 MatlabRevised/balle.m create mode 100644 MatlabRevised/bess.m create mode 100644 MatlabRevised/colider.m create mode 100644 MatlabRevised/contents.txt create mode 100644 MatlabRevised/dftcs.m create mode 100644 MatlabRevised/dsmceq.m create mode 100644 MatlabRevised/dsmcne.m create mode 100644 MatlabRevised/errintg.m create mode 100644 MatlabRevised/fftpoi.m create mode 100644 MatlabRevised/fnewt.m create mode 100644 MatlabRevised/ftdemo.asv create mode 100644 MatlabRevised/ftdemo.m create mode 100644 MatlabRevised/gravrk.m create mode 100644 MatlabRevised/interp.m create mode 100644 MatlabRevised/intrpf.m create mode 100644 MatlabRevised/legndr.m create mode 100644 MatlabRevised/linreg.m create mode 100644 MatlabRevised/lorenz.m create mode 100644 MatlabRevised/lorzrk.m create mode 100644 MatlabRevised/lsfdemo.asv create mode 100644 MatlabRevised/lsfdemo.m create mode 100644 MatlabRevised/mover.m create mode 100644 MatlabRevised/neutrn.m create mode 100644 MatlabRevised/newtn.asv create mode 100644 MatlabRevised/newtn.m create mode 100644 MatlabRevised/orbit.m create mode 100644 MatlabRevised/orthog.m create mode 100644 MatlabRevised/pendul.m create mode 100644 MatlabRevised/pollsf.m create mode 100644 MatlabRevised/relax.asv create mode 100644 MatlabRevised/relax.m create mode 100644 MatlabRevised/rk4.asv create mode 100644 MatlabRevised/rk4.m create mode 100644 MatlabRevised/rka.m create mode 100644 MatlabRevised/rombf.asv create mode 100644 MatlabRevised/rombf.m create mode 100644 MatlabRevised/sampler.m create mode 100644 MatlabRevised/schro.m create mode 100644 MatlabRevised/sorter.m create mode 100644 MatlabRevised/sprfft.asv create mode 100644 MatlabRevised/sprfft.m create mode 100644 MatlabRevised/sprrk.m create mode 100644 MatlabRevised/traffic.asv create mode 100644 MatlabRevised/traffic.m create mode 100644 MatlabRevised/tri_ge.m create mode 100644 MatlabRevised/zeroj.m create mode 100644 Misc/Barrow.txt create mode 100644 Misc/Mauna.txt create mode 100644 Misc/readme.txt create mode 100644 Python/.ipynb_checkpoints/Advect-checkpoint.ipynb create mode 100644 Python/.ipynb_checkpoints/Balle-checkpoint.ipynb create mode 100644 Python/.ipynb_checkpoints/Bess-checkpoint.ipynb create mode 100644 Python/.ipynb_checkpoints/Dftcs-checkpoint.ipynb create mode 100644 Python/.ipynb_checkpoints/Dsmceq-checkpoint.ipynb create mode 100644 Python/.ipynb_checkpoints/Fftpoi-checkpoint.ipynb create mode 100644 Python/.ipynb_checkpoints/Ftdemo-checkpoint.ipynb create mode 100644 Python/.ipynb_checkpoints/Interp-checkpoint.ipynb create mode 100644 Python/.ipynb_checkpoints/Legndr-checkpoint.ipynb create mode 100644 Python/.ipynb_checkpoints/Lorenz-checkpoint.ipynb create mode 100644 Python/.ipynb_checkpoints/Lsfdemo-checkpoint.ipynb create mode 100644 Python/.ipynb_checkpoints/Neutrn-checkpoint.ipynb create mode 100644 Python/.ipynb_checkpoints/Newtn-checkpoint.ipynb create mode 100644 Python/.ipynb_checkpoints/Orbit-checkpoint.ipynb create mode 100644 Python/.ipynb_checkpoints/Orthog-checkpoint.ipynb create mode 100644 Python/.ipynb_checkpoints/Pendul-checkpoint.ipynb create mode 100644 Python/.ipynb_checkpoints/Relax-checkpoint.ipynb create mode 100644 Python/.ipynb_checkpoints/Rk4-checkpoint.ipynb create mode 100644 Python/.ipynb_checkpoints/Rombf-checkpoint.ipynb create mode 100644 Python/.ipynb_checkpoints/Schro-checkpoint.ipynb create mode 100644 Python/.ipynb_checkpoints/Schro_T-checkpoint.ipynb create mode 100644 Python/.ipynb_checkpoints/Sprfft-checkpoint.ipynb create mode 100644 Python/.ipynb_checkpoints/Test_bess-checkpoint.ipynb create mode 100644 Python/.ipynb_checkpoints/Test_legndr-checkpoint.ipynb create mode 100644 Python/.ipynb_checkpoints/Traffic-checkpoint.ipynb create mode 100644 Python/.ipynb_checkpoints/Untitled-checkpoint.ipynb create mode 100644 Python/.ipynb_checkpoints/Zeroj-checkpoint.ipynb create mode 100644 Python/Advect.ipynb create mode 100644 Python/Balle.ipynb create mode 100644 Python/Bess.ipynb create mode 100644 Python/Dftcs.ipynb create mode 100644 Python/Dsmceq.ipynb create mode 100644 Python/Fftpoi.ipynb create mode 100644 Python/Ftdemo.ipynb create mode 100644 Python/Interp.ipynb create mode 100644 Python/Legndr.ipynb create mode 100644 Python/Lorenz.ipynb create mode 100644 Python/Lsfdemo.ipynb create mode 100644 Python/Neutrn.ipynb create mode 100644 Python/Newtn.ipynb create mode 100644 Python/Orbit.ipynb create mode 100644 Python/Orthog.ipynb create mode 100644 Python/Pendul.ipynb create mode 100644 Python/Relax.ipynb create mode 100644 Python/Rk4.ipynb create mode 100644 Python/Rombf.ipynb create mode 100644 Python/Schro.ipynb create mode 100644 Python/Schro_T.ipynb create mode 100644 Python/Sprfft.ipynb create mode 100644 Python/Test_bess.ipynb create mode 100644 Python/Test_legndr.ipynb create mode 100644 Python/Traffic.ipynb create mode 100644 Python/Untitled.ipynb diff --git a/Cpp/Matrix.h b/Cpp/Matrix.h new file mode 100644 index 0000000..53ac462 --- /dev/null +++ b/Cpp/Matrix.h @@ -0,0 +1,93 @@ +#include // Defines the assert function. + +class Matrix { + +public: + +// Default Constructor. Creates a 1 by 1 matrix; sets value to zero. +Matrix () { + nRow_ = 1; nCol_ = 1; + data_ = new double [1]; // Allocate memory + set(0.0); // Set value of data_[0] to 0.0 +} + +// Regular Constructor. Creates an nR by nC matrix; sets values to zero. +// If number of columns is not specified, it is set to 1. +Matrix(int nR, int nC = 1) { + assert(nR > 0 && nC > 0); // Check that nC and nR both > 0. + nRow_ = nR; nCol_ = nC; + data_ = new double [nR*nC]; // Allocate memory + assert(data_ != 0); // Check that memory was allocated + set(0.0); // Set values of data_[] to 0.0 +} + +// Copy Constructor. +// Used when a copy of an object is produced +// (e.g., passing to a function by value) +Matrix(const Matrix& mat) { + this->copy(mat); // Call private copy function. +} + +// Destructor. Called when a Matrix object goes out of scope. +~Matrix() { + delete [] data_; // Release allocated memory +} + +// Assignment operator function. +// Overloads the equal sign operator to work with +// Matrix objects. +Matrix& operator=(const Matrix& mat) { + if( this == &mat ) return *this; // If two sides equal, do nothing. + delete [] data_; // Delete data on left hand side + this->copy(mat); // Copy right hand side to l.h.s. + return *this; +} + +// Simple "get" functions. Return number of rows or columns. +int nRow() const { return nRow_; } +int nCol() const { return nCol_; } + +// Parenthesis operator function. +// Allows access to values of Matrix via (i,j) pair. +// Example: a(1,1) = 2*b(2,3); +// If column is unspecified, take as 1. +double& operator() (int i, int j = 1) { + assert(i > 0 && i <= nRow_); // Bounds checking for rows + assert(j > 0 && j <= nCol_); // Bounds checking for columns + return data_[ nCol_*(i-1) + (j-1) ]; // Access appropriate value +} + +// Parenthesis operator function (const version). +const double& operator() (int i, int j = 1) const{ + assert(i > 0 && i <= nRow_); // Bounds checking for rows + assert(j > 0 && j <= nCol_); // Bounds checking for columns + return data_[ nCol_*(i-1) + (j-1) ]; // Access appropriate value +} + +// Set function. Sets all elements of a matrix to a given value. +void set(double value) { + int i, iData = nRow_*nCol_; + for( i=0; i +#include +#include +#include +#include "Matrix.h" diff --git a/Cpp/SampList.h b/Cpp/SampList.h new file mode 100644 index 0000000..e76d6c0 --- /dev/null +++ b/Cpp/SampList.h @@ -0,0 +1,53 @@ +class SampList { + +public: + +// Class data (sorting lists) +int ncell, nsamp; +double *ave_n, *ave_ux, *ave_uy, *ave_uz, *ave_T; + +// Default Constructor. +SampList() { + initLists(1); +} + +// Regular Constructor. +SampList(int ncell_in) { + initLists(ncell_in); +} + + +// Destructor. Called when a SampList object goes out of scope. +~SampList() { + delete [] ave_n; // Release allocated memory + delete [] ave_ux; + delete [] ave_uy; + delete [] ave_uz; + delete [] ave_T; +} + +//********************************************************* + +private: + +// Initialization routine +void initLists(int ncell_in) { + ncell = ncell_in; + nsamp = 0; + ave_n = new double [ncell+1]; // Allocate memory + ave_ux = new double [ncell+1]; + ave_uy = new double [ncell+1]; + ave_uz = new double [ncell+1]; + ave_T = new double [ncell+1]; + int i; + for( i=1; i<=ncell; i++ ) { + ave_n[i] = 0; + ave_ux[i] = 0; + ave_uy[i] = 0; + ave_uz[i] = 0; + ave_T[i] = 0; + } +} + +}; // Class SampList + diff --git a/Cpp/SortList.h b/Cpp/SortList.h new file mode 100644 index 0000000..c0ccf8d --- /dev/null +++ b/Cpp/SortList.h @@ -0,0 +1,47 @@ +class SortList { + +public: + +// Class data (sorting lists) +int ncell, npart, *cell_n, *index, *Xref; + +// Default Constructor. +SortList() { + initLists(1,1); +} + +// Regular Constructor. +SortList(int ncell_in, int npart_in) { + initLists(ncell_in,npart_in); +} + + +// Destructor. Called when a SortList object goes out of scope. +~SortList() { + delete [] cell_n; // Release allocated memory + delete [] index; + delete [] Xref; +} + +//********************************************************* + +private: + +// Initialization routine +void initLists(int ncell_in, int npart_in) { + ncell = ncell_in; + npart = npart_in; + cell_n = new int [ncell+1]; // Allocate memory + index = new int [ncell+1]; + Xref = new int [npart+1]; + int i; + for( i=1; i<=ncell; i++ ) { + cell_n[i] = 0; + index[i] = 0; + } + for( i=1; i<=npart; i++ ) + Xref[i] = 0; +} + +}; // Class SortList + diff --git a/Cpp/advect.cpp b/Cpp/advect.cpp new file mode 100644 index 0000000..a2702a9 --- /dev/null +++ b/Cpp/advect.cpp @@ -0,0 +1,109 @@ +// advect - Program to solve the advection equation +// using the various hyperbolic PDE schemes +#include "NumMeth.h" + +void main() { + + //* Select numerical parameters (time step, grid spacing, etc.). + cout << "Choose a numerical method: 1) FTCS, 2) Lax, 3) Lax-Wendroff : "; + int method; cin >> method; + cout << "Enter number of grid points: "; int N; cin >> N; + double L = 1.; // System size + double h = L/N; // Grid spacing + double c = 1; // Wave speed + cout << "Time for wave to move one grid spacing is " << h/c << endl; + cout << "Enter time step: "; double tau; cin >> tau; + double coeff = -c*tau/(2.*h); // Coefficient used by all schemes + double coefflw = 2*coeff*coeff; // Coefficient used by L-W scheme + cout << "Wave circles system in " << L/(c*tau) << " steps" << endl; + cout << "Enter number of steps: "; int nStep; cin >> nStep; + + //* Set initial and boundary conditions. + const double pi = 3.141592654; + double sigma = 0.1; // Width of the Gaussian pulse + double k_wave = pi/sigma; // Wave number of the cosine + Matrix x(N), a(N), a_new(N); + int i,j; + for( i=1; i<=N; i++ ) { + x(i) = (i-0.5)*h - L/2; // Coordinates of grid points + // Initial condition is a Gaussian-cosine pulse + a(i) = cos(k_wave*x(i)) * exp(-x(i)*x(i)/(2*sigma*sigma)); + } + // Use periodic boundary conditions + int *ip, *im; ip = new int [N+1]; im = new int [N+1]; + for( i=2; i> y1; + r1[1] = 0; r1[2] = y1; // Initial vector position + cout << "Enter initial speed (m/s): "; cin >> speed; + cout << "Enter initial angle (degrees): "; cin >> theta; + const double pi = 3.141592654; + v1[1] = speed*cos(theta*pi/180); // Initial velocity (x) + v1[2] = speed*sin(theta*pi/180); // Initial velocity (y) + r[1] = r1[1]; r[2] = r1[2]; // Set initial position and velocity + v[1] = v1[1]; v[2] = v1[2]; + + //* Set physical parameters (mass, Cd, etc.) + double Cd = 0.35; // Drag coefficient (dimensionless) + double area = 4.3e-3; // Cross-sectional area of projectile (m^2) + double grav = 9.81; // Gravitational acceleration (m/s^2) + double mass = 0.145; // Mass of projectile (kg) + double airFlag, rho; + cout << "Air resistance? (Yes:1, No:0): "; cin >> airFlag; + if( airFlag == 0 ) + rho = 0; // No air resistance + else + rho = 1.2; // Density of air (kg/m^3) + double air_const = -0.5*Cd*rho*area/mass; // Air resistance constant + + //* Loop until ball hits ground or max steps completed + double tau; + cout << "Enter timestep, tau (sec): "; cin >> tau; + int iStep, maxStep = 1000; // Maximum number of steps + double *xplot, *yplot, *xNoAir, *yNoAir; + xplot = new double [maxStep+1]; yplot = new double [maxStep+1]; + xNoAir = new double [maxStep+1]; yNoAir = new double [maxStep+1]; + for( iStep=1; iStep<=maxStep; iStep++ ) { + + //* Record position (computed and theoretical) for plotting + xplot[iStep] = r[1]; // Record trajectory for plot + yplot[iStep] = r[2]; + double t = (iStep-1)*tau; // Current time + xNoAir[iStep] = r1[1] + v1[1]*t; + yNoAir[iStep] = r1[2] + v1[2]*t - 0.5*grav*t*t; + + //* Calculate the acceleration of the ball + double normV = sqrt( v[1]*v[1] + v[2]*v[2] ); + accel[1] = air_const*normV*v[1]; // Air resistance + accel[2] = air_const*normV*v[2]; // Air resistance + accel[2] -= grav; // Gravity + + //* Calculate the new position and velocity using Euler method + r[1] += tau*v[1]; // Euler step + r[2] += tau*v[2]; + v[1] += tau*accel[1]; + v[2] += tau*accel[2]; + + //* If ball reaches ground (y<0), break out of the loop + if( r[2] < 0 ) { + xplot[iStep+1] = r[1]; // Record last values computed + yplot[iStep+1] = r[2]; + break; // Break out of the for loop + } + } + + //* Print maximum range and time of flight + cout << "Maximum range is " << r[1] << " meters" << endl; + cout << "Time of flight is " << iStep*tau << " seconds" << endl; + + //* Print out the plotting variables: + // xplot, yplot, xNoAir, yNoAir + ofstream xplotOut("xplot.txt"), yplotOut("yplot.txt"), + xNoAirOut("xNoAir.txt"), yNoAirOut("yNoAir.txt"); + int i; + for( i=1; i<=iStep+1; i++ ) { + xplotOut << xplot[i] << endl; + yplotOut << yplot[i] << endl; + } + for( i=1; i<=iStep; i++ ) { + xNoAirOut << xNoAir[i] << endl; + yNoAirOut << yNoAir[i] << endl; + } + + delete [] xplot, yplot, xNoAir, yNoAir; // Release memory + +} +/***** To plot in MATLAB; use the script below ******************** +load xplot.txt; load yplot.txt; load xNoAir.txt; load yNoAir.txt; +clf; figure(gcf); % Clear figure window and bring it forward +% Mark the location of the ground by a straight line +xground = [0 max(xNoAir)]; yground = [0 0]; +% Plot the computed trajectory and parabolic, no-air curve +plot(xplot,yplot,'+',xNoAir,yNoAir,'-',xground,yground,'-'); +legend('Euler method','Theory (No air)'); +xlabel('Range (m)'); ylabel('Height (m)'); +title('Projectile motion'); +******************************************************************/ diff --git a/Cpp/bess.cpp b/Cpp/bess.cpp new file mode 100644 index 0000000..d1a4285 --- /dev/null +++ b/Cpp/bess.cpp @@ -0,0 +1,29 @@ +#include "NumMeth.h" + +void bess( int m_max, double x, Matrix& jj ) { +// Bessel function +// Inputs +// m_max Largest desired order +// x = Value at which Bessel function J(x) is evaluated +// Output +// jj = Vector of J(x) for order m = 0, 1, ..., m_max + + //* Perform downward recursion from initial guess + int maxmx = (m_max > x) ? m_max : ((int)x); // Max(m,x) + // Recursion is downward from m_top (which is even) + int m_top = 2*((int)( (maxmx+15)/2 + 1 )); + Matrix j(m_top+1); + j(m_top+1) = 0.0; + j(m_top) = 1.0; + double tinyNumber = 1e-16; + int m; + for( m=m_top-2; m>=0; m--) // Downward recursion + j(m+1) = 2*(m+1)/(x+tinyNumber)*j(m+2) - j(m+3); + + //* Normalize using identity and return requested values + double norm = j(1); // NOTE: Be careful, m=0,1,... but + for( m=2; m<=m_top; m+=2 ) // vector goes j(1),j(2),... + norm += 2*j(m+1); + for( m=0; m<=m_max; m++ ) // Send back only the values for + jj(m+1) = j(m+1)/norm; // m=0,...,m_max and discard values +} // for m=m_max+1,...,m_top diff --git a/Cpp/cinv.cpp b/Cpp/cinv.cpp new file mode 100644 index 0000000..0240371 --- /dev/null +++ b/Cpp/cinv.cpp @@ -0,0 +1,114 @@ +#include "NumMeth.h" + +// Compute inverse of complex matrix +void cinv( Matrix RealA, Matrix ImagA, + Matrix& RealAinv, Matrix& ImagAinv ) +// Inputs +// RealA - Real part of matrix A (N by N) +// ImagA - Imaginary part of matrix A (N by N) +// Outputs +// RealAinv - Real part of inverse of matrix A (N by N) +// ImagAinv - Imaginary part of A inverse (N by N) +{ + + int N = RealA.nRow(); + assert( N == RealA.nCol() && N == ImagA.nRow() + && N == ImagA.nCol()); + RealAinv = RealA; // Copy matrices to ensure they are same size + ImagAinv = ImagA; + + int i, j, k; + Matrix scale(N); // Scale factor + int *index; index = new int [N+1]; + + //* Matrix B is initialized to the identity matrix + Matrix RealB(N,N), ImagB(N,N); + RealB.set(0.0); ImagB.set(0.0); + for( i=1; i<=N; i++ ) + RealB(i,i) = 1.0; + + //* Set scale factor, scale(i) = max( |a(i,j)| ), for each row + for( i=1; i<=N; i++ ) { + index[i] = i; // Initialize row index list + double scaleMax = 0.; + for( j=1; j<=N; j++ ) { + double MagA = RealA(i,j)*RealA(i,j) + ImagA(i,j)*ImagA(i,j); + scaleMax = (scaleMax > MagA) ? scaleMax : MagA; + } + scale(i) = scaleMax; + } + + //* Loop over rows k = 1, ..., (N-1) + for( k=1; k<=N-1; k++ ) { + //* Select pivot row from max( |a(j,k)/s(j)| ) + double ratiomax = 0.0; + int jPivot = k; + for( i=k; i<=N; i++ ) { + double MagA = RealA(index[i],k)*RealA(index[i],k) + + ImagA(index[i],k)*ImagA(index[i],k); + double ratio = MagA/scale(index[i]); + if( ratio > ratiomax ) { + jPivot=i; + ratiomax = ratio; + } + } + //* Perform pivoting using row index list + int indexJ = index[k]; + if( jPivot != k ) { // Pivot + indexJ = index[jPivot]; + index[jPivot] = index[k]; // Swap index jPivot and k + index[k] = indexJ; + } + //* Perform forward elimination + for( i=k+1; i<=N; i++ ) { + double denom = RealA(indexJ,k)*RealA(indexJ,k) + + ImagA(indexJ,k)*ImagA(indexJ,k); + double RealCoeff = (RealA(index[i],k)*RealA(indexJ,k) + + ImagA(index[i],k)*ImagA(indexJ,k))/denom; + double ImagCoeff = (ImagA(index[i],k)*RealA(indexJ,k) + - RealA(index[i],k)*ImagA(indexJ,k))/denom; + for( j=k+1; j<=N; j++ ) { + RealA(index[i],j) -= RealCoeff*RealA(indexJ,j) + - ImagCoeff*ImagA(indexJ,j); + ImagA(index[i],j) -= RealCoeff*ImagA(indexJ,j) + + ImagCoeff*RealA(indexJ,j); + } + RealA(index[i],k) = RealCoeff; + ImagA(index[i],k) = ImagCoeff; + for( j=1; j<=N; j++ ) { + RealB(index[i],j) -= RealA(index[i],k)*RealB(indexJ,j) + - ImagA(index[i],k)*ImagB(indexJ,j); + ImagB(index[i],j) -= RealA(index[i],k)*ImagB(indexJ,j) + + ImagA(index[i],k)*RealB(indexJ,j); + } + } + } + + //* Perform backsubstitution + for( k=1; k<=N; k++ ) { + double denom = RealA(index[N],N)*RealA(index[N],N) + + ImagA(index[N],N)*ImagA(index[N],N); + RealAinv(N,k) = (RealB(index[N],k)*RealA(index[N],N) + + ImagB(index[N],k)*ImagA(index[N],N))/denom; + ImagAinv(N,k) = (ImagB(index[N],k)*RealA(index[N],N) + - RealB(index[N],k)*ImagA(index[N],N))/denom; + for( i=N-1; i>=1; i--) { + double RealSum = RealB(index[i],k); + double ImagSum = ImagB(index[i],k); + for( j=i+1; j<=N; j++ ) { + RealSum -= RealA(index[i],j)*RealAinv(j,k) + - ImagA(index[i],j)*ImagAinv(j,k); + ImagSum -= RealA(index[i],j)*ImagAinv(j,k) + + ImagA(index[i],j)*RealAinv(j,k); + } + double denom = RealA(index[i],i)*RealA(index[i],i) + + ImagA(index[i],i)*ImagA(index[i],i); + RealAinv(i,k) = (RealSum*RealA(index[i],i) + + ImagSum*ImagA(index[i],i))/denom; + ImagAinv(i,k) = (ImagSum*RealA(index[i],i) + - RealSum*ImagA(index[i],i))/denom; + } + } + + delete [] index; // Release allocated memory +} diff --git a/Cpp/colider.cpp b/Cpp/colider.cpp new file mode 100644 index 0000000..ec6a33d --- /dev/null +++ b/Cpp/colider.cpp @@ -0,0 +1,84 @@ +#include "NumMeth.h" +#include "SortList.h" + +double rand( long& seed ); + +int colider( Matrix& v, Matrix& crmax, double tau, long& seed, + Matrix& selxtra, double coeff, SortList& sD ) { + +// colide - Function to process collisions in cells +// Inputs +// v Velocities of the particles +// crmax Estimated maximum relative speed in a cell +// tau Time step +// seed Current random number seed +// selxtra Extra selections carried over from last timestep +// coeff Coefficient in computing number of selected pairs +// sD Object containing sorting lists +// Outputs +// v Updated velocities of the particles +// crmax Updated maximum relative speed +// selxtra Extra selections carried over to next timestep +// col Total number of collisions processed (Return value) + + int ncell = sD.ncell; + int col = 0; // Count number of collisions + const double pi = 3.141592654; + + //* Loop over cells, processing collisions in each cell + int jcell; + for( jcell=1; jcell<=ncell; jcell++ ) { + + //* Skip cells with only one particle + int number = sD.cell_n[jcell]; + if( number < 2 ) continue; // Skip to the next cell + + //* Determine number of candidate collision pairs + // to be selected in this cell + double select = coeff*number*(number-1)*crmax(jcell) + selxtra(jcell); + int nsel = (int)(select); // Number of pairs to be selected + selxtra(jcell) = select-nsel; // Carry over any left-over fraction + double crm = crmax(jcell); // Current maximum relative speed + + //* Loop over total number of candidate collision pairs + int isel; + for( isel=1; isel<=nsel; isel++ ) { + + //* Pick two particles at random out of this cell + int k = (int)(rand(seed)*number); + int kk = ((int)(k+rand(seed)*(number-1))+1) % number; + int ip1 = sD.Xref[ k+sD.index[jcell] ]; // First particle + int ip2 = sD.Xref[ kk+sD.index[jcell] ]; // Second particle + + //* Calculate pair's relative speed + double cr = sqrt( pow(v(ip1,1)-v(ip2,1),2) + + pow(v(ip1,2)-v(ip2,2),2) + // Relative speed + pow(v(ip1,3)-v(ip2,3),2) ); + if( cr > crm ) // If relative speed larger than crm, + crm = cr; // then reset crm to larger value + + //* Accept or reject candidate pair according to relative speed + if( cr/crmax(jcell) > rand(seed) ) { + //* If pair accepted, select post-collision velocities + col++; // Collision counter + Matrix vcm(3), vrel(3); + int k; + for( k=1; k<=3; k++ ) + vcm(k) = 0.5*(v(ip1,k) + v(ip2,k)); // Center of mass velocity + double cos_th = 1.0 - 2.0*rand(seed); // Cosine and sine of + double sin_th = sqrt(1.0 - cos_th*cos_th); // collision angle theta + double phi = 2.0*pi*rand(seed); // Collision angle phi + vrel(1) = cr*cos_th; // Compute post-collision + vrel(2) = cr*sin_th*cos(phi); // relative velocity + vrel(3) = cr*sin_th*sin(phi); + for( k=1; k<=3; k++ ) { + v(ip1,k) = vcm(k) + 0.5*vrel(k); // Update post-collision + v(ip2,k) = vcm(k) - 0.5*vrel(k); // velocities + } + + } // Loop over pairs + crmax(jcell) = crm; // Update max relative speed + } + } // Loop over cells + return( col ); +} diff --git a/Cpp/contents.txt b/Cpp/contents.txt new file mode 100644 index 0000000..f9206e1 --- /dev/null +++ b/Cpp/contents.txt @@ -0,0 +1,57 @@ +% Numerical Methods for Physics, 2nd Ed. (C++). +% Version 1.0a 2-Oct-99 +% Copyright (c) 1999 by Alejandro Garcia. + +% Matrix.h Matrix C++ class +% NumMeth.h General C++ header +% SampList.h C++ class for DSMC sampling lists +% SortList.h C++ class for DSMC sorting lists +% advect.cpp Advection PDE solver using various methods +% balle.cpp Projectile motion (baseball) program +% barrow.txt Carbon dioxide data for Barrow, Alaska +% bess.cpp Bessel function routine +% cinv.cpp Complex matrix inverse routine +% colider.cpp DSMC particle collision routine +% dftcs.cpp Diffusion PDE solver using FTCS method +% dsmceq.cpp Relaxation to equilibrium using DSMC method +% dsmcne.cpp Couette flow routine using DSMC method +% errintg.cpp Integrand of error function +% fft.cpp Fast Fourier transform function +% fft2.cpp Two-dimensional FFT routine +% fftpoi.cpp Poisson PDE solver using MFT method +% fnewtn.cpp Lorenz model ODEs and Jacobian routine +% ftdemo.cpp Fourier transform demo program +% ge.cpp Gaussian elimination routine +% gravrk.cpp Function for Kepler equations of motion +% ifft.cpp Inverse fast Fourier transform function +% ifft2.cpp Two-dimensional inverse FFT routine +% interp.cpp Interpolation program +% intrpf.cpp Interpolation function +% inv.cpp Matrix inverse routine +% legndr.cpp Legendre polynomial function +% linreg.cpp Linear curve fit routine +% lorenz.cpp Lorenz model program +% lorzrk.cpp Function for Lorenz model ODEs +% lsfdemo.cpp Least square fit demo program +% mauna.txt Carbon dioxide data for Mauna Loa, Hawaii +% mover.cpp DSMC particle moving routine +% neutrn.cpp Neutron diffusion PDE solver +% newtn.cpp Root finding by Newton's method +% orbit.cpp Orbits of comets program +% orthog.cpp Program to test vector orthogonality +% pendul.cpp Simple pendulum program +% pollsf.cpp Polynomial curve fit routine +% rand.cpp Uniformly distributed random number function +% randn.cpp Normal (Gaussian) dist. random number function +% relax.cpp Laplace PDE solver using relaxation methods +% rk4.cpp Runge-Kutta routine +% rka.cpp Adaptive Runge-Kutta routine +% rombf.cpp Romberg integration routine +% sampler.cpp DSMC particle sampling routine +% schro.cpp Schrodinger PDE solver using Crank-Nicolson +% sorter.cpp DSMC particle sorting routine +% sprfft.cpp Spring-mass oscillations program +% sprrk.cpp Function for Spring-mass ODEs +% traffic.cpp Traffic PDE solver using various methods +% tri_ge.cpp Gaussian elimination for tridiagonal matrices +% zeroj.cpp Zeros of Bessel function routine diff --git a/Cpp/dftcs.cpp b/Cpp/dftcs.cpp new file mode 100644 index 0000000..b465b18 --- /dev/null +++ b/Cpp/dftcs.cpp @@ -0,0 +1,83 @@ +// dftcs - Program to solve the diffusion equation +// using the Forward Time Centered Space (FTCS) scheme. +#include "NumMeth.h" + +void main() { + + //* Initialize parameters (time step, grid spacing, etc.). + cout << "Enter time step: "; double tau; cin >> tau; + cout << "Enter the number of grid points: "; int N; cin >> N; + double L = 1.; // The system extends from x=-L/2 to x=L/2 + double h = L/(N-1); // Grid size + double kappa = 1.; // Diffusion coefficient + double coeff = kappa*tau/(h*h); + if( coeff < 0.5 ) + cout << "Solution is expected to be stable" << endl; + else + cout << "WARNING: Solution is expected to be unstable" << endl; + + //* Set initial and boundary conditions. + Matrix tt(N), tt_new(N); + tt.set(0.0); // Initialize temperature to zero at all points + tt(N/2) = 1/h; // Initial cond. is delta function in center + //// The boundary conditions are tt(1) = tt(N) = 0 + tt_new.set(0.0); // End points are unchanged during iteration + + //* Set up loop and plot variables. + int iplot = 1; // Counter used to count plots + int nStep = 300; // Maximum number of iterations + int plot_step = 6; // Number of time steps between plots + int nplots = nStep/plot_step + 1; // Number of snapshots (plots) + Matrix xplot(N), tplot(nplots), ttplot(N,nplots); + int i,j; + for( i=1; i<=N; i++ ) + xplot(i) = (i-1)*h - L/2; // Record the x scale for plots + + //* Loop over the desired number of time steps. + int iStep; + for( iStep=1; iStep<=nStep; iStep++ ) { + + //* Compute new temperature using FTCS scheme. + for( i=2; i<=(N-1); i++ ) + tt_new(i) = tt(i) + coeff*(tt(i+1) + tt(i-1) - 2*tt(i)); + + tt = tt_new; // Reset temperature to new values + + //* Periodically record temperature for plotting. + if( (iStep%plot_step) < 1 ) { // Every plot_step steps + for( i=1; i<=N; i++ ) // record tt(i) for plotting + ttplot(i,iplot) = tt(i); + tplot(iplot) = iStep*tau; // Record time for plots + iplot++; + } + } + nplots = iplot-1; // Number of plots actually recorded + + //* Print out the plotting variables: tplot, xplot, ttplot + ofstream tplotOut("tplot.txt"), xplotOut("xplot.txt"), + ttplotOut("ttplot.txt"); + for( i=1; i<=nplots; i++ ) + tplotOut << tplot(i) << endl; + for( i=1; i<=N; i++ ) { + xplotOut << xplot(i) << endl; + for( j=1; j> npart; + double eff_num = density/mass*L*L*L/npart; + cout << "Each particle represents " << eff_num << " atoms" << endl; + + //* Assign random positions and velocities to particles + long seed = 1; // Initial seed for rand (DO NOT USE ZERO) + double v_init = sqrt(3.0*boltz*T/mass); // Initial speed + Matrix x(npart), v(npart,3); + int i; + for( i=1; i<=npart; i++ ) { + x(i) = L*rand(seed); // Assign random positions + int plusMinus = (1 - 2*((int)(2*rand(seed)))); + v(i,1) = plusMinus * v_init; + v(i,2) = 0.0; // Only x-component is non-zero + v(i,3) = 0.0; + } + + //* Record inital particle speeds + Matrix vmagI(npart); + for( i=1; i<=npart; i++ ) + vmagI(i) = sqrt( v(i,1)*v(i,1) + v(i,2)*v(i,2) + v(i,3)*v(i,3) ); + + //* Initialize variables used for evaluating collisions + int ncell = 15; // Number of cells + double tau = 0.2*(L/ncell)/v_init; // Set timestep tau + Matrix vrmax(ncell), selxtra(ncell); + vrmax.set(3*v_init); // Estimated max rel. speed + selxtra.set(0.0); // Used by routine "colider" + double coeff = 0.5*eff_num*pi*diam*diam*tau/(L*L*L/ncell); + int coltot = 0; // Count total collisions + + //* Declare object for lists used in sorting + SortList sortData(ncell,npart); + + //* Loop for the desired number of time steps + cout << "Enter total number of time steps: "; + int istep, nstep; cin >> nstep; + for( istep = 1; istep<=nstep; istep++ ) { + + //* Move all the particles ballistically + for( i=1; i<=npart; i++ ) { + x(i) += v(i,1)*tau; // Update x position of particle + x(i) = fmod(x(i)+L,L); // Periodic boundary conditions + } + //* Sort the particles into cells + sorter(x,L,sortData); + + //* Evaluate collisions among the particles + int col = colider(v,vrmax,tau,seed,selxtra,coeff,sortData); + coltot += col; // Increment collision count + + //* Periodically display the current progress + if( (istep%10) < 1 ) + cout << "Done " << istep << " of " << nstep << " steps; " << + coltot << " collisions" << endl; + } + + // Record final particle speeds + Matrix vmagF(npart); + for( i=1; i<=npart; i++ ) + vmagF(i) = sqrt( v(i,1)*v(i,1) + v(i,2)*v(i,2) + v(i,3)*v(i,3) ); + + //* Print out the plotting variables: vmagI, vmagF + ofstream vmagIOut("vmagI.txt"), vmagFOut("vmagF.txt"); + for( i=1; i<=npart; i++ ) { + vmagIOut << vmagI(i) << endl; + vmagFOut << vmagF(i) << endl; + } +} +/***** To plot in MATLAB; use the script below ******************** +load vmagI.txt; load vmagF.txt; +%* Plot the histogram of the initial speed distribution +vbin = 50:100:1050; % Bins for histogram +hist(vmagI,vbin); title('Initial speed distribution'); +xlabel('Speed (m/s)'); ylabel('Number'); +%* Plot the histogram of the final speed distribution +figure(2); clf; +hist(vmagF,vbin); +title(sprintf('Final speed distribution')); +xlabel('Speed (m/s)'); ylabel('Number'); +******************************************************************/ + diff --git a/Cpp/dsmcne.cpp b/Cpp/dsmcne.cpp new file mode 100644 index 0000000..46d1622 --- /dev/null +++ b/Cpp/dsmcne.cpp @@ -0,0 +1,173 @@ +// dsmcne - Program to simulate a dilute gas using DSMC algorithm +// This version simulates planar Couette flow + +#include "NumMeth.h" +#include "SortList.h" +#include "SampList.h" + +double rand( long& seed ); +double randn( long& seed ); +int colider( Matrix& v, Matrix& crmax, double tau, long& seed, + Matrix& selxtra, double coeff, SortList& sD ); +void sorter( Matrix& x, double L, SortList &sD ); +void mover( Matrix& x, Matrix& v, int npart, double L, + double mpv, double vwall, double tau, + Matrix& strikes, Matrix& delv, long& seed ); +void sampler( Matrix& x, Matrix& v, int npart, double L, + SampList& sampD ); + +void main() { + + //* Initialize constants (particle mass, diameter, etc.) + const double pi = 3.141592654; + const double boltz = 1.3806e-23; // Boltzmann's constant (J/K) + double mass = 6.63e-26; // Mass of argon atom (kg) + double diam = 3.66e-10; // Effective diameter of argon atom (m) + double T = 273; // Temperature (K) + double density = 2.685e25; // Number density of argon at STP (m^-3) + double L = 1e-6; // System size is one micron + double Volume = L*L*L; // Volume of the system + cout << "Enter number of simulation particles: "; + int npart; cin >> npart; + double eff_num = density*L*L*L/npart; + cout << "Each particle represents " << eff_num << " atoms" << endl; + double mfp = Volume/(sqrt(2.0)*pi*diam*diam*npart*eff_num); + cout << "System width is " << L/mfp << " mean free paths" << endl; + double mpv = sqrt(2*boltz*T/mass); // Most probable initial velocity + cout << "Enter wall velocity as Mach number: "; + double vwall_m; cin >> vwall_m; + double vwall = vwall_m * sqrt(5./3. * boltz*T/mass); + cout << "Wall velocities are " << -vwall << " and " + << vwall << " m/s" << endl; + + //* Assign random positions and velocities to particles + long seed = 1; // Initial seed for rand (DO NOT USE ZERO) + Matrix x(npart), v(npart,3); + int i; + for( i=1; i<=npart; i++ ) { + x(i) = L*rand(seed); // Assign random positions + // Initial velocities are Maxwell-Boltzmann distributed + v(i,1) = sqrt(boltz*T/mass) * randn(seed); + v(i,2) = sqrt(boltz*T/mass) * randn(seed); + v(i,3) = sqrt(boltz*T/mass) * randn(seed); + // Add velocity gradient to the y-component + v(i,2) += vwall * 2*(x(i)/L - 0.5); + } + + //* Initialize variables used for evaluating collisions + int ncell = 20; // Number of cells + double tau = 0.2*(L/ncell)/mpv; // Set timestep tau + Matrix vrmax(ncell), selxtra(ncell); + vrmax.set(3*mpv); // Estimated max rel. speed + selxtra.set(0.0); // Used by routine "colider" + double coeff = 0.5*eff_num*pi*diam*diam*tau/(L*L*L/ncell); + + //* Declare object for lists used in sorting + SortList sortData(ncell,npart); + + //* Initialize object and variables used in statistical sampling + SampList sampData(ncell); + double tsamp = 0; // Total sampling time + Matrix dvtot(2), dverr(2); + dvtot.set(0.0); // Total momentum change at a wall + dverr.set(0.0); // Used to find error in dvtot + + //* Loop for the desired number of time steps + int colSum = 0; // Count total collisions + Matrix strikes(2), strikeSum(2); + strikeSum.set(0.0); // Count strikes on each wall + cout << "Enter total number of time steps: "; + int istep, nstep; cin >> nstep; + for( istep = 1; istep<=nstep; istep++ ) { + + //* Move all the particles + Matrix delv(2); delv.set(0.0); + mover( x, v, npart, L, mpv, vwall, + tau, strikes, delv, seed ); + strikeSum(1) += strikes(1); + strikeSum(2) += strikes(2); + + //* Sort the particles into cells + sorter(x,L,sortData); + + //* Evaluate collisions among the particles + int col = colider(v,vrmax,tau,seed,selxtra,coeff,sortData); + colSum += col; // Increment collision count + + //* After initial transient, accumulate statistical samples + if(istep > nstep/10) { + sampler(x,v,npart,L,sampData); + // Cummulative velocity change for particles striking walls + dvtot(1) += delv(1); dvtot(2) += delv(2); + dverr(1) += delv(1)*delv(1); dverr(2) += delv(2)*delv(2); + tsamp += tau; + } + + //* Periodically display the current progress + if( (istep%100) < 1 ) { + cout << "Done " << istep << " of " << nstep << " steps; " << + colSum << " collisions" << endl; + cout << "Total wall strikes: " << strikeSum(1) << " (left) " + << strikeSum(2) << " (right)" << endl; + } + } + + //* Normalize the accumulated statistics + int nsamp = sampData.nsamp; + for( i=1; i<=ncell; i++ ) { + sampData.ave_n[i] *= (eff_num/(Volume/ncell))/nsamp; + sampData.ave_ux[i] /= nsamp; + sampData.ave_uy[i] /= nsamp; + sampData.ave_uz[i] /= nsamp; + sampData.ave_T[i] *= mass/(3*boltz*nsamp); + } + dverr(1) = dverr(1)/(nsamp-1) - (dvtot(1)/nsamp)*(dvtot(1)/nsamp); + dverr(1) = sqrt(dverr(1)*nsamp); + dverr(2) = dverr(2)/(nsamp-1) - (dvtot(2)/nsamp)*(dvtot(2)/nsamp); + dverr(2) = sqrt(dverr(2)*nsamp); + + //* Compute viscosity from drag force on the walls + Matrix force(2), ferr(2); + force(1) = (eff_num*mass*dvtot(1))/(tsamp*L*L); + force(2) = (eff_num*mass*dvtot(2))/(tsamp*L*L); + ferr(1) = (eff_num*mass*dverr(1))/(tsamp*L*L); + ferr(2) = (eff_num*mass*dverr(2))/(tsamp*L*L); + cout << "Force per unit area is" << endl; + cout << "Left wall: " << force(1) << " +/- " << ferr(1) << endl; + cout << "Right wall: " << force(2) << " +/- " << ferr(2) << endl; + double vgrad = 2*vwall/L; // Velocity gradient + double visc = 0.5*(-force(1)+force(2))/vgrad; // Average viscosity + double viscerr = 0.5*(ferr(1)+ferr(2))/vgrad; // Error + cout << "Viscosity = " << visc << " +/- " << viscerr + << "N s/m^2" << endl; + double eta = 5.*pi/32.*mass*density*(2./sqrt(pi)*mpv)*mfp; + cout << "Theoretical value of viscoisty is " << eta + << "N s/m^2" << endl; + + + //* Print out the plotting variables: + // xcell, ave_n, ave_ux, ave_uy, ave_uz, ave_T + ofstream xcellOut("xcell.txt"), ave_nOut("ave_n.txt"), + ave_uxOut("ave_ux.txt"), ave_uyOut("ave_uy.txt"), + ave_uzOut("ave_uz.txt"), ave_TOut("ave_T.txt"); + for( i=1; i<=ncell; i++ ) { + xcellOut << (i-0.5)*L/ncell << endl; + ave_nOut << sampData.ave_n[i] << endl; + ave_uxOut << sampData.ave_ux[i] << endl; + ave_uyOut << sampData.ave_uy[i] << endl; + ave_uzOut << sampData.ave_uz[i] << endl; + ave_TOut << sampData.ave_T[i] << endl; + } +} +/***** To plot in MATLAB; use the script below ******************** +load xcell.txt; load ave_n.txt; load ave_ux.txt; +load ave_uy.txt; load ave_uz.txt; load ave_T.txt; +figure(1); clf; +plot(xcell,ave_n); xlabel('position'); ylabel('Number density'); +figure(2); clf; +plot(xcell,ave_ux,xcell,ave_uy,xcell,ave_uz); +xlabel('position'); ylabel('Velocities'); +legend('x-component','y-component','z-component'); +figure(3); clf; +plot(xcell,ave_T); xlabel('position'); ylabel('Temperature'); +******************************************************************/ diff --git a/Cpp/errintg.cpp b/Cpp/errintg.cpp new file mode 100644 index 0000000..a89dba5 --- /dev/null +++ b/Cpp/errintg.cpp @@ -0,0 +1,12 @@ +#include "NumMeth.h" + +double errintg( double x, Matrix param) { +// Error function integrand +// Inputs +// x Value where integrand is evaluated +// param Parameter list (not used) +// Output +// f Integrand of the error function + double f = exp(-x*x); + return( f ); +} diff --git a/Cpp/fft.cpp b/Cpp/fft.cpp new file mode 100644 index 0000000..4241b5f --- /dev/null +++ b/Cpp/fft.cpp @@ -0,0 +1,68 @@ +#include "NumMeth.h" + +void fft( Matrix& RealA, Matrix& ImagA) { +// Routine to compute discrete Fourier transform using FFT algorithm +// Inputs +// RealA, ImagA Real and imaginary parts of data vector +// Outputs +// RealA, ImagA Real and imaginary parts of transform + + double RealU, RealW, RealT, ImagU, ImagW, ImagT; + + //* Determine size of input data and check that it is power of 2 + int N = RealA.nRow(); // Number of data points + int M = (int)(log( (double)N )/log(2.0) + 0.5); // N = 2^M + int NN = (int)(pow(2.0,(double)M) + 0.5); + if( N != NN ) { + cerr << "ERROR in fft(): Number of data points not power of 2" << endl; + return; + } + const double pi = 3.141592654; + int N_half = N/2; + int Nm1 = N-1; + + //* Bit-scramble the input data by swapping elements + int i,k,j=1; + for( i=1; i<=Nm1; i++ ) { + if( i < j ) { + RealT = RealA(j); ImagT = ImagA(j); // Swap elements i and j + RealA(j) = RealA(i); ImagA(j) = ImagA(i); // of RealA and ImagA + RealA(i) = RealT; ImagA(i) = ImagT; + } + k = N_half; + while( k < j ) { + j -= k; + k /= 2; + } + j += k; + } + + //* Loop over number of layers, M = log_2(N) + for( k=1; k<=M; k++ ) { + int ke = (int)(pow(2.0,(double)k) + 0.5); + int ke1 = ke/2; + //* Compute lowest, non-zero power of W for this layer + RealU = 1.0; ImagU = 0.0; + double angle = -pi/ke1; + RealW = cos(angle); ImagW = sin(angle); + //* Loop over elements in binary order (outer loop) + for( j=1; j<=ke1; j++ ) { + //* Loop over elements in binary order (inner loop) + for( i=j; i<=N; i+=ke ) { + int ip = i + ke1; + //* Compute the y(.)*W^. factor for this element + RealT = RealA(ip)*RealU - ImagA(ip)*ImagU; // T = A(ip)*U + ImagT = RealA(ip)*ImagU + ImagA(ip)*RealU; + //* Update the current element and its binary pair + RealA(ip) = RealA(i)-RealT; + ImagA(ip) = ImagA(i)-ImagT; // A(ip) = A(i) - T + RealA(i) += RealT; + ImagA(i) += ImagT; // A(i) = A(i) + T + } + //* Increment the power of W for next set of elements + double temp = RealU*RealW - ImagU*ImagW; + ImagU = RealU*ImagW + ImagU*RealW; // U = U * W + RealU = temp; + } + } +} diff --git a/Cpp/fft2.cpp b/Cpp/fft2.cpp new file mode 100644 index 0000000..de80253 --- /dev/null +++ b/Cpp/fft2.cpp @@ -0,0 +1,48 @@ +#include "NumMeth.h" + +void fft( Matrix& RealA, Matrix& ImagA); + +void fft2( Matrix& RealA, Matrix& ImagA) { +// Routine to compute two dimensional Fourier transform +// using FFT algorithm +// Inputs +// RealA, ImagA Real and imaginary parts of data array +// Outputs +// RealA, ImagA Real and imaginary parts of transform + + int i, j, N = RealA.nRow(); + Matrix RealT(N), ImagT(N); // Temporary work vector + + //* Loop over the columns of the matrix + for( j=1; j<=N; j++ ) { + //* Copy out a column into a vector + for( i=1; i<=N; i++ ) { + RealT(i) = RealA(i,j); + ImagT(i) = ImagA(i,j); + } + //* Take FFT of the vector + fft(RealT,ImagT); + //* Copy the transformed vector back into the column + for( i=1; i<=N; i++ ) { + RealA(i,j) = RealT(i); + ImagA(i,j) = ImagT(i); + } + } + + //* Loop over the rows of the matrix + for( i=1; i<=N; i++ ) { + //* Copy out a row into a vector + for( j=1; j<=N; j++ ) { + RealT(j) = RealA(i,j); + ImagT(j) = ImagA(i,j); + } + //* Take FFT of the vector + fft(RealT,ImagT); + //* Copy the transformed vector back into the row + for( j=1; j<=N; j++ ) { + RealA(i,j) = RealT(j); + ImagA(i,j) = ImagT(j); + } + } +} + diff --git a/Cpp/fftpoi.cpp b/Cpp/fftpoi.cpp new file mode 100644 index 0000000..2c77d09 --- /dev/null +++ b/Cpp/fftpoi.cpp @@ -0,0 +1,95 @@ +// fftpoi - Program to solve the Poisson equation using +// MFT method (periodic boundary conditions) +#include "NumMeth.h" + +void fft2( Matrix& RealA, Matrix& ImagA); +void ifft2( Matrix& RealA, Matrix& ImagA); + +void main() { + + //* Initialize parameters (system size, grid spacing, etc.) + double eps0 = 8.8542e-12; // Permittivity (C^2/(N m^2)) + int N = 64; // Number of grid points on a side (square grid) + double L = 1; // System size + double h = L/N; // Grid spacing for periodic boundary conditions + Matrix x(N), y(N); + int i,j; + for( i=1; i<=N; i++ ) + x(i) = (i-0.5)*h; // Coordinates of grid points + y = x; // Square grid + cout << "System is a square of length " << L << endl; + + //* Set up charge density rho(i,j) + Matrix rho(N,N); + rho.set(0.0); // Initialize charge density to zero + cout << "Enter number of line charges: "; int M; cin >> M; + for( i=1; i<=M; i++ ) { + cout << "For charge #" << i << endl; + cout << "Enter x coordinate: "; double xc; cin >> xc; + cout << "Enter y coordinate: "; double yc; cin >> yc; + int ii = (int)(xc/h) + 1; // Place charge at nearest + int jj = (int)(yc/h) + 1; // grid point + cout << "Enter charge density: "; double q; cin >> q; + rho(ii,jj) += q/(h*h); + } + + //* Compute matrix P + const double pi = 3.141592654; + Matrix cx(N), cy(N); + for( i=1; i<=N; i++ ) + cx(i) = cos((2*pi/N)*(i-1)); + cy = cx; + Matrix RealP(N,N), ImagP(N,N); + double numerator = -h*h/(2*eps0); + double tinyNumber = 1e-20; // Avoids division by zero + for( i=1; i<=N; i++ ) + for( j=1; j<=N; j++ ) + RealP(i,j) = numerator/(cx(i)+cy(j)-2+tinyNumber); + ImagP.set(0.0); + + //* Compute potential using MFT method + Matrix RealR(N,N), ImagR(N,N), RealF(N,N), ImagF(N,N); + for( i=1; i<=N; i++ ) + for( j=1; j<=N; j++ ) { + RealR(i,j) = rho(i,j); + ImagR(i,j) = 0.0; // Copy rho into R for input to fft2 + } + fft2(RealR,ImagR); // Transform rho into wavenumber domain + // Compute phi in the wavenumber domain + for( i=1; i<=N; i++ ) + for( j=1; j<=N; j++ ) { + RealF(i,j) = RealR(i,j)*RealP(i,j) - ImagR(i,j)*ImagP(i,j); + ImagF(i,j) = RealR(i,j)*ImagP(i,j) + ImagR(i,j)*RealP(i,j); + } + Matrix phi(N,N); + ifft2(RealF,ImagF); // Inv. transf. phi into the coord. domain + for( i=1; i<=N; i++ ) + for( j=1; j<=N; j++ ) + phi(i,j) = RealF(i,j); + + //* Print out the plotting variables: x, y, phi + ofstream xOut("x.txt"), yOut("y.txt"), phiOut("phi.txt"); + for( i=1; i<=N; i++ ) { + xOut << x(i) << endl; + yOut << y(i) << endl; + for( j=1; j> N; + cout << "Enter frequency of the sine wave: "; + double freq; cin >> freq; + cout << "Enter phase of the sine wave: "; + double phase; cin >> phase; + double tau = 1; // Time increment + const double pi = 3.141592654; + Matrix t(N), y(N), f(N); + int i,j,k; + for( i=1; i<=N; i++ ) { + t(i) = (i-1)*tau; // t = [0, tau, 2*tau, ... ] + y(i) = sin(2*pi*t(i)*freq + phase); // Sine wave time series + f(i) = (i-1)/(N*tau); // f = [0, 1/(N*tau), ... ] + } + + //* Compute the transform using desired method: direct summation + // or fast Fourier transform (FFT) algorithm. + Matrix ytReal(N), ytImag(N); + cout << "Compute transform by, 1) Direct summation; 2) FFT: "; + int method; cin >> method; + if( method == 1 ) { // Direct summation + double twoPiN = -2*pi/N; + for( k=0; k fabs(A(i,j))) ? scaleMax : fabs(A(i,j)); + scale(i) = scaleMax; + } + + //* Loop over rows k = 1, ..., (N-1) + int signDet = 1; + for( k=1; k<=(N-1); k++ ) { + //* Select pivot row from max( |A(j,k)/s(j)| ) + double ratiomax = 0.0; + int jPivot = k; + for( i=k; i<=N; i++ ) { + double ratio = fabs(A(index[i],k))/scale(index[i]); + if( ratio > ratiomax ) { + jPivot = i; + ratiomax = ratio; + } + } + //* Perform pivoting using row index list + int indexJ = index[k]; + if( jPivot != k ) { // Pivot + indexJ = index[jPivot]; + index[jPivot] = index[k]; // Swap index jPivot and k + index[k] = indexJ; + signDet *= -1; // Flip sign of determinant + } + //* Perform forward elimination + for( i=k+1; i<=N; i++ ) { + double coeff = A(index[i],k)/A(indexJ,k); + for( j=k+1; j<=N; j++ ) + A(index[i],j) -= coeff*A(indexJ,j); + A(index[i],k) = coeff; + b(index[i]) -= A(index[i],k)*b(indexJ); + } + } + //* Compute determinant as product of diagonal elements + double determ = signDet; // Sign of determinant + for( i=1; i<=N; i++ ) + determ *= A(index[i],i); + + //* Perform backsubstitution + x(N) = b(index[N])/A(index[N],N); + for( i=N-1; i>=1; i-- ) { + double sum = b(index[i]); + for( j=i+1; j<=N; j++ ) + sum -= A(index[i],j)*x(j); + x(i) = sum/A(index[i],i); + } + + delete [] index; // Release allocated memory + return( determ ); +} diff --git a/Cpp/gravrk.cpp b/Cpp/gravrk.cpp new file mode 100644 index 0000000..8abc837 --- /dev/null +++ b/Cpp/gravrk.cpp @@ -0,0 +1,23 @@ +#include "NumMeth.h" + +void gravrk(double x[], double t, double param[], double deriv[]) { +// Returns right-hand side of Kepler ODE; used by Runge-Kutta routines +// Inputs +// x State vector [r(1) r(2) v(1) v(2)] +// t Time (not used) +// param Parameter G*M (gravitational const. * solar mass) +// Output +// deriv Derivatives [dr(1)/dt dr(2)/dt dv(1)/dt dv(2)/dt] + + //* Compute acceleration + double GM = param[1]; + double r1 = x[1], r2 = x[2]; // Unravel the vector s into + double v1 = x[3], v2 = x[4]; // position and velocity + double normR = sqrt( r1*r1 + r2*r2 ); + double accel1 = -GM*r1/(normR*normR*normR); // Gravitational acceleration + double accel2 = -GM*r2/(normR*normR*normR); + + //* Return derivatives [dr[1]/dt dr[2]/dt dv[1]/dt dv[2]/dt] + deriv[1] = v1; deriv[2] = v2; + deriv[3] = accel1; deriv[4] = accel2; +} diff --git a/Cpp/ifft.cpp b/Cpp/ifft.cpp new file mode 100644 index 0000000..b2528c9 --- /dev/null +++ b/Cpp/ifft.cpp @@ -0,0 +1,27 @@ +#include "NumMeth.h" + +void fft( Matrix& RealA, Matrix& ImagA); + +void ifft( Matrix& RealA, Matrix& ImagA) { +// Routine to compute inverse Fourier transform using FFT algorithm +// Inputs +// RealA, ImagA Real and imaginary parts of transform +// Outputs +// RealA, ImagA Real and imaginary parts of time series + + int i, N = RealA.nRow(); // Number of data points + + //* Take complex conjugate of input transform + for( i=1; i<=N; i++ ) + ImagA(i) *= -1.0; // Complex conjugate + + //* Evaluate fast fourier transform + fft( RealA, ImagA ); + + //* Take complex conjugate and normalize by N + double invN = 1.0/N; + for( i=1; i<=N; i++ ) { + RealA(i) *= invN; + ImagA(i) *= -invN; // Normalize and complex conjugate + } +} diff --git a/Cpp/ifft2.cpp b/Cpp/ifft2.cpp new file mode 100644 index 0000000..33cdc8b --- /dev/null +++ b/Cpp/ifft2.cpp @@ -0,0 +1,50 @@ +#include "NumMeth.h" + +void fft( Matrix& RealA, Matrix& ImagA); + +void ifft2( Matrix& RealA, Matrix& ImagA) { +// Routine to compute inverse two dimensional Fourier transform +// using FFT algorithm +// Inputs +// RealA, ImagA Real and imaginary parts of transform array +// Outputs +// RealA, ImagA Real and imaginary parts of data array + + int i, j, N = RealA.nRow(); + Matrix RealT(N), ImagT(N); // Temporary work vector + + //* Loop over the columns of the matrix + for( j=1; j<=N; j++ ) { + //* Copy out a column into a vector and take its complex conjugate + for( i=1; i<=N; i++ ) { + RealT(i) = RealA(i,j); + ImagT(i) = -1.0*ImagA(i,j); + } + //* Take FFT of the vector + fft(RealT,ImagT); + //* Copy the transformed vector back into the column + for( i=1; i<=N; i++ ) { + RealA(i,j) = RealT(i); + ImagA(i,j) = ImagT(i); + } + } + + //* Loop over the rows of the matrix + double invN2 = 1.0/(N*N); + for( i=1; i<=N; i++ ) { + //* Copy out a row into a vector and take its complex conjugate + for( j=1; j<=N; j++ ) { + RealT(j) = RealA(i,j); + ImagT(j) = ImagA(i,j); + } + //* Take FFT of the vector + fft(RealT,ImagT); + //* Copy the transformed vector back, taking its complex conjugate + // and applying the 1/N normalization + for( j=1; j<=N; j++ ) { + RealA(i,j) = RealT(j)*invN2; + ImagA(i,j) = -1.0*ImagT(j)*invN2; + } + } +} + diff --git a/Cpp/interp.cpp b/Cpp/interp.cpp new file mode 100644 index 0000000..b752cbe --- /dev/null +++ b/Cpp/interp.cpp @@ -0,0 +1,56 @@ +// interp - Program to interpolate data using Lagrange +// polynomial to fit quadratic to three data points +#include "NumMeth.h" + +double intrpf( double xi, double x[], double y[]); + +void main() { + + //* Initialize the data points to be fit by quadratic + double x[3+1], y[3+1]; + cout << "Enter data points:" << endl; + int i; + for( i=1; i<=3; i++ ) { + cout << "x[" << i << "] = "; + cin >> x[i]; + cout << "y[" << i << "] = "; + cin >> y[i]; + } + + //* Establish the range of interpolation (from x_min to x_max) + double x_min, x_max; + cout << "Enter minimum value of x: "; cin >> x_min; + cout << "Enter maximum value of x: "; cin >> x_max; + + //* Find yi for the desired interpolation values xi using + // the function intrpf + int nplot = 100; // Number of points for interpolation curve + double *xi, *yi; + xi = new double [nplot+1]; // Allocate memory for these + yi = new double [nplot+1]; // arrays (nplot+1 elements) + for( i=1; i<=nplot; i++ ) { + xi[i] = x_min + (x_max-x_min)*(i-1)/(nplot-1); + yi[i] = intrpf(xi[i],x,y); // Use intrpf function to interpolate + } + + //* Print out the plotting variables: x, y, xi, yi + ofstream xOut("x.txt"), yOut("y.txt"), xiOut("xi.txt"), + yiOut("yi.txt"); + for( i=1; i<=3; i++ ) { + xOut << x[i] << endl; + yOut << y[i] << endl; + } + for( i=1; i<=nplot; i++ ) { + xiOut << xi[i] << endl; + yiOut << yi[i] << endl; + } + + delete [] xi, yi; // Release memory allocated by "new" +} +/***** To plot in MATLAB; use the script below ******************** +load x.txt; load y.txt; load xi.txt; load yi.txt; +plot(x,y,'*',xi,yi,'-'); +xlabel('x'); ylabel('y'); +title('Three point interpolation'); +legend('Data points','Interpolation'); +******************************************************************/ diff --git a/Cpp/intrpf.cpp b/Cpp/intrpf.cpp new file mode 100644 index 0000000..4125ee3 --- /dev/null +++ b/Cpp/intrpf.cpp @@ -0,0 +1,16 @@ +double intrpf( double xi, double x[], double y[]) { +// Function to interpolate between data points +// using Lagrange polynomial (quadratic) +// Inputs +// xi The x value where interpolation is computed +// x Vector of x coordinates of data points (3 values) +// y Vector of y coordinates of data points (3 values) +// Output +// yi The interpolation polynomial evaluated at xi + + //* Calculate yi = p(xi) using Lagrange polynomial + double yi = (xi-x[2])*(xi-x[3])/((x[1]-x[2])*(x[1]-x[3]))*y[1] + + (xi-x[1])*(xi-x[3])/((x[2]-x[1])*(x[2]-x[3]))*y[2] + + (xi-x[1])*(xi-x[2])/((x[3]-x[1])*(x[3]-x[2]))*y[3]; + return (yi); +}; diff --git a/Cpp/inv.cpp b/Cpp/inv.cpp new file mode 100644 index 0000000..51fb555 --- /dev/null +++ b/Cpp/inv.cpp @@ -0,0 +1,84 @@ +#include "NumMeth.h" + +// Compute inverse of matrix +double inv(Matrix A, Matrix& Ainv) +// Input +// A - Matrix A (N by N) +// Outputs +// Ainv - Inverse of matrix A (N by N) +// determ - Determinant of matrix A (return value) +{ + + int N = A.nRow(); + assert( N == A.nCol() ); + + Ainv = A; // Copy matrix to ensure Ainv is same size + + int i, j, k; + Matrix scale(N), b(N,N); // Scale factor and work array + int *index; index = new int [N+1]; + + //* Matrix b is initialized to the identity matrix + b.set(0.0); + for( i=1; i<=N; i++ ) + b(i,i) = 1.0; + + //* Set scale factor, scale(i) = max( |a(i,j)| ), for each row + for( i=1; i<=N; i++ ) { + index[i] = i; // Initialize row index list + double scalemax = 0.; + for( j=1; j<=N; j++ ) + scalemax = (scalemax > fabs(A(i,j))) ? scalemax : fabs(A(i,j)); + scale(i) = scalemax; + } + + //* Loop over rows k = 1, ..., (N-1) + int signDet = 1; + for( k=1; k<=N-1; k++ ) { + //* Select pivot row from max( |a(j,k)/s(j)| ) + double ratiomax = 0.0; + int jPivot = k; + for( i=k; i<=N; i++ ) { + double ratio = fabs(A(index[i],k))/scale(index[i]); + if( ratio > ratiomax ) { + jPivot=i; + ratiomax = ratio; + } + } + //* Perform pivoting using row index list + int indexJ = index[k]; + if( jPivot != k ) { // Pivot + indexJ = index[jPivot]; + index[jPivot] = index[k]; // Swap index jPivot and k + index[k] = indexJ; + signDet *= -1; // Flip sign of determinant + } + //* Perform forward elimination + for( i=k+1; i<=N; i++ ) { + double coeff = A(index[i],k)/A(indexJ,k); + for( j=k+1; j<=N; j++ ) + A(index[i],j) -= coeff*A(indexJ,j); + A(index[i],k) = coeff; + for( j=1; j<=N; j++ ) + b(index[i],j) -= A(index[i],k)*b(indexJ,j); + } + } + //* Compute determinant as product of diagonal elements + double determ = signDet; // Sign of determinant + for( i=1; i<=N; i++ ) + determ *= A(index[i],i); + + //* Perform backsubstitution + for( k=1; k<=N; k++ ) { + Ainv(N,k) = b(index[N],k)/A(index[N],N); + for( i=N-1; i>=1; i--) { + double sum = b(index[i],k); + for( j=i+1; j<=N; j++ ) + sum -= A(index[i],j)*Ainv(j,k); + Ainv(i,k) = sum/A(index[i],i); + } + } + + delete [] index; // Release allocated memory + return( determ ); +} diff --git a/Cpp/legndr.cpp b/Cpp/legndr.cpp new file mode 100644 index 0000000..269a705 --- /dev/null +++ b/Cpp/legndr.cpp @@ -0,0 +1,19 @@ +#include "NumMeth.h" + +void legndr( int n, double x, Matrix& p) { +// Legendre polynomials function +// Inputs +// n Highest order polynomial returned +// x Value at which polynomial is evaluated +// Output +// p Vector containing P(x) for order 0,1,...,n + + //* Perform upward recursion + p(1) = 1; // P(x) for n=0 + if(n == 0) return; + p(2) = x; // P(x) for n=1 + // Use upward recursion to obtain other n's + int i; + for( i=3; i<=(n+1); i++ ) + p(i) = ((2*i-3)*x*p(i-1) - (i-2)*p(i-2))/(i-1); +} diff --git a/Cpp/linreg.cpp b/Cpp/linreg.cpp new file mode 100644 index 0000000..cb11732 --- /dev/null +++ b/Cpp/linreg.cpp @@ -0,0 +1,45 @@ +#include "NumMeth.h" + +void linreg(Matrix x, Matrix y, Matrix sigma, + Matrix &a_fit, Matrix &sig_a, Matrix &yy, double &chisqr) { +// Function to perform linear regression (fit a line) +// Inputs +// x Independent variable +// y Dependent variable +// sigma Estimated error in y +// Outputs +// a_fit Fit parameters; a(1) is intercept, a(2) is slope +// sig_a Estimated error in the parameters a() +// yy Curve fit to the data +// chisqr Chi squared statistic + + //* Evaluate various sigma sums + int i, nData = x.nRow(); + double sigmaTerm; + double s = 0.0, sx = 0.0, sy = 0.0, sxy = 0.0, sxx = 0.0; + for( i=1; i<=nData; i++ ) { + sigmaTerm = 1.0/(sigma(i)*sigma(i)); + s += sigmaTerm; + sx += x(i) * sigmaTerm; + sy += y(i) * sigmaTerm; + sxy += x(i) * y(i) * sigmaTerm; + sxx += x(i) * x(i) * sigmaTerm; + } + double denom = s*sxx - sx*sx; + + //* Compute intercept a_fit(1) and slope a_fit(2) + a_fit(1) = (sxx*sy - sx*sxy)/denom; + a_fit(2) = (s*sxy - sx*sy)/denom; + + //* Compute error bars for intercept and slope + sig_a(1) = sqrt(sxx/denom); + sig_a(2) = sqrt(s/denom); + + //* Evaluate curve fit at each data point and compute Chi^2 + chisqr = 0.0; + for( i=1; i<=nData; i++ ) { + yy(i) = a_fit(1)+a_fit(2)*x(i); // Curve fit to the data + double delta = (y(i)-yy(i))/sigma(i); + chisqr += delta*delta; // Chi square + } +} diff --git a/Cpp/lorenz.cpp b/Cpp/lorenz.cpp new file mode 100644 index 0000000..5cc0337 --- /dev/null +++ b/Cpp/lorenz.cpp @@ -0,0 +1,104 @@ +// lorenz - Program to compute the trajectories of the Lorenz +// equations using the adaptive Runge-Kutta method. +#include "NumMeth.h" + +void lorzrk(double x[], double t, double param[], double deriv[]); +void rka( double x[], int nX, double& t, double& tau, double err, + void (*derivsRK)(double x[], double t, double param[], double deriv[]), + double param[]); + +void main() { + + //* Set initial state x,y,z and parameters r,sigma,b + cout << "Enter initial state (x,y,z)" << endl; + double x; cout << "x = "; cin >> x; + double y; cout << "y = "; cin >> y; + double z; cout << "z = "; cin >> z; + const int nState = 3; // Number of elements in state + double state[nState+1]; + state[1] = x; state[2] = y; state[3] = z; + cout << "Enter the parameter r: "; + double r; cin >> r; + double sigma = 10.; // Parameter sigma + double b = 8./3.; // Parameter b + double param[3+1]; // Vector of parameters passed to rka + param[1] = r; param[2] = sigma; param[3] = b; + double tau = 1.0; // Initial guess for the timestep + double err = 1.e-3; // Error tolerance + + //* Loop over the desired number of steps + double time = 0; + cout << "Enter number of steps: "; + int iStep, nStep; cin >> nStep; + double *tplot, *tauplot, *xplot, *yplot, *zplot; + tplot = new double [nStep+1]; tauplot = new double [nStep+1]; + xplot = new double [nStep+1]; // Plotting variables + yplot = new double [nStep+1]; zplot = new double [nStep+1]; + for( iStep=1; iStep<=nStep; iStep++ ) { + + //* Record values for plotting + x = state[1]; y = state[2]; z = state[3]; + tplot[iStep] = time; tauplot[iStep] = tau; + xplot[iStep] = x; yplot[iStep] = y; zplot[iStep] = z; + if( (iStep % 50) < 1 ) + cout << "Finished " << iStep << " steps out of " + << nStep << endl; + + //* Find new state using adaptive Runge-Kutta + rka(state,nState,time,tau,err,lorzrk,param); + } + + //* Print max and min time step returned by rka + double maxTau = tauplot[2], minTau = tauplot[2]; + int i; + for( i=3; i<=nStep; i++ ) { + maxTau = (maxTau > tauplot[i]) ? maxTau:tauplot[i]; + minTau = (minTau < tauplot[i]) ? minTau:tauplot[i]; + } + cout << "Adaptive time step: Max = " << maxTau << + " Min = " << minTau << endl; + + // Find the location of the three steady states + double x_ss[3+1], y_ss[3+1], z_ss[3+1]; + x_ss[1] = 0; y_ss[1] = 0; z_ss[1] = 0; + x_ss[2] = sqrt(b*(r-1)); y_ss[2] = x_ss[2]; z_ss[2] = r-1; + x_ss[3] = -sqrt(b*(r-1)); y_ss[3] = x_ss[3]; z_ss[3] = r-1; + + //* Print out the plotting variables: + // tplot, xplot, yplot, zplot, x_ss, y_ss, z_ss + ofstream tplotOut("tplot.txt"), xplotOut("xplot.txt"), + yplotOut("yplot.txt"), zplotOut("zplot.txt"), + x_ssOut("x_ss.txt"), y_ssOut("y_ss.txt"), + z_ssOut("z_ss.txt"); + for( i=1; i<=nStep; i++ ) { + tplotOut << tplot[i] << endl; + xplotOut << xplot[i] << endl; + yplotOut << yplot[i] << endl; + zplotOut << zplot[i] << endl; + } + for( i=1; i<=3; i++ ) { + x_ssOut << x_ss[i] << endl; + y_ssOut << y_ss[i] << endl; + z_ssOut << z_ss[i] << endl; + } + + delete [] tplot, tauplot, xplot, yplot, zplot; // Release memory + +} +/***** To plot in MATLAB; use the script below ******************** +load tplot.txt; load xplot.txt; load yplot.txt; load zplot.txt; +load x_ss.txt; load y_ss.txt; load z_ss.txt; +%* Graph the time series x(t) +figure(1); clf; % Clear figure 1 window and bring forward +plot(tplot,xplot,'-') +xlabel('Time'); ylabel('x(t)') +title('Lorenz model time series') +pause(1) % Pause 1 second +%* Graph the x,y,z phase space trajectory +figure(2); clf; % Clear figure 2 window and bring forward +plot3(xplot,yplot,zplot,'-',x_ss,y_ss,z_ss,'*') +view([30 20]); % Rotate to get a better view +grid; % Add a grid to aid perspective +xlabel('x'); ylabel('y'); zlabel('z'); +title('Lorenz model phase space'); +******************************************************************/ diff --git a/Cpp/lorzrk.cpp b/Cpp/lorzrk.cpp new file mode 100644 index 0000000..f0af465 --- /dev/null +++ b/Cpp/lorzrk.cpp @@ -0,0 +1,21 @@ +#include "NumMeth.h" + +void lorzrk(double X[], double t, double param[], double deriv[]) { +// Returns right-hand side of Lorenz model ODEs +// Inputs +// X State vector [x y z] +// t Time (not used) +// param Parameters [r sigma b] +// Output +// deriv Derivatives [dx/dt dy/dt dz/dt] + + //* For clarity, unravel input vectors + double x = X[1]; double y = X[2]; double z = X[3]; + double r = param[1]; double sigma = param[2]; double b = param[3]; + + //* Return the derivatives [dx/dt dy/dt dz/dt] + deriv[1] = sigma*(y-x); + deriv[2] = r*x - y - x*z; + deriv[3] = x*y - b*z; + return; +} \ No newline at end of file diff --git a/Cpp/lsfdemo.cpp b/Cpp/lsfdemo.cpp new file mode 100644 index 0000000..240a4dd --- /dev/null +++ b/Cpp/lsfdemo.cpp @@ -0,0 +1,66 @@ +// lsfdemo - Program for demonstrating least squares fit routines +#include "NumMeth.h" + +void linreg( Matrix x, Matrix y, Matrix sigma, + Matrix &a_fit, Matrix &sig_a, Matrix &yy, double &chisqr ); +void pollsf( Matrix x, Matrix y, Matrix sigma, int M, + Matrix& a_fit, Matrix& sig_a, Matrix& yy, double& chisqr ); +double randn( long& iseed ); + +void main() { + + //* Initialize data to be fit. Data is quadratic plus random number. + Matrix c(3); + cout << "Curve fit data is created using the quadratic" << endl; + cout << " y(x) = c(1) + c(2)*x + c(3)*x^2" << endl; + cout << "Enter the coefficients:" << endl; + cout << "c(1) = "; cin >> c(1); + cout << "c(2) = "; cin >> c(2); + cout << "c(3) = "; cin >> c(3); + double alpha; + cout << "Enter estimated error bar: "; cin >> alpha; + int i, N = 50; // Number of data points + long seed = 1234; // Seed for random number generator + Matrix x(N), y(N), sigma(N); + for( i=1; i<=N; i++ ) { + x(i) = i; // x = [1, 2, ..., N] + y(i) = c(1) + c(2)*x(i) + c(3)*x(i)*x(i) + alpha*randn(seed); + sigma(i) = alpha; // Constant error bar + } + + //* Fit the data to a straight line or a more general polynomial + cout << "Enter number of fit parameters (=2 for line): "; + int M; cin >> M; + Matrix a_fit(M), sig_a(M), yy(N); double chisqr; + if( M == 2 ) //* Linear regression (Straight line) fit + linreg( x, y, sigma, a_fit, sig_a, yy, chisqr); + else //* Polynomial fit + pollsf( x, y, sigma, M, a_fit, sig_a, yy, chisqr); + + //* Print out the fit parameters, including their error bars. + cout << "Fit parameters:" << endl; + for( i=1; i<=M; i++ ) + cout << " a(" << i << ") = " << a_fit(i) << + " +/- " << sig_a(i) << endl; + + cout << "Chi square = " << chisqr << "; N-M = " << N-M << endl; + + //* Print out the plotting variables: x, y, sigma, yy + ofstream xOut("x.txt"), yOut("y.txt"), + sigmaOut("sigma.txt"), yyOut("yy.txt"); + for( i=1; i<=N; i++ ) { + xOut << x(i) << endl; + yOut << y(i) << endl; + sigmaOut << sigma(i) << endl; + yyOut << yy(i) << endl; + } +} +/***** To plot in MATLAB; use the script below ******************** +load x.txt; load y.txt; load sigma.txt; load yy.txt +%* Graph the data, with error bars, and fitting function. +figure(1); clf; % Bring figure 1 window forward +errorbar(x,y,sigma,'o'); % Graph data with error bars +hold on; % Freeze the plot to add the fit +plot(x,yy,'-'); % Plot the fit on same graph as data +xlabel('x_i'); ylabel('y_i and Y(x)'); +******************************************************************/ diff --git a/Cpp/mover.cpp b/Cpp/mover.cpp new file mode 100644 index 0000000..0e4645d --- /dev/null +++ b/Cpp/mover.cpp @@ -0,0 +1,69 @@ +#include "NumMeth.h" + +double rand( long& seed ); +double randn( long& seed ); + +void mover( Matrix& x, Matrix& v, int npart, double L, + double mpv, double vwall, double tau, + Matrix& strikes, Matrix& delv, long& seed ) { + +// mover - Function to move particles by free flight +// Also handles collisions with walls +// Inputs +// x Positions of the particles +// v Velocities of the particles +// npart Number of particles in the system +// L System length +// mpv Most probable velocity off the wall +// vwall Wall velocities +// tau Time step +// seed Random number seed +// Outputs +// x,v Updated positions and velocities +// strikes Number of particles striking each wall +// delv Change of y-velocity at each wall +// seed Random number seed + + //* Move all particles pretending walls are absent + Matrix x_old(npart); + x_old = x; // Remember original position + int i; + for( i=1; i<= npart; i++ ) + x(i) = x_old(i) + v(i,1)*tau; + + //* Check each particle to see if it strikes a wall + strikes.set(0.0); delv.set(0.0); + Matrix xwall(2), vw(2), direction(2); + xwall(1) = 0; xwall(2) = L; // Positions of walls + vw(1) = -vwall; vw(2) = vwall; // Velocities of walls + double stdev = mpv/sqrt(2.); + // Direction of particle leaving wall + direction(1) = 1; direction(2) = -1; + for( i=1; i<=npart; i++ ) { + + //* Test if particle strikes either wall + int flag = 0; + if( x(i) <= 0 ) + flag=1; // Particle strikes left wall + else if( x(i) >= L ) + flag=2; // Particle strikes right wall + + //* If particle strikes a wall, reset its position + // and velocity. Record velocity change. + if( flag > 0 ) { + strikes(flag)++; + double vyInitial = v(i,2); + //* Reset velocity components as biased Maxwellian, + // Exponential dist. in x; Gaussian in y and z + v(i,1) = direction(flag)*sqrt(-log(1.-rand(seed))) * mpv; + v(i,2) = stdev*randn(seed) + vw(flag); // Add wall velocity + v(i,3) = stdev*randn(seed); + // Time of flight after leaving wall + double dtr = tau*(x(i)-xwall(flag))/(x(i)-x_old(i)); + //* Reset position after leaving wall + x(i) = xwall(flag) + v(i,1)*dtr; + //* Record velocity change for force measurement + delv(flag) += (v(i,2) - vyInitial); + } + } +} diff --git a/Cpp/neutrn.cpp b/Cpp/neutrn.cpp new file mode 100644 index 0000000..d6b24e9 --- /dev/null +++ b/Cpp/neutrn.cpp @@ -0,0 +1,90 @@ +// neutrn - Program to solve the neutron diffusion equation +// using the Forward Time Centered Space (FTCS) scheme. +#include "NumMeth.h" + +void main() { + + //* Initialize parameters (time step, grid spacing, etc.). + cout << "Enter time step: "; double tau; cin >> tau; + cout << "Enter the number of grid points: "; int N; cin >> N; + cout << "Enter system length: "; double L; cin >> L; + // The system extends from x=-L/2 to x=L/2 + double h = L/(N-1); // Grid size + double D = 1.; // Diffusion coefficient + double C = 1.; // Generation rate + double coeff = D*tau/(h*h); + double coeff2 = C*tau; + if( coeff < 0.5 ) + cout << "Solution is expected to be stable" << endl; + else + cout << "WARNING: Solution is expected to be unstable" << endl; + + //* Set initial and boundary conditions. + Matrix nn(N), nn_new(N); + nn.set(0.0); // Initialize density to zero at all points + nn(N/2) = 1/h; // Initial cond. is delta function in center + //// The boundary conditions are nn(1) = nn(N) = 0 + nn_new.set(0.0); // End points are unchanged during iteration + + //* Set up loop and plot variables. + int iplot = 1; // Counter used to count plots + cout << "Enter number of time steps: "; int nStep; cin >> nStep; + int plot_step = 200; // Number of time steps between plots + int nplots = nStep/plot_step + 1; // Number of snapshots (plots) + Matrix xplot(N), tplot(nplots), nnplot(N,nplots), nAve(nplots); + int i,j; + for( i=1; i<=N; i++ ) + xplot(i) = (i-1)*h - L/2; // Record the x scale for plots + + //* Loop over the desired number of time steps. + int iStep; + for( iStep=1; iStep<=nStep; iStep++ ) { + + //* Compute new density using FTCS scheme. + for( i=2; i<=(N-1); i++ ) + nn_new(i) = nn(i) + coeff*(nn(i+1) + nn(i-1) - 2*nn(i)) + + coeff2*nn(i); + + nn = nn_new; // Reset density to new values + + //* Periodically record density for plotting. + if( (iStep%plot_step) < 1 ) { // Every plot_step steps ... + double nSum = 0; + for( i=1; i<=N; i++ ) { + nnplot(i,iplot) = nn(i); // Record tt(i) for plotting + nSum += nn(i); + } + nAve(iplot) = nSum/N; + tplot(iplot) = iStep*tau; // Record time for plots + iplot++; + } + } + nplots = iplot-1; // Number of plots actually recorded + + //* Print out the plotting variables: tplot, xplot, nnplot, nAve + ofstream tplotOut("tplot.txt"), xplotOut("xplot.txt"), + nnplotOut("nnplot.txt"), nAveOut("nAve.txt"); + for( i=1; i<=nplots; i++ ) { + tplotOut << tplot(i) << endl; + nAveOut << nAve(i) << endl; + } + for( i=1; i<=N; i++ ) { + xplotOut << xplot(i) << endl; + for( j=1; j> r0; + cout << "Enter initial tangential velocity (AU/yr): "; cin >> v0; + double r[2+1], v[2+1], state[4+1], accel[2+1]; + r[1] = r0; r[2] = 0; v[1] = 0; v[2] = v0; + state[1] = r[1]; state[2] = r[2]; // Used by R-K routines + state[3] = v[1]; state[4] = v[2]; + int nState = 4; // Number of elements in state vector + + //* Set physical parameters (mass, G*M) + const double pi = 3.141592654; + double GM = 4*pi*pi; // Grav. const. * Mass of Sun (au^3/yr^2) + double param[1+1]; param[1] = GM; + double mass = 1.; // Mass of comet + double adaptErr = 1.e-3; // Error parameter used by adaptive Runge-Kutta + double time = 0; + + //* Loop over desired number of steps using specified + // numerical method. + cout << "Enter number of steps: "; + int nStep; cin >> nStep; + cout << "Enter time step (yr): "; + double tau; cin >> tau; + cout << "Choose a numerical method:" << endl; + cout << "1) Euler, 2) Euler-Cromer, " << endl + << "3) Runge-Kutta, 4) Adaptive R-K: "; + int method; cin >> method; + double *rplot, *thplot, *tplot, *kinetic, *potential; // Plotting variables + rplot = new double [nStep+1]; thplot = new double [nStep+1]; + tplot = new double [nStep+1]; + kinetic = new double [nStep+1]; potential = new double [nStep+1]; + int iStep; + for( iStep=1; iStep<=nStep; iStep++ ) { + + //* Record position and energy for plotting. + double normR = sqrt( r[1]*r[1] + r[2]*r[2] ); + double normV = sqrt( v[1]*v[1] + v[2]*v[2] ); + rplot[iStep] = normR; // Record position for plotting + thplot[iStep] = atan2(r[2],r[1]); + tplot[iStep] = time; + kinetic[iStep] = 0.5*mass*normV*normV; // Record energies + potential[iStep] = - GM*mass/normR; + + //* Calculate new position and velocity using desired method. + if( method == 1 ) { + accel[1] = -GM*r[1]/(normR*normR*normR); + accel[2] = -GM*r[2]/(normR*normR*normR); + r[1] += tau*v[1]; // Euler step + r[2] += tau*v[2]; + v[1] += tau*accel[1]; + v[2] += tau*accel[2]; + time += tau; + } + else if( method == 2 ) { + accel[1] = -GM*r[1]/(normR*normR*normR); + accel[2] = -GM*r[2]/(normR*normR*normR); + v[1] += tau*accel[1]; + v[2] += tau*accel[2]; + r[1] += tau*v[1]; // Euler-Cromer step + r[2] += tau*v[2]; + time += tau; + } + else if( method == 3 ) { + rk4( state, nState, time, tau, gravrk, param ); + r[1] = state[1]; r[2] = state[2]; // 4th order Runge-Kutta + v[1] = state[3]; v[2] = state[4]; + time += tau; + } + else { + rka( state, nState, time, tau, adaptErr, gravrk, param ); + r[1] = state[1]; r[2] = state[2]; // Adaptive Runge-Kutta + v[1] = state[3]; v[2] = state[4]; + } + + } + + //* Print out the plotting variables: + // thplot, rplot, potential, kinetic + ofstream thplotOut("thplot.txt"), rplotOut("rplot.txt"), + tplotOut("tplot.txt"), potentialOut("potential.txt"), + kineticOut("kinetic.txt"); + int i; + for( i=1; i<=nStep; i++ ) { + thplotOut << thplot[i] << endl; + rplotOut << rplot[i] << endl; + tplotOut << tplot[i] << endl; + potentialOut << potential[i] << endl; + kineticOut << kinetic[i] << endl; + } + + delete [] rplot, thplot, tplot, kinetic, potential; + +} +/***** To plot in MATLAB; use the script below ******************** +load thplot.txt; load rplot.txt; load tplot.txt; +load potential.txt; load kinetic.txt; +%* Graph the trajectory of the comet. +figure(1); clf; % Clear figure 1 window and bring forward +polar(thplot,rplot,'+'); % Use polar plot for graphing orbit +xlabel('Distance (AU)'); grid; +pause(1) % Pause for 1 second before drawing next plot +%* Graph the energy of the comet versus time. +figure(2); clf; % Clear figure 2 window and bring forward +totalE = kinetic + potential; % Total energy +plot(tplot,kinetic,'-.',tplot,potential,'--',tplot,totalE,'-') +legend('Kinetic','Potential','Total'); +xlabel('Time (yr)'); ylabel('Energy (M AU^2/yr^2)'); +******************************************************************/ diff --git a/Cpp/orthog.cpp b/Cpp/orthog.cpp new file mode 100644 index 0000000..b64f305 --- /dev/null +++ b/Cpp/orthog.cpp @@ -0,0 +1,34 @@ +// orthog - Program to test if a pair of vectors +// is orthogonal. Assumes vectors are in 3D space +#include + +void main() { + + //* Initialize the vectors a and b + double a[3+1], b[3+1]; + cout << "Enter the first vector" << endl; + int i; + for( i=1; i<=3; i++ ) { + cout << " a[" << i << "] = "; + cin >> a[i]; + } + cout << "Enter the second vector" << endl; + for( i=1; i<=3; i++ ) { + cout << " b[" << i << "] = "; + cin >> b[i]; + } + + //* Evaluate the dot product as sum over products of elements + double a_dot_b = 0.0; + for( i=1; i<=3; i++ ) + a_dot_b += a[i]*b[i]; + + + //* Print dot product and state whether vectors are orthogonal + if( a_dot_b == 0.0 ) + cout << "Vectors are orthogonal" << endl; + else { + cout << "Vectors are NOT orthogonal" << endl; + cout << "Dot product = " << a_dot_b << endl; + } +} diff --git a/Cpp/pendul.cpp b/Cpp/pendul.cpp new file mode 100644 index 0000000..240dcbf --- /dev/null +++ b/Cpp/pendul.cpp @@ -0,0 +1,102 @@ +// pendul - Program to compute the motion of a simple pendulum +// using the Euler or Verlet method +#include "NumMeth.h" + +void main() { + + //* Select the numerical method to use: Euler or Verlet + cout << "Choose a numerical method 1) Euler, 2) Verlet: "; + int method; cin >> method; + + //* Set initial position and velocity of pendulum + cout << "Enter initial angle (in degrees): "; + double theta0; cin >> theta0; + const double pi = 3.141592654; + double theta = theta0*pi/180; // Convert angle to radians + double omega = 0.0; // Set the initial velocity + + //* Set the physical constants and other variables + double g_over_L = 1.0; // The constant g/L + double time = 0.0; // Initial time + double time_old; // Time of previous reversal + int irev = 0; // Used to count number of reversals + cout << "Enter time step: "; + double tau; cin >> tau; + + //* Take one backward step to start Verlet + double accel = -g_over_L*sin(theta); // Gravitational acceleration + double theta_old = theta - omega*tau + 0.5*tau*tau*accel; + + //* Loop over desired number of steps with given time step + // and numerical method + cout << "Enter number of time steps: "; + int nStep; cin >> nStep; + double *t_plot, *th_plot, *period; // Plotting variables + t_plot = new double [nStep+1]; th_plot = new double [nStep+1]; + period = new double [nStep+1]; + int iStep; + for( iStep=1; iStep<=nStep; iStep++ ) { + + //* Record angle and time for plotting + t_plot[iStep] = time; + th_plot[iStep] = theta*180/pi; // Convert angle to degrees + time += tau; + + //* Compute new position and velocity using + // Euler or Verlet method + accel = -g_over_L*sin(theta); // Gravitational acceleration + if( method == 1 ) { + theta_old = theta; // Save previous angle + theta += tau*omega; // Euler method + omega += tau*accel; + } + else { + double theta_new = 2*theta - theta_old + tau*tau*accel; + theta_old = theta; // Verlet method + theta = theta_new; + } + + //* Test if the pendulum has passed through theta = 0; + // if yes, use time to estimate period + if( theta*theta_old < 0 ) { // Test position for sign change + cout << "Turning point at time t = " << time << endl; + if( irev == 0 ) // If this is the first change, + time_old = time; // just record the time + else { + period[irev] = 2*(time - time_old); + time_old = time; + } + irev++; // Increment the number of reversals + } + } + int nPeriod = irev-1; // Number of times period is measured + + //* Estimate period of oscillation, including error bar + double AvePeriod = 0.0, ErrorBar = 0.0; + int i; + for( i=1; i<=nPeriod; i++ ) { + AvePeriod += period[i]; + } + AvePeriod /= nPeriod; + for( i=1; i<=nPeriod; i++ ) { + ErrorBar += (period[i] - AvePeriod)*(period[i] - AvePeriod); + } + ErrorBar = sqrt(ErrorBar/(nPeriod*(nPeriod-1))); + cout << "Average period = " << AvePeriod << " +/- " << ErrorBar << endl; + + //* Print out the plotting variables: t_plot, th_plot + ofstream t_plotOut("t_plot.txt"), th_plotOut("th_plot.txt"); + for( i=1; i<=nStep; i++ ) { + t_plotOut << t_plot[i] << endl; + th_plotOut << th_plot[i] << endl; + } + + delete [] t_plot, th_plot, period; + +} +/***** To plot in MATLAB; use the script below ******************** +load t_plot.txt; load th_plot.txt; +clf; figure(gcf); % Clear and forward figure window +plot(t_plot,th_plot,'+'); +xlabel('Time'); ylabel('Theta (degrees)'); +******************************************************************/ diff --git a/Cpp/pollsf.cpp b/Cpp/pollsf.cpp new file mode 100644 index 0000000..d2815d7 --- /dev/null +++ b/Cpp/pollsf.cpp @@ -0,0 +1,61 @@ +#include "NumMeth.h" + +void inv(Matrix a, Matrix& aInv); + +void pollsf( Matrix x, Matrix y, Matrix sigma, int M, + Matrix& a_fit, Matrix& sig_a, Matrix& yy, double& chisqr) { +// Function to fit a polynomial to data +// Inputs +// x Independent variable +// y Dependent variable +// sigma Estimate error in y +// M Number of parameters used to fit data +// Outputs +// a_fit Fit parameters; a(1) is intercept, a(2) is slope +// sig_a Estimated error in the parameters a() +// yy Curve fit to the data +// chisqr Chi squared statistic + + //* Form the vector b and design matrix A + int i, j, k, N = x.nRow(); + Matrix b(N), A(N,M); + for( i=1; i<=N; i++ ) { + b(i) = y(i)/sigma(i); + for( j=1; j<=M; j++ ) + A(i,j) = pow(x(i),(double)(j-1))/sigma(i); + } + + + //* Compute the correlation matrix C + Matrix C(M,M), Cinv(M,M); + for( i=1; i<=M; i++ ) { // (C inverse) = (A transpose) * A + for( j=1; j<=M; j++ ) { + Cinv(i,j) = 0.0; + for( k=1; k<=N; k++ ) + Cinv(i,j) += A(k,i)*A(k,j); + } + } + inv( Cinv, C ); // C = ( (C inverse) inverse) + + //* Compute the least squares polynomial coefficients a_fit + for( k=1; k<=M; k++ ) { + a_fit(k) = 0.0; + for( j=1; j<=M; j++ ) + for( i=1; i<=N; i++ ) + a_fit(k) += C(k,j) * A(i,j) * b(i); + } + + //* Compute the estimated error bars for the coefficients + for( j=1; j<=M; j++ ) + sig_a(j) = sqrt(C(j,j)); + + //* Evaluate curve fit at each data point and compute Chi^2 + chisqr = 0.0; + for( i=1; i<=N; i++ ) { + yy(i) = 0.0; // yy is the curve fit + for( j=1; j<=M; j++ ) + yy(i) += a_fit(j) * pow( x(i), (double)(j-1) ); + double delta = (y(i)-yy(i))/sigma(i); + chisqr += delta*delta; // Chi square + } +} diff --git a/Cpp/rand.cpp b/Cpp/rand.cpp new file mode 100644 index 0000000..e0ccf0d --- /dev/null +++ b/Cpp/rand.cpp @@ -0,0 +1,16 @@ +#include "NumMeth.h" + +// Random number generator; Uniform dist. in [0,1) +double rand( long& seed ) { +// Input +// seed Integer seed (DO NOT USE A SEED OF ZERO) +// Output +// rand Random number uniformly distributed in [0,1) + + const double a = 16807.0; + const double m = 2147483647.0; + double temp = a * seed; + seed = (long)(fmod(temp,m)); + double rand = seed/m; + return( rand ); +} \ No newline at end of file diff --git a/Cpp/randn.cpp b/Cpp/randn.cpp new file mode 100644 index 0000000..f6910dc --- /dev/null +++ b/Cpp/randn.cpp @@ -0,0 +1,15 @@ +#include "NumMeth.h" + +double rand( long& seed ); + +// Random number generator; Normal (Gaussian) dist. +double randn( long& seed ) { +// Input +// seed Integer seed (DO NOT USE A SEED OF ZERO) +// Output +// randn Random number, Gaussian distributed + + double randn = sqrt( -2.0*log(1.0 - rand(seed)) ) + * cos( 6.283185307 * rand(seed) ); + return( randn ); +} \ No newline at end of file diff --git a/Cpp/relax.cpp b/Cpp/relax.cpp new file mode 100644 index 0000000..e42103c --- /dev/null +++ b/Cpp/relax.cpp @@ -0,0 +1,126 @@ +// relax - Program to solve the Laplace equation using +// Jacobi, Gauss-Seidel and SOR methods on a square grid +#include "NumMeth.h" + +void main() { + + //* Initialize parameters (system size, grid spacing, etc.) + cout << "Select a numerical method: 1) Jacobi, 2) Gauss-Seidel, 3) SOR : "; + int method; cin >> method; + cout << "Enter number of grid points on a side: "; int N; cin >> N; + double L = 1; // System size (length) + double h = L/(N-1); // Grid spacing + Matrix x(N), y(N); + int i,j; + for( i=1; i<=N; i++ ) + x(i) = (i-1)*h; // x coordinate + y = x; // y coordinate + + //* Select over-relaxation factor (SOR only) + double omega, omegaOpt, pi = 3.141592654; + if( method == 3 ) { + omegaOpt = 2.0/(1.0+sin(pi/N)); // Theoretical optimum + cout << "Theoretical optimum omega = " << omegaOpt << endl; + cout << "Enter desired omega: "; cin >> omega; + } + + //* Set initial guess as first term in separation of variables soln. + double phi0 = 1; // Potential at y=L + double coeff = phi0 * 4/(pi*sinh(pi)); + Matrix phi(N,N); + for( i=1; i<=N; i++ ) + for( j=1; j<=N; j++ ) + phi(i,j) = coeff * sin(pi*x(i)/L) * sinh(pi*y(j)/L); + + //* Set boundary conditions + for( i=1; i<=N; i++ ) { + phi(i,1) = 0.0; + phi(i,N) = phi0; + } + for( j=1; j<=N; j++ ) { + phi(1,j) = 0.0; + phi(N,j) = 0.0; + } + cout << "Potential at y=L equals " << phi0 << endl; + cout << "Potential is zero on all other boundaries" << endl; + + //* Loop until desired fractional change per iteration is obtained + Matrix newphi(N,N); // Copy of the solution (used only by Jacobi) + newphi = phi; + double phiTemp; // Temporary value used by GS and SOR + int iterMax = N*N; // Set max to avoid excessively long runs + double changeDesired = 1e-4; // Stop when the change is given fraction + cout << "Desired fractional change = " << changeDesired << endl; + Matrix change(iterMax); // Record fractional change at each iteration + int iter, nIter; // Iterations counters + for( iter=1; iter<=iterMax; iter++ ) { + + double changeSum = 0; + if( method == 1 ) { //// Jacobi method //// + for( i=2; i<=(N-1); i++ ) // Loop over interior points only + for( j=2; j<=(N-1); j++ ) { + newphi(i,j) = 0.25*(phi(i+1,j)+phi(i-1,j)+ + phi(i,j-1)+phi(i,j+1)); + changeSum += fabs(1-phi(i,j)/newphi(i,j)); + } + phi = newphi; // Copy new values into phi + } + else if( method == 2 ) //// G-S method //// + for( i=2; i<=(N-1); i++ ) // Loop over interior points only + for( j=2; j<=(N-1); j++ ) { + phiTemp = 0.25*(phi(i+1,j)+phi(i-1,j)+ + phi(i,j-1)+phi(i,j+1)); + changeSum += fabs(1-phi(i,j)/phiTemp); + phi(i,j) = phiTemp; + } + else //// SOR method //// + for( i=2; i<=(N-1); i++ ) // Loop over interior points only + for( j=2; j<=(N-1); j++ ) { + phiTemp = 0.25*omega*(phi(i+1,j)+phi(i-1,j)+ + phi(i,j-1)+phi(i,j+1)) + (1-omega)*phi(i,j); + changeSum += fabs(1-phi(i,j)/phiTemp); + phi(i,j) = phiTemp; + } + + //* Check if fractional change is small enough to halt the iteration + change(iter) = changeSum/((N-2)*(N-2)); + if( (iter%10) < 1 ) + cout << "After " << iter << " iterations, fractional change = " + << change(iter) << endl; + if( change(iter) < changeDesired ) { + cout << "Desired accuracy achieved after " << iter + << " iterations" << endl; + cout << "Breaking out of main loop" << endl; + nIter = iter; + break; // Break out of the main loop + } + } + + //* Print out the plotting variables: x, y, phi, change + ofstream xOut("x.txt"), yOut("y.txt"), + phiOut("phi.txt"), changeOut("change.txt"); + for( i=1; i<=N; i++ ) { + xOut << x(i) << endl; + yOut << y(i) << endl; + for( j=1; j ratio ) ? errorRatio:ratio; + } + + //* Estimate new tau value (including safety factors) + double tau_old = tau; + tau = safe1*tau_old*pow(errorRatio, -0.20); + tau = (tau > tau_old/safe2) ? tau:tau_old/safe2; + tau = (tau < safe2*tau_old) ? tau:safe2*tau_old; + + //* If error is acceptable, return computed values + if (errorRatio < 1) { + for( i=1; i<=nX; i++ ) + x[i] = xSmall[i]; + return; + } + } + + //* Issue error message if error bound never satisfied + cout << "ERROR: Adaptive Runge-Kutta routine failed" << endl; +} + diff --git a/Cpp/rombf.cpp b/Cpp/rombf.cpp new file mode 100644 index 0000000..b5dfe3c --- /dev/null +++ b/Cpp/rombf.cpp @@ -0,0 +1,43 @@ +#include "NumMeth.h" + +void rombf( double a, double b, int N, + double (*func)( double x, Matrix param ), + Matrix param, Matrix& R) { +// Function to compute integrals by Romberg algorithm +// R = rombf(a,b,N,func,param) +// Inputs +// a,b Lower and upper bound of the integral +// N Romberg table is N by N +// func Integrand function; the calling sequence +// is: double (*func)( double x, Matrix param ) +// param Set of parameters to be passed to function +// Output +// R Romberg table; Entry R(N,N) is best estimate of +// the value of the integral + + //* Compute the first term R(1,1) + double h = b - a; // This is the coarsest panel size + int np = 1; // Current number of panels + R(1,1) = h/2 * ((*func)(a,param) + (*func)(b,param)); + + //* Loop over the desired number of rows, i = 2,...,N + int i,j,k; + for( i=2; i<=N; i++ ) { + + //* Compute the summation in the recursive trapezoidal rule + h /= 2.0; // Use panels half the previous size + np *= 2; // Use twice as many panels + double sumT = 0.0; + for( k=1; k<=(np-1); k+=2 ) + sumT += (*func)( a + k*h, param); + + //* Compute Romberg table entries R(i,1), R(i,2), ..., R(i,i) + R(i,1) = 0.5 * R(i-1,1) + h * sumT; + int m = 1; + for( j=2; j<=i; j++ ) { + m *= 4; + R(i,j) = R(i,j-1) + (R(i,j-1) - R(i-1,j-1))/(m-1); + } + } +} + diff --git a/Cpp/sampler.cpp b/Cpp/sampler.cpp new file mode 100644 index 0000000..041de4b --- /dev/null +++ b/Cpp/sampler.cpp @@ -0,0 +1,61 @@ +#include "NumMeth.h" +#include "SampList.h" + +void sampler( Matrix& x, Matrix& v, int npart, double L, + SampList& sampD ) { + +// sampler - Function to sample density, velocity and temperature +// Inputs +// x Particle positions +// v Particle velocities +// npart Number of particles +// L System size +// sampD Object with sampling data +// Outputs +// sampD Structure with sampling data + + //* Compute cell location for each particle + int ncell = sampD.ncell; + int *jx; jx = new int [npart+1]; + int i; + for( i=1; i<=npart; i++ ) + jx[i] = (int)ceil(ncell*x(i)/L); + + //* Initialize running sums of number, velocity and v^2 + Matrix sum_n(ncell), sum_vx(ncell), sum_vy(ncell), + sum_vz(ncell), sum_v2(ncell); + sum_n.set(0.0); + sum_vx.set(0.0); + sum_vy.set(0.0); + sum_vz.set(0.0); + sum_v2.set(0.0); + + //* For each particle, accumulate running sums for its cell + for( i=1; i<=npart; i++ ) { + int jcell = jx[i]; // Particle i is in cell jcell + sum_n(jcell)++; + sum_vx(jcell) += v(i,1); + sum_vy(jcell) += v(i,2); + sum_vz(jcell) += v(i,3); + sum_v2(jcell) += v(i,1)*v(i,1) + + v(i,2)*v(i,2) + v(i,3)*v(i,3); +} + + //* Use current sums to update sample number, velocity + // and temperature + for( i=1; i<=ncell; i++ ) { + sum_vx(i) /= sum_n(i); + sum_vy(i) /= sum_n(i); + sum_vz(i) /= sum_n(i); + sum_v2(i) /= sum_n(i); + sampD.ave_n[i] += sum_n(i); + sampD.ave_ux[i] += sum_vx(i); + sampD.ave_uy[i] += sum_vy(i); + sampD.ave_uz[i] += sum_vz(i); + sampD.ave_T[i] += sum_v2(i) - (sum_vx(i)*sum_vx(i) + + sum_vy(i)*sum_vy(i) + sum_vz(i)*sum_vz(i)); + } + sampD.nsamp++; + + delete [] jx; +} diff --git a/Cpp/schro.cpp b/Cpp/schro.cpp new file mode 100644 index 0000000..bcfa3a4 --- /dev/null +++ b/Cpp/schro.cpp @@ -0,0 +1,142 @@ +// schro - Program to solve the Schrodinger equation +// for a free particle using the Crank-Nicolson scheme +#include "NumMeth.h" + +void cinv( Matrix RealA, Matrix ImagA, + Matrix& RealAinv, Matrix& ImagAinv ); + +void main() { + + //* Initialize parameters (grid spacing, time step, etc.) + cout << "Enter number of grid points: "; int N; cin >> N; + double L = 100; // System extends from -L/2 to L/2 + double h = L/(N-1); // Grid size + double h_bar = 1; double mass = 1; // Natural units + cout << "Enter time step: "; double tau; cin >> tau; + Matrix x(N); + int i, j, k; + for( i=1; i<=N; i++ ) + x(i) = h*(i-1) - L/2; // Coordinates of grid points + + //* Set up the Hamiltonian operator matrix + Matrix eye(N,N), ham(N,N); + eye.set(0.0); // Set all elements to zero + for( i=1; i<=N; i++ ) // Identity matrix + eye(i,i) = 1.0; + ham.set(0.0); // Set all elements to zero + double coeff = -h_bar*h_bar/(2*mass*h*h); + for( i=2; i<=(N-1); i++ ) { + ham(i,i-1) = coeff; + ham(i,i) = -2*coeff; // Set interior rows + ham(i,i+1) = coeff; + } + // First and last rows for periodic boundary conditions + ham(1,N) = coeff; ham(1,1) = -2*coeff; ham(1,2) = coeff; + ham(N,N-1) = coeff; ham(N,N) = -2*coeff; ham(N,1) = coeff; + + //* Compute the Crank-Nicolson matrix + Matrix RealA(N,N), ImagA(N,N), RealB(N,N), ImagB(N,N); + for( i=1; i<=N; i++ ) + for( j=1; j<=N; j++ ) { + RealA(i,j) = eye(i,j); + ImagA(i,j) = 0.5*tau/h_bar*ham(i,j); + RealB(i,j) = eye(i,j); + ImagB(i,j) = -0.5*tau/h_bar*ham(i,j); + } + Matrix RealAi(N,N), ImagAi(N,N); + cout << "Computing matrix inverse ... " << flush; + cinv( RealA, ImagA, RealAi, ImagAi ); // Complex matrix inverse + cout << "done" << endl; + Matrix RealD(N,N), ImagD(N,N); // Crank-Nicolson matrix + for( i=1; i<=N; i++ ) + for( j=1; j<=N; j++ ) { + RealD(i,j) = 0.0; // Matrix (complex) multiplication + ImagD(i,j) = 0.0; + for( k=1; k<=N; k++ ) { + RealD(i,j) += RealAi(i,k)*RealB(k,j) - ImagAi(i,k)*ImagB(k,j); + ImagD(i,j) += RealAi(i,k)*ImagB(k,j) + ImagAi(i,k)*RealB(k,j); + } + } + + //* Initialize the wavefunction + const double pi = 3.141592654; + double x0 = 0; // Location of the center of the wavepacket + double velocity = 0.5; // Average velocity of the packet + double k0 = mass*velocity/h_bar; // Average wavenumber + double sigma0 = L/10; // Standard deviation of the wavefunction + double Norm_psi = 1/(sqrt(sigma0*sqrt(pi))); // Normalization + Matrix RealPsi(N), ImagPsi(N), rpi(N), ipi(N); + for( i=1; i<=N; i++ ) { + double expFactor = exp(-(x(i)-x0)*(x(i)-x0)/(2*sigma0*sigma0)); + RealPsi(i) = Norm_psi * cos(k0*x(i)) * expFactor; + ImagPsi(i) = Norm_psi * sin(k0*x(i)) * expFactor; + rpi(i) = RealPsi(i); // Record initial wavefunction + ipi(i) = ImagPsi(i); // for plotting + } + + //* Initialize loop and plot variables + int nStep = (int)(L/(velocity*tau)); // Particle should circle system + int nplots = 20; // Number of plots to record + double plotStep = nStep/nplots; // Iterations between plots + Matrix p_plot(N,nplots+2); + for( i=1; i<=N; i++ ) // Record initial condition + p_plot(i,1) = RealPsi(i)*RealPsi(i) + ImagPsi(i)*ImagPsi(i); + int iplot = 1; + + //* Loop over desired number of steps (wave circles system once) + int iStep; + Matrix RealNewPsi(N), ImagNewPsi(N); + for( iStep=1; iStep<=nStep; iStep++ ) { + + //* Compute new wave function using the Crank-Nicolson scheme + RealNewPsi.set(0.0); ImagNewPsi.set(0.0); + for( i=1; i<=N; i++ ) // Matrix multiply D*psi + for( j=1; j<=N; j++ ) { + RealNewPsi(i) += RealD(i,j)*RealPsi(j) - ImagD(i,j)*ImagPsi(j); + ImagNewPsi(i) += RealD(i,j)*ImagPsi(j) + ImagD(i,j)*RealPsi(j); + } + RealPsi = RealNewPsi; // Copy new values into Psi + ImagPsi = ImagNewPsi; + + //* Periodically record values for plotting + if( fmod(iStep,plotStep) < 1 ) { + iplot++; + for( i=1; i<=N; i++ ) + p_plot(i,iplot) = RealPsi(i)*RealPsi(i) + ImagPsi(i)*ImagPsi(i); + cout << "Finished " << iStep << " of " << nStep << " steps" << endl; + } + } + // Record final probability density + iplot++; + for( i=1; i<=N; i++ ) + p_plot(i,iplot) = RealPsi(i)*RealPsi(i) + ImagPsi(i)*ImagPsi(i); + nplots = iplot; // Actual number of plots recorded + + //* Print out the plotting variables: x, rpi, ipi, p_plot + ofstream xOut("x.txt"), rpiOut("rpi.txt"), ipiOut("ipi.txt"), + p_plotOut("p_plot.txt"); + for( i=1; i<=N; i++ ) { + xOut << x(i) << endl; + rpiOut << rpi(i) << endl; + ipiOut << ipi(i) << endl; + for( j=1; j> tau; + double k_over_m = 1; // Ratio of spring const. over mass + double param[1+1]; param[1] = k_over_m; + + //* Loop over the desired number of time steps. + double time = 0; // Set initial time + int nStep = 256; // Number of steps in the main loop + int nprint = nStep/8; // Number of steps between printing progress + Matrix xplot(nStep,3), tplot(nStep); // Plotting variables + int i, iStep; + for( iStep=1; iStep<=nStep; iStep++ ) { + + //* Use Runge-Kutta to find new displacements of the masses. + rk4(state,nState,time,tau,sprrk,param); + time = time + tau; + + //* Record the positions for graphing and to compute spectra. + xplot(iStep,1) = state[1]; // Record positions + xplot(iStep,2) = state[2]; xplot(iStep,3) = state[3]; + tplot(iStep) = time; + if( (iStep%nprint) < 1 ) + cout << "Finished " << iStep << " out of " << + nStep << " steps" << endl; + } + + //* Calculate the power spectrum of the time series for mass #1 + Matrix f(nStep), x1fftR(nStep), x1fftI(nStep), spect(nStep); + for( i=1; i<=nStep; i++ ) { + f(i) = (i-1)/(tau*nStep); // Frequency + double x1 = xplot(i,1); // Displacement of mass 1 + x1fftR(i) = x1; + x1fftI(i) = 0.0; // Copy data for input to fft + } + fft(x1fftR, x1fftI); // Fourier transform of displacement + for( i=1; i<=nStep; i++ ) // Power spectrum of displacement + spect(i) = x1fftR(i)*x1fftR(i) + x1fftI(i)*x1fftI(i); + + //* Apply the Hanning window to the time series and calculate + // the resulting power spectrum + double window, pi = 3.141592654; + Matrix x1fftRw(nStep), x1fftIw(nStep), spectw(nStep); + for( i=1; i<=nStep; i++ ) { + window = 0.5*(1.0-cos(2.0*pi*(i-1.0)/nStep)); // Hanning window + double x1w = xplot(i,1) * window; // Windowed time series + x1fftRw(i) = x1w; + x1fftIw(i) = 0.0; // Copy data for input to fft + } + fft(x1fftRw, x1fftIw); // Fourier transf. (windowed data) + for( i=1; i<=nStep; i++ ) // Power spectrum (windowed data) + spectw(i) = x1fftRw(i)*x1fftRw(i) + x1fftIw(i)*x1fftIw(i); + + //* Print out the plotting variables: + // tplot, xplot, f, spect, spectw + ofstream tplotOut("tplot.txt"), xplotOut("xplot.txt"), fOut("f.txt"), + spectOut("spect.txt"), spectwOut("spectw.txt"); + for( i=1; i<=nStep; i++ ) { + tplotOut << tplot(i) << endl; + xplotOut << xplot(i,1) << ", " << xplot(i,2) << ", " + << xplot(i,3) << endl; + fOut << f(i) << endl; + spectOut << spect(i) << endl; + spectwOut << spectw(i) << endl; + } +} +/***** To plot in MATLAB; use the script below ******************** +load tplot.txt; load xplot.txt; load f.txt; +load spect.txt; load spectw.txt +nstep = length(tplot); nprint = nstep/8; +%* Graph the displacements of the three masses. +figure(1); clf; % Clear figure 1 window and bring forward +ipr = 1:nprint:nstep; % Used to graph limited number of symbols +plot(tplot(ipr),xplot(ipr,1),'o',tplot(ipr),xplot(ipr,2),'+',... + tplot(ipr),xplot(ipr,3),'*',... + tplot,xplot(:,1),'-',tplot,xplot(:,2),'-.',... + tplot,xplot(:,3),'--'); +legend('Mass #1','Mass #2','Mass #3'); +title('Displacement of masses (relative to rest positions)'); +xlabel('Time'); ylabel('Displacement'); +%* Graph the power spectra for original and windowed data +figure(2); clf; % Clear figure 2 window and bring forward +semilogy(f(1:(nstep/2)),spect(1:(nstep/2)),'-',... + f(1:(nstep/2)),spectw(1:(nstep/2)),'--'); +title('Power spectrum (dashed is windowed data)'); +xlabel('Frequency'); ylabel('Power'); +******************************************************************/ diff --git a/Cpp/sprrk.cpp b/Cpp/sprrk.cpp new file mode 100644 index 0000000..8f2a239 --- /dev/null +++ b/Cpp/sprrk.cpp @@ -0,0 +1,18 @@ +void sprrk(double x[], double t, double param[], double deriv[]) { +// Returns right-hand side of 3 mass-spring system +// equations of motion +// Inputs +// x State vector [x(1) x(2) ... v(3)] +// t Time (not used) +// param (Spring constant)/(Block mass) +// Output +// deriv [dx(1)/dt dx(2)/dt ... dv(3)/dt] + deriv[1] = x[4]; + deriv[2] = x[5]; + deriv[3] = x[6]; + double param2 = -2*param[1]; + deriv[4] = param2*x[1] + param[1]*x[2]; + deriv[5] = param2*x[2] + param[1]*(x[1]+x[3]); + deriv[6] = param2*x[3] + param[1]*x[2]; + return; +} \ No newline at end of file diff --git a/Cpp/traffic.cpp b/Cpp/traffic.cpp new file mode 100644 index 0000000..a484fc7 --- /dev/null +++ b/Cpp/traffic.cpp @@ -0,0 +1,123 @@ +// traffic - Program to solve the generalized Burger +// equation for the traffic at a stop light problem +#include "NumMeth.h" + +void main() { + + //* Select numerical parameters (time step, grid spacing, etc.). + cout << "Choose a numerical method: 1) FTCS, 2) Lax, 3) Lax-Wendroff : "; + int method; cin >> method; + cout << "Enter the number of grid points: "; int N; cin >> N; + double L = 400; // System size (meters) + double h = L/N; // Grid spacing for periodic boundary conditions + double v_max = 25; // Maximum car speed (m/s) + cout << "Suggested timestep is " << h/v_max << endl; + cout << "Enter time step (tau): "; double tau; cin >> tau; + cout << "Last car starts moving after " + << (L/4)/(v_max*tau) << " steps" << endl; + cout << "Enter number of steps: "; int nStep; cin >> nStep; + double coeff = tau/(2*h); // Coefficient used by all schemes + double coefflw = tau*tau/(2*h*h); // Coefficient used by Lax-Wendroff + double cp, cm; // Variables used by Lax-Wendroff + + //* Set initial and boundary conditions + double rho_max = 1.0; // Maximum density + double Flow_max = 0.25*rho_max*v_max; // Maximum Flow + // Initial condition is a square pulse from x = -L/4 to x = 0 + Matrix rho(N), rho_new(N); + int i,j, iBack = N/4, iFront = N/2 - 1; + for( i=1; i<=N; i++ ) + if( iBack <= i && i <= iFront ) rho(i) = rho_max; + else rho(i) = 0.0; + rho(iFront+1) = rho_max/2; // Try running without this line + // Use periodic boundary conditions + int *ip, *im; ip = new int [N+1]; im = new int [N+1]; + for( i=2; i=1; i--) + x(i) = (b(i) - gamma(i)*x(i+1))/beta(i); + + return( determ ); +} diff --git a/Cpp/zeroj.cpp b/Cpp/zeroj.cpp new file mode 100644 index 0000000..b2da4cc --- /dev/null +++ b/Cpp/zeroj.cpp @@ -0,0 +1,30 @@ +#include "NumMeth.h" + +void bess( int m_max, double x, Matrix& jj ) ; + +double zeroj( int m_order, int n_zero) { +// Zeros of the Bessel function J(x) +// Inputs +// m_order Order of the Bessel function +// n_zero Index of the zero (first, second, etc.) +// Output +// z The "n_zero"th zero of the Bessel function + + //* Use asymtotic formula for initial guess + double beta = (n_zero + 0.5*m_order - 0.25)*(3.141592654); + double mu = 4*m_order*m_order; + double beta8 = 8*beta; + double z = beta - (mu-1)/beta8 + - 4*(mu-1)*(7*mu-31)/(3*beta8*beta8*beta8); + + //* Use Newton's method to locate the root + Matrix jj(m_order+2); + int i; double deriv; + for( i=1; i<=5; i++ ) { + bess( m_order+1, z, jj ); // Remember j(1) is J_0(z) + // Use the recursion relation to evaluate derivative + deriv = -jj(m_order+2) + m_order/z * jj(m_order+1); + z -= jj(m_order+1)/deriv; // Newton's root finding + } + return(z); +} diff --git a/Fortran/Barrow.txt b/Fortran/Barrow.txt new file mode 100644 index 0000000..ec277ab --- /dev/null +++ b/Fortran/Barrow.txt @@ -0,0 +1,230 @@ + 3.4420000e+02 + 3.4483000e+02 + 3.4520000e+02 + 3.4537000e+02 + 3.4541000e+02 + 3.4542000e+02 + 3.4552000e+02 + 3.4579000e+02 + 3.4621000e+02 + 3.4656000e+02 + 3.4647000e+02 + 3.4551000e+02 + 3.4342000e+02 + 3.4024000e+02 + 3.3650000e+02 + 3.3306000e+02 + 3.3085000e+02 + 3.3045000e+02 + 3.3184000e+02 + 3.3440000e+02 + 3.3720000e+02 + 3.3952000e+02 + 3.4117000e+02 + 3.4239000e+02 + 3.4349000e+02 + 3.4452000e+02 + 3.4539000e+02 + 3.4595000e+02 + 3.4644000e+02 + 3.4701000e+02 + 3.4757000e+02 + 3.4788000e+02 + 3.4782000e+02 + 3.4762000e+02 + 3.4756000e+02 + 3.4767000e+02 + 3.4760000e+02 + 3.4687000e+02 + 3.4518000e+02 + 3.4259000e+02 + 3.3941000e+02 + 3.3615000e+02 + 3.3346000e+02 + 3.3202000e+02 + 3.3224000e+02 + 3.3401000e+02 + 3.3666000e+02 + 3.3931000e+02 + 3.4139000e+02 + 3.4283000e+02 + 3.4391000e+02 + 3.4491000e+02 + 3.4589000e+02 + 3.4655000e+02 + 3.4689000e+02 + 3.4708000e+02 + 3.4729000e+02 + 3.4755000e+02 + 3.4776000e+02 + 3.4786000e+02 + 3.4793000e+02 + 3.4812000e+02 + 3.4830000e+02 + 3.4798000e+02 + 3.4660000e+02 + 3.4392000e+02 + 3.4029000e+02 + 3.3655000e+02 + 3.3367000e+02 + 3.3237000e+02 + 3.3293000e+02 + 3.3517000e+02 + 3.3843000e+02 + 3.4178000e+02 + 3.4435000e+02 + 3.4582000e+02 + 3.4648000e+02 + 3.4699000e+02 + 3.4787000e+02 + 3.4896000e+02 + 3.4992000e+02 + 3.5041000e+02 + 3.5038000e+02 + 3.5005000e+02 + 3.4969000e+02 + 3.4957000e+02 + 3.4977000e+02 + 3.5019000e+02 + 3.5045000e+02 + 3.4998000e+02 + 3.4829000e+02 + 3.4533000e+02 + 3.4166000e+02 + 3.3824000e+02 + 3.3601000e+02 + 3.3545000e+02 + 3.3640000e+02 + 3.3828000e+02 + 3.4036000e+02 + 3.4216000e+02 + 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mode 100644 index 0000000..2bc41ba --- /dev/null +++ b/Fortran/advect.f @@ -0,0 +1,130 @@ +! advect - Program to solve the advection equation +! using the various hyperbolic PDE schemes + + program advect + integer*4 MAXN, MAXnplots + parameter( MAXN = 500, MAXnplots = 500 ) + integer*4 method, N, nStep, i, j, ip(MAXN), im(MAXN) + integer*4 iplot, nplots, iStep + real*8 L, h, c, tau, coeff, coefflw, pi, sigma, k_wave + real*8 x(MAXN), a(MAXN), a_new(MAXN), plotStep + real*8 aplot(MAXN,MAXnplots+1), tplot(MAXnplots+1) + + !* Select numerical parameters (time step, grid spacing, etc.). + write(*,*) 'Choose a numerical method: ' + write(*,*) ' 1) FTCS, 2) Lax, 3) Lax-Wendroff : ' + read(*,*) method + write(*,*) 'Enter number of grid points: ' + read(*,*) N + L = 1. ! System size + h = L/N ! Grid spacing + c = 1 ! Wave speed + write(*,*) 'Time for wave to move one grid spacing is ', h/c + write(*,*) 'Enter time step: ' + read(*,*) tau + coeff = -c*tau/(2.*h) ! Coefficient used by all schemes + coefflw = 2*coeff*coeff ! Coefficient used by L-W scheme + write(*,*) 'Wave circles system in ', L/(c*tau), ' steps' + write(*,*) 'Enter number of steps: ' + read(*,*) nStep + + !* Set initial and boundary conditions. + pi = 3.141592654 + sigma = 0.1 ! Width of the Gaussian pulse + k_wave = pi/sigma ! Wave number of the cosine + do i=1,N + x(i) = (i-0.5)*h - L/2 ! Coordinates of grid points + ! Initial condition is a Gaussian-cosine pulse + a(i) = cos(k_wave*x(i)) * exp(-x(i)**2/(2*sigma**2)) + enddo + ! Use periodic boundary conditions + do i=2,(N-1) + ip(i) = i+1 ! ip(i) = i+1 with periodic b.c. + im(i) = i-1 ! im(i) = i-1 with periodic b.c. + enddo + ip(1) = 2 + ip(N) = 1 + im(1) = N + im(N) = N-1 + + !* Initialize plotting variables. + iplot = 1 ! Plot counter + nplots = 50 ! Desired number of plots + plotStep = float(nStep)/nplots + tplot(1) = 0 ! Record the initial time (t=0) + do i=1,N + aplot(i,1) = a(i) ! Record the initial state + enddo + + !* Loop over desired number of steps. + do iStep=1,nStep + + !* Compute new values of wave amplitude using FTCS, + ! Lax or Lax-Wendroff method. + if( method .eq. 1 ) then !!! FTCS method !!! + do i=1,N + a_new(i) = a(i) + coeff*( a(ip(i))-a(im(i)) ) + enddo + else if( method .eq. 2 ) then !!! Lax method !!! + do i=1,N + a_new(i) = 0.5*( a(ip(i))+a(im(i)) ) + + & coeff*( a(ip(i))-a(im(i)) ) + enddo + else !!! Lax-Wendroff method !!! + do i=1,N + a_new(i) = a(i) + coeff*( a(ip(i))-a(im(i)) ) + + & coefflw*( a(ip(i))+a(im(i))-2*a(i) ) + enddo + endif + + do i=1,N + a(i) = a_new(i) ! Reset with new amplitude values + enddo + + !* Periodically record a(t) for plotting. + if( (iStep-int(iStep/plotStep)*plotStep) .lt. 1 ) then + iplot = iplot+1 + tplot(iplot) = tau*iStep + do i=1,N + aplot(i,iplot) = a(i) ! Record a(i) for ploting + enddo + write(*,*) iStep, ' out of ', nStep, ' steps completed' + endif + enddo + nplots = iplot ! Actual number of plots recorded + + !* Print out the plotting variables: x, a, tplot, aplot + open(11,file='x.txt',status='unknown') + open(12,file='a.txt',status='unknown') + open(13,file='tplot.txt',status='unknown') + open(14,file='aplot.txt',status='unknown') + do i=1,N + write(11,*) x(i) + write(12,*) a(i) + do j=1,(nplots-1) + write(14,1001) aplot(i,j) + enddo + write(14,*) aplot(i,nplots) + enddo + do i=1,nplots + write(13,*) tplot(i) + enddo +1001 format(e12.6,', ',$) ! The $ suppresses the carriage return + + stop + end + +!***** To plot in MATLAB; use the script below ******************** +!load x.txt; load a.txt; load tplot.txt; load aplot.txt; +!%* Plot the initial and final states. +!figure(1); clf; % Clear figure 1 window and bring forward +!plot(x,aplot(:,1),'-',x,a,'--'); +!legend('Initial','Final'); +!xlabel('x'); ylabel('a(x,t)'); +!pause(1); % Pause 1 second between plots +!%* Plot the wave amplitude versus position and time +!figure(2); clf; % Clear figure 2 window and bring forward +!mesh(tplot,x,aplot); +!ylabel('Position'); xlabel('Time'); zlabel('Amplitude'); +!view([-70 50]); % Better view from this angle +!****************************************************************** diff --git a/Fortran/balle.f b/Fortran/balle.f new file mode 100644 index 0000000..f1a8513 --- /dev/null +++ b/Fortran/balle.f @@ -0,0 +1,111 @@ +! balle - Program to compute the trajectory of a baseball +! using the Euler method. + + program balle + integer*4 MAXmaxStep + parameter( MAXmaxStep = 100000 ) + integer*4 iStep, maxStep, i + real*8 y1, speed, theta, pi, airFlag, rho, Cd, area, grav, mass + real*8 air_const, tau, t, normV + real*8 r1(2), v1(2), r(2), v(2), accel(2) + real*8 xplot(MAXmaxStep), yplot(MAXmaxStep) + real*8 xNoAir(MAXmaxStep), yNoAir(MAXmaxStep) + + !* Set initial position and velocity of the baseball + write(*,*) 'Enter initial height (meters): ' + read(*,*) y1 + r1(1) = 0 ! Initial vector position + r1(2) = y1 + write(*,*) 'Enter initial speed (m/s): ' + read(*,*) speed + write(*,*) 'Enter initial angle (degrees): ' + read(*,*) theta + pi = 3.141592654 + v1(1) = speed*cos(theta*pi/180) ! Initial velocity (x) + v1(2) = speed*sin(theta*pi/180) ! Initial velocity (y) + r(1) = r1(1) + r(2) = r1(2) ! Set initial position and velocity + v(1) = v1(1) + v(2) = v1(2) + + !* Set physical parameters (mass, Cd, etc.) + Cd = 0.35 ! Drag coefficient (dimensionless) + area = 4.3e-3 ! Cross-sectional area of projectile (m^2) + grav = 9.81 ! Gravitational acceleration (m/s^2) + mass = 0.145 ! Mass of projectile (kg) + + write(*,*) 'Air resistance? (Yes:1, No:0): ' + read(*,*) airFlag + if( airFlag .eq. 0 ) then + rho = 0 ! No air resistance + else + rho = 1.2 ! Density of air (kg/m^3) + endif + air_const = -0.5*Cd*rho*area/mass ! Air resistance constant + + !* Loop until ball hits ground or max steps completed + write(*,*) 'Enter timestep, tau (sec): ' + read(*,*) tau + maxStep = 1000 ! Maximum number of steps + do iStep=1,maxStep + + !* Record position (computed and theoretical) for plotting + xplot(iStep) = r(1) ! Record trajectory for plot + yplot(iStep) = r(2) + t = (iStep-1)*tau ! Current time + xNoAir(iStep) = r1(1) + v1(1)*t + yNoAir(iStep) = r1(2) + v1(2)*t - 0.5*grav*t**2 + + !* Calculate the acceleration of the ball + normV = sqrt( v(1)*v(1) + v(2)*v(2) ) + accel(1) = air_const*normV*v(1) ! Air resistance + accel(2) = air_const*normV*v(2) ! Air resistance + accel(2) = accel(2) - grav ! Gravity + + !* Calculate the new position and velocity using Euler method + r(1) = r(1) + tau*v(1) ! Euler step + r(2) = r(2) + tau*v(2) + v(1) = v(1) + tau*accel(1) + v(2) = v(2) + tau*accel(2) + + !* If ball reaches ground (y<0), break out of the loop + if( r(2) .lt. 0 ) then + xplot(iStep+1) = r(1) ! Record last values computed + yplot(iStep+1) = r(2) + goto 100 ! Break out of the for loop + endif + enddo +100 continue + + !* Print maximum range and time of flight + write(*,*) 'Maximum range is ', r(1), ' meters' + write(*,*) 'Time of flight is ', iStep*tau, ' seconds' + + !* Print out the plotting variables: + ! xplot, yplot, xNoAir, yNoAir + open(11,file='xplot.txt',status='unknown') + open(12,file='yplot.txt',status='unknown') + open(13,file='xNoAir.txt',status='unknown') + open(14,file='yNoAir.txt',status='unknown') + do i=1,iStep+1 + write(11,*) xplot(i) + write(12,*) yplot(i) + enddo + do i=1,iStep + write(13,*) xNoAir(i) + write(14,*) yNoAir(i) + enddo + stop + end + +!***** To plot in MATLAB; use the script below ******************** +!load xplot.txt; load yplot.txt; load xNoAir.txt; load yNoAir.txt; +!clf; figure(gcf); % Clear figure window and bring it forward +!% Mark the location of the ground by a straight line +!xground = [0 max(xNoAir)]; yground = [0 0]; +!% Plot the computed trajectory and parabolic, no-air curve +!plot(xplot,yplot,'+',xNoAir,yNoAir,'-',xground,yground,'-'); +!legend('Euler method','Theory (No air)'); +!xlabel('Range (m)'); ylabel('Height (m)'); +!title('Projectile motion'); +!***************************************************************** diff --git a/Fortran/bess.f b/Fortran/bess.f new file mode 100644 index 0000000..877013f --- /dev/null +++ b/Fortran/bess.f @@ -0,0 +1,40 @@ + subroutine bess( m_max, x, jj ) + integer*4 m_max + real*8 x, jj(*) +! Bessel function +! Inputs +! m_max Largest desired order +! x = Value at which Bessel function J(x) is evaluated +! Output +! jj = Vector of J(x) for order m = 0, 1, ..., m_max + + integer*4 MAXm_top + parameter( MAXm_top = 1000 ) + integer*4 maxmx, m_top, m + real*8 tinyNumber, j(MAXm_top+1), norm + + !* Perform downward recursion from initial guess + if( m_max .gt. x ) then + maxmx = m_max + else ! maxmx = Max(m_max,x) + maxmx = int(x) + endif + ! Recursion is downward from m_top (which is even) + m_top = 2*(int( (maxmx+15)/2 + 1 )) + j(m_top+1) = 0.0 + j(m_top) = 1.0 + tinyNumber = 1e-16 + do m=(m_top-2), 0, -1 ! Downward recursion + j(m+1) = 2*(m+1)/(x+tinyNumber)*j(m+2) - j(m+3) + enddo + + !* Normalize using identity and return requested values + norm = j(1) ! NOTE: Be careful, m=0,1,... but + do m=2, m_top, 2 ! vector goes j(1),j(2),... + norm = norm + 2*j(m+1) + enddo + do m=0,m_max ! Send back only the values for + jj(m+1) = j(m+1)/norm ! m=0,...,m_max and discard values + enddo ! for m=m_max+1,...,m_top + return + end diff --git a/Fortran/cinv.f b/Fortran/cinv.f new file mode 100644 index 0000000..cee811c --- /dev/null +++ b/Fortran/cinv.f @@ -0,0 +1,90 @@ +! Compute inverse of complex matrix + + subroutine cinv( A, N, MAXN, Ainv ) + integer*4 N, MAXN + complex*16 A(MAXN,MAXN), Ainv(MAXN,MAXN) +! Inputs +! A Matrix A to be inverted +! N Elements used in matrix A (N by N) +! MAXN Matrix dimenstions as A(MAXN,MAXN) +! Outputs +! Ainv Inverse of matrix A + + integer*4 MAXMAXN + parameter( MAXMAXN = 200 ) + integer*4 i, j, k, index(MAXMAXN), jPivot, indexJ + real*8 scale(MAXMAXN), scaleMax, ratio, ratioMax + complex*16 AA(MAXMAXN,MAXMAXN), B(MAXMAXN,MAXMAXN), coeff, sum + + if( MAXN .gt. MAXMAXN ) then + write(*,*) 'ERROR in cinv: Matrix too large' + stop + endif + + !* Matrix B is initialized to the identity matrix + do i=1,N + do j=1,N + AA(i,j) = A(i,j) ! Copy matrix so as not to overwrite + B(i,j) = 0.0 + enddo + B(i,i) = 1.0 + enddo + + !* Set scale factor, scale(i) = max( |a(i,j)| ), for each row + do i=1,N + index(i) = i ! Initialize row index list + scaleMax = 0.0 + do j=1,N + if( abs(AA(i,j)) .gt. scaleMax ) then + scaleMax = abs(AA(i,j)) + endif + enddo + scale(i) = scaleMax + enddo + + !* Loop over rows k = 1, ..., (N-1) + do k=1,(N-1) + !* Select pivot row from max( |a(j,k)/s(j)| ) + ratiomax = 0.0 + jPivot = k + do i=k,N + ratio = abs(AA(index(i),k))/scale(index(i)) + if( ratio .gt. ratiomax ) then + jPivot=i + ratiomax = ratio + endif + enddo + !* Perform pivoting using row index list + indexJ = index(k) + if( jPivot .ne. k ) then ! Pivot + indexJ = index(jPivot) + index(jPivot) = index(k) ! Swap index jPivot and k + index(k) = indexJ + endif + !* Perform forward elimination + do i=k+1,N + coeff = AA(index(i),k)/AA(indexJ,k) + do j=k+1,N + AA(index(i),j) = AA(index(i),j) - coeff*AA(indexJ,j) + enddo + AA(index(i),k) = coeff + do j=1,N + B(index(i),j) = B(index(i),j) - AA(index(i),k)*B(indexJ,j) + enddo + enddo + enddo + + !* Perform backsubstitution + do k=1,N + Ainv(N,k) = B(index(N),k)/AA(index(N),N) + do i=N-1,1,-1 + sum = B(index(i),k) + do j=i+1,N + sum = sum - AA(index(i),j)*Ainv(j,k) + enddo + Ainv(i,k) = sum/AA(index(i),i) + enddo + enddo + + return + end diff --git a/Fortran/colider.f b/Fortran/colider.f new file mode 100644 index 0000000..8a2c9a7 --- /dev/null +++ b/Fortran/colider.f @@ -0,0 +1,90 @@ + integer*4 function colider( v, crmax, tau, seed, + & selxtra, coeff ) + integer*4 MAXnpart, MAXncell + parameter( MAXnpart = 10000, MAXncell = 500 ) + integer*4 seed + real*8 v(MAXnpart,3), crmax(MAXncell), tau, + & selxtra(MAXncell), coeff +! colide - Function to process collisions in cells +! Inputs +! v Velocities of the particles +! crmax Estimated maximum relative speed in a cell +! tau Time step +! seed Current random number seed +! selxtra Extra selections carried over from last timestep +! coeff Coefficient in computing number of selected pairs +! Outputs +! v Updated velocities of the particles +! crmax Updated maximum relative speed +! selxtra Extra selections carried over to next timestep +! col Total number of collisions processed (Return value) + + integer*4 col, jcell, number, nsel, isel, k, kk, ip1, ip2 + real*8 pi, select, cr, crm, vcm(3), vrel(3), cos_th, sin_th, phi + integer*4 ncell, npart + integer*4 cell_n(MAXncell), index(MAXncell), Xref(MAXnpart) + common /SortList/ ncell, npart, cell_n, index, Xref + real*8 rand + + col = 0 ! Count number of collisions + pi = 3.141592654 + + !* Loop over cells, processing collisions in each cell + do jcell=1,ncell + + !* Skip cells with only one particle + number = cell_n(jcell) + if( number .gt. 1 ) then + + !* Determine number of candidate collision pairs + ! to be selected in this cell + select = coeff*number**2*crmax(jcell) + selxtra(jcell) + nsel = int(select) ! Number of pairs to be selected + selxtra(jcell) = select-nsel ! Carry over any left-over fraction + crm = crmax(jcell) ! Current maximum relative speed + + !* Loop over total number of candidate collision pairs + do isel=1,nsel + + !* Pick two particles at random out of this cell + k = int(rand(seed)*number) + kk = mod( int(k+rand(seed)*(number-1))+1, number ) + ip1 = Xref( k+index(jcell) ) ! First particle + ip2 = Xref( kk+index(jcell) ) ! Second particle + + !* Calculate pair's relative speed + cr = sqrt( (v(ip1,1)-v(ip2,1))**2 + + & (v(ip1,2)-v(ip2,2))**2 + + & (v(ip1,3)-v(ip2,3))**2 ) + if( cr .gt. crm ) then ! If relative speed larger than crm, + crm = cr ! then reset crm to larger value + endif + + !* Accept or reject candidate pair according to relative speed + if( cr/crmax(jcell) .gt. rand(seed) ) then + !* If pair accepted, select post-collision velocities + col = col + 1 ! Collision counter + do k=1,3 + vcm(k) = 0.5*(v(ip1,k) + v(ip2,k)) ! Center of mass velocity + enddo + cos_th = 1.0 - 2.0*rand(seed) ! Cosine and sine of + sin_th = sqrt(1.0 - cos_th**2) ! collision angle theta + phi = 2.0*pi*rand(seed) ! Collision angle phi + vrel(1) = cr*cos_th ! Compute post-collision + vrel(2) = cr*sin_th*cos(phi) ! relative velocity + vrel(3) = cr*sin_th*sin(phi) + do k=1,3 + v(ip1,k) = vcm(k) + 0.5*vrel(k) ! Update post-collision + v(ip2,k) = vcm(k) - 0.5*vrel(k) ! velocities + enddo + + endif + crmax(jcell) = crm ! Update max relative speed + + enddo ! Loop over pairs + endif + enddo ! Loop over cells + + colider = col ! Return the number of collisions + return + end diff --git a/Fortran/contents.txt b/Fortran/contents.txt new file mode 100644 index 0000000..826cc51 --- /dev/null +++ b/Fortran/contents.txt @@ -0,0 +1,53 @@ +% Numerical Methods for Physics, 2nd Ed. (FORTRAN). +% Version 1.0a 2-Oct-99 +% Copyright (c) 1999 by Alejandro Garcia. + +% advect.f Advection PDE solver using various methods +% balle.f Projectile motion (baseball) program +% barrow.txt Carbon dioxide data for Barrow, Alaska +% bess.f Bessel function routine +% cinv.f Complex matrix inverse routine +% colider.f DSMC particle collision routine +% dftcs.f Diffusion PDE solver using FTCS method +% dsmceq.f Relaxation to equilibrium using DSMC method +% dsmcne.f Couette flow routine using DSMC method +% errintg.f Integrand of error function +% fft.f Fast Fourier transform function +% fft2.f Two-dimensional FFT routine +% fftpoi.f Poisson PDE solver using MFT method +% fnewtn.f Lorenz model ODEs and Jacobian routine +% ftdemo.f Fourier transform demo program +% ge.f Gaussian elimination routine +% gravrk.f Function for Kepler equations of motion +% ifft.f Inverse fast Fourier transform function +% ifft2.f Two-dimensional inverse FFT routine +% interp.f Interpolation program +% intrpf.f Interpolation function +% inv.f Matrix inverse routine +% legndr.f Legendre polynomial function +% linreg.f Linear curve fit routine +% lorenz.f Lorenz model program +% lorzrk.f Function for Lorenz model ODEs +% lsfdemo.f Least square fit demo program +% mauna.txt Carbon dioxide data for Mauna Loa, Hawaii +% mover.f DSMC particle moving routine +% neutrn.f Neutron diffusion PDE solver +% newtn.f Root finding by Newton's method +% orbit.f Orbits of comets program +% orthog.f Program to test vector orthogonality +% pendul.f Simple pendulum program +% pollsf.f Polynomial curve fit routine +% rand.f Uniformly distributed random number function +% randn.f Normal (Gaussian) dist. random number function +% relax.f Laplace PDE solver using relaxation methods +% rk4.f Runge-Kutta routine +% rka.f Adaptive Runge-Kutta routine +% rombf.f Romberg integration routine +% sampler.f DSMC particle sampling routine +% schro.f Schrodinger PDE solver using Crank-Nicolson +% sorter.f DSMC particle sorting routine +% sprfft.f Spring-mass oscillations program +% sprrk.f Function for Spring-mass ODEs +% traffic.f Traffic PDE solver using various methods +% tri_ge.f Gaussian elimination for tridiagonal matrices +% zeroj.f Zeros of Bessel function routine diff --git a/Fortran/dftcs.f b/Fortran/dftcs.f new file mode 100644 index 0000000..5fbc4ee --- /dev/null +++ b/Fortran/dftcs.f @@ -0,0 +1,97 @@ +! dftcs - Program to solve the diffusion equation +! using the Forward Time Centered Space (FTCS) scheme. + + program dftcs + integer*4 MAXN, MAXnplots + parameter( MAXN = 300, MAXnplots = 500 ) + integer*4 N, i, j, iplot, nStep, plot_step, nplots, iStep + real*8 tau, L, h, kappa, coeff, tt(MAXN), tt_new(MAXN) + real*8 xplot(MAXN), tplot(MAXnplots), ttplot(MAXN,MAXnplots) + + !* Initialize parameters (time step, grid spacing, etc.). + write(*,*) 'Enter time step: ' + read(*,*) tau + write(*,*) 'Enter the number of grid points: ' + read(*,*) N + L = 1. ! The system extends from x=-L/2 to x=L/2 + h = L/(N-1) ! Grid size + kappa = 1. ! Diffusion coefficient + coeff = kappa*tau/h**2 + if( coeff .lt. 0.5 ) then + write(*,*) 'Solution is expected to be stable' + else + write(*,*) 'WARNING: Solution is expected to be unstable' + endif + + !* Set initial and boundary conditions. + do i=1,N + tt(i) = 0.0 ! Initialize temperature to zero at all points + tt_new(i) = 0.0 + enddo + tt(N/2) = 1/h ! Initial cond. is delta function in center + !! The boundary conditions are tt(1) = tt(N) = 0 + !! End points are unchanged during iteration + + !* Set up loop and plot variables. + iplot = 1 ! Counter used to count plots + nStep = 300 ! Maximum number of iterations + plot_step = 6 ! Number of time steps between plots + nplots = nStep/plot_step + 1 ! Number of snapshots (plots) + do i=1,N + xplot(i) = (i-1)*h - L/2 ! Record the x scale for plots + enddo + + !* Loop over the desired number of time steps. + do iStep=1,nStep + + !* Compute new temperature using FTCS scheme. + do i=2,(N-1) + tt_new(i) = tt(i) + coeff*(tt(i+1) + tt(i-1) - 2*tt(i)) + enddo + do i=2,(N-1) + tt(i) = tt_new(i) ! Reset temperature to new values + enddo + + !* Periodically record temperature for plotting. + if( mod(iStep,plot_step) .lt. 1 ) then ! Every plot_step steps + do i=1,N ! record tt(i) for plotting + ttplot(i,iplot) = tt(i) + enddo + tplot(iplot) = iStep*tau ! Record time for plots + iplot = iplot+1 + endif + enddo + nplots = iplot-1 ! Number of plots actually recorded + + !* Print out the plotting variables: tplot, xplot, ttplot + open(11,file='tplot.txt',status='unknown') + open(12,file='xplot.txt',status='unknown') + open(13,file='ttplot.txt',status='unknown') + do i=1,nplots + write(11,*) tplot(i) + enddo + do i=1,N + write(12,*) xplot(i) + do j=1,(nplots-1) + write(13,1001) ttplot(i,j) + enddo + write(13,*) ttplot(i,nplots) + enddo +1001 format(e12.6,', ',$) ! The $ suppresses the carriage return + stop + end +!***** To plot in MATLAB; use the script below ******************** +!load tplot.txt; load xplot.txt; load ttplot.txt; +!%* Plot temperature versus x and t as wire-mesh and contour plots. +!figure(1); clf; +!mesh(tplot,xplot,ttplot); % Wire-mesh surface plot +!xlabel('Time'); ylabel('x'); zlabel('T(x,t)'); +!title('Diffusion of a delta spike'); +!pause(1); +!figure(2); clf; +!contourLevels = 0:0.5:10; contourLabels = 0:5; +!cs = contour(tplot,xplot,ttplot,contourLevels); % Contour plot +!clabel(cs,contourLabels); % Add labels to selected contour levels +!xlabel('Time'); ylabel('x'); +!title('Temperature contour plot'); +!****************************************************************** diff --git a/Fortran/dsmceq.f b/Fortran/dsmceq.f new file mode 100644 index 0000000..4f2ed33 --- /dev/null +++ b/Fortran/dsmceq.f @@ -0,0 +1,113 @@ +! dsmceq - Dilute gas simulation using DSMC algorithm +! This version illustrates the approach to equilibrium + + program dsmceq + integer*4 MAXnpart, MAXncell + parameter( MAXnpart = 10000, MAXncell = 500 ) + integer*4 npart, seed, i, plusMinus, ncell, coltot, col + integer*4 istep, nstep + integer*4 cell_n(MAXncell), index(MAXncell), Xref(MAXnpart) + real*8 pi, boltz, mass, diam, T, density, L, eff_num, v_init + real*8 x(MAXnpart), v(MAXnpart,3) + real*8 vmagI(MAXnpart), vmagF(MAXnpart) + real*8 tau, vrmax(MAXncell), selxtra(MAXncell), coeff + common /SortList/ ncell, npart, cell_n, index, Xref + integer*4 colider + real*8 rand + + !* Initialize constants (particle mass, diameter, etc.) + pi = 3.141592654 + boltz = 1.3806e-23 ! Boltzmann's constant (J/K) + mass = 6.63e-26 ! Mass of argon atom (kg) + diam = 3.66e-10 ! Effective diameter of argon atom (m) + T = 273 ! Temperature (K) + density = 1.78 ! Density of argon at STP (kg/m^3) + L = 1e-6 ! System size is one micron + write(*,*) 'Enter number of simulation particles: ' + read(*,*) npart + eff_num = density/mass*L**3/npart + write(*,*) 'Each particle represents ', eff_num, ' atoms' + + !* Assign random positions and velocities to particles + seed = 1 ! Initial seed for rand (DO NOT USE ZERO) + v_init = sqrt(3.0*boltz*T/mass) ! Initial speed + do i=1,npart + x(i) = L*rand(seed) ! Assign random positions + plusMinus = (1 - 2*int(2*rand(seed))) ! +1 or -1 (equal prob.) + v(i,1) = plusMinus * v_init + v(i,2) = 0.0 ! Only x-component is non-zero + v(i,3) = 0.0 + enddo + + !* Record inital particle speeds + do i=1,npart + vmagI(i) = sqrt( v(i,1)**2 + v(i,2)**2 + v(i,3)**2 ) + enddo + + !* Initialize variables used for evaluating collisions + ncell = 15 ! Number of cells + tau = 0.2*(L/ncell)/v_init ! Set timestep tau + do i=1,ncell + vrmax(i) = 3*v_init ! Estimated max rel. speed + selxtra(i) = 0.0 ! Used by routine 'colider' + enddo + coeff = 0.5*eff_num*pi*diam**2*tau/(L**3/ncell) + coltot = 0 ! Count total collisions + + !* Declare object for lists used in sorting + !! FORTRAN program uses common blocks to pass these lists + + !* Loop for the desired number of time steps + write(*,*) 'Enter total number of time steps: ' + read(*,*) nstep + do istep = 1,nstep + + !* Move all the particles ballistically + do i=1,npart + x(i) = x(i) + v(i,1)*tau ! Update x position of particle + x(i) = dmod(x(i)+L,L) ! Periodic boundary conditions + enddo + + !* Sort the particles into cells + call sorter(x,L) + + !* Evaluate collisions among the particles + col = colider(v,vrmax,tau,seed,selxtra,coeff) + coltot = coltot + col ! Increment collision count + + !* Periodically display the current progress + if( mod(istep,10) .lt. 1 ) then + write(*,*) 'Done ', istep, ' of ', nstep, ' steps; ', + & coltot, ' collisions' + endif + enddo + + ! Record final particle speeds + do i=1,npart + vmagF(i) = sqrt( v(i,1)**2 + v(i,2)**2 + v(i,3)**2 ) + enddo + + !* Print out the plotting variables: vmagI, vmagF + open(11,file='vmagI.txt',status='unknown') + open(12,file='vmagF.txt',status='unknown') + do i=1,npart + write(11,*) vmagI(i) + write(12,*) vmagF(i) + enddo + + stop + end + +!***** To plot in MATLAB; use the script below ******************** +!load vmagI.txt; load vmagF.txt; +!%* Plot the histogram of the initial speed distribution +!figure(1); clf; +!vbin = 50:100:1050; % Bins for histogram +!hist(vmagI,vbin); title('Initial speed distribution'); +!xlabel('Speed (m/s)'); ylabel('Number'); +!%* Plot the histogram of the final speed distribution +!figure(2); clf; +!hist(vmagF,vbin); +!title(sprintf('Final speed distribution')); +!xlabel('Speed (m/s)'); ylabel('Number'); +!***************************************************************** diff --git a/Fortran/dsmcne.f b/Fortran/dsmcne.f new file mode 100644 index 0000000..4eaae32 --- /dev/null +++ b/Fortran/dsmcne.f @@ -0,0 +1,187 @@ +! dsmcne - Program to simulate a dilute gas using DSMC algorithm +! This version simulates planar Couette flow + + program dsmcne + integer*4 MAXnpart, MAXncell + parameter( MAXnpart = 10000, MAXncell = 500 ) + integer*4 npart, i, ncell, colSum, strikes(2), strikeSum(2) + integer*4 istep, nstep, col, nsamp, seed + integer*4 cell_n(MAXncell), index(MAXncell), Xref(MAXnpart) + real*8 pi, boltz, mass, diam, T, density, L, Volume, eff_num + real*8 mfp, mpv, vwall_m, vwall, x(MAXnpart), v(MAXnpart,3) + real*8 tau, vrmax(MAXncell), selxtra(MAXncell), coeff, delv(2) + real*8 tsamp, dvtot(2), dverr(2) + real*8 ave_n(MAXncell), ave_ux(MAXncell), ave_uy(MAXncell) + real*8 ave_uz(MAXncell), ave_T(MAXncell) + real*8 force(2), ferr(2), vgrad, visc, viscerr, eta + integer*4 colider + real*8 rand, randn + common /SortList/ ncell, npart, cell_n, index, Xref + common /SampList/ ave_n, ave_ux, ave_uy, ave_uz, ave_T, + & nsamp + + !* Initialize constants (particle mass, diameter, etc.) + pi = 3.141592654 + boltz = 1.3806e-23 ! Boltzmann's constant (J/K) + mass = 6.63e-26 ! Mass of argon atom (kg) + diam = 3.66e-10 ! Effective diameter of argon atom (m) + T = 273 ! Temperature (K) + density = 2.685e25 ! Number density of argon at STP (m^-3) + L = 1e-6 ! System size is one micron + Volume = L**3 ! Volume of the system + write(*,*) 'Enter number of simulation particles: ' + read(*,*) npart + eff_num = density*L**3/npart + write(*,*) 'Each particle represents ', eff_num, ' atoms' + mfp = Volume/(sqrt(2.0)*pi*diam**2*npart*eff_num) + write(*,*) 'System width is ', L/mfp, ' mean free paths' + mpv = sqrt(2*boltz*T/mass) ! Most probable initial velocity + write(*,*) 'Enter wall velocity as Mach number: ' + read(*,*) vwall_m + vwall = vwall_m * sqrt(5./3. * boltz*T/mass) + write(*,*) 'Wall velocities are ', -vwall, ' and ', + & vwall, ' m/s' + + !* Assign random positions and velocities to particles + seed = 1 ! Initial seed for rand (DO NOT USE ZERO) + do i=1,npart + x(i) = L*rand(seed) ! Assign random positions + ! Initial velocities are Maxwell-Boltzmann distributed + v(i,1) = sqrt(boltz*T/mass) * randn(seed) + v(i,2) = sqrt(boltz*T/mass) * randn(seed) + v(i,3) = sqrt(boltz*T/mass) * randn(seed) + ! Add velocity gradient to the y-component + v(i,2) = v(i,2) + vwall * 2*(x(i)/L - 0.5) + enddo + + !* Initialize variables used for evaluating collisions + ncell = 20 ! Number of cells + tau = 0.2*(L/ncell)/mpv ! Set timestep tau + do i=1, ncell + vrmax(i) = 3*mpv ! Estimated max rel. speed + selxtra(i) = 0.0 ! Used by routine 'colider' + enddo + coeff = 0.5*eff_num*pi*diam**2*tau/(L**3/ncell) + + !* Declare object for lists used in sorting + !! FORTRAN program uses common blocks to pass these lists + + !* Initialize object and variables used in statistical sampling + !! FORTRAN program uses common blocks to pass statistics lists + nsamp = 0 + do i=1,ncell + ave_n(i) = 0.0 + ave_ux(i) = 0.0 + ave_uy(i) = 0.0 + ave_uz(i) = 0.0 + ave_T(i) = 0.0 + enddo + tsamp = 0.0 ! Total sampling time + dvtot(1) = 0.0 ! Total momentum change at a wall + dvtot(2) = 0.0 + dverr(1) = 0.0 ! Used to find error in dvtot + dverr(2) = 0.0 + + !* Loop for the desired number of time steps + colSum = 0 ! Count total collisions + strikeSum(1) = 0.0 ! Count strikes on each wall + strikeSum(2) = 0.0 + write(*,*) 'Enter total number of time steps: ' + read(*,*) nstep + do istep = 1,nstep + + !* Move all the particles + delv(1) = 0.0 + delv(2) = 0.0 + call mover( x, v, npart, L, mpv, vwall, + & tau, strikes, delv, seed ) + strikeSum(1) = strikeSum(1) + strikes(1) + strikeSum(2) = strikeSum(2) + strikes(2) + + !* Sort the particles into cells + call sorter(x,L) + + !* Evaluate collisions among the particles + col = colider(v,vrmax,tau,seed,selxtra,coeff) + colSum = colSum + col ! Increment collision count + + !* After initial transient, accumulate statistical samples + if(istep .gt. nstep/10) then + call sampler(x,v,npart,ncell,L) + ! Cummulative velocity change for particles striking walls + dvtot(1) = dvtot(1) + delv(1) + dvtot(2) = dvtot(2) + delv(2) + dverr(1) = dverr(1) + delv(1)*delv(1) + dverr(2) = dverr(2) + delv(2)*delv(2) + tsamp = tsamp + tau + endif + + !* Periodically display the current progress + if( mod(istep,100) .lt. 1 ) then + write(*,*) 'Done ', istep, ' of ', nstep, ' steps; ', + & colSum, ' collisions' + write(*,*) 'Total wall strikes: ', strikeSum(1), ' (left) ', + & strikeSum(2), ' (right)' + endif + enddo + + !* Normalize the accumulated statistics + do i=1,ncell + ave_n(i) = ave_n(i)*(eff_num/(Volume/ncell))/nsamp + ave_ux(i) = ave_ux(i)/nsamp + ave_uy(i) = ave_uy(i)/nsamp + ave_uz(i) = ave_uz(i)/nsamp + ave_T(i) = ave_T(i) * mass/(3*boltz*nsamp) + enddo + dverr(1) = dverr(1)/(nsamp-1) - (dvtot(1)/nsamp)*(dvtot(1)/nsamp) + dverr(1) = sqrt(dverr(1)*nsamp) + dverr(2) = dverr(2)/(nsamp-1) - (dvtot(2)/nsamp)*(dvtot(2)/nsamp) + dverr(2) = sqrt(dverr(2)*nsamp) + + !* Compute viscosity from drag force on the walls + force(1) = (eff_num*mass*dvtot(1))/(tsamp*L**2) + force(2) = (eff_num*mass*dvtot(2))/(tsamp*L**2) + ferr(1) = (eff_num*mass*dverr(1))/(tsamp*L**2) + ferr(2) = (eff_num*mass*dverr(2))/(tsamp*L**2) + write(*,*) 'Force per unit area is' + write(*,*) 'Left wall: ', force(1), ' +/- ', ferr(1) + write(*,*) 'Right wall: ', force(2), ' +/- ', ferr(2) + vgrad = 2*vwall/L ! Velocity gradient + visc = 0.5*(-force(1)+force(2))/vgrad ! Average viscosity + viscerr = 0.5*(ferr(1)+ferr(2))/vgrad ! Error + write(*,*) 'Viscosity = ', visc, ' +/- ', viscerr, 'N s/m^2' + eta = 5.*pi/32.*mass*density*(2./sqrt(pi)*mpv)*mfp + write(*,*) 'Theoretical value of viscoisty is ', eta, 'N s/m^2' + + + !* Print out the plotting variables: + ! xcell, ave_n, ave_ux, ave_uy, ave_uz, ave_T + open(11,file='xcell.txt',status='unknown') + open(12,file='ave_n.txt',status='unknown') + open(13,file='ave_ux.txt',status='unknown') + open(14,file='ave_uy.txt',status='unknown') + open(15,file='ave_uz.txt',status='unknown') + open(16,file='ave_T.txt',status='unknown') + do i=1,ncell + write(11,*) (i-0.5)*L/ncell + write(12,*) ave_n(i) + write(13,*) ave_ux(i) + write(14,*) ave_uy(i) + write(15,*) ave_uz(i) + write(16,*) ave_T(i) + enddo + + stop + end +!***** To plot in MATLAB; use the script below ******************** +!load xcell.txt; load ave_n.txt; load ave_ux.txt; +!load ave_uy.txt; load ave_uz.txt; load ave_T.txt; +!figure(1); clf; +!plot(xcell,ave_n); xlabel('position'); ylabel('Number density'); +!figure(2); clf; +!plot(xcell,ave_ux,xcell,ave_uy,xcell,ave_uz); +!xlabel('position'); ylabel('Velocities'); +!legend('x-component','y-component','z-component'); +!figure(3); clf; +!plot(xcell,ave_T); xlabel('position'); ylabel('Temperature'); +!****************************************************************** diff --git a/Fortran/errintg.f b/Fortran/errintg.f new file mode 100644 index 0000000..fea5045 --- /dev/null +++ b/Fortran/errintg.f @@ -0,0 +1,12 @@ + real*8 function errintg( x, param ) + real*8 x, param(*) +! Error function integrand +! Inputs +! x Value where integrand is evaluated +! param Parameter list (not used) +! Output +! errintg Integrand of the error function + + errintg = exp(-x*x) + return + end diff --git a/Fortran/fft.f b/Fortran/fft.f new file mode 100644 index 0000000..6bbb721 --- /dev/null +++ b/Fortran/fft.f @@ -0,0 +1,66 @@ + subroutine fft( A, N ) + integer*4 N + complex*16 A(N) +! Routine to compute discrete Fourier transform using FFT algorithm +! Inputs +! A Complex data vector +! Outputs +! A Complex transform of input data vector + + integer*4 M, NN, N_half, Nm1, i, j, k, ke, ke1, ip + real*8 pi, angle, temp + complex*16 U, W, T + + !* Determine size of input data and check that it is power of 2 + M = int( alog(float(N))/alog(2.0) + 0.5) ! N = 2^M + NN = int( 2.0**M + 0.5 ) + if( N .ne. NN ) then + write(*,*) "ERROR in fft(): Number of points not power of 2" + return + endif + pi = 4.0d0*datan(1.0d0) + N_half = N/2 + Nm1 = N-1 + + !* Bit-scramble the input data by swapping elements + j=1 + do i=1,Nm1 + if( i .lt. j ) then + T = A(j) ! Swap elements i and j + A(j) = A(i) ! of RealA and ImagA + A(i) = T + endif + k = N_half +1 if( k .ge. j ) goto 2 ! While loop + j = j-k + k = k/2 + goto 1 +2 continue + j = j+k + enddo + + !* Loop over number of layers, M = log_2(N) + do k=1,M + ke = 2**k + ke1 = ke/2 + !* Compute lowest, non-zero power of W for this layer + U = (1.0, 0.0) + angle = -pi/ke1 + W = cmplx(cos(angle), sin(angle)) + !* Loop over elements in binary order (outer loop) + do j=1,ke1 + !* Loop over elements in binary order (inner loop) + do i=j,N,ke + ip = i + ke1 + !* Compute the y(.)*W^. factor for this element + T = A(ip)*U + !* Update the current element and its binary pair + A(ip) = A(i)-T + A(i) = A(i)+T + enddo + !* Increment the power of W for next set of elements + U = U*W + enddo + enddo + return + end diff --git a/Fortran/fft2.f b/Fortran/fft2.f new file mode 100644 index 0000000..2b262b4 --- /dev/null +++ b/Fortran/fft2.f @@ -0,0 +1,46 @@ + subroutine fft2( A, N, MAXN ) + integer*4 N, MAXN + complex*16 A(MAXN,MAXN) +! Routine to compute two dimensional Fourier transform +! using FFT algorithm +! Inputs +! A Complex input data array +! N Elements transformed are A(1,1) to A(N,N) +! MAXN Array dimensioned as A(MAXN,MAXN) +! Outputs +! A Complex transform of data + + integer*4 MAXNT + parameter( MAXNT = 2048 ) + integer*4 i, j + complex*16 T(MAXNT) ! Temporary work vector + + !* Loop over the columns of the matrix + do j=1,N + !* Copy out a column into a vector + do i=1,N + T(i) = A(i,j) + enddo + !* Take FFT of the vector + call fft(T,N) + !* Copy the transformed vector back into the column + do i=1,N + A(i,j) = T(i) + enddo + enddo + + !* Loop over the rows of the matrix + do i=1,N + !* Copy out a row into a vector + do j=1,N + T(j) = A(i,j) + enddo + !* Take FFT of the vector + call fft(T,N) + !* Copy the transformed vector back into the row + do j=1,N + A(i,j) = T(j) + enddo + enddo + return + end diff --git a/Fortran/fftpoi.f b/Fortran/fftpoi.f new file mode 100644 index 0000000..8f43790 --- /dev/null +++ b/Fortran/fftpoi.f @@ -0,0 +1,108 @@ +! fftpoi - Program to solve the Poisson equation using +! MFT method (periodic boundary conditions) + + program fftpoi + integer*4 MAXN + parameter( MAXN = 300 ) + integer*4 N, i, j, M, ii, jj + real*8 eps0, L, h, x(MAXN), y(MAXN), rho(MAXN,MAXN) + real*8 xc, yc, q, pi, cx(MAXN), cy(MAXN), numerator + real*8 tinyNumber, phi(MAXN,MAXN) + complex*16 P(MAXN,MAXN), R(MAXN,MAXN), F(MAXN,MAXN) + + !* Initialize parameters (system size, grid spacing, etc.) + eps0 = 8.8542e-12 ! Permittivity (C^2/(N m^2)) + N = 64 ! Number of grid points on a side (square grid) + L = 1 ! System size + h = L/N ! Grid spacing for periodic boundary conditions + do i=1,N + x(i) = (i-0.5)*h ! Coordinates of grid points + y(i) = x(i) ! on a square grid + enddo + write(*,*) 'System is a square of length ', L + + !* Set up charge density rho(i,j) + do i=1,N + do j=1,N + rho(i,j) = 0.0 ! Initialize charge density to zero + enddo + enddo + write(*,*) 'Enter number of line charges: ' + read(*,*) M + do i=1,M + write(*,*) 'For charge #', i + write(*,*) 'Enter x,y coordinates: ' + read(*,*) xc,yc + ii = int(xc/h) + 1 ! Place charge at nearest + jj = int(yc/h) + 1 ! grid point + write(*,*) 'Enter charge density: ' + read(*,*) q + rho(ii,jj) = rho(ii,jj) + q/h**2 + enddo + + !* Compute matrix P + pi = 3.141592654 + do i=1,N + cx(i) = cos((2*pi/N)*(i-1)) + cy(i) = cx(i) + enddo + numerator = -h**2/(2*eps0) + tinyNumber = 1e-20 ! Avoids division by zero + do i=1,N + do j=1,N + P(i,j) = numerator/(cx(i)+cy(j)-2.0+tinyNumber) + enddo + enddo + + !* Compute potential using MFT method + do i=1,N + do j=1,N + R(i,j) = rho(i,j) ! Copy rho into R for input to fft2 + enddo + enddo + call fft2(R,N,MAXN) ! Transform rho into wavenumber domain + ! Compute phi in the wavenumber domain + do i=1,N + do j=1,N + F(i,j) = R(i,j)*P(i,j) + enddo + enddo + call ifft2(F,N,MAXN) ! Inv. transf. phi into the coord. domain + do i=1,N + do j=1,N + phi(i,j) = real(F(i,j)) + enddo + enddo + + !* Print out the plotting variables: x, y, phi + open(11,file='x.txt',status='unknown') + open(12,file='y.txt',status='unknown') + open(13,file='phi.txt',status='unknown') + do i=1,N + write(11,*) x(i) + write(12,*) y(i) + do j=1,(N-1) + write(13,1001) phi(i,j) + enddo + write(13,*) phi(i,N) + enddo +1001 format(e12.6,', ',$) ! The $ suppresses the carriage return + + stop + end +!***** To plot in MATLAB; use the script below ******************** +!load x.txt; load y.txt; load phi.txt; +!%* Compute electric field as E = - grad phi +![Ex Ey] = gradient(flipud(rot90(phi))); +!magnitude = sqrt(Ex.^2 + Ey.^2); +!Ex = -Ex ./ magnitude; % Normalize components so +!Ey = -Ey ./ magnitude; % vectors have equal length +!%* Plot potential and electric field +!figure(1); clf; +!contour3(x,y,flipud(rot90(phi,1)),35); +!xlabel('x'); ylabel('y'); zlabel('\Phi(x,y)'); +!figure(2); clf; +!quiver(x,y,Ex,Ey) % Plot E field with vectors +!title('E field (Direction)'); xlabel('x'); ylabel('y'); +!axis('square'); axis([0 1 0 1]); +!***************************************************************** diff --git a/Fortran/fnewt.f b/Fortran/fnewt.f new file mode 100644 index 0000000..10aea6a --- /dev/null +++ b/Fortran/fnewt.f @@ -0,0 +1,30 @@ + subroutine fnewt( x, a, Nm, f, D) + integer*4 Nm + real*8 x(Nm), a(Nm), f(Nm), D(Nm,Nm) +! Function used by the N-variable Newton's method +! Inputs +! x State vector [x y z] +! a Parameters [r sigma b] +! Nm Max number of variables +! Outputs +! f Lorenz model r.h.s. [dx/dt dy/dt dz/dt] +! D Jacobian matrix, D(i,j) = df(j)/dx(i) + + ! Evaluate f(i) + f(1) = a(2)*(x(2)-x(1)) + f(2) = a(1)*x(1)-x(2)-x(1)*x(3) + f(3) = x(1)*x(2)-a(3)*x(3) + + ! Evaluate D(i,j) + D(1,1) = -a(2) ! df(1)/dx(1) + D(1,2) = a(1)-x(3) ! df(2)/dx(1) + D(1,3) = x(2) ! df(3)/dx(1) + D(2,1) = a(2) ! df(1)/dx(2) + D(2,2) = -1 ! df(2)/dx(2) + D(2,3) = x(1) ! df(3)/dx(2) + D(3,1) = 0 ! df(1)/dx(3) + D(3,2) = -x(1) ! df(2)/dx(3) + D(3,3) = -a(3) ! df(3)/dx(3) + + return + end diff --git a/Fortran/ftdemo.f b/Fortran/ftdemo.f new file mode 100644 index 0000000..a8ec58c --- /dev/null +++ b/Fortran/ftdemo.f @@ -0,0 +1,88 @@ +! ftdemo - Discrete Fourier transform demonstration program + program ftdemo + integer*4 MAXN + parameter( MAXN = 16384 ) + integer*4 N, i, j, k, method + real*8 twoPiN, freq, phase, tau, pi, t(MAXN), y(MAXN) + real*8 f(MAXN), powSpec(MAXN) + complex*16 ii, yt(MAXN) + + !* Initialize the sine wave time series to be transformed. + write(*,*) 'Enter the number of points: ' + read(*,*) N + write(*,*) 'Enter frequency of the sine wave: ' + read(*,*) freq + write(*,*) 'Enter phase of the sine wave: ' + read(*,*) phase + tau = 1 ! Time increment + pi = 3.141592654 + do i=1,N + t(i) = (i-1)*tau ! t = [0, tau, 2*tau, ... ] + y(i) = sin(2*pi*t(i)*freq + phase) ! Sine wave time series + f(i) = (i-1)/(N*tau) ! f = [0, 1/(N*tau), ... ] + enddo + + !* Compute the transform using desired method: direct summation + ! or fast Fourier transform (FFT) algorithm. + write(*,*) 'Compute transform by, 1) Direct summation; 2) FFT: ' + read(*,*) method + if( method .eq. 1 ) then ! Direct summation + twoPiN = -2*pi/N + ii = (0., 1.) ! ii = sqrt(-1) + do k=0,N + yt(k+1) = (0.0, 0.0) + do j=0,(N-1) + yt(k+1) = yt(k+1) + + & y(j+1)*cos(twoPiN*j*k) + + & ii*y(j+1)*sin(twoPiN*j*k) + enddo + enddo + else ! Fast Fourier transform + do i=1,N + yt(i) = y(i) ! Copy data for input to fft + enddo + call fft(yt,N) + endif + !* Compute the power spectrum + do k=1,N + powSpec(k) = abs(yt(k))**2 + enddo + + !* Print out the plotting variables: + ! t, y, f, ytReal, ytImag, powspec + open(11,file='t.txt',status='unknown') + open(12,file='y.txt',status='unknown') + open(13,file='f.txt',status='unknown') + open(14,file='ytReal.txt',status='unknown') + open(15,file='ytImag.txt',status='unknown') + open(16,file='powSpec.txt',status='unknown') + do i=1,N + write(11,*) t(i) + write(12,*) y(i) + write(13,*) f(i) + write(14,*) real(yt(i)) + write(15,*) imag(yt(i)) + write(16,*) powSpec(i) + enddo + stop + end + +!***** To plot in MATLAB; use the script below ******************** +!load t.txt; load y.txt; load f.txt; +!load ytReal.txt; load ytImag.txt; load powSpec.txt; +!%* Graph the time series and its transform. +!figure(1); clf; % Clear figure 1 window and bring forward +!plot(t,y); +!title('Original time series'); +!ylabel('Amplitude'); xlabel('Time'); +!figure(2); clf; % Clear figure 2 window and bring forward +!plot(f,ytReal,'-',f,ytImag,'--'); +!legend('Real','Imaginary'); +!title('Fourier transform'); +!ylabel('Transform'); xlabel('Frequency'); +!%* Compute and graph the power spectrum of the time series. +!figure(3); clf; % Clear figure 3 window and bring forward +!semilogy(f,powSpec,'-'); +!title('Power spectrum (unnormalized)'); +!ylabel('Power'); xlabel('Frequency'); +!****************************************************************** diff --git a/Fortran/ge.f b/Fortran/ge.f new file mode 100644 index 0000000..ea8d99d --- /dev/null +++ b/Fortran/ge.f @@ -0,0 +1,96 @@ + real*8 function ge( AA, bb, N, Nm, x ) + integer*4 N, Nm + real*8 AA(Nm,Nm), bb(Nm), x(Nm) +! ge - Function to perform Gaussian elimination to solve A*x = b +! using scaled column pivoting +! Inputs +! AA - Matrix A (N by N) +! bb - Vector b (N by 1) +! N - Dimension of A, b, and x (used) +! Nm - Dimension of A, b, and x (allocated memory) +! Outputs +! x - Vector x (N by 1) +! determ - Determinant of matrix A (return value) + + integer*4 MAXN + parameter( MAXN = 500 ) + + integer*4 i, j, k, index(MAXN), signDet, jPivot, indexJ + real*8 scale(MAXN), scaleMax, ratiomax, ratio, coeff + real*8 determ, sum, A(MAXN,MAXN), b(MAXN) + + if( Nm .gt. MAXN ) then + write(*,*) 'ERROR - Matrix is too large for ge routine' + stop + endif + + ! Copy matrix A and vector b so as not to modify original + do i=1,N + b(i) = bb(i) + do j=1,N + A(i,j) = AA(i,j) + enddo + enddo + + !* Set scale factor, scale(i) = max( |A(i,j)| ), for each row + do i=1,N + index(i) = i ! Initialize row index list + scaleMax = 0.0 + do j=1,N + if( abs(A(i,j)) .gt. scaleMax ) then + scaleMax = abs(A(i,j)) + endif + enddo + scale(i) = scaleMax + enddo + + !* Loop over rows k = 1, ..., (N-1) + signDet = 1 + do k=1,N-1 + !* Select pivot row from max( |A(j,k)/s(j)| ) + ratiomax = 0.0 + jPivot = k + do i=k,N + ratio = abs(A(index(i),k))/scale(index(i)) + if( ratio .gt. ratiomax ) then + jPivot = i + ratiomax = ratio + endif + enddo + !* Perform pivoting using row index list + indexJ = index(k) + if( jPivot .ne. k ) then ! Pivot + indexJ = index(jPivot) + index(jPivot) = index(k) ! Swap index jPivot and k + index(k) = indexJ + signDet = -1*signDet ! Flip sign of determinant + endif + !* Perform forward elimination + do i=k+1,N + coeff = A(index(i),k)/A(indexJ,k) + do j=k+1,N + A(index(i),j) = A(index(i),j) - coeff*A(indexJ,j) + enddo + A(index(i),k) = coeff + b(index(i)) = b(index(i)) - A(index(i),k)*b(indexJ) + enddo + enddo + !* Compute determinant as product of diagonal elements + determ = signDet ! Sign of determinant + do i=1,N + determ = determ * A(index(i),i) + enddo + + !* Perform backsubstitution + x(N) = b(index(N))/A(index(N),N) + do i=N-1,1,-1 + sum = b(index(i)) + do j=i+1,N + sum = sum - A(index(i),j)*x(j) + enddo + x(i) = sum/A(index(i),i) + enddo + + ge = determ + return + end diff --git a/Fortran/gravrk.f b/Fortran/gravrk.f new file mode 100644 index 0000000..f6e7bef --- /dev/null +++ b/Fortran/gravrk.f @@ -0,0 +1,28 @@ + subroutine gravrk( x, t, param, deriv ) + real*8 x(*), t, param(*), deriv(*) +! Returns right-hand side of Kepler ODE; used by Runge-Kutta routines +! Inputs +! x State vector [r(1) r(2) v(1) v(2)] +! t Time (not used) +! param Parameter G*M (gravitational const. * solar mass) +! Output +! deriv Derivatives [dr(1)/dt dr(2)/dt dv(1)/dt dv(2)/dt] + real*8 GM, r1, r2, v1, v2, normR, accel1, accel2 + + !* Compute acceleration + GM = param(1) + r1 = x(1) + r2 = x(2) ! Unravel the vector x into + v1 = x(3) ! position and velocity + v2 = x(4) + normR = sqrt( r1*r1 + r2*r2 ) + accel1 = -GM*r1/(normR**3) ! Gravitational acceleration + accel2 = -GM*r2/(normR**3) + + !* Return derivatives [dr(1)/dt dr(2)/dt dv(1)/dt dv(2)/dt] + deriv(1) = v1 + deriv(2) = v2 + deriv(3) = accel1 + deriv(4) = accel2 + return + end diff --git a/Fortran/ifft.f b/Fortran/ifft.f new file mode 100644 index 0000000..65d9d55 --- /dev/null +++ b/Fortran/ifft.f @@ -0,0 +1,27 @@ + subroutine ifft( A, N ) + integer*4 N + complex*16 A(*) +! Routine to compute inverse Fourier transform using FFT algorithm +! Inputs +! A Complex transform data vector +! N Number of data points +! Outputs +! A Complex time series + + integer*4 i + + !* Take complex conjugate of input transform + do i=1,N + A(i) = conjg(A(i)) ! Complex conjugate + enddo + + !* Evaluate fast fourier transform + call fft( A, N ) + + !* Take complex conjugate and normalize by N + do i=1,N + A(i) = conjg(A(i))/N ! Normalize and complex conjugate + enddo + + return + end diff --git a/Fortran/ifft2.f b/Fortran/ifft2.f new file mode 100644 index 0000000..91ff59c --- /dev/null +++ b/Fortran/ifft2.f @@ -0,0 +1,50 @@ + subroutine ifft2( A, N, MAXN ) + integer*4 N, MAXN + complex*16 A(MAXN,MAXN) +! Routine to compute inverse two dimensional Fourier transform +! using FFT algorithm +! Inputs +! A Complex transform array +! N Elements transformed are A(1,1) to A(N,N) +! MAXN Array dimensioned as A(MAXN,MAXN) +! Outputs +! A Complex data array + + integer*4 MAXNT + parameter( MAXNT = 2048 ) + integer*4 i, j + real*8 invN2 + complex*16 T(MAXNT) ! Temporary work vector + + !* Loop over the columns of the matrix + do j=1,N + !* Copy out a column into a vector and take its complex conjugate + do i=1,N + T(i) = conjg(A(i,j)) + enddo + !* Take FFT of the vector + call fft( T, N ) + !* Copy the transformed vector back into the column + do i=1,N + A(i,j) = T(i) + enddo + enddo + + !* Loop over the rows of the matrix + invN2 = 1.0/N**2 + do i=1,N + !* Copy out a row into a vector and take its complex conjugate + do j=1,N + T(j) = A(i,j) + enddo + !* Take FFT of the vector + call fft( T, N ) + !* Copy the transformed vector back, taking its complex conjugate + ! and applying the 1/N normalization + do j=1,N + A(i,j) = conjg(T(j))*invN2 + enddo + enddo + + return + end diff --git a/Fortran/interp.f b/Fortran/interp.f new file mode 100644 index 0000000..f8810ff --- /dev/null +++ b/Fortran/interp.f @@ -0,0 +1,54 @@ +! interp - Program to interpolate data using Lagrange +! polynomial to fit quadratic to three data points + + program interp + integer*4 MAXnplot + parameter(MAXnplot = 1000) + !* Initialize the data points to be fit by quadratic + integer*4 i, nplot + real*8 x(3), y(3), x_min, x_max, xi(MAXnplot), yi(MAXnplot) + real*8 intrpf + write(*,*) 'Enter data points:' + do i=1,3 + write(*,*) 'x(', i, ') = ' + read(*,*) x(i) + write(*,*) 'y(', i, ') = ' + read(*,*) y(i) + enddo + + !* Establish the range of interpolation (from x_min to x_max) + write(*,*) 'Enter minimum value of x: ' + read(*,*) x_min + write(*,*) 'Enter maximum value of x: ' + read(*,*) x_max + + !* Find yi for the desired interpolation values xi using + ! the function intrpf + nplot = 100 ! Number of points for interpolation curve + do i=1,nplot + xi(i) = x_min + (x_max-x_min)*(i-1)/(nplot-1) + yi(i) = intrpf(xi(i),x,y) ! Use intrpf function to interpolate + enddo + + !* Print out the plotting variables: x, y, xi, yi + open(11,file='x.txt',status='unknown') + open(12,file='y.txt',status='unknown') + open(13,file='xi.txt',status='unknown') + open(14,file='yi.txt',status='unknown') + do i=1,3 + write(11,*) x(i) + write(12,*) y(i) + enddo + do i=1,nplot + write(13,*) xi(i) + write(14,*) yi(i) + enddo + stop + end +!***** To plot in MATLAB; use the script below ******************** +!load x.txt; load y.txt; load xi.txt; load yi.txt; +!plot(x,y,'*',xi,yi,'-'); +!xlabel('x'); ylabel('y'); +!title('Three point interpolation'); +!legend('Data points','Interpolation'); +!****************************************************************** diff --git a/Fortran/intrpf.f b/Fortran/intrpf.f new file mode 100644 index 0000000..8ed98e8 --- /dev/null +++ b/Fortran/intrpf.f @@ -0,0 +1,18 @@ + real*8 function intrpf( xi, x, y ) +! Function to interpolate between data points +! using Lagrange polynomial (quadratic) +! Inputs +! xi The x value where interpolation is computed +! x Vector of x coordinates of data points (3 values) +! y Vector of y coordinates of data points (3 values) +! Output +! yi The interpolation polynomial evaluated at xi + real*8 xi, x(3), y(3), yi + + !* Calculate yi = p(xi) using Lagrange polynomial + yi = (xi-x(2))*(xi-x(3))/((x(1)-x(2))*(x(1)-x(3)))*y(1) + & + (xi-x(1))*(xi-x(3))/((x(2)-x(1))*(x(2)-x(3)))*y(2) + & + (xi-x(1))*(xi-x(2))/((x(3)-x(1))*(x(3)-x(2)))*y(3) + intrpf = yi + return + end diff --git a/Fortran/inv.f b/Fortran/inv.f new file mode 100644 index 0000000..a4a48c5 --- /dev/null +++ b/Fortran/inv.f @@ -0,0 +1,109 @@ + real function inv(AA, N, Nm, Ainv) + integer*4 N, Nm + real*8 AA(Nm,Nm), Ainv(Nm,Nm) +! Compute inverse of matrix +! Input +! AA - Matrix A (N by N) +! N - Dimension of matrix A (used) +! Nm - Dimension of matrix A (allocated memory) +! Outputs +! Ainv - Inverse of matrix A (N by N) +! determ - Determinant of matrix A (return value) + + integer*4 MAXN + parameter( MAXN = 500 ) + integer*4 i, j, k, index(MAXN), signDet, jPivot, indexJ + real*8 scale(MAXN), b(MAXN,MAXN) ! Scale factor and work array + real*8 A(MAXN,MAXN) ! Working copy of input matrix + real*8 scalemax, ratio, ratiomax, coeff, determ, sum + + if( Nm .gt. MAXN ) then + write(*,*) 'ERROR - Matrix is too large for inv routine' + stop + endif + + ! Copy matrix A so as not to modify original + do i=1,N + do j=1,N + A(i,j) = AA(i,j) + enddo + enddo + + !* Matrix b is initialized to the identity matrix + do i=1,N + do j=1,N + if( i .eq. j ) then + b(i,j) = 1.0 + else + b(i,j) = 0.0 + endif + enddo + enddo + + !* Set scale factor, scale(i) = max( |a(i,j)| ), for each row + do i=1,N + index(i) = i ! Initialize row index list + scalemax = 0.0 + do j=1,N + if( abs(A(i,j)) .gt. scalemax ) then + scalemax = abs(A(i,j)) + endif + enddo + scale(i) = scalemax + enddo + + !* Loop over rows k = 1, ..., (N-1) + signDet = 1 + do k=1,N-1 + !* Select pivot row from max( |a(j,k)/s(j)| ) + ratiomax = 0.0 + jPivot = k + do i=k,N + ratio = abs(A(index(i),k))/scale(index(i)) + if( ratio .gt. ratiomax ) then + jPivot=i + ratiomax = ratio + endif + enddo + !* Perform pivoting using row index list + indexJ = index(k) + if( jPivot .ne. k ) then ! Pivot + indexJ = index(jPivot) + index(jPivot) = index(k) ! Swap index jPivot and k + index(k) = indexJ + signDet = -1*signDet ! Flip sign of determinant + endif + !* Perform forward elimination + do i=k+1,N + coeff = A(index(i),k)/A(indexJ,k) + do j=k+1,N + A(index(i),j) = A(index(i),j) - coeff*A(indexJ,j) + enddo + A(index(i),k) = coeff + do j=1,N + b(index(i),j) = b(index(i),j) - A(index(i),k)*b(indexJ,j) + enddo + enddo + enddo + + !* Compute determinant as product of diagonal elements + determ = signDet ! Sign of determinant + do i=1,N + determ = determ*A(index(i),i) + enddo + + !* Perform backsubstitution + do k=1,N + Ainv(N,k) = b(index(N),k)/A(index(N),N) + do i=N-1,1,-1 + sum = b(index(i),k) + do j=i+1,N + sum = sum - A(index(i),j)*Ainv(j,k) + enddo + Ainv(i,k) = sum/A(index(i),i) + enddo + enddo + + inv = determ ! Return the determinant + return + end diff --git a/Fortran/legndr.f b/Fortran/legndr.f new file mode 100644 index 0000000..a1ea5ad --- /dev/null +++ b/Fortran/legndr.f @@ -0,0 +1,21 @@ + subroutine legndr( n, x, p) + integer*4 n + real*8 x, p(*) +! Legendre polynomials function +! Inputs +! n Highest order polynomial returned +! x Value at which polynomial is evaluated +! Output +! p Vector containing P(x) for order 0,1,...,n + + integer*4 i + !* Perform upward recursion + p(1) = 1 ! P(x) for n=0 + if(n .eq. 0) return + p(2) = x ! P(x) for n=1 + ! Use upward recursion to obtain other n's + do i=3,(n+1) + p(i) = ((2*i-3)*x*p(i-1) - (i-2)*p(i-2))/(i-1) + enddo + return + end diff --git a/Fortran/linreg.f b/Fortran/linreg.f new file mode 100644 index 0000000..bda7c58 --- /dev/null +++ b/Fortran/linreg.f @@ -0,0 +1,52 @@ + subroutine linreg( x, y, sigma, N, a_fit, sig_a, yy, chisqr ) + integer*4 N + real*8 x(N), y(N), sigma(N), a_fit(2), sig_a(2) + real*8 yy(N), chisqr +! Function to perform linear regression (fit a line) +! Inputs +! x Independent variable +! y Dependent variable +! sigma Estimated error in y +! N Number of data points +! Outputs +! a_fit Fit parameters; a(1) is intercept, a(2) is slope +! sig_a Estimated error in the parameters a() +! yy Curve fit to the data +! chisqr Chi squared statistic + + integer*4 i + real*8 sigmaTerm, s, sx, sy, sxy, sxx, denom, delta + + !* Evaluate various sigma sums + s = 0.0 + sx = 0.0 + sy = 0.0 + sxy = 0.0 + sxx = 0.0 + do i=1,N + sigmaTerm = 1.0/sigma(i)**2 + s = s + sigmaTerm + sx = sx + x(i) * sigmaTerm + sy = sy + y(i) * sigmaTerm + sxy = sxy + x(i) * y(i) * sigmaTerm + sxx = sxx + x(i) * x(i) * sigmaTerm + enddo + denom = s*sxx - sx*sx + + !* Compute intercept a_fit(1) and slope a_fit(2) + a_fit(1) = (sxx*sy - sx*sxy)/denom + a_fit(2) = (s*sxy - sx*sy)/denom + + !* Compute error bars for intercept and slope + sig_a(1) = sqrt(sxx/denom) + sig_a(2) = sqrt(s/denom) + + !* Evaluate curve fit at each data point and compute Chi^2 + chisqr = 0.0 + do i=1,N + yy(i) = a_fit(1)+a_fit(2)*x(i) ! Curve fit to the data + delta = (y(i)-yy(i))/sigma(i) + chisqr = chisqr + delta**2 ! Chi square + enddo + return + end diff --git a/Fortran/lorenz.f b/Fortran/lorenz.f new file mode 100644 index 0000000..84b18ee --- /dev/null +++ b/Fortran/lorenz.f @@ -0,0 +1,118 @@ +! lorenz - Program to compute the trajectories of the Lorenz +! equations using the adaptive Runge-Kutta method. + + program lorenz + integer*4 nState, MAXnStep + parameter( nState = 3, MAXnStep = 100000 ) + integer*4 iStep, nStep, i + real*8 x, y, z, state(nState), r, sigma, b, param(3) + real*8 tau, err, time, maxTau, minTau + real*8 tplot(MAXnStep), tauplot(MAXnStep) ! Plotting variables + real*8 xplot(MAXnStep), yplot(MAXnStep), zplot(MAXnStep) + real*8 x_ss(3), y_ss(3), z_ss(3) + external lorzrk + + !* Set initial state x,y,z and parameters r,sigma,b + write(*,*) 'Enter initial state (x,y,z)' + write(*,*) 'x, y, z = ' + read(*,*) x, y, z + state(1) = x + state(2) = y + state(3) = z + write(*,*) 'Enter the parameter r: ' + read(*,*) r + sigma = 10. ! Parameter sigma + b = 8./3. ! Parameter b + param(1) = r + param(2) = sigma + param(3) = b + tau = 1.0 ! Initial guess for the timestep + err = 1.e-3 ! Error tolerance + + !* Loop over the desired number of steps + time = 0 + write(*,*) 'Enter number of steps: ' + read(*,*) nStep + do iStep=1,nStep + + !* Record values for plotting + x = state(1) + y = state(2) + z = state(3) + tplot(iStep) = time + tauplot(iStep) = tau + xplot(iStep) = x + yplot(iStep) = y + zplot(iStep) = z + if( mod(iStep, 50) .eq. 0 ) then + write(*,*) 'Finished ', iStep, ' steps out of ', nStep + endif + + !* Find new state using adaptive Runge-Kutta + call rka(state,nState,time,tau,err,lorzrk,param) + enddo + + !* Print max and min time step returned by rka + maxTau = tauplot(2) + minTau = tauplot(2) + do i=3,nStep + if( tauplot(i) .gt. maxTau ) then + maxTau = tauplot(i) + else if( tauplot(i) .lt. minTau ) then + minTau = tauplot(i) + endif + enddo + write(*,*) 'Adaptive time step: Max = ', maxTau, + & ' Min = ', minTau + + ! Find the location of the three steady states + x_ss(1) = 0 + y_ss(1) = 0 + z_ss(1) = 0 + x_ss(2) = sqrt(b*(r-1)) + y_ss(2) = x_ss(2) + z_ss(2) = r-1 + x_ss(3) = -sqrt(b*(r-1)) + y_ss(3) = x_ss(3) + z_ss(3) = r-1 + + !* Print out the plotting variables: + ! tplot, xplot, yplot, zplot, x_ss, y_ss, z_ss + open(11,file='tplot.txt',status='unknown') + open(12,file='xplot.txt',status='unknown') + open(13,file='yplot.txt',status='unknown') + open(14,file='zplot.txt',status='unknown') + open(15,file='x_ss.txt',status='unknown') + open(16,file='y_ss.txt',status='unknown') + open(17,file='z_ss.txt',status='unknown') + do i=1,nStep + write(11,*) tplot(i) + write(12,*) xplot(i) + write(13,*) yplot(i) + write(14,*) zplot(i) + enddo + do i=1,3 + write(15,*) x_ss(i) + write(16,*) y_ss(i) + write(17,*) z_ss(i) + enddo + stop + end + +!***** To plot in MATLAB; use the script below ******************** +!load tplot.txt; load xplot.txt; load yplot.txt; load zplot.txt; +!load x_ss.txt; load y_ss.txt; load z_ss.txt; +!%* Graph the time series x(t) +!figure(1); clf; % Clear figure 1 window and bring forward +!plot(tplot,xplot,'-') +!xlabel('Time'); ylabel('x(t)') +!title('Lorenz model time series') +!pause(1) % Pause 1 second +!%* Graph the x,y,z phase space trajectory +!figure(2); clf; % Clear figure 2 window and bring forward +!plot3(xplot,yplot,zplot,'-',x_ss,y_ss,z_ss,'*') +!view([30 20]); % Rotate to get a better view +!grid; % Add a grid to aid perspective +!xlabel('x'); ylabel('y'); zlabel('z'); +!title('Lorenz model phase space'); +!***************************************************************** diff --git a/Fortran/lorzrk.f b/Fortran/lorzrk.f new file mode 100644 index 0000000..3b690d5 --- /dev/null +++ b/Fortran/lorzrk.f @@ -0,0 +1,26 @@ + subroutine lorzrk( xx, t, param, deriv ) + real*8 xx(*), t, param(*), deriv(*) +! Returns right-hand side of Lorenz model ODEs +! Inputs +! X State vector [x y z] +! t Time (not used) +! param Parameters [r sigma b] +! Output +! deriv Derivatives [dx/dt dy/dt dz/dt] + + real*8 x, y, z, r, sigma, b + + !* For clarity, unravel input vectors + x = xx(1) + y = xx(2) + z = xx(3) + r = param(1) + sigma = param(2) + b = param(3) + + !* Return the derivatives [dx/dt dy/dt dz/dt] + deriv(1) = sigma*(y-x) + deriv(2) = r*x - y - x*z + deriv(3) = x*y - b*z + return + end diff --git a/Fortran/lsfdemo.f b/Fortran/lsfdemo.f new file mode 100644 index 0000000..4d18a56 --- /dev/null +++ b/Fortran/lsfdemo.f @@ -0,0 +1,65 @@ +! lsfdemo - Program for demonstrating least squares fit routines + + program lsfdemo + integer*4 MAXN, MAXM + parameter( MAXN = 10000, MAXM = 50 ) + integer*4 i, N, seed, M + real*8 c(3), alpha, x(MAXN), y(MAXN), sigma(MAXN) + real*8 a_fit(MAXM), sig_a(MAXM), yy(MAXN), chisqr + real*8 randn + + !* Initialize data to be fit. Data is quadratic plus random number. + write(*,*) 'Curve fit data is created using the quadratic' + write(*,*) ' y(x) = c(1) + c(2)*x + c(3)*x^2' + write(*,*) 'Enter the coefficients:' + write(*,*) 'c(1), c(2), c(3) = ' + read(*,*) c(1), c(2), c(3) + write(*,*) 'Enter estimated error bar: ' + read(*,*) alpha + N = 50 ! Number of data points + seed = 1234 ! Seed for random number generator (DO NOT USE ZERO) + do i=1,N + x(i) = i ! x = [1, 2, ..., N] + y(i) = c(1) + c(2)*x(i) + c(3)*x(i)**2 + alpha*randn(seed) + sigma(i) = alpha ! Constant error bar + enddo + + !* Fit the data to a straight line or a more general polynomial + write(*,*) 'Enter number of fit parameters (=2 for line): ' + read(*,*) M + if( M .eq. 2 ) then !* Linear regression (Straight line) fit + call linreg( x, y, sigma, N, a_fit, sig_a, yy, chisqr) + else !* Polynomial fit + call pollsf( x, y, sigma, N, M, a_fit, sig_a, yy, chisqr) + endif + + !* Print out the fit parameters, including their error bars. + write(*,*) 'Fit parameters:' + do i=1,M + write(*,*) ' a(', i, ') = ', a_fit(i), ' +/- ', sig_a(i) + enddo + write(*,*) 'Chi square = ', chisqr, '; N-M = ', N-M + + !* Print out the plotting variables: x, y, sigma, yy + open(11,file='x.txt',status='unknown') + open(12,file='y.txt',status='unknown') + open(13,file='sigma.txt',status='unknown') + open(14,file='yy.txt',status='unknown') + do i=1,N + write(11,*) x(i) + write(12,*) y(i) + write(13,*) sigma(i) + write(14,*) yy(i) + enddo + stop + end + +!***** To plot in MATLAB; use the script below ******************** +!load x.txt; load y.txt; load sigma.txt; load yy.txt +!%* Graph the data, with error bars, and fitting function. +!figure(1); clf; % Bring figure 1 window forward +!errorbar(x,y,sigma,'o'); % Graph data with error bars +!hold on; % Freeze the plot to add the fit +!plot(x,yy,'-'); % Plot the fit on same graph as data +!xlabel('x_i'); ylabel('y_i and Y(x)'); +!****************************************************************** diff --git a/Fortran/mover.f b/Fortran/mover.f new file mode 100644 index 0000000..2ffdb5b --- /dev/null +++ b/Fortran/mover.f @@ -0,0 +1,79 @@ + subroutine mover( x, v, npart, L, mpv, vwall, tau, + & strikes, delv, seed ) + integer*4 MAXnpart, MAXncell + parameter( MAXnpart = 10000, MAXncell = 500 ) + integer*4 npart, seed, strikes(2) + real*8 x(MAXnpart), v(MAXnpart,3), L, mpv, vwall, tau, delv(2) + +! mover - Function to move particles by free flight +! Also handles collisions with walls +! Inputs +! x Positions of the particles +! v Velocities of the particles +! npart Number of particles in the system +! L System length +! mpv Most probable velocity off the wall +! vwall Wall velocities +! tau Time step +! seed Random number seed +! Outputs +! x,v Updated positions and velocities +! strikes Number of particles striking each wall +! delv Change of y-velocity at each wall +! seed Random number seed + + integer*4 i, flag + real*8 x_old(MAXnpart), xwall(2), vw(2), direction(2), stdev + real*8 vyInitial, dtr + real*8 rand, randn + + !* Move all particles pretending walls are absent + do i=1,npart + x_old(i) = x(i) ! Remember original position + x(i) = x_old(i) + v(i,1)*tau + enddo + + !* Check each particle to see if it strikes a wall + strikes(1) = 0 + strikes(2) = 0 + delv(1) = 0.0 + delv(2) = 0.0 + xwall(1) = 0 + xwall(2) = L ! Positions of walls + vw(1) = -vwall + vw(2) = vwall ! Velocities of walls + stdev = mpv/sqrt(2.0) + + direction(1) = 1 + direction(2) = -1 ! Direction of particle leaving wall + do i=1,npart + + !* Test if particle strikes either wall + flag = 0 + if( x(i) .le. 0 ) then + flag=1 ! Particle strikes left wall + else if( x(i) .ge. L ) then + flag=2 ! Particle strikes right wall + endif + + !* If particle strikes a wall, reset its position + ! and velocity. Record velocity change. + if( flag .ne. 0 ) then + strikes(flag) = strikes(flag) + 1 + vyInitial = v(i,2) + !* Reset velocity components as biased Maxwellian, + ! Exponential dist. in x; Gaussian in y and z + v(i,1) = direction(flag)*sqrt(-dlog(1.0-rand(seed))) * mpv + v(i,2) = stdev*randn(seed) + vw(flag) ! Add wall velocity + v(i,3) = stdev*randn(seed) + ! Time of flight after leaving wall + dtr = tau*(x(i)-xwall(flag))/(x(i)-x_old(i)) + !* Reset position after leaving wall + x(i) = xwall(flag) + v(i,1)*dtr + !* Record velocity change for force measurement + delv(flag) = delv(flag) + (v(i,2) - vyInitial) + endif + enddo + + return + end diff --git a/Fortran/neutrn.f b/Fortran/neutrn.f new file mode 100644 index 0000000..c1d9478 --- /dev/null +++ b/Fortran/neutrn.f @@ -0,0 +1,107 @@ +! neutrn - Program to solve the neutron diffusion equation +! using the Forward Time Centered Space (FTCS) scheme. + + program neutrn + integer*4 MAXN, MAXnplots + parameter( MAXN = 500, MAXnplots = 500 ) + integer*4 N, iplot, nplots, plot_step, i, j, iStep, nStep + real*8 tau, L, h, D, C, coeff, coeff2, nSum + real*8 nn(MAXN), nn_new(MAXN), nAve(MAXnplots) + real*8 xplot(MAXN), tplot(MAXnplots), nnplot(MAXN,MAXnplots) + + !* Initialize parameters (time step, grid spacing, etc.). + write(*,*) 'Enter time step: ' + read(*,*) tau + write(*,*) 'Enter the number of grid points: ' + read(*,*) N + write(*,*) 'Enter system length: ' + read(*,*) L + ! The system extends from x=-L/2 to x=L/2 + h = L/(N-1) ! Grid size + D = 1. ! Diffusion coefficient + C = 1. ! Generation rate + coeff = D*tau/(h*h) + coeff2 = C*tau + if( coeff .lt. 0.5 ) then + write(*,*) 'Solution is expected to be stable' + else + write(*,*) 'WARNING: Solution is expected to be unstable' + endif + + !* Set initial and boundary conditions. + do i=1,N + nn(i) = 0.0 ! Initialize density to zero at all points + nn_new(i) = 0.0 + enddo + nn(N/2) = 1/h ! Initial cond. is delta function in center + !! The boundary conditions are nn(1) = nn(N) = 0 + !! End points are unchanged during iteration + + !* Set up loop and plot variables. + iplot = 1 ! Counter used to count plots + write(*,*) 'Enter number of time steps: ' + read(*,*) nStep + plot_step = 200 ! Number of time steps between plots + nplots = nStep/plot_step + 1 ! Number of snapshots (plots) + do i=1,N + xplot(i) = (i-1)*h - L/2 ! Record the x scale for plots + enddo + + !* Loop over the desired number of time steps. + do iStep=1,nStep + + !* Compute new density using FTCS scheme. + do i=2,(N-1) + nn_new(i) = nn(i) + coeff*(nn(i+1) + nn(i-1) - 2*nn(i)) + & + coeff2*nn(i) + enddo + do i=2,(N-1) + nn(i) = nn_new(i) ! Reset density to new values + enddo + + !* Periodically record density for plotting. + if( mod(iStep,plot_step) .lt. 1 ) then ! Every plot_step steps ... + nSum = 0 + do i=1,N + nnplot(i,iplot) = nn(i) ! Record tt(i) for plotting + nSum = nSum + nn(i) + enddo + nAve(iplot) = nSum/N + tplot(iplot) = iStep*tau ! Record time for plots + iplot = iplot+1 + endif + enddo + nplots = iplot-1 ! Number of plots actually recorded + + !* Print out the plotting variables: tplot, xplot, nnplot, nAve + open(11,file='tplot.txt',status='unknown') + open(12,file='xplot.txt',status='unknown') + open(13,file='nnplot.txt',status='unknown') + open(14,file='nAve.txt',status='unknown') + do i=1,nplots + write(11,*) tplot(i) + write(14,*) nAve(i) + enddo + do i=1,N + write(12,*) xplot(i) + do j=1,(nplots-1) + write(13,1001) nnplot(i,j) + enddo + write(13,*) nnplot(i,nplots) + enddo +1001 format(e12.6,', ',$) ! The $ suppresses the carriage return + stop + end + +!***** To plot in MATLAB; use the script below ******************** +!load tplot.txt; load xplot.txt; load nnplot.txt; load nAve.txt; +!%* Plot density versus x and t as a 3D-surface plot +!figure(1); clf; +!surf(tplot,xplot,nnplot); +!xlabel('Time'); ylabel('x'); zlabel('n(x,t)'); +!title('Neutron diffusion'); +!%* Plot average neutron density versus time +!figure(2); clf; +!plot(tplot,nAve,'*'); +!xlabel('Time'); ylabel('Average density'); +!****************************************************************** diff --git a/Fortran/newtn.f b/Fortran/newtn.f new file mode 100644 index 0000000..8cd2f18 --- /dev/null +++ b/Fortran/newtn.f @@ -0,0 +1,94 @@ +! newtn - Program to solve a system of nonlinear equations +! using Newton's method. Equations defined by function fnewt. + + program newtn + integer*4 MAXnVars, MAXnParams, MAXnStep + parameter( MAXnVars = 20, MAXnParams = 20, MAXnStep = 100 ) + integer*4 iStep, nStep, nVars, nParams, i, j + real*8 temp + real*8 x(MAXnVars), xp(MAXnVars,MAXnStep+1), a(MAXnParams) + real*8 f(MAXnVars), D(MAXnVars,MAXnVars), dx(MAXnVars) + real*8 ge, determ + + !* Set initial guess and parameters + nStep = 10 ! Number of iterations before stopping + nVars = 3 ! Number of variables + nParams = 3 ! Number of parameters + write(*,*) 'Enter the initial guess: ' + do i=1,nVars + write(*,*) ' x(', i, ') = ' + read(*,*) x(i) + xp(i,1) = x(i) ! Record initial guess for plotting + enddo + write(*,*) 'Enter the parameters: ' + do i=1,nParams + write(*,*) 'a(', i, ') = ' + read(*,*) a(i) + enddo + + !* Loop over desired number of steps + do iStep=1,nStep + + !* Evaluate function f and its Jacobian matrix D + call fnewt(x,a,MAXnVars,f,D) ! fnewt returns value of f and D + do i=1,nVars + do j=i+1,nVars + temp = D(i,j) + D(i,j) = D(j,i) ! Transpose of matrix D + D(j,i) = temp + enddo + enddo + + !* Find dx by Gaussian elimination + determ = ge(D,f,nVars,MAXnVars,dx) ! Determinant returned but not used + + !* Update the estimate for the root + do i=1,nVars + x(i) = x(i) - dx(i) ! Newton iteration for new x + xp(i,iStep+1) = x(i) ! Save current estimate for plotting + enddo + enddo + + !* Print the final estimate for the root + write(*,*) 'After ', nStep, ' iterations the root is:' + do i=1,nVars + write(*,*) 'x(', i, ') = ', x(i) + enddo + + !* Print out the plotting variable: xp + open(11,file='xp.txt',status='unknown') + do i=1,nVars + do j=1,nStep + write(11,1001) xp(i,j) + enddo + write(11,*) xp(i,nStep+1) + enddo +1001 format(e12.6,', ',$) ! The $ suppresses the carriage return + stop + end + +!***** To plot in MATLAB; use the script below ******************** +!load xp.txt; +!%* Plot the iterations from initial guess to final estimate +!figure(1); clf; % Clear figure 1 window and bring forward +!subplot(1,2,1) % Left plot +! plot3(xp(1,:),xp(2,:),xp(3,:),'o-'); +! xlabel('x'); ylabel('y'); zlabel('z'); +! view([-37.5, 30]); % Viewing angle +! grid; drawnow; +!subplot(1,2,2) % Right plot +! plot3(xp(1,:),xp(2,:),xp(3,:),'o-'); +! xlabel('x'); ylabel('y'); zlabel('z'); +! view([-127.5, 30]); % Viewing angle +! grid; drawnow; +!% Plot data from lorenz (if available). +!flag = input('Plot data from lorenz program? (1=Yes/0=No): '); +!if( flag == 1 ) +! figure(2); clf; % Clear figure 1 window and bring forward +! load xplot.txt; load yplot.txt; load zplot.txt; +! plot3(xplot,yplot,zplot,'-',xp(1,:),xp(2,:),xp(3,:),'o--'); +! xlabel('x'); ylabel('y'); zlabel('z'); +! view([40 10]); % Rotate to get a better view +! grid; % Add a grid to aid perspective +!end +!****************************************************************** diff --git a/Fortran/orbit.f b/Fortran/orbit.f new file mode 100644 index 0000000..3eaa144 --- /dev/null +++ b/Fortran/orbit.f @@ -0,0 +1,122 @@ +! orbit - Program to compute the orbit of a comet. + + program orbit + integer*4 MAXnStep + parameter( MAXnStep = 100000 ) + integer*4 nState, nStep, method, iStep, i + real*8 r0, v0, r(2), v(2), state(4), accel(2), GM, param(1) + real*8 pi, mass, adaptErr, time, tau, normR, normV + real*8 rplot(MAXnStep), thplot(MAXnStep), tplot(MAXnStep) + real*8 kinetic(MAXnStep), potential(MAXnStep) + external gravrk ! Function which defines equations of motion + + !* Set initial position and velocity of the comet. + write(*,*) 'Enter initial radial distance (AU): ' + read(*,*) r0 + write(*,*) 'Enter initial tangential velocity (AU/yr): ' + read(*,*) v0 + r(1) = r0 + r(2) = 0 + v(1) = 0 + v(2) = v0 + state(1) = r(1) + state(2) = r(2) ! Used by R-K routines + state(3) = v(1) + state(4) = v(2) + nState = 4 ! Number of elements in state vector + + !* Set physical parameters (mass, G*M) + pi = 3.141592654 + GM = 4*pi**2 ! Grav. const. * Mass of Sun (au^3/yr^2) + param(1) = GM + mass = 1. ! Mass of comet + adaptErr = 1.e-3 ! Error parameter used by adaptive Runge-Kutta + time = 0 + + !* Loop over desired number of steps using specified + ! numerical method. + write(*,*) 'Enter number of steps: ' + read(*,*) nStep + write(*,*) 'Enter time step (yr): ' + read(*,*) tau + write(*,*) 'Choose a numerical method:' + write(*,*) '1) Euler, 2) Euler-Cromer, ' + write(*,*) '3) Runge-Kutta, 4) Adaptive R-K: ' + read(*,*) method + do iStep=1,nStep + + !* Record position and energy for plotting. + normR = sqrt( r(1)*r(1) + r(2)*r(2) ) + normV = sqrt( v(1)*v(1) + v(2)*v(2) ) + rplot(iStep) = normR ! Record position for plotting + thplot(iStep) = atan2(r(2),r(1)) + tplot(iStep) = time + kinetic(iStep) = 0.5*mass*normV**2 ! Record energies + potential(iStep) = -GM*mass/normR + + !* Calculate new position and velocity using desired method. + if( method .eq. 1 ) then + accel(1) = -GM*r(1)/(normR**3) + accel(2) = -GM*r(2)/(normR**3) + r(1) = r(1) + tau*v(1) ! Euler step + r(2) = r(2) + tau*v(2) + v(1) = v(1) + tau*accel(1) + v(2) = v(2) + tau*accel(2) + time = time + tau + else if( method .eq. 2 ) then + accel(1) = -GM*r(1)/(normR**3) + accel(2) = -GM*r(2)/(normR**3) + v(1) = v(1) + tau*accel(1) + v(2) = v(2) + tau*accel(2) + r(1) = r(1) + tau*v(1) ! Euler-Cromer step + r(2) = r(2) + tau*v(2) + time = time + tau + else if( method .eq. 3 ) then + call rk4( state, nState, time, tau, gravrk, param ) + r(1) = state(1) + r(2) = state(2) ! 4th order Runge-Kutta + v(1) = state(3) + v(2) = state(4) + time = time + tau + else + call rka( state, nState, time, tau, adaptErr, gravrk, param ) + r(1) = state(1) + r(2) = state(2) ! Adaptive Runge-Kutta + v(1) = state(3) + v(2) = state(4) + endif + + enddo + + !* Print out the plotting variables: + ! thplot, rplot, potential, kinetic + open(11,file='thplot.txt',status='unknown') + open(12,file='rplot.txt',status='unknown') + open(13,file='tplot.txt',status='unknown') + open(14,file='potential.txt',status='unknown') + open(15,file='kinetic.txt',status='unknown') + do i=1,nStep + write(11,*) thplot(i) + write(12,*) rplot(i) + write(13,*) tplot(i) + write(14,*) potential(i) + write(15,*) kinetic(i) + enddo + stop + end + +!***** To plot in MATLAB; use the script below ******************** +!load thplot.txt; load rplot.txt; load tplot.txt; +!load potential.txt; load kinetic.txt; +!%* Graph the trajectory of the comet. +!figure(1); clf; % Clear figure 1 window and bring forward +!polar(thplot,rplot,'+'); % Use polar plot for graphing orbit +!xlabel('Distance (AU)'); grid; +!pause(1) % Pause for 1 second before drawing next plot +!%* Graph the energy of the comet versus time. +!figure(2); clf; % Clear figure 2 window and bring forward +!totalE = kinetic + potential; % Total energy +!plot(tplot,kinetic,'-.',tplot,potential,'--',tplot,totalE,'-') +!legend('Kinetic','Potential','Total'); +!xlabel('Time (yr)'); ylabel('Energy (M AU^2/yr^2)'); +!***************************************************************** diff --git a/Fortran/orthog.f b/Fortran/orthog.f new file mode 100644 index 0000000..ab465fc --- /dev/null +++ b/Fortran/orthog.f @@ -0,0 +1,34 @@ +! orthog - Program to test if a pair of vectors +! is orthogonal. Assumes vectors are in 3D space + + program orthog + + !* Initialize the vectors a and b + integer*4 i + real*8 a(3), b(3), a_dot_b + write(*,*) 'Enter the first vector' + do i=1,3 + write(*,*) ' a(', i, ') = ' + read(*,*) a(i) + enddo + write(*,*) 'Enter the second vector' + do i=1,3 + write(*,*) ' b(', i, ') = ' + read(*,*) b(i) + enddo + + !* Evaluate the dot product as sum over products of elements + a_dot_b = 0.0 + do i=1,3 + a_dot_b = a_dot_b + a(i)*b(i) + enddo + + !* Print dot product and state whether vectors are orthogonal + if( a_dot_b .eq. 0.0 ) then + write(*,*) 'Vectors are orthogonal' + else + write(*,*) 'Vectors are NOT orthogonal' + write(*,*) 'Dot product = ', a_dot_b + endif + stop + end diff --git a/Fortran/pendul.f b/Fortran/pendul.f new file mode 100644 index 0000000..a269774 --- /dev/null +++ b/Fortran/pendul.f @@ -0,0 +1,102 @@ +! pendul - Program to compute the motion of a simple pendulum +! using the Euler or Verlet method + + program pendul + integer*4 MAXnStep + parameter( MAXnStep = 100000 ) + integer*4 method, irev, iStep, nStep, nPeriod, i + real*8 theta0, pi, theta, omega, g_over_L, time, time_old + real*8 tau, accel, theta_old, theta_new, AvePeriod, ErrorBar + real*8 t_plot(MAXnStep), th_plot(MAXnStep), period(MAXnStep) + + !* Select the numerical method to use: Euler or Verlet + write(*,*) 'Choose a numerical method 1) Euler, 2) Verlet: ' + read(*,*) method + + !* Set initial position and velocity of pendulum + write(*,*) 'Enter initial angle (in degrees): ' + read(*,*) theta0 + pi = 3.141592654 + theta = theta0*pi/180 ! Convert angle to radians + omega = 0.0 ! Set the initial velocity + + !* Set the physical constants and other variables + g_over_L = 1.0 ! The constant g/L + time = 0.0 ! Initial time + irev = 0 ! Used to count number of reversals + write(*,*) 'Enter time step: ' + read(*,*) tau + + !* Take one backward step to start Verlet + accel = -g_over_L*sin(theta) ! Gravitational acceleration + theta_old = theta - omega*tau + 0.5*tau**2*accel + + !* Loop over desired number of steps with given time step + ! and numerical method + write(*,*) 'Enter number of time steps: ' + read(*,*) nStep + do iStep=1, nStep + + !* Record angle and time for plotting + t_plot(iStep) = time + th_plot(iStep) = theta*180/pi ! Convert angle to degrees + time = time + tau + + !* Compute new position and velocity using + ! Euler or Verlet method + accel = -g_over_L*sin(theta) ! Gravitational acceleration + if( method .eq. 1 ) then + theta_old = theta ! Save previous angle + theta = theta + tau*omega ! Euler method + omega = omega + tau*accel + else + theta_new = 2*theta - theta_old + accel*tau**2 + theta_old = theta ! Verlet method + theta = theta_new + endif + + !* Test if the pendulum has passed through theta = 0; + ! if yes, use time to estimate period + if( theta*theta_old .lt. 0 ) then ! Test position for sign change + write(*,*) 'Turning point at time t = ', time + if( irev .eq. 0 ) then ! If this is the first change, + time_old = time ! just record the time + else + period(irev) = 2*(time - time_old) + time_old = time + endif + irev = irev+1 ! Increment the number of reversals + endif + + enddo + nPeriod = irev-1 ! Number of times period is measured + + !* Estimate period of oscillation, including error bar + AvePeriod = 0.0 + ErrorBar = 0.0 + do i=1,nPeriod + AvePeriod = AvePeriod + period(i) + enddo + AvePeriod = AvePeriod/nPeriod + do i=1,nPeriod + ErrorBar = ErrorBar + (period(i) - AvePeriod)**2 + enddo + ErrorBar = sqrt(ErrorBar/(nPeriod*(nPeriod-1))) + write(*,*) 'Average period = ', AvePeriod, ' +/- ', ErrorBar + + !* Print out the plotting variables: t_plot, th_plot + open(11,file='t_plot.txt',status='unknown') + open(12,file='th_plot.txt',status='unknown') + do i=1,nStep + write(11,*) t_plot(i) + write(12,*) th_plot(i) + enddo + stop + end + +!***** To plot in MATLAB; use the script below ******************** +!load t_plot.txt; load th_plot.txt; +!clf; figure(gcf); % Clear and forward figure window +!plot(t_plot,th_plot,'+'); +!xlabel('Time'); ylabel('Theta (degrees)'); +!****************************************************************** diff --git a/Fortran/pollsf.f b/Fortran/pollsf.f new file mode 100644 index 0000000..b05927f --- /dev/null +++ b/Fortran/pollsf.f @@ -0,0 +1,69 @@ + subroutine pollsf( x, y, sigma, N, M, a_fit, sig_a, yy, chisqr ) + integer*4 MAXN, MAXM + parameter( MAXN = 10000, MAXM = 50 ) + integer*4 N, M + real*8 x(N), y(N), sigma(N), a_fit(M), sig_a(M) + real*8 yy(N), chisqr +! Function to fit a polynomial to data +! Inputs +! x Independent variable +! y Dependent variable +! sigma Estimate error in y +! M Number of parameters used to fit data +! Outputs +! a_fit Fit parameters; a(1) is intercept, a(2) is slope +! sig_a Estimated error in the parameters a() +! yy Curve fit to the data +! chisqr Chi squared statistic + + integer*4 i, j, k + real*8 b(MAXN), A(MAXN,MAXM), C(MAXM,MAXM), Cinv(MAXM,MAXM) + real*8 delta, determ, inv + + !* Form the vector b and design matrix A + do i=1,N + b(i) = y(i)/sigma(i) + do j=1,M + A(i,j) = (x(i)**(j-1))/sigma(i) + enddo + enddo + + !* Compute the correlation matrix C + do i=1,M ! (C inverse) = (A transpose) * A + do j=1,M + Cinv(i,j) = 0.0 + do k=1,N + Cinv(i,j) = Cinv(i,j) + A(k,i)*A(k,j) + enddo + enddo + enddo + ! C = ( (C inverse) inverse) + determ = inv( Cinv, M, MAXM, C ) ! Determinant returned but unused + + !* Compute the least squares polynomial coefficients a_fit + do k=1,M + a_fit(k) = 0.0 + do j=1,M + do i=1,N + a_fit(k) = a_fit(k) + C(k,j) * A(i,j) * b(i) + enddo + enddo + enddo + + !* Compute the estimated error bars for the coefficients + do j=1,M + sig_a(j) = sqrt(C(j,j)) + enddo + + !* Evaluate curve fit at each data point and compute Chi^2 + chisqr = 0.0 + do i=1,N + yy(i) = 0.0 ! yy is the curve fit + do j=1,M + yy(i) = yy(i) + a_fit(j) * x(i)**(j-1) + enddo + delta = (y(i)-yy(i))/sigma(i) + chisqr = chisqr + delta**2 ! Chi square + enddo + return + end diff --git a/Fortran/rand.f b/Fortran/rand.f new file mode 100644 index 0000000..ad30369 --- /dev/null +++ b/Fortran/rand.f @@ -0,0 +1,18 @@ + real*8 function rand( seed ) + integer*4 seed +! Random number generator; Uniform dist. in [0,1) +! Input +! seed Integer seed (DO NOT USE A SEED OF ZERO) +! Output +! rand Random number uniformly distributed in [0,1) + + static a,m + real*8 a,m,temp + data a,m/16807.0, 2147483647.0/ + + temp = a*seed + seed = dmod(temp,m) + rand = seed/m + + return + end diff --git a/Fortran/randn.f b/Fortran/randn.f new file mode 100644 index 0000000..1293f6b --- /dev/null +++ b/Fortran/randn.f @@ -0,0 +1,14 @@ + real*8 function randn( seed ) + integer*4 seed +! Random number generator; Normal (Gaussian) dist. +! Input +! seed Integer seed (DO NOT USE A SEED OF ZERO) +! Output +! randn Random number, Gaussian distributed + real*8 rand + + randn = sqrt(-2*dlog(1.-rand(seed))) + & * cos(6.283185307 * rand(seed)) + + return + end diff --git a/Fortran/relax.f b/Fortran/relax.f new file mode 100644 index 0000000..7929a8f --- /dev/null +++ b/Fortran/relax.f @@ -0,0 +1,150 @@ +! relax - Program to solve the Laplace equation using +! Jacobi, Gauss-Seidel and SOR methods on a square grid + + program relax + integer*4 MAXN, MAXiterMax + parameter( MAXN = 200, MAXiterMax = MAXN*MAXN ) + integer*4 method, N, i, j, iterMax, iter, nIter + real*8 L, h, x(MAXN), y(MAXN), omega, omegaOpt, pi, phi0 + real*8 coeff, phi(MAXN,MAXN), newphi(MAXN,MAXN), phiTemp + real*8 changeDesired, change(MAXiterMax), changeSum + + !* Initialize parameters (system size, grid spacing, etc.) + write(*,*) 'Select a numerical method:' + write(*,*) ' 1) Jacobi, 2) Gauss-Seidel, 3) SOR : ' + read(*,*) method + write(*,*) 'Enter number of grid points on a side: ' + read(*,*) N + L = 1 ! System size (length) + h = L/(N-1) ! Grid spacing + do i=1,N + x(i) = (i-1)*h ! x coordinate + y(i) = x(i) ! y coordinate + enddo + + !* Select over-relaxation factor (SOR only) + pi = 3.141592654 + if( method .eq. 3 ) then + omegaOpt = 2.0/(1.0+sin(pi/N)) ! Theoretical optimum + write(*,*) 'Theoretical optimum omega = ', omegaOpt + write(*,*) 'Enter desired omega: ' + read(*,*) omega + endif + + !* Set initial guess as first term in separation of variables soln. + phi0 = 1 ! Potential at y=L + coeff = phi0 * 4/(pi*sinh(pi)) + do i=1,N + do j=1,N + phi(i,j) = coeff * sin(pi*x(i)/L) * sinh(pi*y(j)/L) + enddo + enddo + + !* Set boundary conditions + do i=1,N + phi(i,1) = 0.0 + phi(i,N) = phi0 + enddo + do j=1,N + phi(1,j) = 0.0 + phi(N,j) = 0.0 + enddo + write(*,*) 'Potential at y=L equals ', phi0 + write(*,*) 'Potential is zero on all other boundaries' + + !* Loop until desired fractional change per iteration is obtained + do i=1,N + do j=1,N + newphi(i,j) = phi(i,j) ! Copy of the solution (used only by Jacobi) + enddo + enddo + iterMax = N*N ! Set max to avoid excessively long runs + changeDesired = 1e-4 ! Stop when the change is given fraction + write(*,*) 'Desired fractional change = ', changeDesired + do iter=1,iterMax + + changeSum = 0 + if( method .eq. 1 ) then !! Jacobi method !! + do i=2,(N-1) ! Loop over interior points only + do j=2,(N-1) + newphi(i,j) = 0.25*(phi(i+1,j)+phi(i-1,j)+ + & phi(i,j-1)+phi(i,j+1)) + changeSum = changeSum + abs(1-phi(i,j)/newphi(i,j)) + enddo + enddo + do i=2,(N-1) ! Loop over interior points only + do j=2,(N-1) + phi(i,j) = newphi(i,j) ! Copy new values into phi + enddo + enddo + else if( method .eq. 2 ) then !! G-S method !! + do i=2,(N-1) ! Loop over interior points only + do j=2,(N-1) + phiTemp = 0.25*(phi(i+1,j)+phi(i-1,j)+ + & phi(i,j-1)+phi(i,j+1)) + changeSum = changeSum + abs(1-phi(i,j)/phiTemp) + phi(i,j) = phiTemp + enddo + enddo + else !! SOR method !! + do i=2,(N-1) ! Loop over interior points only + do j=2,(N-1) + phiTemp = 0.25*omega*(phi(i+1,j)+phi(i-1,j)+ + & phi(i,j-1)+phi(i,j+1)) + (1-omega)*phi(i,j) + changeSum = changeSum + abs(1-phi(i,j)/phiTemp) + phi(i,j) = phiTemp + enddo + enddo + endif + + !* Check if fractional change is small enough to halt the iteration + change(iter) = changeSum/(N-2)**2 + if( mod(iter,10) .lt. 1 ) then + write(*,*) "After ", iter, + & " iterations, fractional change = ", change(iter) + endif + if( change(iter) .lt. changeDesired ) then + write(*,*) "Desired accuracy achieved after ", iter, + & " iterations" + write(*,*) "Breaking out of main loop" + nIter = iter + goto 1 ! Break out of the main loop + endif + enddo +1 continue + + !* Print out the plotting variables: x, y, phi, change + open(11,file='x.txt',status='unknown') + open(12,file='y.txt',status='unknown') + open(13,file='phi.txt',status='unknown') + open(14,file='change.txt',status='unknown') + do i=1,N + write(11,*) x(i) + write(12,*) y(i) + do j=1,(N-1) + write(13,1001) phi(i,j) + enddo + write(13,*) phi(i,N) + enddo + do i=1,nIter + write(14,*) change(i) + enddo +1001 format(e12.6,', ',$) ! The $ suppresses the carriage return + + stop + end +!***** To plot in MATLAB; use the script below ******************** +!load x.txt; load y.txt; load phi.txt; load change.txt; +!%* Plot final estimate of potential as contour and surface plots +!figure(1); clf; +!cLevels = 0:(0.1):1; % Contour levels +!cs = contour(x,y,flipud(rot90(phi)),cLevels); +!xlabel('x'); ylabel('y'); clabel(cs); +!figure(2); clf; +!mesh(x,y,flipud(rot90(phi))); +!xlabel('x'); ylabel('y'); zlabel('\Phi(x,y)'); +!%* Plot the fractional change versus iteration +!figure(3); clf; +!semilogy(change); +!xlabel('Iteration'); ylabel('Fractional change'); +!****************************************************************** diff --git a/Fortran/rk4.f b/Fortran/rk4.f new file mode 100644 index 0000000..96f1024 --- /dev/null +++ b/Fortran/rk4.f @@ -0,0 +1,53 @@ + subroutine rk4( x, nX, t, tau, derivsRK, param ) + integer*4 MAXnX, MAXnparam + parameter( MAXnX = 50, MAXnparam = 1000 ) + integer*4 nX + real*8 x(nX), t, tau, param(MAXnparam) +! Runge-Kutta integrator (4th order) +! Inputs +! x Current value of dependent variable +! nX Number of elements in dependent variable x +! t Independent variable (usually time) +! tau Step size (usually time step) +! derivsRK Right hand side of the ODE; derivsRK is the +! name of the function which returns dx/dt +! Calling format derivsRK(x,t,param,dxdt). +! param Extra parameters passed to derivsRK +! Output +! x New value of x after a step of size tau + + integer*4 i + real*8 half_tau, t_half, t_full + real*8 F1(MAXnX), F2(MAXnX), F3(MAXnX), F4(MAXnX), xtemp(MAXnX) + + !* Evaluate F1 = f(x,t). + call derivsRK( x, t, param, F1 ) + + !* Evaluate F2 = f( x+tau*F1/2, t+tau/2 ). + half_tau = 0.5*tau + t_half = t + half_tau + do i=1,nX + xtemp(i) = x(i) + half_tau*F1(i) + enddo + call derivsRK( xtemp, t_half, param, F2 ) + + !* Evaluate F3 = f( x+tau*F2/2, t+tau/2 ). + do i=1,nX + xtemp(i) = x(i) + half_tau*F2(i) + enddo + call derivsRK( xtemp, t_half, param, F3 ) + + !* Evaluate F4 = f( x+tau*F3, t+tau ). + t_full = t + tau + do i=1,nX + xtemp(i) = x(i) + tau*F3(i) + enddo + call derivsRK( xtemp, t_full, param, F4 ) + + !* Return x(t+tau) computed from fourth-order R-K. + do i=1,nX + x(i) = x(i) + tau/6.*(F1(i) + F4(i) + 2.*(F2(i)+F3(i))) + enddo + + return + end diff --git a/Fortran/rka.f b/Fortran/rka.f new file mode 100644 index 0000000..7bfb4e3 --- /dev/null +++ b/Fortran/rka.f @@ -0,0 +1,87 @@ + subroutine rka( x, nX, t, tau, err, derivsRK, param ) + integer*4 MAXnX, MAXnparam + parameter( MAXnX = 50, MAXnparam = 1000 ) + integer*4 nX + real*8 x(MAXnX), t, tau, err, param(MAXnparam) + external derivsRK + +! Adaptive Runge-Kutta routine +! Inputs +! x Current value of the dependent variable +! nX Number of elements in dependent variable x +! t Independent variable (usually time) +! tau Step size (usually time step) +! err Desired fractional local truncation error +! derivsRK Right hand side of the ODE; derivsRK is the +! name of the function which returns dx/dt +! Calling format derivsRK(x,t,param). +! param Extra parameters passed to derivsRK +! Outputs +! x New value of the dependent variable +! t New value of the independent variable +! tau Suggested step size for next call to rka + + integer*4 i, iTry, maxTry + real*8 tSave, safe1, safe2, xSmall(MAXnX), xBig(MAXnX) + real*8 errorRatio, eps, scale, xDiff, ratio, tau_old, half_tau + + !* Set initial variables + tSave = t ! Save initial value + safe1 = 0.9 + safe2 = 4.0 ! Safety factors + + !* Loop over maximum number of attempts to satisfy error bound + maxTry = 100 + do iTry=1,maxTry + + !* Take the two small time steps + half_tau = 0.5 * tau + do i=1,nX + xSmall(i) = x(i) + enddo + call rk4(xSmall,nX,tSave,half_tau,derivsRK,param) + t = tSave + half_tau + call rk4(xSmall,nX,t,half_tau,derivsRK,param) + + !* Take the single big time step + t = tSave + tau + do i=1,nX + xBig(i) = x(i) + enddo + call rk4(xBig,nX,tSave,tau,derivsRK,param) + + !* Compute the estimated truncation error + errorRatio = 0.0 + eps = 1.0e-16 + do i=1,nX + scale = err * (abs(xSmall(i)) + abs(xBig(i)))/2.0 + xDiff = xSmall(i) - xBig(i) + ratio = abs(xDiff)/(scale + eps) + if( ratio .gt. errorRatio ) then + errorRatio = ratio + endif + enddo + + !* Estimate new tau value (including safety factors) + tau_old = tau + tau = safe1*tau_old*errorRatio**(-0.20) + if( tau .lt. tau_old/safe2 ) then + tau = tau_old/safe2 + else if( tau .gt. safe2*tau_old ) then + tau = safe2*tau_old + endif + + !* If error is acceptable, return computed values + if (errorRatio .lt. 1) then + do i=1,nX + x(i) = xSmall(i) + enddo + return + endif + enddo + + !* Issue error message if error bound never satisfied + write(*,*) 'ERROR: Adaptive Runge-Kutta routine failed' + + return + end diff --git a/Fortran/rombf.f b/Fortran/rombf.f new file mode 100644 index 0000000..a6af8a4 --- /dev/null +++ b/Fortran/rombf.f @@ -0,0 +1,47 @@ + subroutine rombf( a, b, N,MAXN, func, param, R ) + integer*4 N, MAXN + real*8 a, b, param(*), R(MAXN,MAXN) + external func +! Function to compute integrals by Romberg algorithm +! R = rombf(a,b,N,MAXN,func,param) +! Inputs +! a,b Lower and upper bound of the integral +! N Romberg table is computed to N by N +! R Array R is dimensioned as R(MAXN,MAXN) +! func Integrand function; the calling sequence +! is: double (*func)( double x, Matrix param ) +! param Set of parameters to be passed to function +! Output +! R Romberg table; Entry R(N,N) is best estimate of +! the value of the integral + + integer*4 np, i, j, k, m + real*8 h, sumT + + !* Compute the first term R(1,1) + h = b - a ! This is the coarsest panel size + np = 1 ! Current number of panels + R(1,1) = h/2 * ( func(a,param) + func(b,param) ) + + !* Loop over the desired number of rows, i = 2,...,N + do i=2,N + + !* Compute the summation in the recursive trapezoidal rule + h = h/2.0 ! Use panels half the previous size + np = 2*np ! Use twice as many panels + sumT = 0.0 + do k=1,(np-1),2 + sumT = sumT + func( a + k*h, param) + enddo + + !* Compute Romberg table entries R(i,1), R(i,2), ..., R(i,i) + R(i,1) = 0.5 * R(i-1,1) + h * sumT + m = 1 + do j=2,i + m = 4*m; + R(i,j) = R(i,j-1) + (R(i,j-1) - R(i-1,j-1))/(m-1) + enddo + enddo + + return + end diff --git a/Fortran/sampler.f b/Fortran/sampler.f new file mode 100644 index 0000000..64d254f --- /dev/null +++ b/Fortran/sampler.f @@ -0,0 +1,68 @@ + subroutine sampler( x, v, npart, ncell, L ) + integer*4 MAXnpart, MAXncell + parameter( MAXnpart = 10000, MAXncell = 500 ) + integer*4 npart, ncell + real*8 x(MAXnpart), v(MAXnpart,3), L +! sampler - Function to sample density, velocity and temperature +! Inputs +! x Particle positions +! v Particle velocities +! npart Number of particles +! ncell Number of cells +! L System size +! SampList Common block with sampling data +! Outputs +! SampList Common block with (updated) sampling data + + integer*4 jx(MAXnpart), i, jCell + real*8 sum_n(MAXncell), sum_vx(MAXncell), sum_vy(MAXncell), + & sum_vz(MAXncell), sum_v2(MAXncell) + integer*4 nsamp + real*8 ave_n(MAXncell), ave_ux(MAXncell), ave_uy(MAXncell) + real*8 ave_uz(MAXncell), ave_T(MAXncell) + common /SampList/ ave_n, ave_ux, ave_uy, ave_uz, ave_T, + & nsamp + + !* Compute cell location for each particle + do i=1,npart + jx(i) = int(ncell*x(i)/L) + 1 + enddo + + !* Initialize running sums of number, velocity and v^2 + do i=1,ncell + sum_n(i) = 0.0 + sum_vx(i) = 0.0 + sum_vy(i) = 0.0 + sum_vz(i) = 0.0 + sum_v2(i) = 0.0 + enddo + + !* For each particle, accumulate running sums for its cell + do i=1,npart + jcell = jx(i) ! Particle i is in cell jcell + sum_n(jcell) = sum_n(jcell) + 1 + sum_vx(jcell) = sum_vx(jcell) + v(i,1) + sum_vy(jcell) = sum_vy(jcell) + v(i,2) + sum_vz(jcell) = sum_vz(jcell) + v(i,3) + sum_v2(jcell) = sum_v2(jcell) + v(i,1)**2 + + & v(i,2)**2 + v(i,3)**2 + enddo + + !* Use current sums to update sample number, velocity + ! and temperature + do i=1,ncell + sum_vx(i) = sum_vx(i)/sum_n(i) + sum_vy(i) = sum_vy(i)/sum_n(i) + sum_vz(i) = sum_vz(i)/sum_n(i) + sum_v2(i) = sum_v2(i)/sum_n(i) + ave_n(i) = ave_n(i) + sum_n(i) + ave_ux(i) = ave_ux(i) + sum_vx(i) + ave_uy(i) = ave_uy(i) + sum_vy(i) + ave_uz(i) = ave_uz(i) + sum_vz(i) + ave_T(i) = ave_T(i) + sum_v2(i) - (sum_vx(i)**2 + + & sum_vy(i)**2 + sum_vz(i)**2) + enddo + nsamp = nsamp + 1 + + return + end diff --git a/Fortran/schro.f b/Fortran/schro.f new file mode 100644 index 0000000..c931726 --- /dev/null +++ b/Fortran/schro.f @@ -0,0 +1,158 @@ +! schro - Program to solve the Schrodinger equation +! for a free particle using the Crank-Nicolson scheme + + program schro + integer*4 MAXN, MAXnplots + parameter( MAXN = 200, MAXnplots = 100 ) + integer*4 N, i, j, k, nStep, nplots, iplot, iStep + real*8 L, h, h_bar, mass, tau, x(MAXN), eye(MAXN,MAXN) + real*8 ham(MAXN,MAXN), coeff, pi, x0, velocity, k0, sigma0 + real*8 Norm_psi, expFactor, plotStep, p_plot(MAXN, MAXnplots+2) + complex*16 iImag, A(MAXN,MAXN), B(MAXN,MAXN), Ai(MAXN,MAXN) + complex*16 D(MAXN,MAXN), Psi(MAXN), PsiInit(MAXN) + complex*16 NewPsi(MAXN) + + !* Initialize parameters (grid spacing, time step, etc.) + write(*,*) 'Enter number of grid points: ' + read(*,*) N + L = 100 ! System extends from -L/2 to L/2 + h = L/(N-1) ! Grid size + h_bar = 1 ! Planck's constant (natural units) + mass = 1 ! Particle mass (natural units) + write(*,*) 'Enter time step: ' + read(*,*) tau + do i=1,N + x(i) = h*(i-1) - L/2 ! Coordinates of grid points + enddo + + !* Set up the Hamiltonian operator matrix + do i=1,N + do j=1,N + eye(i,j) = 0.0 ! Set all elements to zero + ham(i,j) = 0.0 ! then evaluate non-zero elements + enddo + enddo + do i=1,N + eye(i,i) = 1.0 ! Identity matrix + enddo + coeff = -h_bar**2/(2*mass*h**2) + do i=2,(N-1) + ham(i,i-1) = coeff + ham(i,i) = -2*coeff ! Set interior rows + ham(i,i+1) = coeff + enddo + ! First and last rows for periodic boundary conditions + ham(1,N) = coeff + ham(1,1) = -2*coeff + ham(1,2) = coeff + ham(N,N-1) = coeff + ham(N,N) = -2*coeff + ham(N,1) = coeff + + !* Compute the Crank-Nicolson matrix + iImag = ( 0.0, 1.0 ) ! = sqrt(-1) + do i=1,N + do j=1,N + A(i,j) = eye(i,j) + iImag*0.5*tau/h_bar*ham(i,j) + B(i,j) = eye(i,j) - iImag*0.5*tau/h_bar*ham(i,j) + enddo + enddo + write(*,*) 'Computing matrix inverse ... ' + call cinv( A, N, MAXN, Ai ) ! Complex matrix inverse + write(*,*) ' ... done' + do i=1,N + do j=1,N + D(i,j) = 0.0 ! Matrix (complex) multiplication + do k=1,N + D(i,j) = D(i,j) + Ai(i,k)*B(k,j) ! Crank-Nicolson matrix + enddo + enddo + enddo + + !* Initialize the wavefunction + pi = 3.141592654 + x0 = 0 ! Location of the center of the wavepacket + velocity = 0.5 ! Average velocity of the packet + k0 = mass*velocity/h_bar ! Average wavenumber + sigma0 = L/10 ! Standard deviation of the wavefunction + Norm_psi = 1/(sqrt(sigma0*sqrt(pi))) ! Normalization + do i=1,N + expFactor = exp(-(x(i)-x0)**2/(2*sigma0**2)) + Psi(i) = Norm_psi * cos(k0*x(i)) * expFactor + & + iImag* Norm_psi * sin(k0*x(i)) * expFactor + PsiInit(i) = Psi(i) ! Record initial wavefunction + enddo + + !* Initialize loop and plot variables + nStep = int(L/(velocity*tau)) ! Particle should circle system + nplots = 20 ! Number of plots to record + plotStep = nStep/nplots ! Iterations between plots + do i=1,N ! Record initial condition + p_plot(i,1) = abs(Psi(i))**2 + enddo + iplot = 1 + + !* Loop over desired number of steps (wave circles system once) + do iStep=1,nStep + + !* Compute new wave function using the Crank-Nicolson scheme + do i=1,N ! Matrix multiply D*psi + NewPsi(i) = 0 + do j=1,N + NewPsi(i) = NewPsi(i) + D(i,j)*Psi(j) + enddo + enddo + do i=1,N + Psi(i) = NewPsi(i) ! Copy new values into Psi + enddo + + !* Periodically record values for plotting + if( (iStep-int(iStep/plotStep)*plotStep) .lt. 1 ) then + iplot = iplot + 1 + do i=1,N + p_plot(i,iplot) = abs(Psi(i))**2 + enddo + write(*,*) 'Finished ', iStep, ' of ', nStep, ' steps' + endif + enddo + ! Record final probability density + iplot = iplot + 1 + do i=1,N + p_plot(i,iplot) = abs(Psi(i))**2 + enddo + nplots = iplot ! Actual number of plots recorded + + !* Print out the plotting variables: + ! x, real(PsiInit), imag(PsiInit), p_plot + open(11,file='x.txt',status='unknown') + open(12,file='rpi.txt',status='unknown') + open(13,file='ipi.txt',status='unknown') + open(14,file='p_plot.txt',status='unknown') + do i=1,N + write(11,*) x(i) + write(12,*) real(PsiInit(i)) + write(13,*) imag(PsiInit(i)) + do j=1,(nplots-1) + write(14,1001) p_plot(i,j) + enddo + write(14,*) p_plot(i,nplots) + enddo +1001 format(e12.6,', ',$) ! The $ suppresses the carriage return + + stop + end +!***** To plot in MATLAB; use the script below ******************** +!load x.txt; load rpi.txt; load ipi.txt; load p_plot.txt; +!%* Plot the initial wavefunction +!figure(1); clf; +!plot(x,rpi,x,ipi); +!title('Initial wave function'); +!xlabel('x'); ylabel('\psi(x)'); legend('Real','Imag'); +!%* Plot probability versus position at various times +!figure(2); clf; +![mp np] = size(p_plot); +!plot(x,p_plot(:,1:3:np),x,p_plot(:,np)); +!xlabel('x'); ylabel('P(x,t)'); +!title('Probability density at various times'); +!axisV = [-1/2 1/2 0 max(p_plot)]; % Fix axis min and max +!***************************************************************** diff --git a/Fortran/sorter.f b/Fortran/sorter.f new file mode 100644 index 0000000..0ba2a58 --- /dev/null +++ b/Fortran/sorter.f @@ -0,0 +1,54 @@ + subroutine sorter( x, L ) + real*8 x(*), L +! sorter - Routine to sort particles into cells +! Inputs +! x Positions of particles +! L System size +! Outputs +! cell_n Number of particles in a cell (SortList common block) +! index Indexing list (SortList common block) +! Xref Cross-reference list to locate particles in cells +! (SortList common block) + + integer*4 MAXnpart, MAXncell + parameter( MAXnpart = 10000, MAXncell = 500 ) + integer*4 ipart, jx(MAXnpart), j, jcell, m, temp(MAXncell), k + integer*4 ncell, npart + integer*4 cell_n(MAXncell), index(MAXncell), Xref(MAXnpart) + common /SortList/ ncell, npart, cell_n, index, Xref + + !* Find the cell address for each particle + do ipart=1,npart + j = int(x(ipart)*ncell/L) + 1 + jx(ipart) = min0( j, ncell ) + enddo + + !* Count the number of particles in each cell + do jcell=1,ncell + cell_n(jcell) = 0 + enddo + do ipart=1,npart + cell_n( jx(ipart) ) = cell_n( jx(ipart) ) + 1 + enddo + + !* Build index list as cumulative sum of the + ! number of particles in each cell + m = 1 + do jcell=1,ncell + index(jcell) = m + m = m + cell_n(jcell) + enddo + + !* Build cross-reference list + do jcell=1,ncell + temp(jcell) = 0 + enddo + do ipart=1,npart + jcell = jx(ipart) ! Cell address of ipart + k = index(jcell) + temp(jcell) + Xref(k) = ipart + temp(jcell) = temp(jcell) + 1 + enddo + + return + end diff --git a/Fortran/sprfft.f b/Fortran/sprfft.f new file mode 100644 index 0000000..1a3ae64 --- /dev/null +++ b/Fortran/sprfft.f @@ -0,0 +1,110 @@ +! sprfft - Program to compute the power spectrum of a +! coupled mass-spring system. + + program sprfft + integer*4 MAXnStep + parameter( MAXnStep = 100000 ) + integer*4 nState, i, iStep, nStep, nPrint + real*8 x(3), v(3), state(6), param(1) + real*8 time, tau, pi, k_over_m, window + real*8 xplot(MAXnStep,3), tplot(MAXnStep) + real*8 f(MAXnStep), spect(MAXnStep), spectW(MAXnStep) + complex*16 x1fft(MAXnStep), x1fftW(MAXnStep) + external sprrk + !* Set parameters for the system (initial positions, etc.). + nState = 6 + write(*,*) 'Enter initial displacements x(1),x(2),x(3) = ' + read(*,*) x(1), x(2), x(3) + v(1) = 0.0 + v(2) = 0.0 ! Masses are initially at rest + v(3) = 0.0 + state(1) = x(1) + state(2) = x(2) + state(3) = x(3) + state(4) = v(1) + state(5) = v(2) + state(6) = v(3) + write(*,*) 'Enter timestep: ' + read(*,*) tau + k_over_m = 1 ! Ratio of spring const. over mass + param(1) = k_over_m + + !* Loop over the desired number of time steps. + time = 0 ! Set initial time + nStep = 256 ! Number of steps in the main loop + nPrint = nStep/8 ! Number of steps between printing progress + do iStep=1,nStep + + !* Use Runge-Kutta to find new displacements of the masses. + call rk4(state,nState,time,tau,sprrk,param) + time = time + tau + + !* Record the positions for graphing and to compute spectra. + xplot(iStep,1) = state(1) ! Record positions + xplot(iStep,2) = state(2) + xplot(iStep,3) = state(3) + tplot(iStep) = time + if( mod(iStep,nprint) .lt. 1 ) then + write(*,*) 'Finished ', iStep, ' out of ', nStep, ' steps' + endif + enddo + + !* Calculate the power spectrum of the time series for mass #1 + do i=1,nStep + f(i) = (i-1)/(tau*nStep) ! Frequency + x1fft(i) = xplot(i,1) ! Displacement of mass 1 + enddo + call fft(x1fft, nStep) ! Fourier transform of displacement + do i=1,nStep ! Power spectrum of displacement + spect(i) = abs(x1fft(i))**2 + enddo + + !* Apply the Hanning window to the time series and calculate + ! the resulting power spectrum + pi = 3.141592654 + do i=1,nStep + window = 0.5*(1.0-cos(2.0*pi*(i-1.0)/nStep)) ! Hanning window + x1fftW(i) = xplot(i,1) * window ! Windowed time series + enddo + call fft(x1fftW, nStep) ! Fourier transf. (windowed data) + do i=1,nStep ! Power spectrum (windowed data) + spectW(i) = abs(x1fftW(i))**2 + enddo + + !* Print out the plotting variables: + ! tplot, xplot, f, spect, spectw + open(11,file='tplot.txt',status='unknown') + open(12,file='xplot.txt',status='unknown') + open(13,file='f.txt',status='unknown') + open(14,file='spect.txt',status='unknown') + open(15,file='spectw.txt',status='unknown') + do i=1,nStep + write(11,*) tplot(i) + write(12,*) xplot(i,1), xplot(i,2), xplot(i,3) + write(13,*) f(i) + write(14,*) spect(i) + write(15,*) spectW(i) + enddo + stop + end +!***** To plot in MATLAB; use the script below ******************** +!load tplot.txt; load xplot.txt; load f.txt; +!load spect.txt; load spectw.txt +!nstep = length(tplot); nprint = nstep/8; +!%* Graph the displacements of the three masses. +!figure(1); clf; % Clear figure 1 window and bring forward +!ipr = 1:nprint:nstep; % Used to graph limited number of symbols +!plot(tplot(ipr),xplot(ipr,1),'o',tplot(ipr),xplot(ipr,2),'+',... +! tplot(ipr),xplot(ipr,3),'*',... +! tplot,xplot(:,1),'-',tplot,xplot(:,2),'-.',... +! tplot,xplot(:,3),'--'); +!legend('Mass #1','Mass #2','Mass #3'); +!title('Displacement of masses (relative to rest positions)'); +!xlabel('Time'); ylabel('Displacement'); +!%* Graph the power spectra for original and windowed data +!figure(2); clf; % Clear figure 2 window and bring forward +!semilogy(f(1:(nstep/2)),spect(1:(nstep/2)),'-',... +! f(1:(nstep/2)),spectw(1:(nstep/2)),'--'); +!title('Power spectrum (dashed is windowed data)'); +!xlabel('Frequency'); ylabel('Power'); +!****************************************************************** diff --git a/Fortran/sprrk.f b/Fortran/sprrk.f new file mode 100644 index 0000000..8d85529 --- /dev/null +++ b/Fortran/sprrk.f @@ -0,0 +1,22 @@ + subroutine sprrk( x, t, param, deriv ) + real*8 x(*), t, param(*), deriv(*) +! Returns right-hand side of 3 mass-spring system +! equations of motion +! Inputs +! x State vector [x(1) x(2) ... v(3)] +! t Time (not used) +! param (Spring constant)/(Block mass) +! Output +! deriv [dx(1)/dt dx(2)/dt ... dv(3)/dt] + + real*8 param2 + + deriv(1) = x(4) + deriv(2) = x(5) + deriv(3) = x(6) + param2 = -2*param(1) + deriv(4) = param2*x(1) + param(1)*x(2) + deriv(5) = param2*x(2) + param(1)*(x(1)+x(3)) + deriv(6) = param2*x(3) + param(1)*x(2) + return + end diff --git a/Fortran/traffic.f b/Fortran/traffic.f new file mode 100644 index 0000000..aed8044 --- /dev/null +++ b/Fortran/traffic.f @@ -0,0 +1,142 @@ +! traffic - Program to solve the generalized Burger +! equation for the traffic at a stop light problem + + program traffic + integer*4 MAXN, MAXnStep + parameter( MAXN = 200, MAXnStep = 1000 ) + integer*4 method, N, i, j, iFront, iBack, iplot, iStep, nStep + integer*4 ip(MAXN+1), im(MAXN+1), nplots + real*8 L, h, v_max, coeff, coefflw, cp, cm, rho_max, Flow_max + real*8 rho(MAXN), rho_new(MAXN), Flow(MAXN), tau + real*8 tplot(MAXnStep+1), xplot(MAXN), rplot(MAXN,MAXnStep+1) + + !* Select numerical parameters (time step, grid spacing, etc.). + write(*,*) 'Choose a numerical method: ' + write(*,*) ' 1) FTCS, 2) Lax, 3) Lax-Wendroff : ' + read(*,*) method + write(*,*) 'Enter the number of grid points: ' + read(*,*) N + L = 400 ! System size (meters) + h = L/N ! Grid spacing for periodic boundary conditions + v_max = 25 ! Maximum car speed (m/s) + write(*,*) 'Suggested timestep is ', h/v_max + write(*,*) 'Enter time step (tau): ' + read(*,*) tau + write(*,*) 'Last car starts moving after ', + & (L/4)/(v_max*tau), ' steps' + write(*,*) 'Enter number of steps: ' + read(*,*) nStep + coeff = tau/(2*h) ! Coefficient used by all schemes + coefflw = tau**2/(2*h**2) ! Coefficient used by Lax-Wendroff + + !* Set initial and boundary conditions + rho_max = 1.0 ! Maximum density + Flow_max = 0.25*rho_max*v_max ! Maximum Flow + ! Initial condition is a square pulse from x = -L/4 to x = 0 + iBack = N/4 + iFront = N/2 - 1 + do i=1,N + if( iBack .le. i .and. i .le. iFront ) then + rho(i) = rho_max + else + rho(i) = 0.0 + endif + enddo + rho(iFront+1) = rho_max/2 ! Try running without this line + ! Use periodic boundary conditions + do i=2,(N-1) + ip(i) = i+1 ! ip(i) = i+1 with periodic b.c. + im(i) = i-1 ! im(i) = i-1 with periodic b.c. + enddo + ip(1) = 2 + ip(N) = 1 + im(1) = N + im(N) = N-1 + + !* Initialize plotting variables. + iplot = 1 + tplot(1) = 0.0 ! Record initial time + do i=1,N + xplot(i) = (i - 0.5)*h - L/2 ! Record x scale for plot + rplot(i,1) = rho(i) ! Record the initial state + enddo + + !* Loop over desired number of steps. + do iStep=1,nStep + + !* Compute the flow = (Density)*(Velocity) + do i=1,N + Flow(i) = rho(i) * (v_max*(1.0 - rho(i)/rho_max)) + enddo + + !* Compute new values of density using FTCS, + ! Lax or Lax-Wendroff method. + if( method .eq. 1 ) then !!! FTCS method !!! + do i=1,N + rho_new(i) = rho(i) - coeff*(Flow(ip(i))-Flow(im(i))) + enddo + else if( method .eq. 2 ) then !!! Lax method !!! + do i=1,N + rho_new(i) = 0.5*(rho(ip(i))+rho(im(i))) + & - coeff*(Flow(ip(i))-Flow(im(i))) + enddo + else !!! Lax-Wendroff method !!! + do i=1,N + cp = v_max*(1 - (rho(ip(i))+rho(i))/rho_max) + cm = v_max*(1 - (rho(i)+rho(im(i)))/rho_max) + rho_new(i) = rho(i) - coeff*(Flow(ip(i))-Flow(im(i))) + & + coefflw*(cp*(Flow(ip(i))-Flow(i)) + & - cm*(Flow(i)-Flow(im(i)))) + enddo + endif + ! Reset with new density values + do i=1,N + rho(i) = rho_new(i) + enddo + + !* Record density for plotting. + write(*,*) 'Finished ', iStep, ' of ', nStep, ' steps' + iplot = iplot+1 + tplot(iplot) = tau*iStep + do i=1,N + rplot(i,iplot) = rho(i) + enddo + enddo + nplots = iplot ! Number of plots recorded + + !* Print out the plotting variables: tplot, xplot, rplot + open(11,file='tplot.txt',status='unknown') + open(12,file='xplot.txt',status='unknown') + open(13,file='rplot.txt',status='unknown') + do i=1,nplots + write(11,*) tplot(i) + enddo + do i=1,N + write(12,*) xplot(i) + do j=1,(nplots-1) + write(13,1001) rplot(i,j) + enddo + write(13,*) rplot(i,nplots) + enddo +1001 format(e12.6,', ',$) ! The $ suppresses the carriage return + + stop + end +!***** To plot in MATLAB; use the script below ******************** +!load tplot.txt; load xplot.txt; load rplot.txt; +!%* Graph density versus position and time as wire-mesh plot +!figure(1); clf; % Clear figure 1 window and bring forward +!mesh(tplot,xplot,rplot) +!xlabel('t'); ylabel('x'); zlabel('\rho'); +!title('Density versus position and time'); +!view([100 30]); % Rotate the plot for better view point +!pause(1); % Pause 1 second between plots +!%* Graph contours of density versus position and time. +!figure(2); clf; % Clear figure 2 window and bring forward +!% Use rot90 function to graph t vs x since +!% contour(rplot) graphs x vs t. +!clevels = 0:(0.1):1; % Contour levels +!cs = contour(xplot,tplot,flipud(rot90(rplot)),clevels); +!clabel(cs); % Put labels on contour levels +!xlabel('x'); ylabel('time'); title('Density contours'); +!****************************************************************** diff --git a/Fortran/trige.f b/Fortran/trige.f new file mode 100644 index 0000000..cdcf9cb --- /dev/null +++ b/Fortran/trige.f @@ -0,0 +1,47 @@ + real*8 function trige( A, b, N, x) + integer*4 N + real*8 A(*,3), b(*), x(*) +! Function to solve b = A*x by Gaussian elimination where +! the matrix A is a packed tridiagonal matrix +! Inputs +! A Packed tridiagonal matrix, N by N unpacked +! b Column vector +! N Number of elements used in matrix A and vector b +! Output +! x Solution of b = A*x +! determ Determinant of A + + parameter( MAXN = 500 ) + integer*4 i + real*8 alpha(MAXN), beta(MAXN), gamma(MAXN), coeff, determ + + !* Unpack diagonals of triangular matrix into vectors + do i=1,(N-1) + alpha(i) = A(i+1,1) + beta(i) = A(i,2) + gamma(i) = A(i,) + enddo + beta(N) = A(N,2) + + !* Perform forward elimination + do i=2,N + coeff = alpha(i-1)/beta(i-1) + beta(i) = beta(i) - coeff*gamma(i-1) + b(i) = b(i) - coeff*b(i-1) + enddo + + !* Compute determinant as product of diagonal elements + determ = 1.0 + do i=1,N + determ = determ*beta(i) + enddo + + !* Perform back substitution + x(N) = b(N)/beta(N) + do i=(N-1),1,-1 + x(i) = (b(i) - gamma(i)*x(i+1))/beta(i) + enddo + + trige = determ ! Return the determinant + return + end diff --git a/Fortran/zeroj.f b/Fortran/zeroj.f new file mode 100644 index 0000000..6a74b7e --- /dev/null +++ b/Fortran/zeroj.f @@ -0,0 +1,33 @@ + real*8 function zeroj( m_order, n_zero) + integer*4 m_order, n_zero +! Zeros of the Bessel function J(x) +! Inputs +! m_order Order of the Bessel function +! n_zero Index of the zero (first, second, etc.) +! Output +! z The "n_zero"th zero of the Bessel function (Return value) +! NOTE: Uses the subroutine bess.f + + integer*4 MAXm_order + parameter( MAXm_order = 200 ) + integer*4 i + real*8 beta, mu, beta8, z, jj(MAXm_order+2), deriv + + !* Use asymtotic formula for initial guess + beta = (n_zero + 0.5*m_order - 0.25)*(3.141592654) + mu = 4*m_order**2 + beta8 = 8*beta + z = beta - (mu-1)/beta8 + & - 4*(mu-1)*(7*mu-31)/(3*beta8**3) + + !* Use Newton's method to locate the root + do i=1,5 + call bess( m_order+1, z, jj ) ! Remember j(1) is J_0(z) + ! Use the recursion relation to evaluate derivative + deriv = -jj(m_order+2) + m_order/z * jj(m_order+1) + z = z - jj(m_order+1)/deriv ! Newton's root finding + enddo + zeroj = z + + return + end diff --git a/Matlab/Barrow.txt b/Matlab/Barrow.txt new file mode 100644 index 0000000..ec277ab --- /dev/null +++ b/Matlab/Barrow.txt @@ -0,0 +1,230 @@ + 3.4420000e+02 + 3.4483000e+02 + 3.4520000e+02 + 3.4537000e+02 + 3.4541000e+02 + 3.4542000e+02 + 3.4552000e+02 + 3.4579000e+02 + 3.4621000e+02 + 3.4656000e+02 + 3.4647000e+02 + 3.4551000e+02 + 3.4342000e+02 + 3.4024000e+02 + 3.3650000e+02 + 3.3306000e+02 + 3.3085000e+02 + 3.3045000e+02 + 3.3184000e+02 + 3.3440000e+02 + 3.3720000e+02 + 3.3952000e+02 + 3.4117000e+02 + 3.4239000e+02 + 3.4349000e+02 + 3.4452000e+02 + 3.4539000e+02 + 3.4595000e+02 + 3.4644000e+02 + 3.4701000e+02 + 3.4757000e+02 + 3.4788000e+02 + 3.4782000e+02 + 3.4762000e+02 + 3.4756000e+02 + 3.4767000e+02 + 3.4760000e+02 + 3.4687000e+02 + 3.4518000e+02 + 3.4259000e+02 + 3.3941000e+02 + 3.3615000e+02 + 3.3346000e+02 + 3.3202000e+02 + 3.3224000e+02 + 3.3401000e+02 + 3.3666000e+02 + 3.3931000e+02 + 3.4139000e+02 + 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schemes +clear all; help advect; % Clear memory and print header + +%* Select numerical parameters (time step, grid spacing, etc.). +method = menu('Choose a numerical method:', ... + 'FTCS','Lax','Lax-Wendroff'); +N = input('Enter number of grid points: '); +L = 1.; % System size +h = L/N; % Grid spacing +c = 1; % Wave speed +fprintf('Time for wave to move one grid spacing is %g\n',h/c); +tau = input('Enter time step: '); +coeff = -c*tau/(2.*h); % Coefficient used by all schemes +coefflw = 2*coeff^2; % Coefficient used by L-W scheme +fprintf('Wave circles system in %g steps\n',L/(c*tau)); +nStep = input('Enter number of steps: '); + +%* Set initial and boundary conditions. +sigma = 0.1; % Width of the Gaussian pulse +k_wave = pi/sigma; % Wave number of the cosine +x = ((1:N)-1/2)*h - L/2; % Coordinates of grid points +% Initial condition is a Gaussian-cosine pulse +a = cos(k_wave*x) .* exp(-x.^2/(2*sigma^2)); +% Use periodic boundary conditions +ip(1:(N-1)) = 2:N; ip(N) = 1; % ip = i+1 with periodic b.c. +im(2:N) = 1:(N-1); im(1) = N; % im = i-1 with periodic b.c. + +%* Initialize plotting variables. +iplot = 1; % Plot counter +aplot(:,1) = a(:); % Record the initial state +tplot(1) = 0; % Record the initial time (t=0) +nplots = 50; % Desired number of plots +plotStep = nStep/nplots; % Number of steps between plots + +%* Loop over desired number of steps. +for iStep=1:nStep %% MAIN LOOP %% + + %* Compute new values of wave amplitude using FTCS, + % Lax or Lax-Wendroff method. + if( method == 1 ) %%% FTCS method %%% + a(1:N) = a(1:N) + coeff*(a(ip)-a(im)); + elseif( method == 2 ) %%% Lax method %%% + a(1:N) = .5*(a(ip)+a(im)) + coeff*(a(ip)-a(im)); + else %%% Lax-Wendroff method %%% + a(1:N) = a(1:N) + coeff*(a(ip)-a(im)) + ... + coefflw*(a(ip)+a(im)-2*a(1:N)); + end + + %* Periodically record a(t) for plotting. + if( rem(iStep,plotStep) < 1 ) % Every plot_iter steps record + iplot = iplot+1; + aplot(:,iplot) = a(:); % Record a(i) for ploting + tplot(iplot) = tau*iStep; + fprintf('%g out of %g steps completed\n',iStep,nStep); + end +end + +%* Plot the initial and final states. +figure(1); clf; % Clear figure 1 window and bring forward +plot(x,aplot(:,1),'-',x,a,'--'); +legend('Initial ','Final'); +xlabel('x'); ylabel('a(x,t)'); +pause(1); % Pause 1 second between plots + +%* Plot the wave amplitude versus position and time +figure(2); clf; % Clear figure 2 window and bring forward +mesh(tplot,x,aplot); +ylabel('Position'); xlabel('Time'); zlabel('Amplitude'); +view([-70 50]); % Better view from this angle diff --git a/Matlab/balle.m b/Matlab/balle.m new file mode 100644 index 0000000..d44a21d --- /dev/null +++ b/Matlab/balle.m @@ -0,0 +1,67 @@ +% balle - Program to compute the trajectory of a baseball +% using the Euler method. +clear; help balle; % Clear memory and print header + +%* Set initial position and velocity of the baseball +y1 = input('Enter initial height (meters): '); +r1 = [0, y1]; % Initial vector position +speed = input('Enter initial speed (m/s): '); +theta = input('Enter initial angle (degrees): '); +v1 = [speed*cos(theta*pi/180), ... + speed*sin(theta*pi/180)]; % Initial velocity +r = r1; v = v1; % Set initial position and velocity + +%* Set physical parameters (mass, Cd, etc.) +Cd = 0.35; % Drag coefficient (dimensionless) +area = 4.3e-3; % Cross-sectional area of projectile (m^2) +grav = 9.81; % Gravitational acceleration (m/s^2) +mass = 0.145; % Mass of projectile (kg) +airFlag = input('Air resistance? (Yes:1, No:0): '); +if( airFlag == 0 ) + rho = 0; % No air resistance +else + rho = 1.2; % Density of air (kg/m^3) +end +air_const = -0.5*Cd*rho*area/mass; % Air resistance constant + +%* Loop until ball hits ground or max steps completed +tau = input('Enter timestep, tau (sec): '); % (sec) +maxstep = 1000; % Maximum number of steps +for istep=1:maxstep + + %* Record position (computed and theoretical) for plotting + xplot(istep) = r(1); % Record trajectory for plot + yplot(istep) = r(2); + t = (istep-1)*tau; % Current time + xNoAir(istep) = r1(1) + v1(1)*t; + yNoAir(istep) = r1(2) + v1(2)*t - 0.5*grav*t^2; + + %* Calculate the acceleration of the ball + accel = air_const*norm(v)*v; % Air resistance + accel(2) = accel(2)-grav; % Gravity + + %* Calculate the new position and velocity using Euler method + r = r + tau*v; % Euler step + v = v + tau*accel; + + %* If ball reaches ground (y<0), break out of the loop + if( r(2) < 0 ) + xplot(istep+1) = r(1); % Record last values computed + yplot(istep+1) = r(2); + break; % Break out of the for loop + end +end + +%* Print maximum range and time of flight +fprintf('Maximum range is %g meters\n',r(1)); +fprintf('Time of flight is %g seconds\n',istep*tau); + +%* Graph the trajectory of the baseball +clf; figure(gcf); % Clear figure window and bring it forward +% Mark the location of the ground by a straight line +xground = [0 max(xNoAir)]; yground = [0 0]; +% Plot the computed trajectory and parabolic, no-air curve +plot(xplot,yplot,'+',xNoAir,yNoAir,'-',xground,yground,'-'); +legend('Euler method','Theory (No air) '); +xlabel('Range (m)'); ylabel('Height (m)'); +title('Projectile motion'); diff --git a/Matlab/bess.m b/Matlab/bess.m new file mode 100644 index 0000000..d5939f9 --- /dev/null +++ b/Matlab/bess.m @@ -0,0 +1,25 @@ +function jj = bess(m_max,x) +% Bessel function +% Inputs +% m_max = Largest desired order +% x = Value at which Bessel function J(x) is evaluated +% Output +% jj = Vector of J(x) for all orders <= m_max + +%* Perform downward recursion from initial guess +m_top = max(m_max,x)+15; % Top value of m for recursion +m_top = 2*ceil( m_top/2 ); % Round up to an even number +j(m_top+1) = 0; +j(m_top) = 1; +for m=m_top-2:-1:0 % Downward recursion + j(m+1) = 2*(m+1)/(x+eps)*j(m+2) - j(m+3); +end + +%* Normalize using identity and return requested values +norm = j(1); % NOTE: Be careful, m=0,1,... but +for m=2:2:m_top % vector goes j(1),j(2),... + norm = norm + 2*j(m+1); +end +for m=0:m_max % Send back only the values for + jj(m+1) = j(m+1)/norm; % m=0,...,m_max and discard values +end % for m=m_max+1,...,m_top diff --git a/Matlab/colider.m b/Matlab/colider.m new file mode 100644 index 0000000..15dd2fb --- /dev/null +++ b/Matlab/colider.m @@ -0,0 +1,69 @@ +function [v,crmax,selxtra,col] = ... + colider(v,crmax,tau,selxtra,coeff,sD) +% colide - Function to process collisions in cells +% [v,crmax,selxtra,col] = colider(v,crmax,tau,selxtra,coeff,sD) +% Inputs +% v Velocities of the particles +% crmax Estimated maximum relative speed in a cell +% tau Time step +% selxtra Extra selections carried over from last timestep +% coeff Coefficient in computing number of selected pairs +% sD Structure containing sorting lists +% Outputs +% v Updated velocities of the particles +% crmax Updated maximum relative speed +% selxtra Extra selections carried over to next timestep +% col Total number of collisions processed + +ncell = sD.ncell; +col = 0; % Count number of collisions + +%* Loop over cells, processing collisions in each cell +for jcell=1:ncell + + %* Skip cells with only one particle + number = sD.cell_n(jcell); + if( number > 1 ) + + %* Determine number of candidate collision pairs + % to be selected in this cell + select = coeff*number*(number-1)*crmax(jcell) + selxtra(jcell); + nsel = floor(select); % Number of pairs to be selected + selxtra(jcell) = select-nsel; % Carry over any left-over fraction + crm = crmax(jcell); % Current maximum relative speed + + %* Loop over total number of candidate collision pairs + for isel=1:nsel + + %* Pick two particles at random out of this cell + k = floor(rand(1)*number); + kk = rem(ceil(k+rand(1)*(number-1)),number); + ip1 = sD.Xref(k+sD.index(jcell)); % First particle + ip2 = sD.Xref(kk+sD.index(jcell)); % Second particle + + %* Calculate pair's relative speed + cr = norm( v(ip1,:)-v(ip2,:) ); % Relative speed + if( cr > crm ) % If relative speed larger than crm, + crm = cr; % then reset crm to larger value + end + + %* Accept or reject candidate pair according to relative speed + if( cr/crmax(jcell) > rand(1) ) + %* If pair accepted, select post-collision velocities + col = col+1; % Collision counter + vcm = 0.5*(v(ip1,:) + v(ip2,:)); % Center of mass velocity + cos_th = 1 - 2*rand(1); % Cosine and sine of + sin_th = sqrt(1 - cos_th^2); % collision angle theta + phi = 2*pi*rand(1); % Collision angle phi + vrel(1) = cr*cos_th; % Compute post-collision + vrel(2) = cr*sin_th*cos(phi); % relative velocity + vrel(3) = cr*sin_th*sin(phi); + v(ip1,:) = vcm + 0.5*vrel; % Update post-collision + v(ip2,:) = vcm - 0.5*vrel; % velocities + end + + end % Loop over pairs + crmax(jcell) = crm; % Update max relative speed + end +end % Loop over cells +return; diff --git a/Matlab/contents.txt b/Matlab/contents.txt new file mode 100644 index 0000000..fc691e6 --- /dev/null +++ b/Matlab/contents.txt @@ -0,0 +1,44 @@ +% Numerical Methods for Physics, 2nd Ed. (MATLAB). +% Version 1.0a 2-Oct-99 +% Copyright (c) 1999 by Alejandro Garcia. + +% advect.m Advection PDE solver using various methods +% balle.m Projectile motion (baseball) program +% barrow.txt Carbon dioxide data for Barrow, Alaska +% bess.m Bessel function routine +% colider.m DSMC particle collision routine +% dftcs.m Diffusion PDE solver using FTCS method +% dsmceq.m Relaxation to equilibrium using DSMC method +% dsmcne.m Couette flow routine using DSMC method +% errintg.m Integrand of error function +% fftpoi.m Poisson PDE solver using MFT method +% fnewtn.m Lorenz model ODEs and Jacobian routine +% ftdemo.m Fourier transform demo program +% gravrk.m Function for Kepler equations of motion +% interp.m Interpolation program +% intrpf.m Interpolation function +% legndr.m Legendre polynomial function +% linreg.m Linear curve fit routine +% lorenz.m Lorenz model program +% lorzrk.m Function for Lorenz model ODEs +% lsfdemo.m Least square fit demo program +% mauna.txt Carbon dioxide data for Mauna Loa, Hawaii +% mover.m DSMC particle moving routine +% neutrn.m Neutron diffusion PDE solver +% newtn.m Root finding by Newton's method +% orbit.m Orbits of comets program +% orthog.m Program to test vector orthogonality +% pendul.m Simple pendulum program +% pollsf.m Polynomial curve fit routine +% relax.m Laplace PDE solver using relaxation methods +% rk4.m Runge-Kutta routine +% rka.m Adaptive Runge-Kutta routine +% rombf.m Romberg integration routine +% sampler.m DSMC particle sampling routine +% schro.m Schrodinger PDE solver using Crank-Nicolson +% sorter.m DSMC particle sorting routine +% sprfft.m Spring-mass oscillations program +% sprrk.m Function for Spring-mass ODEs +% traffic.m Traffic PDE solver using various methods +% tri_ge.m Gaussian elimination for tridiagonal matrices +% zeroj.m Zeros of Bessel function routine diff --git a/Matlab/dftcs.m b/Matlab/dftcs.m new file mode 100644 index 0000000..930cf17 --- /dev/null +++ b/Matlab/dftcs.m @@ -0,0 +1,56 @@ +% dftcs - Program to solve the diffusion equation +% using the Forward Time Centered Space (FTCS) scheme. +clear; help dftcs; % Clear memory and print header + +%* Initialize parameters (time step, grid spacing, etc.). +tau = input('Enter time step: '); +N = input('Enter the number of grid points: '); +L = 1.; % The system extends from x=-L/2 to x=L/2 +h = L/(N-1); % Grid size +kappa = 1.; % Diffusion coefficient +coeff = kappa*tau/h^2; +if( coeff < 0.5 ) + disp('Solution is expected to be stable'); +else + disp('WARNING: Solution is expected to be unstable'); +end + +%* Set initial and boundary conditions. +tt = zeros(N,1); % Initialize temperature to zero at all points +tt(round(N/2)) = 1/h; % Initial cond. is delta function in center +%% The boundary conditions are tt(1) = tt(N) = 0 + +%* Set up loop and plot variables. +xplot = (0:N-1)*h - L/2; % Record the x scale for plots +iplot = 1; % Counter used to count plots +nstep = 300; % Maximum number of iterations +nplots = 50; % Number of snapshots (plots) to take +plot_step = nstep/nplots; % Number of time steps between plots + +%* Loop over the desired number of time steps. +for istep=1:nstep %% MAIN LOOP %% + + %* Compute new temperature using FTCS scheme. + tt(2:(N-1)) = tt(2:(N-1)) + ... + coeff*(tt(3:N) + tt(1:(N-2)) - 2*tt(2:(N-1))); + + %* Periodically record temperature for plotting. + if( rem(istep,plot_step) < 1 ) % Every plot_step steps + ttplot(:,iplot) = tt(:); % record tt(i) for plotting + tplot(iplot) = istep*tau; % Record time for plots + iplot = iplot+1; + end +end + +%* Plot temperature versus x and t as wire-mesh and contour plots. +figure(1); clf; +mesh(tplot,xplot,ttplot); % Wire-mesh surface plot +xlabel('Time'); ylabel('x'); zlabel('T(x,t)'); +title('Diffusion of a delta spike'); +pause(1); +figure(2); clf; +contourLevels = 0:0.5:10; contourLabels = 0:5; +cs = contour(tplot,xplot,ttplot,contourLevels); % Contour plot +clabel(cs,contourLabels); % Add labels to selected contour levels +xlabel('Time'); ylabel('x'); +title('Temperature contour plot'); diff --git a/Matlab/dsmceq.m b/Matlab/dsmceq.m new file mode 100644 index 0000000..02c66ae --- /dev/null +++ b/Matlab/dsmceq.m @@ -0,0 +1,78 @@ +% dsmceq - Dilute gas simulation using DSMC algorithm +% This version illustrates the approach to equilibrium +clear all; help dsmceq; % Clear memory and print header + +%* Initialize constants (particle mass, diameter, etc.) +boltz = 1.3806e-23; % Boltzmann's constant (J/K) +mass = 6.63e-26; % Mass of argon atom (kg) +diam = 3.66e-10; % Effective diameter of argon atom (m) +T = 273; % Temperature (K) +density = 1.78; % Density of argon at STP (kg/m^3) +L = 1e-6; % System size is one micron +npart = input('Enter number of simulation particles: '); +eff_num = density/mass*L^3/npart; +fprintf('Each particle represents %g atoms\n',eff_num); + +%* Assign random positions and velocities to particles +rand('state',0); % Initialize random number generator +x = L*rand(npart,1); % Assign random positions +v_init = sqrt(3*boltz*T/mass); % Initial speed +v = zeros(npart,3); % Only x-component is non-zero +v(:,1) = v_init * (1 - 2*floor(2*rand(npart,1))); + +%* Plot the initial speed distribution +figure(1); clf; +vmag = sqrt(v(:,1).^2 + v(:,2).^2 + v(:,3).^2); +vbin = 50:100:1050; % Bins for histogram +hist(vmag,vbin); title('Initial speed distribution'); +xlabel('Speed (m/s)'); ylabel('Number'); + +%* Initialize variables used for evaluating collisions +ncell = 15; % Number of cells +tau = 0.2*(L/ncell)/v_init; % Set timestep tau +vrmax = 3*v_init*ones(ncell,1); % Estimated max rel. speed +selxtra = zeros(ncell,1); % Used by routine "colider" +coeff = 0.5*eff_num*pi*diam^2*tau/(L^3/ncell); +coltot = 0; % Count total collisions + +%* Declare structure for lists used in sorting +sortData = struct('ncell',ncell, ... + 'npart',npart, ... + 'cell_n',zeros(ncell,1), ... + 'index',zeros(ncell,1), ... + 'Xref',zeros(npart,1)); + +%* Loop for the desired number of time steps +nstep = input('Enter total number of time steps: '); +for istep = 1:nstep + + %* Move all the particles ballistically + x(:) = x(:) + v(:,1)*tau; % Update x position of particle + x = rem(x+L,L); % Periodic boundary conditions + + %* Sort the particles into cells + sortData = sorter(x,L,sortData); + + %* Evaluate collisions among the particles + [v, vrmax, selxtra, col] = ... + colider(v,vrmax,tau,selxtra,coeff,sortData); + coltot = coltot + col; + + %* Periodically display the current progress + if( rem(istep,10) < 1 ) + figure(2); clf; + vmag = sqrt(v(:,1).^2 + v(:,2).^2 + v(:,3).^2); + hist(vmag,vbin); + title(sprintf('Done %g of %g steps; %g collisions',... + istep,nstep,coltot)); + xlabel('Speed (m/s)'); ylabel('Number'); + drawnow; + end +end + +%* Plot the histogram of the final speed distribution +figure(2); clf; +vmag = sqrt(v(:,1).^2 + v(:,2).^2 + v(:,3).^2); +hist(vmag,vbin); +title(sprintf('Final distrib., Time = %g sec.',nstep*tau)); +xlabel('Speed (m/s)'); ylabel('Number'); diff --git a/Matlab/dsmcne.m b/Matlab/dsmcne.m new file mode 100644 index 0000000..3df33d5 --- /dev/null +++ b/Matlab/dsmcne.m @@ -0,0 +1,120 @@ +% dsmcne - Program to simulate a dilute gas using DSMC algorithm +% This version simulates planar Couette flow +clear all; help dsmcne; % Clear memory and print header + +%* Initialize constants (particle mass, diameter, etc.) +boltz = 1.3806e-23; % Boltzmann's constant (J/K) +mass = 6.63e-26; % Mass of argon atom (kg) +diam = 3.66e-10; % Effective diameter of argon atom (m) +T = 273; % Initial temperature (K) +density = 2.685e25; % Number density of argon at STP (m^-3) +L = 1e-6; % System size is one micron +Volume = L^3; % Volume of the system (m^3) +npart = input('Enter number of simulation particles: '); +eff_num = density*Volume/npart; +fprintf('Each simulation particle represents %g atoms\n',eff_num); +mfp = Volume/(sqrt(2)*pi*diam^2*npart*eff_num); +fprintf('System width is %g mean free paths \n',L/mfp); +mpv = sqrt(2*boltz*T/mass); % Most probable initial velocity +vwall_m = input('Enter wall velocity as Mach number: '); +vwall = vwall_m * sqrt(5/3 * boltz*T/mass); +fprintf('Wall velocities are %g and %g m/s \n',-vwall,vwall); + +%* Assign random positions and velocities to particles +rand('state',1); % Initialize random number generators +randn('state',1); +x = L*rand(npart,1); % Assign random positions +% Assign thermal velocities using Gaussian random numbers +v = sqrt(boltz*T/mass) * randn(npart,3); +% Add velocity gradient to the y-component +v(:,2) = v(:,2) + 2*vwall*(x(:)/L) - vwall; + +%* Initialize variables used for evaluating collisions +ncell = 20; % Number of cells +tau = 0.2*(L/ncell)/mpv; % Set timestep tau +vrmax = 3*mpv*ones(ncell,1); % Estimated max rel. speed in a cell +selxtra = zeros(ncell,1); % Used by collision routine "colider" +coeff = 0.5*eff_num*pi*diam^2*tau/(Volume/ncell); + +%* Declare structure for lists used in sorting +sortData = struct('ncell', ncell, ... + 'npart', npart, ... + 'cell_n', zeros(ncell,1), ... + 'index', zeros(ncell,1), ... + 'Xref', zeros(npart,1)); + +%* Initialize structure and variables used in statistical sampling +sampData = struct('ncell', ncell, ... + 'nsamp', 0, ... + 'ave_n', zeros(ncell,1), ... + 'ave_u', zeros(ncell,3), ... + 'ave_T', zeros(ncell,1)); +tsamp = 0; % Total sampling time +dvtot = zeros(1,2); % Total momentum change at a wall +dverr = zeros(1,2); % Used to find error in dvtot + +%* Loop for the desired number of time steps +colSum = 0; strikeSum = [0 0]; +nstep = input('Enter total number of timesteps: '); +for istep = 1:nstep + + %* Move all the particles + [x, v, strikes, delv] = mover(x,v,npart,L,mpv,vwall,tau); + strikeSum = strikeSum + strikes; + + %* Sort the particles into cells + sortData = sorter(x,L,sortData); + + %* Evaluate collisions among the particles + [v, vrmax, selxtra, col] = ... + colider(v,vrmax,tau,selxtra,coeff,sortData); + colSum = colSum + col; + + %* After initial transient, accumulate statistical samples + if(istep > nstep/10) + sampData = sampler(x,v,npart,L,sampData); + dvtot = dvtot + delv; + dverr = dverr + delv.^2; + tsamp = tsamp + tau; + end + + %* Periodically display the current progress + if( rem(istep,10) < 1 ) + fprintf('Finished %g of %g steps, Collisions = %g\n', ... + istep,nstep,colSum); + fprintf('Total wall strikes: %g (left) %g (right)\n', ... + strikeSum(1),strikeSum(2)); + end +end + +%* Normalize the accumulated statistics +nsamp = sampData.nsamp; +ave_n = (eff_num/(Volume/ncell))*sampData.ave_n/nsamp; +ave_u = sampData.ave_u/nsamp; +ave_T = mass/(3*boltz) * (sampData.ave_T/nsamp); +dverr = dverr/(nsamp-1) - (dvtot/nsamp).^2; +dverr = sqrt(dverr*nsamp); + +%* Compute viscosity from drag force on the walls +force = (eff_num*mass*dvtot)/(tsamp*L^2); +ferr = (eff_num*mass*dverr)/(tsamp *L^2); +fprintf('Force per unit area is \n'); +fprintf('Left wall: %g +/- %g \n',force(1),ferr(1)); +fprintf('Right wall: %g +/- %g \n',force(2),ferr(2)); +vgrad = 2*vwall/L; % Velocity gradient +visc = 1/2*(-force(1)+force(2))/vgrad; % Average viscosity +viscerr = 1/2*(ferr(1)+ferr(2))/vgrad; % Error +fprintf('Viscosity = %g +/- %g N s/m^2\n',visc,viscerr); +eta = 5*pi/32*mass*density*(2/sqrt(pi)*mpv)*mfp; +fprintf('Theoretical value of viscoisty is %g N s/m^2\n',eta); + +%* Plot average density, velocity and temperature +figure(1); clf; +xcell = ((1:ncell)-0.5)/ncell * L; +plot(xcell,ave_n); xlabel('position'); ylabel('Number density'); +figure(2); clf; +plot(xcell,ave_u); xlabel('position'); ylabel('Velocities'); +legend('x-component','y-component','z-component'); +figure(3); clf; +plot(xcell,ave_T); xlabel('position'); ylabel('Temperature'); + diff --git a/Matlab/errintg.m b/Matlab/errintg.m new file mode 100644 index 0000000..7324c4a --- /dev/null +++ b/Matlab/errintg.m @@ -0,0 +1,9 @@ +function f = errintg(x,param) +% Error function integrand +% Inputs +% x Value where integrand is evaluated +% param Parameter list (not used) +% Output +% f Integrand of the error function +f = exp(-x^2); +return; diff --git a/Matlab/fftpoi.m b/Matlab/fftpoi.m new file mode 100644 index 0000000..2f74789 --- /dev/null +++ b/Matlab/fftpoi.m @@ -0,0 +1,57 @@ +% fftpoi - Program to solve the Poisson equation using +% MFT method (periodic boundary conditions) +clear all; help fftpoi; % Clear memory and print header + +%* Initialize parameters (system size, grid spacing, etc.) +eps0 = 8.8542e-12; % Permittivity (C^2/(N m^2)) +N = 50; % Number of grid points on a side (square grid) +L = 1; % System size +h = L/N; % Grid spacing for periodic boundary conditions +x = ((1:N)-1/2)*h; % Coordinates of grid points +y = x; % Square grid +fprintf('System is a square of length %g \n',L); + +%* Set up charge density rho(i,j) +rho = zeros(N,N); % Initialize charge density to zero +M = input('Enter number of line charges: '); +for i=1:M + fprintf('\n For charge #%g \n',i); + r = input('Enter position [x y]: '); + ii=round(r(1)/h + 1/2); % Place charge at nearest + jj=round(r(2)/h + 1/2); % grid point + q = input('Enter charge density: '); + rho(ii,jj) = rho(ii,jj) + q/h^2; +end + +%* Compute matrix P +cx = cos((2*pi/N)*(0:N-1)); +cy = cx; +numerator = -h^2/(2*eps0); +tinyNumber = 1e-20; % Avoids division by zero +for i=1:N + for j=1:N + P(i,j) = numerator/(cx(i)+cy(j)-2+tinyNumber); + end +end + +%* Compute potential using MFT method +rhoT = fft2(rho); % Transform rho into wavenumber domain +phiT = rhoT .* P; % Computing phi in the wavenumber domain +phi = ifft2(phiT); % Inv. transf. phi into the coord. domain +phi = real(phi); % Clean up imaginary part due to round-off + +%* Compute electric field as E = - grad phi +[Ex Ey] = gradient(flipud(rot90(phi))); +magnitude = sqrt(Ex.^2 + Ey.^2); +Ex = -Ex ./ magnitude; % Normalize components so +Ey = -Ey ./ magnitude; % vectors have equal length + +%* Plot potential and electric field +figure(1); clf; +contour3(x,y,flipud(rot90(phi,1)),35); +xlabel('x'); ylabel('y'); zlabel('\Phi(x,y)'); +figure(2); clf; +quiver(x,y,Ex,Ey) % Plot E field with vectors +title('E field (Direction)'); xlabel('x'); ylabel('y'); +axis('square'); axis([0 L 0 L]); + diff --git a/Matlab/fnewt.m b/Matlab/fnewt.m new file mode 100644 index 0000000..65a8ed3 --- /dev/null +++ b/Matlab/fnewt.m @@ -0,0 +1,25 @@ +function [f,D] = fnewt(x,a) +% Function used by the N-variable Newton's method +% Inputs +% x State vector [x y z] +% a Parameters [r sigma b] +% Outputs +% f Lorenz model r.h.s. [dx/dt dy/dt dz/dt] +% D Jacobian matrix, D(i,j) = df(j)/dx(i) + +% Evaluate f(i) +f(1) = a(2)*(x(2)-x(1)); +f(2) = a(1)*x(1)-x(2)-x(1)*x(3); +f(3) = x(1)*x(2)-a(3)*x(3); + +% Evaluate D(i,j) +D(1,1) = -a(2); % df(1)/dx(1) +D(1,2) = a(1)-x(3); % df(2)/dx(1) +D(1,3) = x(2); % df(3)/dx(1) +D(2,1) = a(2); % df(1)/dx(2) +D(2,2) = -1; % df(2)/dx(2) +D(2,3) = x(1); % df(3)/dx(2) +D(3,1) = 0; % df(1)/dx(3) +D(3,2) = -x(1); % df(2)/dx(3) +D(3,3) = -a(3); % df(3)/dx(3) +return; diff --git a/Matlab/ftdemo.m b/Matlab/ftdemo.m new file mode 100644 index 0000000..fd124be --- /dev/null +++ b/Matlab/ftdemo.m @@ -0,0 +1,44 @@ +% ftdemo - Discrete Fourier transform demonstration program +clear all; help ftdemo; % Clear memory and print header + +%* Initialize the sine wave time series to be transformed. +N = input('Enter the number of points: '); +freq = input('Enter frequency of the sine wave: '); +phase = input('Enter phase of the sine wave: '); +tau = 1; % Time increment +t = (0:(N-1))*tau; % t = [0, tau, 2*tau, ... ] +y = sin(2*pi*t*freq + phase); % Sine wave time series +f = (0:(N-1))/(N*tau); % f = [0, 1/(N*tau), ... ] + +%* Compute the transform using desired method: direct summation +% or fast Fourier transform (FFT) algorithm. +flops(0); % Reset the flops counter to zero +Method = menu('Compute transform by','Direct summation','FFT'); +if( Method == 1 ); % Direct summation + twoPiN = -2*pi*sqrt(-1)/N; + for k=0:N-1 + expTerm = exp(twoPiN*(0:N-1)*k); + yt(k+1) = sum(y .* expTerm); + end +else % Fast Fourier transform + yt = fft(y); +end +fprintf('Number of floating point operations = %g\n',flops); + +%* Graph the time series and its transform. +figure(1); clf; % Clear figure 1 window and bring forward +plot(t,y); +title('Original time series'); +ylabel('Amplitude'); xlabel('Time'); +figure(2); clf; % Clear figure 2 window and bring forward +plot(f,real(yt),'-',f,imag(yt),'--'); +legend('Real','Imaginary '); +title('Fourier transform'); +ylabel('Transform'); xlabel('Frequency'); + +%* Compute and graph the power spectrum of the time series. +figure(3); clf; % Clear figure 3 window and bring forward +powspec = abs(yt).^2; +semilogy(f,powspec,'-'); +title('Power spectrum (unnormalized)'); +ylabel('Power'); xlabel('Frequency'); diff --git a/Matlab/gravrk.m b/Matlab/gravrk.m new file mode 100644 index 0000000..4dc8ed2 --- /dev/null +++ b/Matlab/gravrk.m @@ -0,0 +1,17 @@ +function deriv = gravrk(s,t,GM) +% Returns right-hand side of Kepler ODE; used by Runge-Kutta routines +% Inputs +% s State vector [r(1) r(2) v(1) v(2)] +% t Time (not used) +% GM Parameter G*M (gravitational const. * solar mass) +% Output +% deriv Derivatives [dr(1)/dt dr(2)/dt dv(1)/dt dv(2)/dt] + +%* Compute acceleration +r = [s(1) s(2)]; % Unravel the vector s into position and velocity +v = [s(3) s(4)]; +accel = -GM*r/norm(r)^3; % Gravitational acceleration + +%* Return derivatives [dr(1)/dt dr(2)/dt dv(1)/dt dv(2)/dt] +deriv = [v(1) v(2) accel(1) accel(2)]; +return; diff --git a/Matlab/interp.m b/Matlab/interp.m new file mode 100644 index 0000000..850b1a2 --- /dev/null +++ b/Matlab/interp.m @@ -0,0 +1,25 @@ +% interp - Program to interpolate data using Lagrange +% polynomial to fit quadratic to three data points +clear all; help interp; % Clear memory and print header +%* Initialize the data points to be fit by quadratic +disp('Enter data points as x,y pairs (e.g., [1 2])'); +for i=1:3 + temp = input('Enter data point: '); + x(i) = temp(1); + y(i) = temp(2); +end +%* Establish the range of interpolation (from x_min to x_max) +xr = input('Enter range of x values as [x_min x_max]: '); +%* Find yi for the desired interpolation values xi using +% the function intrpf +nplot = 100; % Number of points for interpolation curve +for i=1:nplot + xi(i) = xr(1) + (xr(2)-xr(1))*(i-1)/(nplot-1); + yi(i) = intrpf(xi(i),x,y); % Use intrpf function to interpolate +end +%* Plot the curve given by (xi,yi) and mark original data points +plot(x,y,'*',xi,yi,'-'); +xlabel('x'); +ylabel('y'); +title('Three point interpolation'); +legend('Data points','Interpolation '); \ No newline at end of file diff --git a/Matlab/intrpf.m b/Matlab/intrpf.m new file mode 100644 index 0000000..a787456 --- /dev/null +++ b/Matlab/intrpf.m @@ -0,0 +1,15 @@ +function yi = intrpf(xi,x,y) +% Function to interpolate between data points +% using Lagrange polynomial (quadratic) +% Inputs +% x Vector of x coordinates of data points (3 values) +% y Vector of y coordinates of data points (3 values) +% xi The x value where interpolation is computed +% Output +% yi The interpolation polynomial evaluated at xi + +%* Calculate yi = p(xi) using Lagrange polynomial +yi = (xi-x(2))*(xi-x(3))/((x(1)-x(2))*(x(1)-x(3)))*y(1) ... + + (xi-x(1))*(xi-x(3))/((x(2)-x(1))*(x(2)-x(3)))*y(2) ... + + (xi-x(1))*(xi-x(2))/((x(3)-x(1))*(x(3)-x(2)))*y(3); +return; diff --git a/Matlab/legndr.m b/Matlab/legndr.m new file mode 100644 index 0000000..d50cdab --- /dev/null +++ b/Matlab/legndr.m @@ -0,0 +1,16 @@ +function p = legndr(n,x) +% Legendre polynomials function +% Inputs +% n = Highest order polynomial returned +% x = Value at which polynomial is evaluated +% Output +% p = Vector containing P(x) for order 0,1,...,n + +%* Perform upward recursion +p(1)=1; % P(x) for n=0 +if(n == 0) return; end +p(2)=x; % P(x) for n=1 +for i=3:n+1 % Use upward recursion to obtain other n's + p(i) = ((2*i-3)*x*p(i-1) - (i-2)*p(i-2))/(i-1); +end +return; diff --git a/Matlab/linreg.m b/Matlab/linreg.m new file mode 100644 index 0000000..768fedf --- /dev/null +++ b/Matlab/linreg.m @@ -0,0 +1,33 @@ +function [a_fit, sig_a, yy, chisqr] = linreg(x,y,sigma) +% Function to perform linear regression (fit a line) +% Inputs +% x Independent variable +% y Dependent variable +% sigma Estimated error in y +% Outputs +% a_fit Fit parameters; a(1) is intercept, a(2) is slope +% sig_a Estimated error in the parameters a() +% yy Curve fit to the data +% chisqr Chi squared statistic + +%* Evaluate various sigma sums +sigmaTerm = sigma .^ (-2); +s = sum(sigmaTerm); +sx = sum(x .* sigmaTerm); +sy = sum(y .* sigmaTerm); +sxy = sum(x .* y .* sigmaTerm); +sxx = sum((x .^ 2) .* sigmaTerm); +denom = s*sxx - sx^2; + +%* Compute intercept a_fit(1) and slope a_fit(2) +a_fit(1) = (sxx*sy - sx*sxy)/denom; +a_fit(2) = (s*sxy - sx*sy)/denom; + +%* Compute error bars for intercept and slope +sig_a(1) = sqrt(sxx/denom); +sig_a(2) = sqrt(s/denom); + +%* Evaluate curve fit at each data point and compute Chi^2 +yy = a_fit(1)+a_fit(2)*x; % Curve fit to the data +chisqr = sum( ((y-yy)./sigma).^2 ); % Chi square +return; diff --git a/Matlab/lorenz.m b/Matlab/lorenz.m new file mode 100644 index 0000000..c60f6da --- /dev/null +++ b/Matlab/lorenz.m @@ -0,0 +1,53 @@ +% lorenz - Program to compute the trajectories of the Lorenz +% equations using the adaptive Runge-Kutta method. +clear; help lorenz; + +%* Set initial state x,y,z and parameters r,sigma,b +state = input('Enter the initial position [x y z]: '); +r = input('Enter the parameter r: '); +sigma = 10.; % Parameter sigma +b = 8./3.; % Parameter b +param = [r sigma b]; % Vector of parameters passed to rka +tau = 1; % Initial guess for the timestep +err = 1.e-3; % Error tolerance + +%* Loop over the desired number of steps +time = 0; +nstep = input('Enter number of steps: '); +for istep=1:nstep + + %* Record values for plotting + x = state(1); y = state(2); z = state(3); + tplot(istep) = time; tauplot(istep) = tau; + xplot(istep) = x; yplot(istep) = y; zplot(istep) = z; + if( rem(istep,50) < 1 ) + fprintf('Finished %g steps out of %g\n',istep,nstep); + end + + %* Find new state using adaptive Runge-Kutta + [state, time, tau] = rka(state,time,tau,err,'lorzrk',param); + +end + +%* Print max and min time step returned by rka +fprintf('Adaptive time step: Max = %g, Min = %g \n', ... + max(tauplot(2:nstep)), min(tauplot(2:nstep))); + +%* Graph the time series x(t) +figure(1); clf; % Clear figure 1 window and bring forward +plot(tplot,xplot,'-') +xlabel('Time'); ylabel('x(t)') +title('Lorenz model time series') +pause(1) % Pause 1 second + +%* Graph the x,y,z phase space trajectory +figure(2); clf; % Clear figure 2 window and bring forward +% Mark the location of the three steady states +x_ss(1) = 0; y_ss(1) = 0; z_ss(1) = 0; +x_ss(2) = sqrt(b*(r-1)); y_ss(2) = x_ss(2); z_ss(2) = r-1; +x_ss(3) = -sqrt(b*(r-1)); y_ss(3) = x_ss(3); z_ss(3) = r-1; +plot3(xplot,yplot,zplot,'-',x_ss,y_ss,z_ss,'*') +view([30 20]); % Rotate to get a better view +grid; % Add a grid to aid perspective +xlabel('x'); ylabel('y'); zlabel('z'); +title('Lorenz model phase space'); diff --git a/Matlab/lorzrk.m b/Matlab/lorzrk.m new file mode 100644 index 0000000..e606e93 --- /dev/null +++ b/Matlab/lorzrk.m @@ -0,0 +1,18 @@ +function deriv = lorzrk(s,t,param) +% Returns right-hand side of Lorenz model ODEs +% Inputs +% s State vector [x y z] +% t Time (not used) +% param Parameters [r sigma b] +% Output +% deriv Derivatives [dx/dt dy/dt dz/dt] + +%* For clarity, unravel input vectors +x = s(1); y = s(2); z = s(3); +r = param(1); sigma = param(2); b = param(3); + +%* Return the derivatives [dx/dt dy/dt dz/dt] +deriv(1) = sigma*(y-x); +deriv(2) = r*x - y - x*z; +deriv(3) = x*y - b*z; +return; diff --git a/Matlab/lsfdemo.m b/Matlab/lsfdemo.m new file mode 100644 index 0000000..a904ef7 --- /dev/null +++ b/Matlab/lsfdemo.m @@ -0,0 +1,38 @@ +% lsfdemo - Program for demonstrating least squares fit routines +clear all; help lsfdemo; % Clear memory and print header + +%* Initialize data to be fit. Data is quadratic plus random number. +fprintf('Curve fit data is created using the quadratic\n'); +fprintf(' y(x) = c(1) + c(2)*x + c(3)*x^2 \n'); +c = input('Enter the coefficients as [c(1) c(2) c(3)]: '); +N = 50; % Number of data points +x = 1:N; % x = [1, 2, ..., N] +randn('state',0); % Initialize random number generator +alpha = input('Enter estimated error bar: '); +r = alpha*randn(1,N); % Gaussian distributed random vector +y = c(1) + c(2)*x + c(3)*x.^2 + r; +sigma = alpha*ones(1,N); % Constant error bar + +%* Fit the data to a straight line or a more general polynomial +M = input('Enter number of fit parameters (=2 for line): '); +if( M == 2 ) + %* Linear regression (Straight line) fit + [a_fit sig_a yy chisqr] = linreg(x,y,sigma); +else + %* Polynomial fit + [a_fit sig_a yy chisqr] = pollsf(x,y,sigma,M); +end + +%* Print out the fit parameters, including their error bars. +fprintf('Fit parameters:\n'); +for i=1:M + fprintf(' a(%g) = %g +/- %g \n',i,a_fit(i),sig_a(i)); +end + +%* Graph the data, with error bars, and fitting function. +figure(1); clf; % Bring figure 1 window forward +errorbar(x,y,sigma,'o'); % Graph data with error bars +hold on; % Freeze the plot to add the fit +plot(x,yy,'-'); % Plot the fit on same graph as data +xlabel('x_i'); ylabel('y_i and Y(x)'); +title(['\chi^2 = ',num2str(chisqr),' N-M = ',num2str(N-M)]); diff --git a/Matlab/mover.m b/Matlab/mover.m new file mode 100644 index 0000000..b5dfecc --- /dev/null +++ b/Matlab/mover.m @@ -0,0 +1,55 @@ +function [x,v,strikes,delv] = mover(x,v,npart, ... + L,mpv,vwall,tau) +% mover - Function to move particles by free flight +% Also handles collisions with walls +% Inputs +% x Positions of the particles +% v Velocities of the particles +% npart Number of particles in the system +% L System length +% mpv Most probable velocity off the wall +% vwall Wall velocities +% tau Time step +% Outputs +% x,v Updated positions and velocities +% strikes Number of particles striking each wall +% delv Change of y-velocity at each wall + +%* Move all particles pretending walls are absent +x_old = x; % Remember original position +x(:) = x_old(:) + v(:,1)*tau; + +%* Loop over all particles +strikes = [0 0]; delv = [0 0]; +xwall = [0 L]; vw = [-vwall vwall]; +direction = [1 -1]; % Direction of particle leaving wall +stdev = mpv/sqrt(2); +for i=1:npart + + %* Test if particle strikes either wall + if( x(i) <= 0 ) + flag=1; % Particle strikes left wall + elseif( x(i) >= L ) + flag=2; % Particle strikes right wall + else + flag=0; % Particle strikes neither wall + end + + %* If particle strikes a wall, reset its position + % and velocity. Record velocity change. + if( flag > 0 ) + strikes(flag) = strikes(flag) + 1; + vyInitial = v(i,2); + %* Reset velocity components as biased Maxwellian, + % Exponential dist. in x; Gaussian in y and z + v(i,1) = direction(flag)*sqrt(-log(1-rand(1))) * mpv; + v(i,2) = stdev*randn(1) + vw(flag); % Add wall velocity + v(i,3) = stdev*randn(1); + % Time of flight after leaving wall + dtr = tau*(x(i)-xwall(flag))/(x(i)-x_old(i)); + %* Reset position after leaving wall + x(i) = xwall(flag) + v(i,1)*dtr; + %* Record velocity change for force measurement + delv(flag) = delv(flag) + (v(i,2) - vyInitial); + end +end diff --git a/Matlab/neutrn.m b/Matlab/neutrn.m new file mode 100644 index 0000000..4083cfd --- /dev/null +++ b/Matlab/neutrn.m @@ -0,0 +1,63 @@ +% neutrn - Program to solve the neutron diffusion equation +% using the Forward Time Centered Space (FTCS) scheme. +clear; help neutrn; % Clear memory and print header + +%* Initialize parameters (time step, grid points, etc.). +tau = input('Enter time step: '); +N = input('Enter the number of grid points: '); +L = input('Enter system length: '); +% The system extends from x=-L/2 to x=L/2 +h = L/(N-1); % Grid size +D = 1.; % Diffusion coefficient +C = 1.; % Generation rate +coeff = D*tau/h^2; +coeff2 = C*tau; +if( coeff < 0.5 ) + disp('Solution is expected to be stable'); +else + disp('WARNING: Solution is expected to be unstable'); +end + +%* Set initial and boundary conditions. +nn = zeros(N,1); % Initialize density to zero at all points +nn_new = zeros(N,1); % Initialize temporary array used by FTCS +nn(round(N/2)) = 1/h; % Initial cond. is delta function in center +%% The boundary conditions are nn(1) = nn(N) = 0 + +%* Set up loop and plot variables. +xplot = (0:N-1)*h - L/2; % Record the x scale for plots +iplot = 1; % Counter used to count plots +nstep = input('Enter number of time steps: '); +nplots = 50; % Number of snapshots (plots) to take +plot_step = nstep/nplots; % Number of time steps between plots + +%* Loop over the desired number of time steps. +for istep=1:nstep %% MAIN LOOP %% + + %* Compute the new density using FTCS scheme. + nn_new(2:(N-1)) = nn(2:(N-1)) + ... + coeff*(nn(3:N) + nn(1:(N-2)) - 2*nn(2:(N-1))) + ... + coeff2*nn(2:(N-1)); + nn = nn_new; % Reset temperature to new values + + %* Periodically record the density for plotting. + if( rem(istep,plot_step) < 1 ) % Every plot_step steps + nnplot(:,iplot) = nn(:); % record nn(i) for plotting + tplot(iplot) = istep*tau; % Record time for plots + nAve(iplot) = mean(nn); % Record average density + iplot = iplot+1; + fprintf('Finished %g of %g steps\n',istep,nstep); + end +end + +%* Plot density versus x and t as a 3D-surface plot +figure(1); clf; +mesh(tplot,xplot,nnplot); +xlabel('Time'); ylabel('x'); zlabel('n(x,t)'); +title('Neutron diffusion'); + +%* Plot average neutron density versus time +figure(2); clf; +plot(tplot,nAve,'*'); +xlabel('Time'); ylabel('Average density'); +title(['L = ',num2str(L),' (L_c = \pi)']); diff --git a/Matlab/newtn.m b/Matlab/newtn.m new file mode 100644 index 0000000..1ed12f5 --- /dev/null +++ b/Matlab/newtn.m @@ -0,0 +1,57 @@ +% newtn - Program to solve a system of nonlinear equations +% using Newton's method. Equations defined by function fnewt. +clear all; help newtn; % Clear memory and print header + +%* Set initial guess and parameters +x0 = input('Enter the initial guess (row vector): '); +x = x0; % Copy initial guess +xp(:,1) = x(:); % Record initial guess for plotting +a = input('Enter the parameter a: '); + +%* Loop over desired number of steps +nStep = 10; % Number of iterations before stopping +for iStep=1:nStep + + %* Evaluate function f and its Jacobian matrix D + [f D] = fnewt(x,a); % fnewt returns value of f and D + %* Find dx by Gaussian elimination + dx = f/D; + %* Update the estimate for the root + x = x - dx; % Newton iteration for new x + xp(:,iStep+1) = x(:); % Save current estimate for plotting + +end + +%* Print the final estimate for the root +fprintf('After %g iterations the root is\n',nStep); +disp(x); + +%* Plot the iterations from initial guess to final estimate +figure(1); clf; % Clear figure 1 window and bring forward +subplot(1,2,1) % Left plot + plot3(xp(1,:),xp(2,:),xp(3,:),'o-',... + x(1),x(2),x(3),'*'); + xlabel('x'); ylabel('y'); zlabel('z'); + view([-37.5, 30]); % Viewing angle + title(sprintf('Initial guess is %g %g %g',x0(1),x0(2),x0(3))); + grid; drawnow; +subplot(1,2,2) % Right plot + plot3(xp(1,:),xp(2,:),xp(3,:),'o-',... + x(1),x(2),x(3),'*'); + xlabel('x'); ylabel('y'); zlabel('z'); + view([-127.5, 30]); % Viewing angle + title(sprintf('After %g iterations, root is %g %g %g',... + nStep,x(1),x(2),x(3))); + grid; drawnow; +% Plot data from lorenz (if available). To write lorenz data, use: +% >>save xplot; save yplot; save zplot; +% after running the lornez program. +flag = input('Plot data from lorenz program? (1=Yes/0=No): '); +if( flag == 1 ) + figure(2); clf; % Clear figure 1 window and bring forward + load xplot; load yplot; load zplot; + plot3(xplot,yplot,zplot,'-',xp(1,:),xp(2,:),xp(3,:),'o--'); + xlabel('x'); ylabel('y'); zlabel('z'); + view([40 10]); % Rotate to get a better view + grid; % Add a grid to aid perspective +end \ No newline at end of file diff --git a/Matlab/orbit.m b/Matlab/orbit.m new file mode 100644 index 0000000..6cba47d --- /dev/null +++ b/Matlab/orbit.m @@ -0,0 +1,66 @@ +% orbit - Program to compute the orbit of a comet. +clear all; help orbit; % Clear memory and print header + +%* Set initial position and velocity of the comet. +r0 = input('Enter initial radial distance (AU): '); +v0 = input('Enter initial tangential velocity (AU/yr): '); +r = [r0 0]; v = [0 v0]; +state = [ r(1) r(2) v(1) v(2) ]; % Used by R-K routines + +%* Set physical parameters (mass, G*M) +GM = 4*pi^2; % Grav. const. * Mass of Sun (au^3/yr^2) +mass = 1.; % Mass of comet +adaptErr = 1.e-3; % Error parameter used by adaptive Runge-Kutta +time = 0; + +%* Loop over desired number of steps using specified +% numerical method. +nStep = input('Enter number of steps: '); +tau = input('Enter time step (yr): '); +NumericalMethod = menu('Choose a numerical method:', ... + 'Euler','Euler-Cromer','Runge-Kutta','Adaptive R-K'); +for iStep=1:nStep + + %* Record position and energy for plotting. + rplot(iStep) = norm(r); % Record position for polar plot + thplot(iStep) = atan2(r(2),r(1)); + tplot(iStep) = time; + kinetic(iStep) = .5*mass*norm(v)^2; % Record energies + potential(iStep) = - GM*mass/norm(r); + + %* Calculate new position and velocity using desired method. + if( NumericalMethod == 1 ) + accel = -GM*r/norm(r)^3; + r = r + tau*v; % Euler step + v = v + tau*accel; + time = time + tau; + elseif( NumericalMethod == 2 ) + accel = -GM*r/norm(r)^3; + v = v + tau*accel; + r = r + tau*v; % Euler-Cromer step + time = time + tau; + elseif( NumericalMethod == 3 ) + state = rk4(state,time,tau,'gravrk',GM); + r = [state(1) state(2)]; % 4th order Runge-Kutta + v = [state(3) state(4)]; + time = time + tau; + else + [state time tau] = rka(state,time,tau,adaptErr,'gravrk',GM); + r = [state(1) state(2)]; % Adaptive Runge-Kutta + v = [state(3) state(4)]; + end + +end + +%* Graph the trajectory of the comet. +figure(1); clf; % Clear figure 1 window and bring forward +polar(thplot,rplot,'+'); % Use polar plot for graphing orbit +xlabel('Distance (AU)'); grid; +pause(1) % Pause for 1 second before drawing next plot + +%* Graph the energy of the comet versus time. +figure(2); clf; % Clear figure 2 window and bring forward +totalE = kinetic + potential; % Total energy +plot(tplot,kinetic,'-.',tplot,potential,'--',tplot,totalE,'-') +legend('Kinetic','Potential','Total'); +xlabel('Time (yr)'); ylabel('Energy (M AU^2/yr^2)'); diff --git a/Matlab/orthog.m b/Matlab/orthog.m new file mode 100644 index 0000000..3aedc79 --- /dev/null +++ b/Matlab/orthog.m @@ -0,0 +1,18 @@ +% orthog - Program to test if a pair of vectors +% is orthogonal. Assumes vectors are in 3D space +clear all; help orthog; % Clear the memory and print header +%* Initialize the vectors a and b +a = input('Enter the first vector: '); +b = input('Enter the second vector: '); +%* Evaluate the dot product as sum over products of elements +a_dot_b = 0; +for i=1:3 + a_dot_b = a_dot_b + a(i)*b(i); +end +%* Print dot product and state whether vectors are orthogonal +if( a_dot_b == 0 ) + disp('Vectors are orthogonal'); +else + disp('Vectors are NOT orthogonal'); + fprintf('Dot product = %g \n',a_dot_b); +end diff --git a/Matlab/pendul.m b/Matlab/pendul.m new file mode 100644 index 0000000..2ef4b9c --- /dev/null +++ b/Matlab/pendul.m @@ -0,0 +1,69 @@ +% pendul - Program to compute the motion of a simple pendulum +% using the Euler or Verlet method +clear all; help pendul % Clear the memory and print header + +%* Select the numerical method to use: Euler or Verlet +NumericalMethod = menu('Choose a numerical method:', ... + 'Euler','Verlet'); + +%* Set initial position and velocity of pendulum +theta0 = input('Enter initial angle (in degrees): '); +theta = theta0*pi/180; % Convert angle to radians +omega = 0; % Set the initial velocity + +%* Set the physical constants and other variables +g_over_L = 1; % The constant g/L +time = 0; % Initial time +irev = 0; % Used to count number of reversals +tau = input('Enter time step: '); + +%* Take one backward step to start Verlet +accel = -g_over_L*sin(theta); % Gravitational acceleration +theta_old = theta - omega*tau + 0.5*tau^2*accel; + +%* Loop over desired number of steps with given time step +% and numerical method +nstep = input('Enter number of time steps: '); +for istep=1:nstep + + %* Record angle and time for plotting + t_plot(istep) = time; + th_plot(istep) = theta*180/pi; % Convert angle to degrees + time = time + tau; + + %* Compute new position and velocity using + % Euler or Verlet method + accel = -g_over_L*sin(theta); % Gravitational acceleration + if( NumericalMethod == 1 ) + theta_old = theta; % Save previous angle + theta = theta + tau*omega; % Euler method + omega = omega + tau*accel; + else + theta_new = 2*theta - theta_old + tau^2*accel; + theta_old = theta; % Verlet method + theta = theta_new; + end + + %* Test if the pendulum has passed through theta = 0; + % if yes, use time to estimate period + if( theta*theta_old < 0 ) % Test position for sign change + fprintf('Turning point at time t= %f \n',time); + if( irev == 0 ) % If this is the first change, + time_old = time; % just record the time + else + period(irev) = 2*(time - time_old); + time_old = time; + end + irev = irev + 1; % Increment the number of reversals + end +end + +%* Estimate period of oscillation, including error bar +AvePeriod = mean(period); +ErrorBar = std(period)/sqrt(irev); +fprintf('Average period = %g +/- %g\n', AvePeriod,ErrorBar); + +%* Graph the oscillations as theta versus time +clf; figure(gcf); % Clear and forward figure window +plot(t_plot,th_plot,'+'); +xlabel('Time'); ylabel('\theta (degrees)'); diff --git a/Matlab/pollsf.m b/Matlab/pollsf.m new file mode 100644 index 0000000..0580988 --- /dev/null +++ b/Matlab/pollsf.m @@ -0,0 +1,40 @@ +function [a_fit, sig_a, yy, chisqr] = pollsf(x, y, sigma, M) +% Function to fit a polynomial to data +% Inputs +% x Independent variable +% y Dependent variable +% sigma Estimate error in y +% M Number of parameters used to fit data +% Outputs +% a_fit Fit parameters; a(1) is intercept, a(2) is slope +% sig_a Estimated error in the parameters a() +% yy Curve fit to the data +% chisqr Chi squared statistic + +%* Form the vector b and design matrix A +b = y./sigma; +N = length(x); +for i=1:N + for j=1:M + A(i,j) = x(i)^(j-1)/sigma(i); + end +end + +%* Compute the correlation matrix C +C = inv(A.' * A); + +%* Compute the least squares polynomial coefficients a_fit +a_fit = C * A.' * b.'; + +%* Compute the estimated error bars for the coefficients +for j=1:M + sig_a(j) = sqrt(C(j,j)); +end + +%* Evaluate curve fit at each data point and compute Chi^2 +yy = zeros(1,N); +for j=1:M + yy = yy + a_fit(j)*x.^(j-1); % yy is the curve fit +end +chisqr = sum( ((y-yy)./sigma).^2 ); +return; diff --git a/Matlab/relax.m b/Matlab/relax.m new file mode 100644 index 0000000..620f3fe --- /dev/null +++ b/Matlab/relax.m @@ -0,0 +1,97 @@ +% relax - Program to solve the Laplace equation using +% Jacobi, Gauss-Seidel and SOR methods on a square grid +clear all; help relax; % Clear memory and print header + +%* Initialize parameters (system size, grid spacing, etc.) +method = menu('Numerical Method','Jacobi','Gauss-Seidel','SOR'); +N = input('Enter number of grid points on a side: '); +L = 1; % System size (length) +h = L/(N-1); % Grid spacing +x = (0:N-1)*h; % x coordinate +y = (0:N-1)*h; % y coordinate + +%* Select over-relaxation factor (SOR only) +if( method == 3 ) + omegaOpt = 2/(1+sin(pi/N)); % Theoretical optimum + fprintf('Theoretical optimum omega = %g \n',omegaOpt); + omega = input('Enter desired omega: '); +end + +%* Set initial guess as first term in separation of variables soln. +phi0 = 1; % Potential at y=L +phi = phi0 * 4/(pi*sinh(pi)) * sin(pi*x'/L)*sinh(pi*y/L); + +%* Set boundary conditions +phi(1,:) = 0; phi(N,:) = 0; phi(:,1) = 0; +phi(:,N) = phi0*ones(N,1); +fprintf('Potential at y=L equals %g \n',phi0); +fprintf('Potential is zero on all other boundaries\n'); + +%* Loop until desired fractional change per iteration is obtained +flops(0); % Reset the flops counter to zero; +newphi = phi; % Copy of the solution (used only by Jacobi) +iterMax = N^2; % Set max to avoid excessively long runs +changeDesired = 1e-4; % Stop when the change is given fraction +fprintf('Desired fractional change = %g\n',changeDesired); +for iter=1:iterMax + changeSum = 0; + + if( method == 1 ) %% Jacobi method %% + for i=2:(N-1) % Loop over interior points only + for j=2:(N-1) + newphi(i,j) = .25*(phi(i+1,j)+phi(i-1,j)+ ... + phi(i,j-1)+phi(i,j+1)); + changeSum = changeSum + abs(1-phi(i,j)/newphi(i,j)); + end + end + phi = newphi; + + elseif( method == 2 ) %% G-S method %% + for i=2:(N-1) % Loop over interior points only + for j=2:(N-1) + newphi = .25*(phi(i+1,j)+phi(i-1,j)+ ... + phi(i,j-1)+phi(i,j+1)); + changeSum = changeSum + abs(1-phi(i,j)/newphi); + phi(i,j) = newphi; + end + end + + else %% SOR method %% + for i=2:(N-1) % Loop over interior points only + for j=2:(N-1) + newphi = 0.25*omega*(phi(i+1,j)+phi(i-1,j)+ ... + phi(i,j-1)+phi(i,j+1)) + (1-omega)*phi(i,j); + changeSum = changeSum + abs(1-phi(i,j)/newphi); + phi(i,j) = newphi; + end + end + end + + %* Check if fractional change is small enough to halt the iteration + change(iter) = changeSum/(N-2)^2; + if( rem(iter,10) < 1 ) + fprintf('After %g iterations, fractional change = %g\n',... + iter,change(iter)); + end + if( change(iter) < changeDesired ) + fprintf('Desired accuracy achieved after %g iterations\n',iter); + fprintf('Breaking out of main loop\n'); + break; + end +end + +%* Plot final estimate of potential as contour and surface plots +figure(1); clf; +cLevels = 0:(0.1):1; % Contour levels +cs = contour(x,y,flipud(rot90(phi)),cLevels); +xlabel('x'); ylabel('y'); clabel(cs); +title(sprintf('Potential after %g iterations',iter)); +figure(2); clf; +mesh(x,y,flipud(rot90(phi))); +xlabel('x'); ylabel('y'); zlabel('\Phi(x,y)'); + +%* Plot the fractional change versus iteration +figure(3); clf; +semilogy(change); +xlabel('Iteration'); ylabel('Fractional change'); +title(sprintf('Number of flops = %g\n',flops)); diff --git a/Matlab/rk4.m b/Matlab/rk4.m new file mode 100644 index 0000000..d4525d5 --- /dev/null +++ b/Matlab/rk4.m @@ -0,0 +1,24 @@ +function xout = rk4(x,t,tau,derivsRK,param) +% Runge-Kutta integrator (4th order) +% Input arguments - +% x = current value of dependent variable +% t = independent variable (usually time) +% tau = step size (usually timestep) +% derivsRK = right hand side of the ODE; derivsRK is the +% name of the function which returns dx/dt +% Calling format derivsRK(x,t,param). +% param = extra parameters passed to derivsRK +% Output arguments - +% xout = new value of x after a step of size tau +half_tau = 0.5*tau; +F1 = feval(derivsRK,x,t,param); +t_half = t + half_tau; +xtemp = x + half_tau*F1; +F2 = feval(derivsRK,xtemp,t_half,param); +xtemp = x + half_tau*F2; +F3 = feval(derivsRK,xtemp,t_half,param); +t_full = t + tau; +xtemp = x + tau*F3; +F4 = feval(derivsRK,xtemp,t_full,param); +xout = x + tau/6.*(F1 + F4 + 2.*(F2+F3)); +return; diff --git a/Matlab/rka.m b/Matlab/rka.m new file mode 100644 index 0000000..06030bc --- /dev/null +++ b/Matlab/rka.m @@ -0,0 +1,53 @@ +function [xSmall, t, tau] = rka(x,t,tau,err,derivsRK,param) +% Adaptive Runge-Kutta routine +% Inputs +% x Current value of the dependent variable +% t Independent variable (usually time) +% tau Step size (usually time step) +% err Desired fractional local truncation error +% derivsRK Right hand side of the ODE; derivsRK is the +% name of the function which returns dx/dt +% Calling format derivsRK(x,t,param). +% param Extra parameters passed to derivsRK +% Outputs +% xSmall New value of the dependent variable +% t New value of the independent variable +% tau Suggested step size for next call to rka + +%* Set initial variables +tSave = t; xSave = x; % Save initial values +safe1 = .9; safe2 = 4.; % Safety factors + +%* Loop over maximum number of attempts to satisfy error bound +maxTry = 100; +for iTry=1:maxTry + + %* Take the two small time steps + half_tau = 0.5 * tau; + xTemp = rk4(xSave,tSave,half_tau,derivsRK,param); + t = tSave + half_tau; + xSmall = rk4(xTemp,t,half_tau,derivsRK,param); + + %* Take the single big time step + t = tSave + tau; + xBig = rk4(xSave,tSave,tau,derivsRK,param); + + %* Compute the estimated truncation error + scale = err * (abs(xSmall) + abs(xBig))/2.; + xDiff = xSmall - xBig; + errorRatio = max( abs(xDiff)./(scale + eps) ); + + %* Estimate new tau value (including safety factors) + tau_old = tau; + tau = safe1*tau_old*errorRatio^(-0.20); + tau = max(tau,tau_old/safe2); + tau = min(tau,safe2*tau_old); + + %* If error is acceptable, return computed values + if (errorRatio < 1) return; end +end + +%* Issue error message if error bound never satisfied +error('ERROR: Adaptive Runge-Kutta routine failed'); +return; + diff --git a/Matlab/rombf.m b/Matlab/rombf.m new file mode 100644 index 0000000..ba6eabb --- /dev/null +++ b/Matlab/rombf.m @@ -0,0 +1,39 @@ +function R = rombf(a,b,N,func,param) +% Function to compute integrals by Romberg algorithm +% R = rombf(a,b,N,func,param) +% Inputs +% a,b Lower and upper bound of the integral +% N Romberg table is N by N +% func Name of integrand function in a string such as +% func='errintg'. The calling sequence is func(x,param) +% param Set of parameters to be passed to function +% Output +% R Romberg table; Entry R(N,N) is best estimate of +% the value of the integral + +%* Compute the first term R(1,1) +h = b - a; % This is the coarsest panel size +np = 1; % Current number of panels +R(1,1) = h/2 * (feval(func,a,param) + feval(func,b,param)); + +%* Loop over the desired number of rows, i = 2,...,N +for i=2:N + + %* Compute the summation in the recursive trapezoidal rule + h = h/2; % Use panels half the previous size + np = 2*np; % Use twice as many panels + sumT = 0; + for k=1:2:np-1 % This for loop goes k=1,3,5,...,np-1 + sumT = sumT + feval(func, a + k*h, param); + end + + %* Compute Romberg table entries R(i,1), R(i,2), ..., R(i,i) + R(i,1) = 1/2 * R(i-1,1) + h * sumT; + m = 1; + for j=2:i + m = 4*m; + R(i,j) = R(i,j-1) + (R(i,j-1) - R(i-1,j-1))/(m-1); + end +end +return; + diff --git a/Matlab/sampler.m b/Matlab/sampler.m new file mode 100644 index 0000000..739e9aa --- /dev/null +++ b/Matlab/sampler.m @@ -0,0 +1,41 @@ +function sampD = sampler(x,v,npart,L,sampD) +% sampler - Function to sample density, velocity and temperature +% Inputs +% x Particle positions +% v Particle velocities +% npart Number of particles +% L System size +% sampD Structure with sampling data +% Outputs +% sampD Structure with sampling data + +%* Compute cell location for each particle +ncell = sampD.ncell; +jx=ceil(ncell*x/L); + +%* Initialize running sums of number, velocity and v^2 +sum_n = zeros(ncell,1); +sum_v = zeros(ncell,3); +sum_v2 = zeros(ncell,1); + +%* For each particle, accumulate running sums for its cell +for ipart=1:npart + jcell = jx(ipart); % Particle ipart is in cell jcell + sum_n(jcell) = sum_n(jcell)+1; + sum_v(jcell,:) = sum_v(jcell,:) + v(ipart,:); + sum_v2(jcell) = sum_v2(jcell) + ... + v(ipart,1)^2 + v(ipart,2)^2 + v(ipart,3)^2; +end + +%* Use current sums to update sample number, velocity +% and temperature +for i=1:3 + sum_v(:,i) = sum_v(:,i)./sum_n(:); +end +sum_v2 = sum_v2./sum_n; +sampD.ave_n = sampD.ave_n + sum_n; +sampD.ave_u = sampD.ave_u + sum_v; +sampD.ave_T = sampD.ave_T + sum_v2 - ... + (sum_v(:,1).^2 + sum_v(:,2).^2 + sum_v(:,3).^2); +sampD.nsamp = sampD.nsamp + 1; +return; diff --git a/Matlab/schro.m b/Matlab/schro.m new file mode 100644 index 0000000..941620d --- /dev/null +++ b/Matlab/schro.m @@ -0,0 +1,77 @@ +% schro - Program to solve the Schrodinger equation +% for a free particle using the Crank-Nicolson scheme +clear all; help schro; % Clear memory and print header + +%* Initialize parameters (grid spacing, time step, etc.) +i_imag = sqrt(-1); % Imaginary i +N = input('Enter number of grid points: '); +L = 100; % System extends from -L/2 to L/2 +h = L/(N-1); % Grid size +x = h*(0:N-1) - L/2; % Coordinates of grid points +h_bar = 1; mass = 1; % Natural units +tau = input('Enter time step: '); + +%* Set up the Hamiltonian operator matrix +ham = zeros(N); % Set all elements to zero +coeff = -h_bar^2/(2*mass*h^2); +for i=2:(N-1) + ham(i,i-1) = coeff; + ham(i,i) = -2*coeff; % Set interior rows + ham(i,i+1) = coeff; +end +% First and last rows for periodic boundary conditions +ham(1,N) = coeff; ham(1,1) = -2*coeff; ham(1,2) = coeff; +ham(N,N-1) = coeff; ham(N,N) = -2*coeff; ham(N,1) = coeff; + +%* Compute the Crank-Nicolson matrix +dCN = ( inv(eye(N) + .5*i_imag*tau/h_bar*ham) * ... + (eye(N) - .5*i_imag*tau/h_bar*ham) ); + +%* Initialize the wavefunction +x0 = 0; % Location of the center of the wavepacket +velocity = 0.5; % Average velocity of the packet +k0 = mass*velocity/h_bar; % Average wavenumber +sigma0 = L/10; % Standard deviation of the wavefunction +Norm_psi = 1/(sqrt(sigma0*sqrt(pi))); % Normalization +psi = Norm_psi * exp(i_imag*k0*x') .* ... + exp(-(x'-x0).^2/(2*sigma0^2)); + +%* Plot the initial wavefunction +figure(1); clf; +plot(x,real(psi),'-',x,imag(psi),'--'); +title('Initial wave function'); +xlabel('x'); ylabel('\psi(x)'); legend('Real ','Imag '); +drawnow; pause(1); + +%* Initialize loop and plot variables +max_iter = L/(velocity*tau); % Particle should circle system +plot_iter = max_iter/20; % Produce 20 curves +p_plot(:,1) = psi.*conj(psi); % Record initial condition +iplot = 1; +figure(2); clf; +axisV = [-L/2 L/2 0 max(p_plot)]; % Fix axis min and max + +%* Loop over desired number of steps (wave circles system once) +for iter=1:max_iter + + %* Compute new wave function using the Crank-Nicolson scheme + psi = dCN*psi; + + %* Periodically record values for plotting + if( rem(iter,plot_iter) < 1 ) + iplot = iplot+1; + p_plot(:,iplot) = psi.*conj(psi); + plot(x,p_plot(:,iplot)); % Display snap-shot of P(x) + xlabel('x'); ylabel('P(x,t)'); + title(sprintf('Finished %g of %g iterations',iter,max_iter)); + axis(axisV); drawnow; + end + +end + +%* Plot probability versus position at various times +pFinal = psi.*conj(psi); +plot(x,p_plot(:,1:3:iplot),x,pFinal); +xlabel('x'); ylabel('P(x,t)'); +title('Probability density at various times'); + diff --git a/Matlab/sorter.m b/Matlab/sorter.m new file mode 100644 index 0000000..c63cb71 --- /dev/null +++ b/Matlab/sorter.m @@ -0,0 +1,40 @@ +function sD = sorter(x,L,sD) +% sorter - Function to sort particles into cells +% sD = sorter(x,L,sD) +% Inputs +% x Positions of particles +% L System size +% sD Structure containing sorting lists +% Output +% sD Structure containing sorting lists + +%* Find the cell address for each particle +npart = sD.npart; +ncell = sD.ncell; +jx = floor(x*ncell/L) + 1; +jx = min( jx, ncell*ones(npart,1) ); + +%* Count the number of particles in each cell +sD.cell_n = zeros(ncell,1); +for ipart=1:npart + sD.cell_n( jx(ipart) ) = sD.cell_n( jx(ipart) ) + 1; +end + +%* Build index list as cumulative sum of the +% number of particles in each cell +m=1; +for jcell=1:ncell + sD.index(jcell) = m; + m = m + sD.cell_n(jcell); +end + +%* Build cross-reference list +temp = zeros(ncell,1); % Temporary array +for ipart=1:npart + jcell = jx(ipart); % Cell address of ipart + k = sD.index(jcell) + temp(jcell); + sD.Xref(k) = ipart; + temp(jcell) = temp(jcell) + 1; +end + +return; diff --git a/Matlab/sprfft.m b/Matlab/sprfft.m new file mode 100644 index 0000000..595c75f --- /dev/null +++ b/Matlab/sprfft.m @@ -0,0 +1,60 @@ +% sprfft - Program to compute the power spectrum of a +% coupled mass-spring system. +clear; help sprfft; % Clear memory and print header + +%* Set parameters for the system (initial positions, etc.). +x = input('Enter initial displacement [x1 x2 x3]: '); +v = [0 0 0]; % Masses are initially at rest +state = [x v]; % Positions and velocities; used by rk4 +tau = input('Enter timestep: '); +k_over_m = 1; % Ratio of spring const. over mass + +%* Loop over the desired number of time steps. +time = 0; % Set initial time +nstep = 256; % Number of steps in the main loop +nprint = nstep/8; % Number of steps between printing progress +for istep=1:nstep %%% MAIN LOOP %%% + + %* Use Runge-Kutta to find new displacements of the masses. + state = rk4(state,time,tau,'sprrk',k_over_m); + time = time + tau; + + %* Record the positions for graphing and to compute spectra. + xplot(istep,1:3) = state(1:3); % Record positions + tplot(istep) = time; + if( rem(istep,nprint) < 1 ) + fprintf('Finished %g out of %g steps\n',istep,nstep); + end +end + +%* Graph the displacements of the three masses. +figure(1); clf; % Clear figure 1 window and bring forward +ipr = 1:nprint:nstep; % Used to graph limited number of symbols +plot(tplot(ipr),xplot(ipr,1),'o',tplot(ipr),xplot(ipr,2),'+',... + tplot(ipr),xplot(ipr,3),'*',... + tplot,xplot(:,1),'-',tplot,xplot(:,2),'-.',... + tplot,xplot(:,3),'--'); +legend('Mass #1 ','Mass #2 ','Mass #3 '); +title('Displacement of masses (relative to rest positions)'); +xlabel('Time'); ylabel('Displacement'); +drawnow; + +%* Calculate the power spectrum of the time series for mass #1 +f(1:nstep) = (0:(nstep-1))/(tau*nstep); % Frequency +x1 = xplot(:,1); % Displacement of mass 1 +x1fft = fft(x1); % Fourier transform of displacement +spect = abs(x1fft).^2; % Power spectrum of displacement + +%* Apply the Hanning window to the time series and calculate +% the resulting power spectrum +window = 0.5*(1-cos(2*pi*((1:nstep)-1)/nstep)); % Hanning window +x1w = x1 .* window'; % Windowed time series +x1wfft = fft(x1w); % Fourier transf. (windowed data) +spectw = abs(x1wfft).^2; % Power spectrum (windowed data) + +%* Graph the power spectra for original and windowed data +figure(2); clf; % Clear figure 2 window and bring forward +semilogy(f(1:(nstep/2)),spect(1:(nstep/2)),'-',... + f(1:(nstep/2)),spectw(1:(nstep/2)),'--'); +title('Power spectrum (dashed is windowed data)'); +xlabel('Frequency'); ylabel('Power'); diff --git a/Matlab/sprrk.m b/Matlab/sprrk.m new file mode 100644 index 0000000..02e9e91 --- /dev/null +++ b/Matlab/sprrk.m @@ -0,0 +1,17 @@ +function deriv = sprrk(s,t,param) +% Returns right-hand side of 3 mass-spring system +% equations of motion +% Inputs +% s State vector [x(1) x(2) ... v(3)] +% t Time (not used) +% param (Spring constant)/(Block mass) +% Output +% deriv [dx(1)/dt dx(2)/dt ... dv(3)/dt] +deriv(1) = s(4); +deriv(2) = s(5); +deriv(3) = s(6); +param2 = -2*param; +deriv(4) = param2*s(1) + param*s(2); +deriv(5) = param2*s(2) + param*(s(1)+s(3)); +deriv(6) = param2*s(3) + param*s(2); +return; diff --git a/Matlab/traffic.m b/Matlab/traffic.m new file mode 100644 index 0000000..9ff1926 --- /dev/null +++ b/Matlab/traffic.m @@ -0,0 +1,90 @@ +% traffic - Program to solve the generalized Burger +% equation for the traffic at a stop light problem +clear all; help traffic; % Clear memory and print header + +%* Select numerical parameters (time step, grid spacing, etc.). +method = menu('Choose a numerical method:', ... + 'FTCS','Lax','Lax-Wendroff'); +N = input('Enter the number of grid points: '); +L = 400; % System size (meters) +h = L/N; % Grid spacing for periodic boundary conditions +v_max = 25; % Maximum car speed (m/s) +fprintf('Suggested timestep is %g\n',h/v_max); +tau = input('Enter time step (tau): '); +fprintf('Last car starts moving after %g steps\n', ... + (L/4)/(v_max*tau)); +nstep = input('Enter number of steps: '); +coeff = tau/(2*h); % Coefficient used by all schemes +coefflw = tau^2/(2*h^2); % Coefficient used by Lax-Wendroff + +%* Set initial and boundary conditions +rho_max = 1.0; % Maximum density +Flow_max = 0.25*rho_max*v_max; % Maximum Flow +% Initial condition is a square pulse from x = -L/4 to x = 0 +rho = zeros(1,N); +for i=round(N/4):round(N/2-1) + rho(i) = rho_max; % Max density in the square pulse +end +rho(round(N/2)) = rho_max/2; % Try running without this line +% Use periodic boundary conditions +ip(1:N) = (1:N)+1; ip(N) = 1; % ip = i+1 with periodic b.c. +im(1:N) = (1:N)-1; im(1) = N; % im = i-1 with periodic b.c. + +%* Initialize plotting variables. +iplot = 1; +xplot = ((1:N)-1/2)*h - L/2; % Record x scale for plot +rplot(:,1) = rho(:); % Record the initial state +tplot(1) = 0; +figure(1); clf; % Clear figure 1 window and bring forward + +%* Loop over desired number of steps. +for istep=1:nstep + + %* Compute the flow = (Density)*(Velocity) + Flow = rho .* (v_max*(1 - rho/rho_max)); + + %* Compute new values of density using FTCS, + % Lax or Lax-Wendroff method. + if( method == 1 ) %%% FTCS method %%% + rho(1:N) = rho(1:N) - coeff*(Flow(ip)-Flow(im)); + elseif( method == 2 ) %%% Lax method %%% + rho(1:N) = .5*(rho(ip)+rho(im)) ... + - coeff*(Flow(ip)-Flow(im)); + else %%% Lax-Wendroff method %%% + cp = v_max*(1 - (rho(ip)+rho(1:N))/rho_max); + cm = v_max*(1 - (rho(1:N)+rho(im))/rho_max); + rho(1:N) = rho(1:N) - coeff*(Flow(ip)-Flow(im)) ... + + coefflw*(cp.*(Flow(ip)-Flow(1:N)) ... + - cm.*(Flow(1:N)-Flow(im))); + end + + %* Record density for plotting. + iplot = iplot+1; + rplot(:,iplot) = rho(:); + tplot(iplot) = tau*istep; + + %* Display snap-shot of density versus position + plot(xplot,rho,'-',xplot,Flow/Flow_max,'--'); + xlabel('x'); ylabel('Density and Flow'); + legend('\rho(x,t)','F(x,t)'); + axis([-L/2, L/2, -0.1, 1.1]); + drawnow; +end + +%* Graph density versus position and time as wire-mesh plot +figure(1); clf; % Clear figure 1 window and bring forward +mesh(tplot,xplot,rplot) +xlabel('t'); ylabel('x'); zlabel('\rho'); +title('Density versus position and time'); +view([100 30]); % Rotate the plot for better view point +pause(1); % Pause 1 second between plots + +%* Graph contours of density versus position and time. +figure(2); clf; % Clear figure 2 window and bring forward +% Use rot90 function to graph t vs x since +% contour(rplot) graphs x vs t. +clevels = 0:(0.1):1; % Contour levels +cs = contour(xplot,tplot,flipud(rot90(rplot)),clevels); +clabel(cs); % Put labels on contour levels +xlabel('x'); ylabel('time'); title('Density contours'); + diff --git a/Matlab/tri_ge.m b/Matlab/tri_ge.m new file mode 100644 index 0000000..40abc6a --- /dev/null +++ b/Matlab/tri_ge.m @@ -0,0 +1,35 @@ +function x = tri_ge(a,b) +% Function to solve b = a*x by Gaussian elimination where +% the matrix a is a packed tridiagonal matrix +% Inputs +% a Packed tridiagonal matrix, N by N unpacked +% b Column vector of length N +% Output +% x Solution of b = a*x; Column vector of length N + +%* Check that dimensions of a and b are compatible +[N,M] = size(a); +[NN,MM] = size(b); +if( N ~= NN | MM ~= 1) + error('Problem in tri_GE, inputs are incompatible'); +end + +%* Unpack diagonals of triangular matrix into vectors +alpha(1:N-1) = a(2:N,1); +beta(1:N) = a(1:N,2); +gamma(1:N-1) = a(1:N-1,3); + +%* Perform forward elimination +for i=2:N + coeff = alpha(i-1)/beta(i-1); + beta(i) = beta(i) - coeff*gamma(i-1); + b(i) = b(i) - coeff*b(i-1); +end + +%* Perform back substitution +x(N) = b(N)/beta(N); +for i=N-1:-1:1 + x(i) = (b(i) - gamma(i)*x(i+1))/beta(i); +end +x = x.'; % Transpose x to a column vector +return; diff --git a/Matlab/zeroj.m b/Matlab/zeroj.m new file mode 100644 index 0000000..38f0b2d --- /dev/null +++ b/Matlab/zeroj.m @@ -0,0 +1,21 @@ +function z = zeroj(m_order,n_zero) +% Zeros of the Bessel function J(x) +% Inputs +% m_order = Order of the Bessel function +% n_zero = Index of the zero (first, second, etc.) +% Output +% z = The "n_zero th" zero of the Bessel function + +%* Use asymtotic formula for initial guess +beta = (n_zero + 0.5*m_order - 0.25)*pi; +mu = 4*m_order^2; +z = beta - (mu-1)/(8*beta) - 4*(mu-1)*(7*mu-31)/(3*(8*beta)^3); + +%* Use Newton's method to locate the root +for i=1:5 + jj = bess(m_order+1,z); + % Use the recursion relation to evaluate derivative + deriv = -jj(m_order+2) + m_order/z * jj(m_order+1); + z = z - jj(m_order+1)/deriv; % Newton's root finding +end +return; diff --git a/MatlabRevised/BalleEnergy.asv b/MatlabRevised/BalleEnergy.asv new file mode 100644 index 0000000..42c5ada --- /dev/null +++ b/MatlabRevised/BalleEnergy.asv @@ -0,0 +1,84 @@ +%% balle - Program to compute the trajectory of a baseball +% using the Euler method. +% This version also computes and plots energy +clear; % Clear memory and print header + +%% * Set initial position and velocity of the baseball +y1 = 1; %input('Enter initial height (meters): '); +r1 = [0, y1]; % Initial vector position +speed = 50; %input('Enter initial speed (m/s): '); +theta = input('Enter initial angle (degrees): '); +v1 = [speed*cos(theta*pi/180), ... + speed*sin(theta*pi/180)]; % Initial velocity +r = r1; v = v1; % Set initial position and velocity + +%% * Set physical parameters (mass, Cd, etc.) +Cd = 0.35; % Drag coefficient (dimensionless) +area = 4.3e-3; % Cross-sectional area of projectile (m^2) +grav = 9.81; % Gravitational acceleration (m/s^2) +mass = 0.145; % Mass of projectile (kg) +airFlag = input('Air resistance? (Yes:1, No:0): '); +if( airFlag == 0 ) + rho = 0; % No air resistance +else + rho = 1.2; % Density of air (kg/m^3) +end +air_const = -0.5*Cd*rho*area/mass; % Air resistance constant + +%% * Loop until ball hits ground or max steps completed +tau = input('Enter timestep, tau (sec): '); % (sec) +maxstep = 1000; % Maximum number of steps +for istep=1:maxstep + + %* Record position (computed and theoretical) for plotting + xplot(istep) = r(1); % Record trajectory for plot + yplot(istep) = r(2); + t = (istep-1)*tau; % Current time + xNoAir(istep) = r1(1) + v1(1)*t; + yNoAir(istep) = r1(2) + v1(2)*t - 0.5*grav*t^2; + + %* Compute kinetic and potential energy + KEnergy(istep) = 0.5*mass*norm(v)^2; + PEnergy(istep) = mass*grav*r(2); + + %* Calculate the acceleration of the ball + accel = air_const*norm(v)*v; % Air resistance + accel(2) = accel(2)-grav; % Gravity + + %* Calculate the new position and velocity using Euler method + r = r + tau*v; % Euler step + v = v + tau*accel; + + %* If ball reaches ground (y<0), break out of the loop + if( r(2) < 0 ) + xplot(istep+1) = r(1); % Record last values computed + yplot(istep+1) = r(2); + break; % Break out of the for loop + end +end + +%% * Print maximum range and time of flight +fprintf('Maximum range is %g meters\n',r(1)); +fprintf('Time of flight is %g seconds\n',istep*tau); + +%% * Graph the trajectory of the baseball +figure(1); clf; % Clear figure window #1 and bring it forward +% Mark the location of the ground by a straight line +xground = [0 max(xNoAir)]; yground = [0 0]; +% Plot the computed trajectory and parabolic, no-air curve +plot(xplot,yplot,'+',xNoAir,yNoAir,'-',xground,yground,'-'); +legend('Euler method','Theory (No air) '); +xlabel('Range (m)'); ylabel('Height (m)'); +title('Projectile motion'); + +%% * Graph the energy as a function of time +nE = length(KEnergy); +TotEnergy = KEnergy + PEnergy; +tPlot = tau*(0:(nE-1)); +plot(tPlot,KEnergy,'--',tPlot,PEnergy,'-.',tPlot,TotEnergy,'-'); +xlabel('Time (sec)'); ylabel('Energy (Joules)'); +legend('Kinetic','Potential','Total'); +fprintf('Initial, final energies = %g, %g Joul\n',TotEnergy(1)); +fprintf('Final value of total energy = %g\n',TotEnergy(nE)); +FracEnergy = TotEnergy(nE)/TotEnergy(1) - 1; +fprintf('Fractional change = %g\n',FracEnergy); diff --git a/MatlabRevised/Barrow.txt b/MatlabRevised/Barrow.txt new file mode 100644 index 0000000..ec277ab --- /dev/null +++ b/MatlabRevised/Barrow.txt @@ -0,0 +1,230 @@ + 3.4420000e+02 + 3.4483000e+02 + 3.4520000e+02 + 3.4537000e+02 + 3.4541000e+02 + 3.4542000e+02 + 3.4552000e+02 + 3.4579000e+02 + 3.4621000e+02 + 3.4656000e+02 + 3.4647000e+02 + 3.4551000e+02 + 3.4342000e+02 + 3.4024000e+02 + 3.3650000e+02 + 3.3306000e+02 + 3.3085000e+02 + 3.3045000e+02 + 3.3184000e+02 + 3.3440000e+02 + 3.3720000e+02 + 3.3952000e+02 + 3.4117000e+02 + 3.4239000e+02 + 3.4349000e+02 + 3.4452000e+02 + 3.4539000e+02 + 3.4595000e+02 + 3.4644000e+02 + 3.4701000e+02 + 3.4757000e+02 + 3.4788000e+02 + 3.4782000e+02 + 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3.4913000e+02 + 3.4937000e+02 + 3.4991000e+02 diff --git a/MatlabRevised/advect.m b/MatlabRevised/advect.m new file mode 100644 index 0000000..3cd7678 --- /dev/null +++ b/MatlabRevised/advect.m @@ -0,0 +1,70 @@ +%% advect - Program to solve the advection equation +% using the various hyperbolic PDE schemes +clear all; help advect; % Clear memory and print header + +%% * Select numerical parameters (time step, grid spacing, etc.). +method = menu('Choose a numerical method:', ... + 'FTCS','Lax','Lax-Wendroff'); +N = input('Enter number of grid points: '); +L = 1.; % System size +h = L/N; % Grid spacing +c = 1; % Wave speed +fprintf('Time for wave to move one grid spacing is %g\n',h/c); +tau = input('Enter time step: '); +coeff = -c*tau/(2.*h); % Coefficient used by all schemes +coefflw = 2*coeff^2; % Coefficient used by L-W scheme +fprintf('Wave circles system in %g steps\n',L/(c*tau)); +nStep = input('Enter number of steps: '); + +%% * Set initial and boundary conditions. +sigma = 0.1; % Width of the Gaussian pulse +k_wave = pi/sigma; % Wave number of the cosine +x = ((1:N)-1/2)*h - L/2; % Coordinates of grid points +% Initial condition is a Gaussian-cosine pulse +a = cos(k_wave*x) .* exp(-x.^2/(2*sigma^2)); +% Use periodic boundary conditions +ip(1:(N-1)) = 2:N; ip(N) = 1; % ip = i+1 with periodic b.c. +im(2:N) = 1:(N-1); im(1) = N; % im = i-1 with periodic b.c. + +%% * Initialize plotting variables. +iplot = 1; % Plot counter +aplot(:,1) = a(:); % Record the initial state +tplot(1) = 0; % Record the initial time (t=0) +nplots = 50; % Desired number of plots +plotStep = nStep/nplots; % Number of steps between plots + +%% * Loop over desired number of steps. +for iStep=1:nStep %% MAIN LOOP %% + + %* Compute new values of wave amplitude using FTCS, + % Lax or Lax-Wendroff method. + if( method == 1 ) %%% FTCS method %%% + a(1:N) = a(1:N) + coeff*(a(ip)-a(im)); + elseif( method == 2 ) %%% Lax method %%% + a(1:N) = .5*(a(ip)+a(im)) + coeff*(a(ip)-a(im)); + else %%% Lax-Wendroff method %%% + a(1:N) = a(1:N) + coeff*(a(ip)-a(im)) + ... + coefflw*(a(ip)+a(im)-2*a(1:N)); + end + + %* Periodically record a(t) for plotting. + if( rem(iStep,plotStep) < 1 ) % Every plot_iter steps record + iplot = iplot+1; + aplot(:,iplot) = a(:); % Record a(i) for ploting + tplot(iplot) = tau*iStep; + fprintf('%g out of %g steps completed\n',iStep,nStep); + end +end + +%% * Plot the initial and final states. +figure(1); clf; % Clear figure 1 window and bring forward +plot(x,aplot(:,1),'-',x,a,'--'); +legend('Initial ','Final'); +xlabel('x'); ylabel('a(x,t)'); +pause(1); % Pause 1 second between plots + +%% * Plot the wave amplitude versus position and time +figure(2); clf; % Clear figure 2 window and bring forward +mesh(tplot,x,aplot); +ylabel('Position'); xlabel('Time'); zlabel('Amplitude'); +view([-70 50]); % Better view from this angle diff --git a/MatlabRevised/balle.asv b/MatlabRevised/balle.asv new file mode 100644 index 0000000..04c5da8 --- /dev/null +++ b/MatlabRevised/balle.asv @@ -0,0 +1,67 @@ +%% balle - Program to compute the trajectory of a baseball +% using the Euler method. +clear; help balle; % Clear memory and print header + +%% * Set initial position and velocity of the baseball +y1 = input('Enter initial height (meters): '); +r1 = [0, y1]; % Initial vector position +speed = input('Enter initial speed (m/s): '); +theta = input('Enter initial angle (degrees): '); +v1 = [speed*cos(theta*pi/180), ... + speed*sin(theta*pi/180)]; % Initial velocity +r = r1; v = v1; % Set initial position and velocity + +%% * Set physical parameters (mass, Cd, etc.) +Cd = 0.35; % Drag coefficient (dimensionless) +area = 4.3e-3; % Cross-sectional area of projectile (m^2) +grav = 9.81; % Gravitational acceleration (m/s^2) +mass = 0.145; % Mass of projectile (kg) +airFlag = input('Air resistance? (Yes:1, No:0): '); +if( airFlag == 0 ) + rho = 0; % No air resistance +else + rho = 1.2; % Density of air (kg/m^3) +end +air_const = -0.5*Cd*rho*area/mass; % Air resistance constant + +%% * Loop until ball hits ground or max steps completed +tau = input('Enter timestep, tau (sec): '); % (sec) +maxstep = 1000; % Maximum number of steps +for istep=1:maxstep + + %* Record position (computed and theoretical) for plotting + xplot(istep) = r(1); % Record trajectory for plot + yplot(istep) = r(2); + t = (istep-1)*tau; % Current time + xNoAir(istep) = r1(1) + v1(1)*t; + yNoAir(istep) = r1(2) + v1(2)*t - 0.5*grav*t^2; + + %* Calculate the acceleration of the ball + accel = air_const*norm(v)*v; % Air resistance + accel(2) = accel(2)-grav; % Gravity + + %* Calculate the new position and velocity using Euler method + r = r + tau*v; % Euler step + v = v + tau*accel; + + %* If ball reaches ground (y<0), break out of the loop + if( r(2) < 0 ) + xplot(istep+1) = r(1); % Record last values computed + yplot(istep+1) = r(2); + break; % Break out of the for loop + end +end + +%% * Print maximum range and time of flight +fprintf('Maximum range is %g meters\n',r(1)); +fprintf('Time of flight is %g seconds\n',istep*tau); + +%% * Graph the trajectory of the baseball +clf; figure(gcf); % Clear figure window and bring it forward +% Mark the location of the ground by a straight line +xground = [0 max(xNoAir)]; yground = [0 0]; +% Plot the computed trajectory and parabolic, no-air curve +plot(xplot,yplot,'+',xNoAir,yNoAir,'-',xground,yground,'-'); +legend('Euler method','Theory (No air) '); +xlabel('Range (m)'); ylabel('Height (m)'); +title('Projectile motion'); diff --git a/MatlabRevised/balle.m b/MatlabRevised/balle.m new file mode 100644 index 0000000..bee55f8 --- /dev/null +++ b/MatlabRevised/balle.m @@ -0,0 +1,67 @@ +%% balle - Program to compute the trajectory of a baseball +% using the Euler method. +clear; help balle; % Clear memory and print header + +%% * Set initial position and velocity of the baseball +y1 = input('Enter initial height (meters): '); +r1 = [0, y1]; % Initial vector position +speed = input('Enter initial speed (m/s): '); +theta = input('Enter initial angle (degrees): '); +v1 = [speed*cos(theta*pi/180), ... + speed*sin(theta*pi/180)]; % Initial velocity +r = r1; v = v1; % Set initial position and velocity + +%% * Set physical parameters (mass, Cd, etc.) +Cd = 0.35; % Drag coefficient (dimensionless) +area = 4.3e-3; % Cross-sectional area of projectile (m^2) +grav = 9.81; % Gravitational acceleration (m/s^2) +mass = 0.145; % Mass of projectile (kg) +airFlag = input('Air resistance? (Yes:1, No:0): '); +if( airFlag == 0 ) + rho = 0; % No air resistance +else + rho = 1.2; % Density of air (kg/m^3) +end +air_const = -0.5*Cd*rho*area/mass; % Air resistance constant + +%% * Loop until ball hits ground or max steps completed +tau = input('Enter timestep, tau (sec): '); % (sec) +maxstep = 1000; % Maximum number of steps +for istep=1:maxstep + + %* Record position (computed and theoretical) for plotting + xplot(istep) = r(1); % Record trajectory for plot + yplot(istep) = r(2); + t = (istep-1)*tau; % Current time + xNoAir(istep) = r1(1) + v1(1)*t; + yNoAir(istep) = r1(2) + v1(2)*t - 0.5*grav*t^2; + + %* Calculate the acceleration of the ball + accel = air_const*norm(v)*v; % Air resistance + accel(2) = accel(2)-grav; % Gravity + + %* Calculate the new position and velocity using Euler method + r = r + tau*v; % Euler step + v = v + tau*accel; + + %* If ball reaches ground (y<0), break out of the loop + if( r(2) < 0 ) + xplot(istep+1) = r(1); % Record last values computed + yplot(istep+1) = r(2); + break; % Break out of the for loop + end +end + +%% * Print maximum range and time of flight +fprintf('Maximum range is %g meters\n',r(1)); +fprintf('Time of flight is %g seconds\n',istep*tau); + +%% * Graph the trajectory of the baseball +figure(1); clf; % Clear figure window #1 and bring it forward +% Mark the location of the ground by a straight line +xground = [0 max(xNoAir)]; yground = [0 0]; +% Plot the computed trajectory and parabolic, no-air curve +plot(xplot,yplot,'+',xNoAir,yNoAir,'-',xground,yground,'-'); +legend('Euler method','Theory (No air) '); +xlabel('Range (m)'); ylabel('Height (m)'); +title('Projectile motion'); diff --git a/MatlabRevised/bess.m b/MatlabRevised/bess.m new file mode 100644 index 0000000..d5939f9 --- /dev/null +++ b/MatlabRevised/bess.m @@ -0,0 +1,25 @@ +function jj = bess(m_max,x) +% Bessel function +% Inputs +% m_max = Largest desired order +% x = Value at which Bessel function J(x) is evaluated +% Output +% jj = Vector of J(x) for all orders <= m_max + +%* Perform downward recursion from initial guess +m_top = max(m_max,x)+15; % Top value of m for recursion +m_top = 2*ceil( m_top/2 ); % Round up to an even number +j(m_top+1) = 0; +j(m_top) = 1; +for m=m_top-2:-1:0 % Downward recursion + j(m+1) = 2*(m+1)/(x+eps)*j(m+2) - j(m+3); +end + +%* Normalize using identity and return requested values +norm = j(1); % NOTE: Be careful, m=0,1,... but +for m=2:2:m_top % vector goes j(1),j(2),... + norm = norm + 2*j(m+1); +end +for m=0:m_max % Send back only the values for + jj(m+1) = j(m+1)/norm; % m=0,...,m_max and discard values +end % for m=m_max+1,...,m_top diff --git a/MatlabRevised/colider.m b/MatlabRevised/colider.m new file mode 100644 index 0000000..959e800 --- /dev/null +++ b/MatlabRevised/colider.m @@ -0,0 +1,68 @@ +function [v,crmax,selxtra,col] = ... + colider(v,crmax,selxtra,coeff,sD) +% colide - Function to process collisions in cells +% [v,crmax,selxtra,col] = colider(v,crmax,selxtra,coeff,sD) +% Inputs +% v Velocities of the particles +% crmax Estimated maximum relative speed in a cell +% selxtra Extra selections carried over from last timestep +% coeff Coefficient in computing number of selected pairs +% sD Structure containing sorting lists +% Outputs +% v Updated velocities of the particles +% crmax Updated maximum relative speed +% selxtra Extra selections carried over to next timestep +% col Total number of collisions processed + +ncell = sD.ncell; +col = 0; % Count number of collisions + +%* Loop over cells, processing collisions in each cell +for jcell=1:ncell + + %* Skip cells with only one particle + number = sD.cell_n(jcell); + if( number > 1 ) + + %* Determine number of candidate collision pairs + % to be selected in this cell + select = coeff*number*(number-1)*crmax(jcell) + selxtra(jcell); + nsel = floor(select); % Number of pairs to be selected + selxtra(jcell) = select-nsel; % Carry over any left-over fraction + crm = crmax(jcell); % Current maximum relative speed + + %* Loop over total number of candidate collision pairs + for isel=1:nsel + + %* Pick two particles at random out of this cell + k = floor(rand(1)*number); + kk = rem(ceil(k+rand(1)*(number-1)),number); + ip1 = sD.Xref(k+sD.index(jcell)); % First particle + ip2 = sD.Xref(kk+sD.index(jcell)); % Second particle + + %* Calculate pair's relative speed + cr = norm( v(ip1,:)-v(ip2,:) ); % Relative speed + if( cr > crm ) % If relative speed larger than crm, + crm = cr; % then reset crm to larger value + end + + %* Accept or reject candidate pair according to relative speed + if( cr/crmax(jcell) > rand(1) ) + %* If pair accepted, select post-collision velocities + col = col+1; % Collision counter + vcm = 0.5*(v(ip1,:) + v(ip2,:)); % Center of mass velocity + cos_th = 1 - 2*rand(1); % Cosine and sine of + sin_th = sqrt(1 - cos_th^2); % collision angle theta + phi = 2*pi*rand(1); % Collision angle phi + vrel(1) = cr*cos_th; % Compute post-collision + vrel(2) = cr*sin_th*cos(phi); % relative velocity + vrel(3) = cr*sin_th*sin(phi); + v(ip1,:) = vcm + 0.5*vrel; % Update post-collision + v(ip2,:) = vcm - 0.5*vrel; % velocities + end + + end % Loop over pairs + crmax(jcell) = crm; % Update max relative speed + end +end % Loop over cells +return; diff --git a/MatlabRevised/contents.txt b/MatlabRevised/contents.txt new file mode 100644 index 0000000..fc691e6 --- /dev/null +++ b/MatlabRevised/contents.txt @@ -0,0 +1,44 @@ +% Numerical Methods for Physics, 2nd Ed. (MATLAB). +% Version 1.0a 2-Oct-99 +% Copyright (c) 1999 by Alejandro Garcia. + +% advect.m Advection PDE solver using various methods +% balle.m Projectile motion (baseball) program +% barrow.txt Carbon dioxide data for Barrow, Alaska +% bess.m Bessel function routine +% colider.m DSMC particle collision routine +% dftcs.m Diffusion PDE solver using FTCS method +% dsmceq.m Relaxation to equilibrium using DSMC method +% dsmcne.m Couette flow routine using DSMC method +% errintg.m Integrand of error function +% fftpoi.m Poisson PDE solver using MFT method +% fnewtn.m Lorenz model ODEs and Jacobian routine +% ftdemo.m Fourier transform demo program +% gravrk.m Function for Kepler equations of motion +% interp.m Interpolation program +% intrpf.m Interpolation function +% legndr.m Legendre polynomial function +% linreg.m Linear curve fit routine +% lorenz.m Lorenz model program +% lorzrk.m Function for Lorenz model ODEs +% lsfdemo.m Least square fit demo program +% mauna.txt Carbon dioxide data for Mauna Loa, Hawaii +% mover.m DSMC particle moving routine +% neutrn.m Neutron diffusion PDE solver +% newtn.m Root finding by Newton's method +% orbit.m Orbits of comets program +% orthog.m Program to test vector orthogonality +% pendul.m Simple pendulum program +% pollsf.m Polynomial curve fit routine +% relax.m Laplace PDE solver using relaxation methods +% rk4.m Runge-Kutta routine +% rka.m Adaptive Runge-Kutta routine +% rombf.m Romberg integration routine +% sampler.m DSMC particle sampling routine +% schro.m Schrodinger PDE solver using Crank-Nicolson +% sorter.m DSMC particle sorting routine +% sprfft.m Spring-mass oscillations program +% sprrk.m Function for Spring-mass ODEs +% traffic.m Traffic PDE solver using various methods +% tri_ge.m Gaussian elimination for tridiagonal matrices +% zeroj.m Zeros of Bessel function routine diff --git a/MatlabRevised/dftcs.m b/MatlabRevised/dftcs.m new file mode 100644 index 0000000..6572239 --- /dev/null +++ b/MatlabRevised/dftcs.m @@ -0,0 +1,56 @@ +%% dftcs - Program to solve the diffusion equation +% using the Forward Time Centered Space (FTCS) scheme. +clear; help dftcs; % Clear memory and print header + +%% * Initialize parameters (time step, grid spacing, etc.). +tau = input('Enter time step: '); +N = input('Enter the number of grid points: '); +L = 1.; % The system extends from x=-L/2 to x=L/2 +h = L/(N-1); % Grid size +kappa = 1.; % Diffusion coefficient +coeff = kappa*tau/h^2; +if( coeff < 0.5 ) + disp('Solution is expected to be stable'); +else + disp('WARNING: Solution is expected to be unstable'); +end + +%% * Set initial and boundary conditions. +tt = zeros(N,1); % Initialize temperature to zero at all points +tt(round(N/2)) = 1/h; % Initial cond. is delta function in center +%- The boundary conditions are tt(1) = tt(N) = 0 + +%% * Set up loop and plot variables. +xplot = (0:N-1)*h - L/2; % Record the x scale for plots +iplot = 1; % Counter used to count plots +nstep = 300; % Maximum number of iterations +nplots = 50; % Number of snapshots (plots) to take +plot_step = nstep/nplots; % Number of time steps between plots + +%% * Loop over the desired number of time steps. +for istep=1:nstep %% MAIN LOOP %% + + %* Compute new temperature using FTCS scheme. + tt(2:(N-1)) = tt(2:(N-1)) + ... + coeff*(tt(3:N) + tt(1:(N-2)) - 2*tt(2:(N-1))); + + %* Periodically record temperature for plotting. + if( rem(istep,plot_step) < 1 ) % Every plot_step steps + ttplot(:,iplot) = tt(:); % record tt(i) for plotting + tplot(iplot) = istep*tau; % Record time for plots + iplot = iplot+1; + end +end + +%% * Plot temperature versus x and t as wire-mesh and contour plots. +figure(1); clf; +mesh(tplot,xplot,ttplot); % Wire-mesh surface plot +xlabel('Time'); ylabel('x'); zlabel('T(x,t)'); +title('Diffusion of a delta spike'); +pause(1); +figure(2); clf; +contourLevels = 0:0.5:10; contourLabels = 0:5; +cs = contour(tplot,xplot,ttplot,contourLevels); % Contour plot +clabel(cs,contourLabels); % Add labels to selected contour levels +xlabel('Time'); ylabel('x'); +title('Temperature contour plot'); diff --git a/MatlabRevised/dsmceq.m b/MatlabRevised/dsmceq.m new file mode 100644 index 0000000..7db7c9f --- /dev/null +++ b/MatlabRevised/dsmceq.m @@ -0,0 +1,78 @@ +% dsmceq - Dilute gas simulation using DSMC algorithm +% This version illustrates the approach to equilibrium +clear all; help dsmceq; % Clear memory and print header + +%* Initialize constants (particle mass, diameter, etc.) +boltz = 1.3806e-23; % Boltzmann's constant (J/K) +mass = 6.63e-26; % Mass of argon atom (kg) +diam = 3.66e-10; % Effective diameter of argon atom (m) +T = 273; % Temperature (K) +density = 1.78; % Density of argon at STP (kg/m^3) +L = 1e-6; % System size is one micron +npart = input('Enter number of simulation particles: '); +eff_num = density/mass*L^3/npart; +fprintf('Each particle represents %g atoms\n',eff_num); + +%* Assign random positions and velocities to particles +rand('state',0); % Initialize random number generator +x = L*rand(npart,1); % Assign random positions +v_init = sqrt(3*boltz*T/mass); % Initial speed +v = zeros(npart,3); % Only x-component is non-zero +v(:,1) = v_init * (1 - 2*floor(2*rand(npart,1))); + +%* Plot the initial speed distribution +figure(1); clf; +vmag = sqrt(v(:,1).^2 + v(:,2).^2 + v(:,3).^2); +vbin = 50:100:1050; % Bins for histogram +hist(vmag,vbin); title('Initial speed distribution'); +xlabel('Speed (m/s)'); ylabel('Number'); + +%* Initialize variables used for evaluating collisions +ncell = 15; % Number of cells +tau = 0.2*(L/ncell)/v_init; % Set timestep tau +vrmax = 3*v_init*ones(ncell,1); % Estimated max rel. speed +selxtra = zeros(ncell,1); % Used by routine "colider" +coeff = 0.5*eff_num*pi*diam^2*tau/(L^3/ncell); +coltot = 0; % Count total collisions + +%* Declare structure for lists used in sorting +sortData = struct('ncell',ncell, ... + 'npart',npart, ... + 'cell_n',zeros(ncell,1), ... + 'index',zeros(ncell,1), ... + 'Xref',zeros(npart,1)); + +%* Loop for the desired number of time steps +nstep = input('Enter total number of time steps: '); +for istep = 1:nstep + + %* Move all the particles ballistically + x(:) = x(:) + v(:,1)*tau; % Update x position of particle + x = rem(x+L,L); % Periodic boundary conditions + + %* Sort the particles into cells + sortData = sorter(x,L,sortData); + + %* Evaluate collisions among the particles + [v, vrmax, selxtra, col] = ... + colider(v,vrmax,selxtra,coeff,sortData); + coltot = coltot + col; + + %* Periodically display the current progress + if( rem(istep,10) < 1 ) + figure(2); clf; + vmag = sqrt(v(:,1).^2 + v(:,2).^2 + v(:,3).^2); + hist(vmag,vbin); + title(sprintf('Done %g of %g steps; %g collisions',... + istep,nstep,coltot)); + xlabel('Speed (m/s)'); ylabel('Number'); + drawnow; + end +end + +%* Plot the histogram of the final speed distribution +figure(2); clf; +vmag = sqrt(v(:,1).^2 + v(:,2).^2 + v(:,3).^2); +hist(vmag,vbin); +title(sprintf('Final distrib., Time = %g sec.',nstep*tau)); +xlabel('Speed (m/s)'); ylabel('Number'); diff --git a/MatlabRevised/dsmcne.m b/MatlabRevised/dsmcne.m new file mode 100644 index 0000000..04d724f --- /dev/null +++ b/MatlabRevised/dsmcne.m @@ -0,0 +1,120 @@ +% dsmcne - Program to simulate a dilute gas using DSMC algorithm +% This version simulates planar Couette flow +clear all; help dsmcne; % Clear memory and print header + +%* Initialize constants (particle mass, diameter, etc.) +boltz = 1.3806e-23; % Boltzmann's constant (J/K) +mass = 6.63e-26; % Mass of argon atom (kg) +diam = 3.66e-10; % Effective diameter of argon atom (m) +T = 273; % Initial temperature (K) +density = 2.685e25; % Number density of argon at STP (m^-3) +L = 1e-6; % System size is one micron +Volume = L^3; % Volume of the system (m^3) +npart = input('Enter number of simulation particles: '); +eff_num = density*Volume/npart; +fprintf('Each simulation particle represents %g atoms\n',eff_num); +mfp = Volume/(sqrt(2)*pi*diam^2*npart*eff_num); +fprintf('System width is %g mean free paths \n',L/mfp); +mpv = sqrt(2*boltz*T/mass); % Most probable initial velocity +vwall_m = input('Enter wall velocity as Mach number: '); +vwall = vwall_m * sqrt(5/3 * boltz*T/mass); +fprintf('Wall velocities are %g and %g m/s \n',-vwall,vwall); + +%* Assign random positions and velocities to particles +rand('state',1); % Initialize random number generators +randn('state',1); +x = L*rand(npart,1); % Assign random positions +% Assign thermal velocities using Gaussian random numbers +v = sqrt(boltz*T/mass) * randn(npart,3); +% Add velocity gradient to the y-component +v(:,2) = v(:,2) + 2*vwall*(x(:)/L) - vwall; + +%* Initialize variables used for evaluating collisions +ncell = 20; % Number of cells +tau = 0.2*(L/ncell)/mpv; % Set timestep tau +vrmax = 3*mpv*ones(ncell,1); % Estimated max rel. speed in a cell +selxtra = zeros(ncell,1); % Used by collision routine "colider" +coeff = 0.5*eff_num*pi*diam^2*tau/(Volume/ncell); + +%* Declare structure for lists used in sorting +sortData = struct('ncell', ncell, ... + 'npart', npart, ... + 'cell_n', zeros(ncell,1), ... + 'index', zeros(ncell,1), ... + 'Xref', zeros(npart,1)); + +%* Initialize structure and variables used in statistical sampling +sampData = struct('ncell', ncell, ... + 'nsamp', 0, ... + 'ave_n', zeros(ncell,1), ... + 'ave_u', zeros(ncell,3), ... + 'ave_T', zeros(ncell,1)); +tsamp = 0; % Total sampling time +dvtot = zeros(1,2); % Total momentum change at a wall +dverr = zeros(1,2); % Used to find error in dvtot + +%* Loop for the desired number of time steps +colSum = 0; strikeSum = [0 0]; +nstep = input('Enter total number of timesteps: '); +for istep = 1:nstep + + %* Move all the particles + [x, v, strikes, delv] = mover(x,v,npart,L,mpv,vwall,tau); + strikeSum = strikeSum + strikes; + + %* Sort the particles into cells + sortData = sorter(x,L,sortData); + + %* Evaluate collisions among the particles + [v, vrmax, selxtra, col] = ... + colider(v,vrmax,selxtra,coeff,sortData); + colSum = colSum + col; + + %* After initial transient, accumulate statistical samples + if(istep > nstep/10) + sampData = sampler(x,v,npart,L,sampData); + dvtot = dvtot + delv; + dverr = dverr + delv.^2; + tsamp = tsamp + tau; + end + + %* Periodically display the current progress + if( rem(istep,10) < 1 ) + fprintf('Finished %g of %g steps, Collisions = %g\n', ... + istep,nstep,colSum); + fprintf('Total wall strikes: %g (left) %g (right)\n', ... + strikeSum(1),strikeSum(2)); + end +end + +%* Normalize the accumulated statistics +nsamp = sampData.nsamp; +ave_n = (eff_num/(Volume/ncell))*sampData.ave_n/nsamp; +ave_u = sampData.ave_u/nsamp; +ave_T = mass/(3*boltz) * (sampData.ave_T/nsamp); +dverr = dverr/(nsamp-1) - (dvtot/nsamp).^2; +dverr = sqrt(dverr*nsamp); + +%* Compute viscosity from drag force on the walls +force = (eff_num*mass*dvtot)/(tsamp*L^2); +ferr = (eff_num*mass*dverr)/(tsamp *L^2); +fprintf('Force per unit area is \n'); +fprintf('Left wall: %g +/- %g \n',force(1),ferr(1)); +fprintf('Right wall: %g +/- %g \n',force(2),ferr(2)); +vgrad = 2*vwall/L; % Velocity gradient +visc = 1/2*(-force(1)+force(2))/vgrad; % Average viscosity +viscerr = 1/2*(ferr(1)+ferr(2))/vgrad; % Error +fprintf('Viscosity = %g +/- %g N s/m^2\n',visc,viscerr); +eta = 5*pi/32*mass*density*(2/sqrt(pi)*mpv)*mfp; +fprintf('Theoretical value of viscoisty is %g N s/m^2\n',eta); + +%* Plot average density, velocity and temperature +figure(1); clf; +xcell = ((1:ncell)-0.5)/ncell * L; +plot(xcell,ave_n); xlabel('position'); ylabel('Number density'); +figure(2); clf; +plot(xcell,ave_u); xlabel('position'); ylabel('Velocities'); +legend('x-component','y-component','z-component'); +figure(3); clf; +plot(xcell,ave_T); xlabel('position'); ylabel('Temperature'); + diff --git a/MatlabRevised/errintg.m b/MatlabRevised/errintg.m new file mode 100644 index 0000000..7324c4a --- /dev/null +++ b/MatlabRevised/errintg.m @@ -0,0 +1,9 @@ +function f = errintg(x,param) +% Error function integrand +% Inputs +% x Value where integrand is evaluated +% param Parameter list (not used) +% Output +% f Integrand of the error function +f = exp(-x^2); +return; diff --git a/MatlabRevised/fftpoi.m b/MatlabRevised/fftpoi.m new file mode 100644 index 0000000..b84b714 --- /dev/null +++ b/MatlabRevised/fftpoi.m @@ -0,0 +1,56 @@ +%% fftpoi - Program to solve the Poisson equation using +% MFT method (periodic boundary conditions) +clear all; help fftpoi; % Clear memory and print header + +%% * Initialize parameters (system size, grid spacing, etc.) +eps0 = 8.8542e-12; % Permittivity (C^2/(N m^2)) +N = 50; % Number of grid points on a side (square grid) +L = 1; % System size +h = L/N; % Grid spacing for periodic boundary conditions +x = ((1:N)-1/2)*h; % Coordinates of grid points +y = x; % Square grid +fprintf('System is a square of length %g \n',L); + +%% * Set up charge density rho(i,j) +rho = zeros(N,N); % Initialize charge density to zero +M = input('Enter number of line charges: '); +for i=1:M + fprintf('\n For charge #%g \n',i); + r = input('Enter position [x y]: '); + ii=round(r(1)/h + 1/2); % Place charge at nearest + jj=round(r(2)/h + 1/2); % grid point + q = input('Enter charge density: '); + rho(ii,jj) = rho(ii,jj) + q/h^2; +end + +%% * Compute matrix P +cx = cos((2*pi/N)*(0:N-1)); +cy = cx; +numerator = -h^2/(2*eps0); +tinyNumber = 1e-20; % Avoids division by zero +for i=1:N + for j=1:N + P(i,j) = numerator/(cx(i)+cy(j)-2+tinyNumber); + end +end + +%% * Compute potential using MFT method +rhoT = fft2(rho); % Transform rho into wavenumber domain +phiT = rhoT .* P; % Computing phi in the wavenumber domain +phi = ifft2(phiT); % Inv. transf. phi into the coord. domain +phi = real(phi); % Clean up imaginary part due to round-off + +%% * Compute electric field as E = - grad phi +[Ex Ey] = gradient(flipud(rot90(phi))); +magnitude = sqrt(Ex.^2 + Ey.^2); +Ex = -Ex ./ magnitude; % Normalize components so +Ey = -Ey ./ magnitude; % vectors have equal length + +%% * Plot potential and electric field +figure(1); clf; +contour3(x,y,flipud(rot90(phi,1)),35); +xlabel('x'); ylabel('y'); zlabel('\Phi(x,y)'); +figure(2); clf; +quiver(x,y,Ex,Ey) % Plot E field with vectors +title('E field (Direction)'); xlabel('x'); ylabel('y'); +axis('square'); axis([0 L 0 L]); diff --git a/MatlabRevised/fnewt.m b/MatlabRevised/fnewt.m new file mode 100644 index 0000000..65a8ed3 --- /dev/null +++ b/MatlabRevised/fnewt.m @@ -0,0 +1,25 @@ +function [f,D] = fnewt(x,a) +% Function used by the N-variable Newton's method +% Inputs +% x State vector [x y z] +% a Parameters [r sigma b] +% Outputs +% f Lorenz model r.h.s. [dx/dt dy/dt dz/dt] +% D Jacobian matrix, D(i,j) = df(j)/dx(i) + +% Evaluate f(i) +f(1) = a(2)*(x(2)-x(1)); +f(2) = a(1)*x(1)-x(2)-x(1)*x(3); +f(3) = x(1)*x(2)-a(3)*x(3); + +% Evaluate D(i,j) +D(1,1) = -a(2); % df(1)/dx(1) +D(1,2) = a(1)-x(3); % df(2)/dx(1) +D(1,3) = x(2); % df(3)/dx(1) +D(2,1) = a(2); % df(1)/dx(2) +D(2,2) = -1; % df(2)/dx(2) +D(2,3) = x(1); % df(3)/dx(2) +D(3,1) = 0; % df(1)/dx(3) +D(3,2) = -x(1); % df(2)/dx(3) +D(3,3) = -a(3); % df(3)/dx(3) +return; diff --git a/MatlabRevised/ftdemo.asv b/MatlabRevised/ftdemo.asv new file mode 100644 index 0000000..1c3fde1 --- /dev/null +++ b/MatlabRevised/ftdemo.asv @@ -0,0 +1,45 @@ +%% ftdemo - Discrete Fourier transform demonstration program +clear all; help ftdemo; % Clear memory and print header + +%% * Initialize the sine wave time series to be transformed. +N = input('Enter the number of points: '); +freq = input('Enter frequency of the sine wave: '); +phase = input('Enter phase of the sine wave: '); +tau = 1; % Time increment +t = (0:(N-1))*tau; % t = [0, tau, 2*tau, ... ] +y = sin(2*pi*t*freq + phase); % Sine wave time series +f = (0:(N-1))/(N*tau); % f = [0, 1/(N*tau), ... ] + +%% * Compute the transform using desired method: direct summation +% or fast Fourier transform (FFT) algorithm. +Method = menu('Compute transform by','Direct summation','FFT'); +tStart = cputime; % Start the stopwatch +if( Method == 1 ); % Direct summation + twoPiN = -2*pi*sqrt(-1)/N; + for k=0:N-1 + expTerm = exp(twoPiN*(0:N-1)*k); + yt(k+1) = sum(y .* expTerm); + end +else % Fast Fourier transform + yt = fft(y); +end +t +fprintf('Number of floating point operations = %g\n',flops); + +%% * Graph the time series and its transform. +figure(1); clf; % Clear figure 1 window and bring forward +plot(t,y); +title('Original time series'); +ylabel('Amplitude'); xlabel('Time'); +figure(2); clf; % Clear figure 2 window and bring forward +plot(f,real(yt),'-',f,imag(yt),'--'); +legend('Real','Imaginary '); +title('Fourier transform'); +ylabel('Transform'); xlabel('Frequency'); + +%% * Compute and graph the power spectrum of the time series. +figure(3); clf; % Clear figure 3 window and bring forward +powspec = abs(yt).^2; +semilogy(f,powspec,'-'); +title('Power spectrum (unnormalized)'); +ylabel('Power'); xlabel('Frequency'); diff --git a/MatlabRevised/ftdemo.m b/MatlabRevised/ftdemo.m new file mode 100644 index 0000000..75ff126 --- /dev/null +++ b/MatlabRevised/ftdemo.m @@ -0,0 +1,45 @@ +%% ftdemo - Discrete Fourier transform demonstration program +clear all; help ftdemo; % Clear memory and print header + +%% * Initialize the sine wave time series to be transformed. +N = input('Enter the number of points: '); +freq = input('Enter frequency of the sine wave: '); +phase = input('Enter phase of the sine wave: '); +tau = 1; % Time increment +t = (0:(N-1))*tau; % t = [0, tau, 2*tau, ... ] +y = sin(2*pi*t*freq + phase); % Sine wave time series +f = (0:(N-1))/(N*tau); % f = [0, 1/(N*tau), ... ] + +%% * Compute the transform using desired method: direct summation +% or fast Fourier transform (FFT) algorithm. +Method = menu('Compute transform by','Direct summation','FFT'); +tStart = cputime; % Start the stopwatch +if( Method == 1 ); % Direct summation + twoPiN = -2*pi*sqrt(-1)/N; + for k=0:N-1 + expTerm = exp(twoPiN*(0:N-1)*k); + yt(k+1) = sum(y .* expTerm); + end +else % Fast Fourier transform + yt = fft(y); +end +tStop = cputime; % Stop the stopwatch +fprintf('Elapsed time (sec) = %g\n',tStop-tStart); + +%% * Graph the time series and its transform. +figure(1); clf; % Clear figure 1 window and bring forward +plot(t,y); +title('Original time series'); +ylabel('Amplitude'); xlabel('Time'); +figure(2); clf; % Clear figure 2 window and bring forward +plot(f,real(yt),'-',f,imag(yt),'--'); +legend('Real','Imaginary '); +title('Fourier transform'); +ylabel('Transform'); xlabel('Frequency'); + +%% * Compute and graph the power spectrum of the time series. +figure(3); clf; % Clear figure 3 window and bring forward +powspec = abs(yt).^2; +semilogy(f,powspec,'-'); +title('Power spectrum (unnormalized)'); +ylabel('Power'); xlabel('Frequency'); diff --git a/MatlabRevised/gravrk.m b/MatlabRevised/gravrk.m new file mode 100644 index 0000000..4dc8ed2 --- /dev/null +++ b/MatlabRevised/gravrk.m @@ -0,0 +1,17 @@ +function deriv = gravrk(s,t,GM) +% Returns right-hand side of Kepler ODE; used by Runge-Kutta routines +% Inputs +% s State vector [r(1) r(2) v(1) v(2)] +% t Time (not used) +% GM Parameter G*M (gravitational const. * solar mass) +% Output +% deriv Derivatives [dr(1)/dt dr(2)/dt dv(1)/dt dv(2)/dt] + +%* Compute acceleration +r = [s(1) s(2)]; % Unravel the vector s into position and velocity +v = [s(3) s(4)]; +accel = -GM*r/norm(r)^3; % Gravitational acceleration + +%* Return derivatives [dr(1)/dt dr(2)/dt dv(1)/dt dv(2)/dt] +deriv = [v(1) v(2) accel(1) accel(2)]; +return; diff --git a/MatlabRevised/interp.m b/MatlabRevised/interp.m new file mode 100644 index 0000000..883a1a1 --- /dev/null +++ b/MatlabRevised/interp.m @@ -0,0 +1,25 @@ +%% interp - Program to interpolate data using Lagrange +% polynomial to fit quadratic to three data points +clear all; help interp; % Clear memory and print header +%% * Initialize the data points to be fit by quadratic +disp('Enter data points as x,y pairs (e.g., [1 2])'); +for i=1:3 + temp = input('Enter data point: '); + x(i) = temp(1); + y(i) = temp(2); +end +%% * Establish the range of interpolation (from x_min to x_max) +xr = input('Enter range of x values as [x_min x_max]: '); +%% * Find yi for the desired interpolation values xi using +% the function intrpf +nplot = 100; % Number of points for interpolation curve +for i=1:nplot + xi(i) = xr(1) + (xr(2)-xr(1))*(i-1)/(nplot-1); + yi(i) = intrpf(xi(i),x,y); % Use intrpf function to interpolate +end +%% * Plot the curve given by (xi,yi) and mark original data points +plot(x,y,'*',xi,yi,'-'); +xlabel('x'); +ylabel('y'); +title('Three point interpolation'); +legend('Data points','Interpolation '); \ No newline at end of file diff --git a/MatlabRevised/intrpf.m b/MatlabRevised/intrpf.m new file mode 100644 index 0000000..6f06dc5 --- /dev/null +++ b/MatlabRevised/intrpf.m @@ -0,0 +1,15 @@ +function yi = intrpf(xi,x,y) +%% Function to interpolate between data points +% using Lagrange polynomial (quadratic) +% Inputs +% x Vector of x coordinates of data points (3 values) +% y Vector of y coordinates of data points (3 values) +% xi The x value where interpolation is computed +% Output +% yi The interpolation polynomial evaluated at xi + +%% * Calculate yi = p(xi) using Lagrange polynomial +yi = (xi-x(2))*(xi-x(3))/((x(1)-x(2))*(x(1)-x(3)))*y(1) ... + + (xi-x(1))*(xi-x(3))/((x(2)-x(1))*(x(2)-x(3)))*y(2) ... + + (xi-x(1))*(xi-x(2))/((x(3)-x(1))*(x(3)-x(2)))*y(3); +return; diff --git a/MatlabRevised/legndr.m b/MatlabRevised/legndr.m new file mode 100644 index 0000000..d50cdab --- /dev/null +++ b/MatlabRevised/legndr.m @@ -0,0 +1,16 @@ +function p = legndr(n,x) +% Legendre polynomials function +% Inputs +% n = Highest order polynomial returned +% x = Value at which polynomial is evaluated +% Output +% p = Vector containing P(x) for order 0,1,...,n + +%* Perform upward recursion +p(1)=1; % P(x) for n=0 +if(n == 0) return; end +p(2)=x; % P(x) for n=1 +for i=3:n+1 % Use upward recursion to obtain other n's + p(i) = ((2*i-3)*x*p(i-1) - (i-2)*p(i-2))/(i-1); +end +return; diff --git a/MatlabRevised/linreg.m b/MatlabRevised/linreg.m new file mode 100644 index 0000000..768fedf --- /dev/null +++ b/MatlabRevised/linreg.m @@ -0,0 +1,33 @@ +function [a_fit, sig_a, yy, chisqr] = linreg(x,y,sigma) +% Function to perform linear regression (fit a line) +% Inputs +% x Independent variable +% y Dependent variable +% sigma Estimated error in y +% Outputs +% a_fit Fit parameters; a(1) is intercept, a(2) is slope +% sig_a Estimated error in the parameters a() +% yy Curve fit to the data +% chisqr Chi squared statistic + +%* Evaluate various sigma sums +sigmaTerm = sigma .^ (-2); +s = sum(sigmaTerm); +sx = sum(x .* sigmaTerm); +sy = sum(y .* sigmaTerm); +sxy = sum(x .* y .* sigmaTerm); +sxx = sum((x .^ 2) .* sigmaTerm); +denom = s*sxx - sx^2; + +%* Compute intercept a_fit(1) and slope a_fit(2) +a_fit(1) = (sxx*sy - sx*sxy)/denom; +a_fit(2) = (s*sxy - sx*sy)/denom; + +%* Compute error bars for intercept and slope +sig_a(1) = sqrt(sxx/denom); +sig_a(2) = sqrt(s/denom); + +%* Evaluate curve fit at each data point and compute Chi^2 +yy = a_fit(1)+a_fit(2)*x; % Curve fit to the data +chisqr = sum( ((y-yy)./sigma).^2 ); % Chi square +return; diff --git a/MatlabRevised/lorenz.m b/MatlabRevised/lorenz.m new file mode 100644 index 0000000..8f4b3b1 --- /dev/null +++ b/MatlabRevised/lorenz.m @@ -0,0 +1,53 @@ +% lorenz - Program to compute the trajectories of the Lorenz +% equations using the adaptive Runge-Kutta method. +clear; help lorenz; + +%% * Set initial state x,y,z and parameters r,sigma,b +state = input('Enter the initial position [x y z]: '); +r = input('Enter the parameter r: '); +sigma = 10.; % Parameter sigma +b = 8./3.; % Parameter b +param = [r sigma b]; % Vector of parameters passed to rka +tau = 1; % Initial guess for the timestep +err = 1.e-3; % Error tolerance + +%% * Loop over the desired number of steps +time = 0; +nstep = input('Enter number of steps: '); +for istep=1:nstep + + %* Record values for plotting + x = state(1); y = state(2); z = state(3); + tplot(istep) = time; tauplot(istep) = tau; + xplot(istep) = x; yplot(istep) = y; zplot(istep) = z; + if( rem(istep,50) < 1 ) + fprintf('Finished %g steps out of %g\n',istep,nstep); + end + + %* Find new state using adaptive Runge-Kutta + [state, time, tau] = rka(state,time,tau,err,@lorzrk,param); + +end + +%% * Print max and min time step returned by rka +fprintf('Adaptive time step: Max = %g, Min = %g \n', ... + max(tauplot(2:nstep)), min(tauplot(2:nstep))); + +%% * Graph the time series x(t) +figure(1); clf; % Clear figure 1 window and bring forward +plot(tplot,xplot,'-') +xlabel('Time'); ylabel('x(t)') +title('Lorenz model time series') +pause(1) % Pause 1 second + +%% * Graph the x,y,z phase space trajectory +figure(2); clf; % Clear figure 2 window and bring forward +% Mark the location of the three steady states +x_ss(1) = 0; y_ss(1) = 0; z_ss(1) = 0; +x_ss(2) = sqrt(b*(r-1)); y_ss(2) = x_ss(2); z_ss(2) = r-1; +x_ss(3) = -sqrt(b*(r-1)); y_ss(3) = x_ss(3); z_ss(3) = r-1; +plot3(xplot,yplot,zplot,'-',x_ss,y_ss,z_ss,'*') +view([30 20]); % Rotate to get a better view +grid; % Add a grid to aid perspective +xlabel('x'); ylabel('y'); zlabel('z'); +title('Lorenz model phase space'); diff --git a/MatlabRevised/lorzrk.m b/MatlabRevised/lorzrk.m new file mode 100644 index 0000000..e606e93 --- /dev/null +++ b/MatlabRevised/lorzrk.m @@ -0,0 +1,18 @@ +function deriv = lorzrk(s,t,param) +% Returns right-hand side of Lorenz model ODEs +% Inputs +% s State vector [x y z] +% t Time (not used) +% param Parameters [r sigma b] +% Output +% deriv Derivatives [dx/dt dy/dt dz/dt] + +%* For clarity, unravel input vectors +x = s(1); y = s(2); z = s(3); +r = param(1); sigma = param(2); b = param(3); + +%* Return the derivatives [dx/dt dy/dt dz/dt] +deriv(1) = sigma*(y-x); +deriv(2) = r*x - y - x*z; +deriv(3) = x*y - b*z; +return; diff --git a/MatlabRevised/lsfdemo.asv b/MatlabRevised/lsfdemo.asv new file mode 100644 index 0000000..68f5111 --- /dev/null +++ b/MatlabRevised/lsfdemo.asv @@ -0,0 +1,38 @@ +% lsfdemo - Program for demonstrating least squares fit routines +clear all; help lsfdemo; % Clear memory and print header + +%% * Initialize data to be fit. Data is quadratic plus random number. +fprintf('Curve fit data is created using the quadratic\n'); +fprintf(' y(x) = c(1) + c(2)*x + c(3)*x^2 \n'); +c = input('Enter the coefficients as [c(1) c(2) c(3)]: '); +N = 50; % Number of data points +x = 1:N; % x = [1, 2, ..., N] +randn('state',0); % Initialize random number generator +alpha = input('Enter estimated error bar: '); +r = alpha*randn(1,N); % Gaussian distributed random vector +y = c(1) + c(2)*x + c(3)*x.^2 + r; +sigma = alpha*ones(1,N); % Constant error bar + +%% * Fit the data to a straight line or a more general polynomial +M = input('Enter number of fit parameters (=2 for line): '); +if( M == 2 ) + %* Linear regression (Straight line) fit + [a_fit sig_a yy chisqr] = linreg(x,y,sigma); +else + %* Polynomial fit + [a_fit sig_a yy chisqr] = pollsf(x,y,sigma,M); +end + +%% * Print out the fit parameters, including their error bars. +fprintf('Fit parameters:\n'); +for i=1:M + fprintf(' a(%g) = %g +/- %g \n',i,a_fit(i),sig_a(i)); +end + +%% * Graph the data, with error bars, and fitting function. +figure(1); clf; % Bring figure 1 window forward +errorbar(x,y,sigma,'o'); % Graph data with error bars +hold on; % Freeze the plot to add the fit +plot(x,yy,'-'); % Plot the fit on same graph as data +xlabel('x_i'); ylabel('y_i and Y(x)'); +title(['\chi^2 = ',num2str(chisqr),' N-M = ',num2str(N-M)]); diff --git a/MatlabRevised/lsfdemo.m b/MatlabRevised/lsfdemo.m new file mode 100644 index 0000000..6307a81 --- /dev/null +++ b/MatlabRevised/lsfdemo.m @@ -0,0 +1,38 @@ +%% lsfdemo - Program for demonstrating least squares fit routines +clear all; help lsfdemo; % Clear memory and print header + +%% * Initialize data to be fit. Data is quadratic plus random number. +fprintf('Curve fit data is created using the quadratic\n'); +fprintf(' y(x) = c(1) + c(2)*x + c(3)*x^2 \n'); +c = input('Enter the coefficients as [c(1) c(2) c(3)]: '); +N = 50; % Number of data points +x = 1:N; % x = [1, 2, ..., N] +randn('state',0); % Initialize random number generator +alpha = input('Enter estimated error bar: '); +r = alpha*randn(1,N); % Gaussian distributed random vector +y = c(1) + c(2)*x + c(3)*x.^2 + r; +sigma = alpha*ones(1,N); % Constant error bar + +%% * Fit the data to a straight line or a more general polynomial +M = input('Enter number of fit parameters (=2 for line): '); +if( M == 2 ) + %* Linear regression (Straight line) fit + [a_fit sig_a yy chisqr] = linreg(x,y,sigma); +else + %* Polynomial fit + [a_fit sig_a yy chisqr] = pollsf(x,y,sigma,M); +end + +%% * Print out the fit parameters, including their error bars. +fprintf('Fit parameters:\n'); +for i=1:M + fprintf(' a(%g) = %g +/- %g \n',i,a_fit(i),sig_a(i)); +end + +%% * Graph the data, with error bars, and fitting function. +figure(1); clf; % Bring figure 1 window forward +errorbar(x,y,sigma,'o'); % Graph data with error bars +hold on; % Freeze the plot to add the fit +plot(x,yy,'-'); % Plot the fit on same graph as data +xlabel('x_i'); ylabel('y_i and Y(x)'); +title(['\chi^2 = ',num2str(chisqr),' N-M = ',num2str(N-M)]); diff --git a/MatlabRevised/mover.m b/MatlabRevised/mover.m new file mode 100644 index 0000000..b5dfecc --- /dev/null +++ b/MatlabRevised/mover.m @@ -0,0 +1,55 @@ +function [x,v,strikes,delv] = mover(x,v,npart, ... + L,mpv,vwall,tau) +% mover - Function to move particles by free flight +% Also handles collisions with walls +% Inputs +% x Positions of the particles +% v Velocities of the particles +% npart Number of particles in the system +% L System length +% mpv Most probable velocity off the wall +% vwall Wall velocities +% tau Time step +% Outputs +% x,v Updated positions and velocities +% strikes Number of particles striking each wall +% delv Change of y-velocity at each wall + +%* Move all particles pretending walls are absent +x_old = x; % Remember original position +x(:) = x_old(:) + v(:,1)*tau; + +%* Loop over all particles +strikes = [0 0]; delv = [0 0]; +xwall = [0 L]; vw = [-vwall vwall]; +direction = [1 -1]; % Direction of particle leaving wall +stdev = mpv/sqrt(2); +for i=1:npart + + %* Test if particle strikes either wall + if( x(i) <= 0 ) + flag=1; % Particle strikes left wall + elseif( x(i) >= L ) + flag=2; % Particle strikes right wall + else + flag=0; % Particle strikes neither wall + end + + %* If particle strikes a wall, reset its position + % and velocity. Record velocity change. + if( flag > 0 ) + strikes(flag) = strikes(flag) + 1; + vyInitial = v(i,2); + %* Reset velocity components as biased Maxwellian, + % Exponential dist. in x; Gaussian in y and z + v(i,1) = direction(flag)*sqrt(-log(1-rand(1))) * mpv; + v(i,2) = stdev*randn(1) + vw(flag); % Add wall velocity + v(i,3) = stdev*randn(1); + % Time of flight after leaving wall + dtr = tau*(x(i)-xwall(flag))/(x(i)-x_old(i)); + %* Reset position after leaving wall + x(i) = xwall(flag) + v(i,1)*dtr; + %* Record velocity change for force measurement + delv(flag) = delv(flag) + (v(i,2) - vyInitial); + end +end diff --git a/MatlabRevised/neutrn.m b/MatlabRevised/neutrn.m new file mode 100644 index 0000000..e17dd80 --- /dev/null +++ b/MatlabRevised/neutrn.m @@ -0,0 +1,63 @@ +%% neutrn - Program to solve the neutron diffusion equation +% using the Forward Time Centered Space (FTCS) scheme. +clear; help neutrn; % Clear memory and print header + +%% * Initialize parameters (time step, grid points, etc.). +tau = input('Enter time step: '); +N = input('Enter the number of grid points: '); +L = input('Enter system length: '); +% The system extends from x=-L/2 to x=L/2 +h = L/(N-1); % Grid size +D = 1.; % Diffusion coefficient +C = 1.; % Generation rate +coeff = D*tau/h^2; +coeff2 = C*tau; +if( coeff < 0.5 ) + disp('Solution is expected to be stable'); +else + disp('WARNING: Solution is expected to be unstable'); +end + +%% * Set initial and boundary conditions. +nn = zeros(N,1); % Initialize density to zero at all points +nn_new = zeros(N,1); % Initialize temporary array used by FTCS +nn(round(N/2)) = 1/h; % Initial cond. is delta function in center +%% The boundary conditions are nn(1) = nn(N) = 0 + +%% * Set up loop and plot variables. +xplot = (0:N-1)*h - L/2; % Record the x scale for plots +iplot = 1; % Counter used to count plots +nstep = input('Enter number of time steps: '); +nplots = 50; % Number of snapshots (plots) to take +plot_step = nstep/nplots; % Number of time steps between plots + +%% * Loop over the desired number of time steps. +for istep=1:nstep %% MAIN LOOP %% + + %* Compute the new density using FTCS scheme. + nn_new(2:(N-1)) = nn(2:(N-1)) + ... + coeff*(nn(3:N) + nn(1:(N-2)) - 2*nn(2:(N-1))) + ... + coeff2*nn(2:(N-1)); + nn = nn_new; % Reset temperature to new values + + %* Periodically record the density for plotting. + if( rem(istep,plot_step) < 1 ) % Every plot_step steps + nnplot(:,iplot) = nn(:); % record nn(i) for plotting + tplot(iplot) = istep*tau; % Record time for plots + nAve(iplot) = mean(nn); % Record average density + iplot = iplot+1; + fprintf('Finished %g of %g steps\n',istep,nstep); + end +end + +%% * Plot density versus x and t as a 3D-surface plot +figure(1); clf; +mesh(tplot,xplot,nnplot); +xlabel('Time'); ylabel('x'); zlabel('n(x,t)'); +title('Neutron diffusion'); + +%% * Plot average neutron density versus time +figure(2); clf; +plot(tplot,nAve,'*'); +xlabel('Time'); ylabel('Average density'); +title(['L = ',num2str(L),' (L_c = \pi)']); diff --git a/MatlabRevised/newtn.asv b/MatlabRevised/newtn.asv new file mode 100644 index 0000000..dfc33e3 --- /dev/null +++ b/MatlabRevised/newtn.asv @@ -0,0 +1,57 @@ +%% newtn - Program to solve a system of nonlinear equations +% using Newton's method. Equations defined by function fnewt. +clear all; help newtn; % Clear memory and print header + +%% * Set initial guess and parameters +x0 = input('Enter the initial guess (row vector): '); +x = x0; % Copy initial guess +xp(:,1) = x(:); % Record initial guess for plotting +a = input('Enter the parameter a: '); + +%% * Loop over desired number of steps +nStep = 10; % Number of iterations before stopping +for iStep=1:nStep + + %* Evaluate function f and its Jacobian matrix D + [f D] = fnewt(x,a); % fnewt returns value of f and D + %* Find dx by Gaussian elimination + dx = f/D; + %* Update the estimate for the root + x = x - dx; % Newton iteration for new x + xp(:,iStep+1) = x(:); % Save current estimate for plotting + +end + +%% * Print the final estimate for the root +fprintf('After %g iterations the root is\n',nStep); +disp(x); + +%% * Plot the iterations from initial guess to final estimate +figure(1); clf; % Clear figure 1 window and bring forward +subplot(1,2,1) % Left plot + plot3(xp(1,:),xp(2,:),xp(3,:),'o-',... + x(1),x(2),x(3),'*'); + xlabel('x'); ylabel('y'); zlabel('z'); + view([-37.5, 30]); % Viewing angle + title(sprintf('Initial guess is %g %g %g',x0(1),x0(2),x0(3))); + grid; drawnow; +subplot(1,2,2) % Right plot + plot3(xp(1,:),xp(2,:),xp(3,:),'o-',... + x(1),x(2),x(3),'*'); + xlabel('x'); ylabel('y'); zlabel('z'); + view([-127.5, 30]); % Viewing angle + title(sprintf('After %g iterations, root is %g %g %g',... + nStep,x(1),x(2),x(3))); + grid; drawnow; +%% Plot data from lorenz (if available). To write lorenz data, use: +% >>save xplot; save yplot; save zplot; +% after running the lornez program. +flag = input('Plot data from lorenz program? (1=Yes/0=No): '); +if( flag == 1 ) + figure(2); clf; % Clear figure 1 window and bring forward + load xplot; load yplot; load zplot; + plot3(xplot,yplot,zplot,'-',xp(1,:),xp(2,:),xp(3,:),'o--'); + xlabel('x'); ylabel('y'); zlabel('z'); + view([40 10]); % Rotate to get a better view + grid; % Add a grid to aid perspective +end \ No newline at end of file diff --git a/MatlabRevised/newtn.m b/MatlabRevised/newtn.m new file mode 100644 index 0000000..e95544d --- /dev/null +++ b/MatlabRevised/newtn.m @@ -0,0 +1,59 @@ +%% newtn - Program to solve a system of nonlinear equations +% using Newton's method. Equations defined by user-supplied function. +clear all; help newtn; % Clear memory and print header + +%% * Set initial guess and parameters +fnewtName = input('Enter name of function (e.g., fnewt): ','s'); +fnewtH = str2func(fnewtName); % Convert name into function handle +x0 = input('Enter the initial guess (row vector): '); +x = x0; % Copy initial guess +xp(:,1) = x(:); % Record initial guess for plotting +a = input('Enter the parameter a: '); + +%% * Loop over desired number of steps +nStep = 10; % Number of iterations before stopping +for iStep=1:nStep + + %* Evaluate function f and its Jacobian matrix D + [f D] = fnewtH(x,a); % fnewt returns value of f and D + %* Find dx by Gaussian elimination + dx = f/D; + %* Update the estimate for the root + x = x - dx; % Newton iteration for new x + xp(:,iStep+1) = x(:); % Save current estimate for plotting + +end + +%% * Print the final estimate for the root +fprintf('After %g iterations the root is\n',nStep); +disp(x); + +%% * Plot the iterations from initial guess to final estimate +figure(1); clf; % Clear figure 1 window and bring forward +subplot(1,2,1) % Left plot + plot3(xp(1,:),xp(2,:),xp(3,:),'o-',... + x(1),x(2),x(3),'*'); + xlabel('x'); ylabel('y'); zlabel('z'); + view([-37.5, 30]); % Viewing angle + title(sprintf('Initial guess is %g %g %g',x0(1),x0(2),x0(3))); + grid; drawnow; +subplot(1,2,2) % Right plot + plot3(xp(1,:),xp(2,:),xp(3,:),'o-',... + x(1),x(2),x(3),'*'); + xlabel('x'); ylabel('y'); zlabel('z'); + view([-127.5, 30]); % Viewing angle + title(sprintf('After %g iterations, root is %g %g %g',... + nStep,x(1),x(2),x(3))); + grid; drawnow; +%% Plot data from lorenz (if available). To write lorenz data, use: +% >>save xplot; save yplot; save zplot; +% after running the lornez program. +flag = input('Plot data from lorenz program? (1=Yes/0=No): '); +if( flag == 1 ) + figure(2); clf; % Clear figure 1 window and bring forward + load xplot; load yplot; load zplot; + plot3(xplot,yplot,zplot,'-',xp(1,:),xp(2,:),xp(3,:),'o--'); + xlabel('x'); ylabel('y'); zlabel('z'); + view([40 10]); % Rotate to get a better view + grid; % Add a grid to aid perspective +end \ No newline at end of file diff --git a/MatlabRevised/orbit.m b/MatlabRevised/orbit.m new file mode 100644 index 0000000..1175b67 --- /dev/null +++ b/MatlabRevised/orbit.m @@ -0,0 +1,66 @@ +%% orbit - Program to compute the orbit of a comet. +clear all; help orbit; % Clear memory and print header + +%% * Set initial position and velocity of the comet. +r0 = input('Enter initial radial distance (AU): '); +v0 = input('Enter initial tangential velocity (AU/yr): '); +r = [r0 0]; v = [0 v0]; +state = [ r(1) r(2) v(1) v(2) ]; % Used by R-K routines + +%% * Set physical parameters (mass, G*M) +GM = 4*pi^2; % Grav. const. * Mass of Sun (au^3/yr^2) +mass = 1.; % Mass of comet +adaptErr = 1.e-3; % Error parameter used by adaptive Runge-Kutta +time = 0; + +%% * Loop over desired number of steps using specified +% numerical method. +nStep = input('Enter number of steps: '); +tau = input('Enter time step (yr): '); +NumericalMethod = menu('Choose a numerical method:', ... + 'Euler','Euler-Cromer','Runge-Kutta','Adaptive R-K'); +for iStep=1:nStep + + %* Record position and energy for plotting. + rplot(iStep) = norm(r); % Record position for polar plot + thplot(iStep) = atan2(r(2),r(1)); + tplot(iStep) = time; + kinetic(iStep) = .5*mass*norm(v)^2; % Record energies + potential(iStep) = - GM*mass/norm(r); + + %* Calculate new position and velocity using desired method. + if( NumericalMethod == 1 ) + accel = -GM*r/norm(r)^3; + r = r + tau*v; % Euler step + v = v + tau*accel; + time = time + tau; + elseif( NumericalMethod == 2 ) + accel = -GM*r/norm(r)^3; + v = v + tau*accel; + r = r + tau*v; % Euler-Cromer step + time = time + tau; + elseif( NumericalMethod == 3 ) + state = rk4(state,time,tau,@gravrk,GM); + r = [state(1) state(2)]; % 4th order Runge-Kutta + v = [state(3) state(4)]; + time = time + tau; + else + [state time tau] = rka(state,time,tau,adaptErr,@gravrk,GM); + r = [state(1) state(2)]; % Adaptive Runge-Kutta + v = [state(3) state(4)]; + end + +end + +%% * Graph the trajectory of the comet. +figure(1); clf; % Clear figure 1 window and bring forward +polar(thplot,rplot,'+'); % Use polar plot for graphing orbit +xlabel('Distance (AU)'); grid; +pause(1) % Pause for 1 second before drawing next plot + +%% * Graph the energy of the comet versus time. +figure(2); clf; % Clear figure 2 window and bring forward +totalE = kinetic + potential; % Total energy +plot(tplot,kinetic,'-.',tplot,potential,'--',tplot,totalE,'-') +legend('Kinetic','Potential','Total'); +xlabel('Time (yr)'); ylabel('Energy (M AU^2/yr^2)'); diff --git a/MatlabRevised/orthog.m b/MatlabRevised/orthog.m new file mode 100644 index 0000000..39d0527 --- /dev/null +++ b/MatlabRevised/orthog.m @@ -0,0 +1,18 @@ +%% orthog - Program to test if a pair of vectors +% is orthogonal. Assumes vectors are in 3D space +clear all; help orthog; % Clear the memory and print header +%% * Initialize the vectors a and b +a = input('Enter the first vector: '); +b = input('Enter the second vector: '); +%% * Evaluate the dot product as sum over products of elements +a_dot_b = 0; +for i=1:3 + a_dot_b = a_dot_b + a(i)*b(i); +end +%% * Print dot product and state whether vectors are orthogonal +if( a_dot_b == 0 ) + disp('Vectors are orthogonal'); +else + disp('Vectors are NOT orthogonal'); + fprintf('Dot product = %g \n',a_dot_b); +end diff --git a/MatlabRevised/pendul.m b/MatlabRevised/pendul.m new file mode 100644 index 0000000..d073a41 --- /dev/null +++ b/MatlabRevised/pendul.m @@ -0,0 +1,70 @@ +%% pendul - Program to compute the motion of a simple pendulum +% using the Euler or Verlet method +clear all; help pendul % Clear the memory and print header + +%% * Select the numerical method to use: Euler or Verlet +NumericalMethod = menu('Choose a numerical method:', ... + 'Euler','Verlet'); + +%% * Set initial position and velocity of pendulum +theta0 = input('Enter initial angle (in degrees): '); +theta = theta0*pi/180; % Convert angle to radians +omega = 0; % Set the initial velocity + +%% * Set the physical constants and other variables +g_over_L = 1; % The constant g/L +time = 0; % Initial time +irev = 0; % Used to count number of reversals +period = []; % Used to record period estimates +tau = input('Enter time step: '); + +%% * Take one backward step to start Verlet +accel = -g_over_L*sin(theta); % Gravitational acceleration +theta_old = theta - omega*tau + 0.5*tau^2*accel; + +%% * Loop over desired number of steps with given time step +% and numerical method +nstep = input('Enter number of time steps: '); +for istep=1:nstep + + %* Record angle and time for plotting + t_plot(istep) = time; + th_plot(istep) = theta*180/pi; % Convert angle to degrees + time = time + tau; + + %* Compute new position and velocity using + % Euler or Verlet method + accel = -g_over_L*sin(theta); % Gravitational acceleration + if( NumericalMethod == 1 ) + theta_old = theta; % Save previous angle + theta = theta + tau*omega; % Euler method + omega = omega + tau*accel; + else + theta_new = 2*theta - theta_old + tau^2*accel; + theta_old = theta; % Verlet method + theta = theta_new; + end + + %* Test if the pendulum has passed through theta = 0; + % if yes, use time to estimate period + if( theta*theta_old < 0 ) % Test position for sign change + fprintf('Turning point at time t= %f \n',time); + if( irev == 0 ) % If this is the first change, + time_old = time; % just record the time + else + period(irev) = 2*(time - time_old); + time_old = time; + end + irev = irev + 1; % Increment the number of reversals + end +end + +%% * Estimate period of oscillation, including error bar +AvePeriod = mean(period); +ErrorBar = std(period)/sqrt(irev); +fprintf('Average period = %g +/- %g\n', AvePeriod,ErrorBar); + +%% * Graph the oscillations as theta versus time +figure(1); clf; % Clear figure window #1 and bring it forward +plot(t_plot,th_plot,'+'); +xlabel('Time'); ylabel('\theta (degrees)'); diff --git a/MatlabRevised/pollsf.m b/MatlabRevised/pollsf.m new file mode 100644 index 0000000..0580988 --- /dev/null +++ b/MatlabRevised/pollsf.m @@ -0,0 +1,40 @@ +function [a_fit, sig_a, yy, chisqr] = pollsf(x, y, sigma, M) +% Function to fit a polynomial to data +% Inputs +% x Independent variable +% y Dependent variable +% sigma Estimate error in y +% M Number of parameters used to fit data +% Outputs +% a_fit Fit parameters; a(1) is intercept, a(2) is slope +% sig_a Estimated error in the parameters a() +% yy Curve fit to the data +% chisqr Chi squared statistic + +%* Form the vector b and design matrix A +b = y./sigma; +N = length(x); +for i=1:N + for j=1:M + A(i,j) = x(i)^(j-1)/sigma(i); + end +end + +%* Compute the correlation matrix C +C = inv(A.' * A); + +%* Compute the least squares polynomial coefficients a_fit +a_fit = C * A.' * b.'; + +%* Compute the estimated error bars for the coefficients +for j=1:M + sig_a(j) = sqrt(C(j,j)); +end + +%* Evaluate curve fit at each data point and compute Chi^2 +yy = zeros(1,N); +for j=1:M + yy = yy + a_fit(j)*x.^(j-1); % yy is the curve fit +end +chisqr = sum( ((y-yy)./sigma).^2 ); +return; diff --git a/MatlabRevised/relax.asv b/MatlabRevised/relax.asv new file mode 100644 index 0000000..401c898 --- /dev/null +++ b/MatlabRevised/relax.asv @@ -0,0 +1,106 @@ +%% relax - Program to solve the Laplace equation using +% Jacobi, Gauss-Seidel and SOR methods on a square grid +clear all; help relax; % Clear memory and print header + +%% * Initialize parameters (system size, grid spacing, etc.) +method = menu('Numerical Method','Jacobi','Gauss-Seidel','SOR'); +N = input('Enter number of grid points on a side: '); +L = 1; % System size (length) +h = L/(N-1); % Grid spacing +x = (0:N-1)*h; % x coordinate +y = (0:N-1)*h; % y coordinate + +%% * Select over-relaxation factor (SOR only) +if( method == 3 ) + omegaOpt = 2/(1+sin(pi/N)); % Theoretical optimum + fprintf('Theoretical optimum omega = %g \n',omegaOpt); + omega = input('Enter desired omega: '); +end + +%% * Set initial guess as first term in separation of variables soln. +phi0 = 1; % Potential at y=L +phi = phi0 * 4/(pi*sinh(pi)) * sin(pi*x'/L)*sinh(pi*y/L); + +%% * Set boundary conditions +phi(1,:) = 0; phi(N,:) = 0; phi(:,1) = 0; +phi(:,N) = phi0*ones(N,1); +fprintf('Potential at y=L equals %g \n',phi0); +fprintf('Potential is zero on all other boundaries\n'); + +%% * Loop until desired fractional change per iteration is obtained +newphi = phi; % Copy of the solution (used only by Jacobi) +iterMax = N^2; % Set max to avoid excessively long runs +changeDesired = 1e-4; % Stop when the change is given fraction +fprintf('Desired fractional change = %g\n',changeDesired); +tStart = cputime; % Start the stopwatch +for iter=1:iterMax + changeSum = 0; + + if( method == 1 ) %% Jacobi method %% + for i=2:(N-1) % Loop over interior points only + for j=2:(N-1) + newphi(i,j) = .25*(phi(i+1,j)+phi(i-1,j)+ ... + phi(i,j-1)+phi(i,j+1)); + changeSum = changeSum + abs(1-phi(i,j)/newphi(i,j)); + end + end + phi = newphi; + + elseif( method == 2 ) %% G-S method %% +% for i=2:(N-1) % Loop over interior points only +% for j=2:(N-1) +% newphi = .25*(phi(i+1,j)+phi(i-1,j)+ ... +% phi(i,j-1)+phi(i,j+1)); +% changeSum = changeSum + abs(1-phi(i,j)/newphi); +% phi(i,j) = newphi; +% end +% end + for i=2:(N-1) % Loop over interior points only + for j=2:(N-1) + newphi(i,j) = .25*(phi(i+1,j)+phi(i-1,j)+ ... + phi(i,j-1)+phi(i,j+1)); + changeSum = changeSum + abs(1-phi(i,j)/newphi); + phi(i,j) = newphi; + end + end + + else %% SOR method %% + for i=2:(N-1) % Loop over interior points only + for j=2:(N-1) + newphi = 0.25*omega*(phi(i+1,j)+phi(i-1,j)+ ... + phi(i,j-1)+phi(i,j+1)) + (1-omega)*phi(i,j); + changeSum = changeSum + abs(1-phi(i,j)/newphi); + phi(i,j) = newphi; + end + end + end + + %* Check if fractional change is small enough to halt the iteration + change(iter) = changeSum/(N-2)^2; + if( rem(iter,10) < 1 ) + fprintf('After %g iterations, fractional change = %g\n',... + iter,change(iter)); + end + if( change(iter) < changeDesired ) + fprintf('Desired accuracy achieved after %g iterations\n',iter); + fprintf('Breaking out of main loop\n'); + break; + end +end +tStop = cputime; % Stop the stopwatch + +%% * Plot final estimate of potential as contour and surface plots +figure(1); clf; +cLevels = 0:(0.1):1; % Contour levels +cs = contour(x,y,flipud(rot90(phi)),cLevels); +xlabel('x'); ylabel('y'); clabel(cs); +title(sprintf('Potential after %g iterations',iter)); +figure(2); clf; +mesh(x,y,flipud(rot90(phi))); +xlabel('x'); ylabel('y'); zlabel('\Phi(x,y)'); + +%% * Plot the fractional change versus iteration +figure(3); clf; +semilogy(change); +xlabel('Iteration'); ylabel('Fractional change'); +title(sprintf('Elapsed CPU time = %g seconds',tStop-tStart)); diff --git a/MatlabRevised/relax.m b/MatlabRevised/relax.m new file mode 100644 index 0000000..3c243ea --- /dev/null +++ b/MatlabRevised/relax.m @@ -0,0 +1,98 @@ +%% relax - Program to solve the Laplace equation using +% Jacobi, Gauss-Seidel and SOR methods on a square grid +clear all; help relax; % Clear memory and print header + +%% * Initialize parameters (system size, grid spacing, etc.) +method = menu('Numerical Method','Jacobi','Gauss-Seidel','SOR'); +N = input('Enter number of grid points on a side: '); +L = 1; % System size (length) +h = L/(N-1); % Grid spacing +x = (0:N-1)*h; % x coordinate +y = (0:N-1)*h; % y coordinate + +%% * Select over-relaxation factor (SOR only) +if( method == 3 ) + omegaOpt = 2/(1+sin(pi/N)); % Theoretical optimum + fprintf('Theoretical optimum omega = %g \n',omegaOpt); + omega = input('Enter desired omega: '); +end + +%% * Set initial guess as first term in separation of variables soln. +phi0 = 1; % Potential at y=L +phi = phi0 * 4/(pi*sinh(pi)) * sin(pi*x'/L)*sinh(pi*y/L); + +%% * Set boundary conditions +phi(1,:) = 0; phi(N,:) = 0; phi(:,1) = 0; +phi(:,N) = phi0*ones(N,1); +fprintf('Potential at y=L equals %g \n',phi0); +fprintf('Potential is zero on all other boundaries\n'); + +%% * Loop until desired fractional change per iteration is obtained +newphi = phi; % Copy of the solution (used only by Jacobi) +iterMax = N^2; % Set max to avoid excessively long runs +changeDesired = 1e-4; % Stop when the change is given fraction +fprintf('Desired fractional change = %g\n',changeDesired); +tStart = cputime; % Start the stopwatch +for iter=1:iterMax + changeSum = 0; + + if( method == 1 ) %% Jacobi method %% + for i=2:(N-1) % Loop over interior points only + for j=2:(N-1) + newphi(i,j) = .25*(phi(i+1,j)+phi(i-1,j)+ ... + phi(i,j-1)+phi(i,j+1)); + changeSum = changeSum + abs(1-phi(i,j)/newphi(i,j)); + end + end + phi = newphi; + + elseif( method == 2 ) %% G-S method %% + for i=2:(N-1) % Loop over interior points only + for j=2:(N-1) + newphi = .25*(phi(i+1,j)+phi(i-1,j)+ ... + phi(i,j-1)+phi(i,j+1)); + changeSum = changeSum + abs(1-phi(i,j)/newphi); + phi(i,j) = newphi; + end + end + + else %% SOR method %% + for i=2:(N-1) % Loop over interior points only + for j=2:(N-1) + newphi = 0.25*omega*(phi(i+1,j)+phi(i-1,j)+ ... + phi(i,j-1)+phi(i,j+1)) + (1-omega)*phi(i,j); + changeSum = changeSum + abs(1-phi(i,j)/newphi); + phi(i,j) = newphi; + end + end + end + + %* Check if fractional change is small enough to halt the iteration + change(iter) = changeSum/(N-2)^2; + if( rem(iter,10) < 1 ) + fprintf('After %g iterations, fractional change = %g\n',... + iter,change(iter)); + end + if( change(iter) < changeDesired ) + fprintf('Desired accuracy achieved after %g iterations\n',iter); + fprintf('Breaking out of main loop\n'); + break; + end +end +tStop = cputime; % Stop the stopwatch + +%% * Plot final estimate of potential as contour and surface plots +figure(1); clf; +cLevels = 0:(0.1):1; % Contour levels +cs = contour(x,y,flipud(rot90(phi)),cLevels); +xlabel('x'); ylabel('y'); clabel(cs); +title(sprintf('Potential after %g iterations',iter)); +figure(2); clf; +mesh(x,y,flipud(rot90(phi))); +xlabel('x'); ylabel('y'); zlabel('\Phi(x,y)'); + +%% * Plot the fractional change versus iteration +figure(3); clf; +semilogy(change); +xlabel('Iteration'); ylabel('Fractional change'); +title(sprintf('Elapsed CPU time = %g seconds',tStop-tStart)); diff --git a/MatlabRevised/rk4.asv b/MatlabRevised/rk4.asv new file mode 100644 index 0000000..ec8b75e --- /dev/null +++ b/MatlabRevised/rk4.asv @@ -0,0 +1,24 @@ +function xout = rk4(x,t,tau,derivsRK,param) +% Runge-Kutta integrator (4th order) +% Input arguments - +% x = current value of dependent variable +% t = independent variable (usually time) +% tau = step size (usually timestep) +% derivsRK = right hand side of the ODE; derivsRK is the function +% which returns dx/dt (passed as a function handle) +% Calling format derivsRK(x,t,param). +% param = extra parameters passed to derivsRK +% Output arguments - +% xout = new value of x after a step of size tau +half_tau = 0.5*tau; +F1 = derivsRK(x,t,param); +t_half = t + half_tau; +xtemp = x + half_tau*F1; +F2 = derivsRK(xtemp,t_half,param); +xtemp = x + half_tau*F2; +F3 = derivsRK(xtemp,t_half,param); +t_full = t + tau; +xtemp = x + tau*F3; +F4 = derivsRK(xtemp,t_full,param); +xout = x + tau/6.*(F1 + F4 + 2.*(F2+F3)); +return; diff --git a/MatlabRevised/rk4.m b/MatlabRevised/rk4.m new file mode 100644 index 0000000..ec8b75e --- /dev/null +++ b/MatlabRevised/rk4.m @@ -0,0 +1,24 @@ +function xout = rk4(x,t,tau,derivsRK,param) +% Runge-Kutta integrator (4th order) +% Input arguments - +% x = current value of dependent variable +% t = independent variable (usually time) +% tau = step size (usually timestep) +% derivsRK = right hand side of the ODE; derivsRK is the function +% which returns dx/dt (passed as a function handle) +% Calling format derivsRK(x,t,param). +% param = extra parameters passed to derivsRK +% Output arguments - +% xout = new value of x after a step of size tau +half_tau = 0.5*tau; +F1 = derivsRK(x,t,param); +t_half = t + half_tau; +xtemp = x + half_tau*F1; +F2 = derivsRK(xtemp,t_half,param); +xtemp = x + half_tau*F2; +F3 = derivsRK(xtemp,t_half,param); +t_full = t + tau; +xtemp = x + tau*F3; +F4 = derivsRK(xtemp,t_full,param); +xout = x + tau/6.*(F1 + F4 + 2.*(F2+F3)); +return; diff --git a/MatlabRevised/rka.m b/MatlabRevised/rka.m new file mode 100644 index 0000000..683817f --- /dev/null +++ b/MatlabRevised/rka.m @@ -0,0 +1,53 @@ +function [xSmall, t, tau] = rka(x,t,tau,err,derivsRK,param) +% Adaptive Runge-Kutta routine +% Inputs +% x Current value of the dependent variable +% t Independent variable (usually time) +% tau Step size (usually time step) +% err Desired fractional local truncation error +% derivsRK Right hand side of the ODE; derivsRK is the +% name of the function which returns dx/dt +% Calling format derivsRK(x,t,param). +% param Extra parameters passed to derivsRK +% Outputs +% xSmall New value of the dependent variable +% t New value of the independent variable +% tau Suggested step size for next call to rka + +%* Set initial variables +tSave = t; xSave = x; % Save initial values +safe1 = .9; safe2 = 4.; % Safety factors + +%* Loop over maximum number of attempts to satisfy error bound +maxTry = 100; +for iTry=1:maxTry + + %* Take the two small time steps + half_tau = 0.5 * tau; + xTemp = rk4(xSave,tSave,half_tau,derivsRK,param); + t = tSave + half_tau; + xSmall = rk4(xTemp,t,half_tau,derivsRK,param); + + %* Take the single big time step + t = tSave + tau; + xBig = rk4(xSave,tSave,tau,derivsRK,param); + + %* Compute the estimated truncation error + scale = err * (abs(xSmall) + abs(xBig))/2.; + xDiff = xSmall - xBig; + errorRatio = max( abs(xDiff)./(scale + eps) ); + + %* Estimate new tau value (including safety factors) + tau_old = tau; + tau = safe1*tau_old*errorRatio^(-0.20); + tau = max(tau,tau_old/safe2); + tau = min(tau,safe2*tau_old); + + %* If error is acceptable, return computed values + if (errorRatio < 1) return; end +end + +%* Issue error message if error bound never satisfied +error('ERROR: Adaptive Runge-Kutta routine failed'); + + diff --git a/MatlabRevised/rombf.asv b/MatlabRevised/rombf.asv new file mode 100644 index 0000000..978eb31 --- /dev/null +++ b/MatlabRevised/rombf.asv @@ -0,0 +1,40 @@ +function R = rombf(a,b,N,func,param) +% Function to compute integrals by Romberg algorithm +% R = rombf(a,b,N,func,param) +% Inputs +% a,b Lower and upper bound of the integral +% N Romberg table is N by N +% func Name of integrand function in a string such as +% func='errintg'. The calling sequence is func(x,param) +% param Set of parameters to be passed to function +% Output +% R Romberg table; Entry R(N,N) is best estimate of +% the value of the integral + +%* Compute the first term R(1,1) +h = b - a; % This is the coarsest panel size +np = 1; % Current number of panels +f = str2func(func); % Convert name into function handle +R(1,1) = h/2 * (feval(func,a,param) + feval(func,b,param)); + +%* Loop over the desired number of rows, i = 2,...,N +for i=2:N + + %* Compute the summation in the recursive trapezoidal rule + h = h/2; % Use panels half the previous size + np = 2*np; % Use twice as many panels + sumT = 0; + for k=1:2:np-1 % This for loop goes k=1,3,5,...,np-1 + sumT = sumT + feval(func, a + k*h, param); + end + + %* Compute Romberg table entries R(i,1), R(i,2), ..., R(i,i) + R(i,1) = 1/2 * R(i-1,1) + h * sumT; + m = 1; + for j=2:i + m = 4*m; + R(i,j) = R(i,j-1) + (R(i,j-1) - R(i-1,j-1))/(m-1); + end +end +return; + diff --git a/MatlabRevised/rombf.m b/MatlabRevised/rombf.m new file mode 100644 index 0000000..a44b670 --- /dev/null +++ b/MatlabRevised/rombf.m @@ -0,0 +1,40 @@ +function R = rombf(a,b,N,func,param) +% Function to compute integrals by Romberg algorithm +% R = rombf(a,b,N,func,param) +% Inputs +% a,b Lower and upper bound of the integral +% N Romberg table is N by N +% func Name of integrand function in a string such as +% func='errintg'. The calling sequence is func(x,param) +% param Set of parameters to be passed to function +% Output +% R Romberg table; Entry R(N,N) is best estimate of +% the value of the integral + +%* Compute the first term R(1,1) +h = b - a; % This is the coarsest panel size +np = 1; % Current number of panels +f = str2func(func); % Convert name into function handle +R(1,1) = h/2 * (f(a,param) + f(b,param)); + +%* Loop over the desired number of rows, i = 2,...,N +for i=2:N + + %* Compute the summation in the recursive trapezoidal rule + h = h/2; % Use panels half the previous size + np = 2*np; % Use twice as many panels + sumT = 0; + for k=1:2:np-1 % This for loop goes k=1,3,5,...,np-1 + sumT = sumT + f(a + k*h, param); + end + + %* Compute Romberg table entries R(i,1), R(i,2), ..., R(i,i) + R(i,1) = 1/2 * R(i-1,1) + h * sumT; + m = 1; + for j=2:i + m = 4*m; + R(i,j) = R(i,j-1) + (R(i,j-1) - R(i-1,j-1))/(m-1); + end +end +return; + diff --git a/MatlabRevised/sampler.m b/MatlabRevised/sampler.m new file mode 100644 index 0000000..739e9aa --- /dev/null +++ b/MatlabRevised/sampler.m @@ -0,0 +1,41 @@ +function sampD = sampler(x,v,npart,L,sampD) +% sampler - Function to sample density, velocity and temperature +% Inputs +% x Particle positions +% v Particle velocities +% npart Number of particles +% L System size +% sampD Structure with sampling data +% Outputs +% sampD Structure with sampling data + +%* Compute cell location for each particle +ncell = sampD.ncell; +jx=ceil(ncell*x/L); + +%* Initialize running sums of number, velocity and v^2 +sum_n = zeros(ncell,1); +sum_v = zeros(ncell,3); +sum_v2 = zeros(ncell,1); + +%* For each particle, accumulate running sums for its cell +for ipart=1:npart + jcell = jx(ipart); % Particle ipart is in cell jcell + sum_n(jcell) = sum_n(jcell)+1; + sum_v(jcell,:) = sum_v(jcell,:) + v(ipart,:); + sum_v2(jcell) = sum_v2(jcell) + ... + v(ipart,1)^2 + v(ipart,2)^2 + v(ipart,3)^2; +end + +%* Use current sums to update sample number, velocity +% and temperature +for i=1:3 + sum_v(:,i) = sum_v(:,i)./sum_n(:); +end +sum_v2 = sum_v2./sum_n; +sampD.ave_n = sampD.ave_n + sum_n; +sampD.ave_u = sampD.ave_u + sum_v; +sampD.ave_T = sampD.ave_T + sum_v2 - ... + (sum_v(:,1).^2 + sum_v(:,2).^2 + sum_v(:,3).^2); +sampD.nsamp = sampD.nsamp + 1; +return; diff --git a/MatlabRevised/schro.m b/MatlabRevised/schro.m new file mode 100644 index 0000000..8a1a28c --- /dev/null +++ b/MatlabRevised/schro.m @@ -0,0 +1,77 @@ +% schro - Program to solve the Schrodinger equation +% for a free particle using the Crank-Nicolson scheme +clear all; help schro; % Clear memory and print header + +%% * Initialize parameters (grid spacing, time step, etc.) +i_imag = sqrt(-1); % Imaginary i +N = input('Enter number of grid points: '); +L = 100; % System extends from -L/2 to L/2 +h = L/(N-1); % Grid size +x = h*(0:N-1) - L/2; % Coordinates of grid points +h_bar = 1; mass = 1; % Natural units +tau = input('Enter time step: '); + +%% * Set up the Hamiltonian operator matrix +ham = zeros(N); % Set all elements to zero +coeff = -h_bar^2/(2*mass*h^2); +for i=2:(N-1) + ham(i,i-1) = coeff; + ham(i,i) = -2*coeff; % Set interior rows + ham(i,i+1) = coeff; +end +% First and last rows for periodic boundary conditions +ham(1,N) = coeff; ham(1,1) = -2*coeff; ham(1,2) = coeff; +ham(N,N-1) = coeff; ham(N,N) = -2*coeff; ham(N,1) = coeff; + +%% * Compute the Crank-Nicolson matrix +dCN = ( inv(eye(N) + .5*i_imag*tau/h_bar*ham) * ... + (eye(N) - .5*i_imag*tau/h_bar*ham) ); + +%% * Initialize the wavefunction +x0 = 0; % Location of the center of the wavepacket +velocity = 0.5; % Average velocity of the packet +k0 = mass*velocity/h_bar; % Average wavenumber +sigma0 = L/10; % Standard deviation of the wavefunction +Norm_psi = 1/(sqrt(sigma0*sqrt(pi))); % Normalization +psi = Norm_psi * exp(i_imag*k0*x') .* ... + exp(-(x'-x0).^2/(2*sigma0^2)); + +%% * Plot the initial wavefunction +figure(1); clf; +plot(x,real(psi),'-',x,imag(psi),'--'); +title('Initial wave function'); +xlabel('x'); ylabel('\psi(x)'); legend('Real ','Imag '); +drawnow; pause(1); + +%% * Initialize loop and plot variables +max_iter = L/(velocity*tau); % Particle should circle system +plot_iter = max_iter/20; % Produce 20 curves +p_plot(:,1) = psi.*conj(psi); % Record initial condition +iplot = 1; +figure(2); clf; +axisV = [-L/2 L/2 0 max(p_plot)]; % Fix axis min and max + +%% * Loop over desired number of steps (wave circles system once) +for iter=1:max_iter + + %* Compute new wave function using the Crank-Nicolson scheme + psi = dCN*psi; + + %* Periodically record values for plotting + if( rem(iter,plot_iter) < 1 ) + iplot = iplot+1; + p_plot(:,iplot) = psi.*conj(psi); + plot(x,p_plot(:,iplot)); % Display snap-shot of P(x) + xlabel('x'); ylabel('P(x,t)'); + title(sprintf('Finished %g of %g iterations',iter,max_iter)); + axis(axisV); drawnow; + end + +end + +%% * Plot probability versus position at various times +pFinal = psi.*conj(psi); +plot(x,p_plot(:,1:3:iplot),x,pFinal); +xlabel('x'); ylabel('P(x,t)'); +title('Probability density at various times'); + \ No newline at end of file diff --git a/MatlabRevised/sorter.m b/MatlabRevised/sorter.m new file mode 100644 index 0000000..c63cb71 --- /dev/null +++ b/MatlabRevised/sorter.m @@ -0,0 +1,40 @@ +function sD = sorter(x,L,sD) +% sorter - Function to sort particles into cells +% sD = sorter(x,L,sD) +% Inputs +% x Positions of particles +% L System size +% sD Structure containing sorting lists +% Output +% sD Structure containing sorting lists + +%* Find the cell address for each particle +npart = sD.npart; +ncell = sD.ncell; +jx = floor(x*ncell/L) + 1; +jx = min( jx, ncell*ones(npart,1) ); + +%* Count the number of particles in each cell +sD.cell_n = zeros(ncell,1); +for ipart=1:npart + sD.cell_n( jx(ipart) ) = sD.cell_n( jx(ipart) ) + 1; +end + +%* Build index list as cumulative sum of the +% number of particles in each cell +m=1; +for jcell=1:ncell + sD.index(jcell) = m; + m = m + sD.cell_n(jcell); +end + +%* Build cross-reference list +temp = zeros(ncell,1); % Temporary array +for ipart=1:npart + jcell = jx(ipart); % Cell address of ipart + k = sD.index(jcell) + temp(jcell); + sD.Xref(k) = ipart; + temp(jcell) = temp(jcell) + 1; +end + +return; diff --git a/MatlabRevised/sprfft.asv b/MatlabRevised/sprfft.asv new file mode 100644 index 0000000..f99e840 --- /dev/null +++ b/MatlabRevised/sprfft.asv @@ -0,0 +1,60 @@ +%% sprfft - Program to compute the power spectrum of a +% coupled mass-spring system. +clear; help sprfft; % Clear memory and print header + +%% * Set parameters for the system (initial positions, etc.). +x = input('Enter initial displacement [x1 x2 x3]: '); +v = [0 0 0]; % Masses are initially at rest +state = [x v]; % Positions and velocities; used by rk4 +tau = input('Enter timestep: '); +k_over_m = 1; % Ratio of spring const. over mass + +%% * Loop over the desired number of time steps. +time = 0; % Set initial time +nstep = 1024; % Number of steps in the main loop +nprint = nstep/8; % Number of steps between printing progress +for istep=1:nstep %%% MAIN LOOP %%% + + %* Use Runge-Kutta to find new displacements of the masses. + state = rk4(state,time,tau,@sprrk,k_over_m); + time = time + tau; + + %* Record the positions for graphing and to compute spectra. + xplot(istep,1:3) = state(1:3); % Record positions + tplot(istep) = time; + if( rem(istep,nprint) < 1 ) + fprintf('Finished %g out of %g steps\n',istep,nstep); + end +end + +%% * Graph the displacements of the three masses. +figure(1); clf; % Clear figure 1 window and bring forward +ipr = 1:nprint:nstep; % Used to graph limited number of symbols +plot(tplot(ipr),xplot(ipr,1),'o',tplot(ipr),xplot(ipr,2),'+',... + tplot(ipr),xplot(ipr,3),'*',... + tplot,xplot(:,1),'-',tplot,xplot(:,2),'-.',... + tplot,xplot(:,3),'--'); +legend('Mass #1 ','Mass #2 ','Mass #3 '); +title('Displacement of masses (relative to rest positions)'); +xlabel('Time'); ylabel('Displacement'); +drawnow; + +%% * Calculate the power spectrum of the time series for mass #1 +f(1:nstep) = (0:(nstep-1))/(tau*nstep); % Frequency +x1 = xplot(:,1); % Displacement of mass 1 +x1fft = fft(x1); % Fourier transform of displacement +spect = abs(x1fft).^2; % Power spectrum of displacement + +%% * Apply the Hanning window to the time series and calculate +% the resulting power spectrum +window = 0.5*(1-cos(2*pi*((1:nstep)-1)/nstep)); % Hanning window +x1w = x1 .* window'; % Windowed time series +x1wfft = fft(x1w); % Fourier transf. (windowed data) +spectw = abs(x1wfft).^2; % Power spectrum (windowed data) + +%% * Graph the power spectra for original and windowed data +figure(2); clf; % Clear figure 2 window and bring forward +semilogy(f(1:(nstep/2)),spect(1:(nstep/2)),'-',... + f(1:(nstep/2)),spectw(1:(nstep/2)),'--'); +title('Power spectrum (dashed is windowed data)'); +xlabel('Frequency'); ylabel('Power'); diff --git a/MatlabRevised/sprfft.m b/MatlabRevised/sprfft.m new file mode 100644 index 0000000..a37a921 --- /dev/null +++ b/MatlabRevised/sprfft.m @@ -0,0 +1,60 @@ +%% sprfft - Program to compute the power spectrum of a +% coupled mass-spring system. +clear; help sprfft; % Clear memory and print header + +%% * Set parameters for the system (initial positions, etc.). +x = input('Enter initial displacement [x1 x2 x3]: '); +v = [0 0 0]; % Masses are initially at rest +state = [x v]; % Positions and velocities; used by rk4 +tau = input('Enter timestep: '); +k_over_m = 1; % Ratio of spring const. over mass + +%% * Loop over the desired number of time steps. +time = 0; % Set initial time +nstep = 256; % Number of steps in the main loop +nprint = nstep/8; % Number of steps between printing progress +for istep=1:nstep %%% MAIN LOOP %%% + + %* Use Runge-Kutta to find new displacements of the masses. + state = rk4(state,time,tau,@sprrk,k_over_m); + time = time + tau; + + %* Record the positions for graphing and to compute spectra. + xplot(istep,1:3) = state(1:3); % Record positions + tplot(istep) = time; + if( rem(istep,nprint) < 1 ) + fprintf('Finished %g out of %g steps\n',istep,nstep); + end +end + +%% * Graph the displacements of the three masses. +figure(1); clf; % Clear figure 1 window and bring forward +ipr = 1:nprint:nstep; % Used to graph limited number of symbols +plot(tplot(ipr),xplot(ipr,1),'o',tplot(ipr),xplot(ipr,2),'+',... + tplot(ipr),xplot(ipr,3),'*',... + tplot,xplot(:,1),'-',tplot,xplot(:,2),'-.',... + tplot,xplot(:,3),'--'); +legend('Mass #1 ','Mass #2 ','Mass #3 '); +title('Displacement of masses (relative to rest positions)'); +xlabel('Time'); ylabel('Displacement'); +drawnow; + +%% * Calculate the power spectrum of the time series for mass #1 +f(1:nstep) = (0:(nstep-1))/(tau*nstep); % Frequency +x1 = xplot(:,1); % Displacement of mass 1 +x1fft = fft(x1); % Fourier transform of displacement +spect = abs(x1fft).^2; % Power spectrum of displacement + +%% * Apply the Hanning window to the time series and calculate +% the resulting power spectrum +window = 0.5*(1-cos(2*pi*((1:nstep)-1)/nstep)); % Hanning window +x1w = x1 .* window'; % Windowed time series +x1wfft = fft(x1w); % Fourier transf. (windowed data) +spectw = abs(x1wfft).^2; % Power spectrum (windowed data) + +%% * Graph the power spectra for original and windowed data +figure(2); clf; % Clear figure 2 window and bring forward +semilogy(f(1:(nstep/2)),spect(1:(nstep/2)),'-',... + f(1:(nstep/2)),spectw(1:(nstep/2)),'--'); +title('Power spectrum (dashed is windowed data)'); +xlabel('Frequency'); ylabel('Power'); diff --git a/MatlabRevised/sprrk.m b/MatlabRevised/sprrk.m new file mode 100644 index 0000000..02e9e91 --- /dev/null +++ b/MatlabRevised/sprrk.m @@ -0,0 +1,17 @@ +function deriv = sprrk(s,t,param) +% Returns right-hand side of 3 mass-spring system +% equations of motion +% Inputs +% s State vector [x(1) x(2) ... v(3)] +% t Time (not used) +% param (Spring constant)/(Block mass) +% Output +% deriv [dx(1)/dt dx(2)/dt ... dv(3)/dt] +deriv(1) = s(4); +deriv(2) = s(5); +deriv(3) = s(6); +param2 = -2*param; +deriv(4) = param2*s(1) + param*s(2); +deriv(5) = param2*s(2) + param*(s(1)+s(3)); +deriv(6) = param2*s(3) + param*s(2); +return; diff --git a/MatlabRevised/traffic.asv b/MatlabRevised/traffic.asv new file mode 100644 index 0000000..74c8e27 --- /dev/null +++ b/MatlabRevised/traffic.asv @@ -0,0 +1,90 @@ +%% traffic - Program to solve the generalized Burger +% equation for the traffic at a stop light problem +clear all; help traffic; % Clear memory and print header + +%% * Select numerical parameters (time step, grid spacing, etc.). +method = menu('Choose a numerical method:', ... + 'FTCS','Lax','Lax-Wendroff'); +N = input('Enter the number of grid points: '); +L = 400; % System size (meters) +h = L/N; % Grid spacing for periodic boundary conditions +v_max = 25; % Maximum car speed (m/s) +fprintf('Suggested timestep is %g\n',h/v_max); +tau = input('Enter time step (tau): '); +fprintf('Last car starts moving after %g steps\n', ... + (L/4)/(v_max*tau)); +nstep = input('Enter number of steps: '); +coeff = tau/(2*h); % Coefficient used by all schemes +coefflw = tau^2/(2*h^2); % Coefficient used by Lax-Wendroff + +%% * Set initial and boundary conditions +rho_max = 1.0; % Maximum density +Flow_max = 0.25*rho_max*v_max; % Maximum Flow +% Initial condition is a square pulse from x = -L/4 to x = 0 +rho = zeros(1,N); +for i=round(N/4):round(N/2-1) + rho(i) = rho_max; % Max density in the square pulse +end +rho(round(N/2)) = rho_max/2; % Try running without this line +% Use periodic boundary conditions +ip(1:N) = (1:N)+1; ip(N) = 1; % ip = i+1 with periodic b.c. +im(1:N) = (1:N)-1; im(1) = N; % im = i-1 with periodic b.c. + +%% * Initialize plotting variables. +iplot = 1; +xplot = ((1:N)-1/2)*h - L/2; % Record x scale for plot +rplot(:,1) = rho(:); % Record the initial state +tplot(1) = 0; +figure(1); clf; % Clear figure 1 window and bring forward + +%% * Loop over desired number of steps. +for istep=1:nstep + + %* Compute the flow = (Density)*(Velocity) + Flow = rho .* (v_max*(1 - rho/rho_max)); + + %* Compute new values of density using FTCS, + % Lax or Lax-Wendroff method. + if( method == 1 ) %%% FTCS method %%% + rho(1:N) = rho(1:N) - coeff*(Flow(ip)-Flow(im)); + elseif( method == 2 ) %%% Lax method %%% + rho(1:N) = .5*(rho(ip)+rho(im)) ... + - coeff*(Flow(ip)-Flow(im)); + else %%% Lax-Wendroff method %%% + cp = v_max*(1 - (rho(ip)+rho(1:N))/rho_max); + cm = v_max*(1 - (rho(1:N)+rho(im))/rho_max); + rho(1:N) = rho(1:N) - coeff*(Flow(ip)-Flow(im)) ... + + coefflw*(cp.*(Flow(ip)-Flow(1:N)) ... + - cm.*(Flow(1:N)-Flow(im))); + end + + %* Record density for plotting. + iplot = iplot+1; + rplot(:,iplot) = rho(:); + tplot(iplot) = tau*istep; + + %* Display snap-shot of density versus position + plot(xplot,rho,'-',xplot,Flow/Flow_max,'--'); + xlabel('x'); ylabel('Density and Flow'); + legend('\rho(x,t)','F(x,t)'); + axis([-L/2, L/2, -0.1, 1.1]); + drawnow; +end + +%% * Graph density versus position and time as wire-mesh plot +figure(1); clf; % Clear figure 1 window and bring forward +mesh(tplot,xplot,rplot) +xlabel('t'); ylabel('x'); zlabel('\rho'); +title('Density versus position and time'); +view([100 30]); % Rotate the plot for better view point +pause(1); % Pause 1 second between plots + +%% * Graph contours of density versus position and time. +figure(2); clf; % Clear figure 2 window and bring forward +% Use rot90 function to graph t vs x since +% contour(rplot) graphs x vs t. +clevels = 0:(0.1):1; % Contour levels +cs = contour(xplot,tplot,flipud(rot90(rplot)),clevels); +clabel(cs); % Put labels on contour levels +xlabel('x'); ylabel('time'); title('Density contours'); + diff --git a/MatlabRevised/traffic.m b/MatlabRevised/traffic.m new file mode 100644 index 0000000..74c8e27 --- /dev/null +++ b/MatlabRevised/traffic.m @@ -0,0 +1,90 @@ +%% traffic - Program to solve the generalized Burger +% equation for the traffic at a stop light problem +clear all; help traffic; % Clear memory and print header + +%% * Select numerical parameters (time step, grid spacing, etc.). +method = menu('Choose a numerical method:', ... + 'FTCS','Lax','Lax-Wendroff'); +N = input('Enter the number of grid points: '); +L = 400; % System size (meters) +h = L/N; % Grid spacing for periodic boundary conditions +v_max = 25; % Maximum car speed (m/s) +fprintf('Suggested timestep is %g\n',h/v_max); +tau = input('Enter time step (tau): '); +fprintf('Last car starts moving after %g steps\n', ... + (L/4)/(v_max*tau)); +nstep = input('Enter number of steps: '); +coeff = tau/(2*h); % Coefficient used by all schemes +coefflw = tau^2/(2*h^2); % Coefficient used by Lax-Wendroff + +%% * Set initial and boundary conditions +rho_max = 1.0; % Maximum density +Flow_max = 0.25*rho_max*v_max; % Maximum Flow +% Initial condition is a square pulse from x = -L/4 to x = 0 +rho = zeros(1,N); +for i=round(N/4):round(N/2-1) + rho(i) = rho_max; % Max density in the square pulse +end +rho(round(N/2)) = rho_max/2; % Try running without this line +% Use periodic boundary conditions +ip(1:N) = (1:N)+1; ip(N) = 1; % ip = i+1 with periodic b.c. +im(1:N) = (1:N)-1; im(1) = N; % im = i-1 with periodic b.c. + +%% * Initialize plotting variables. +iplot = 1; +xplot = ((1:N)-1/2)*h - L/2; % Record x scale for plot +rplot(:,1) = rho(:); % Record the initial state +tplot(1) = 0; +figure(1); clf; % Clear figure 1 window and bring forward + +%% * Loop over desired number of steps. +for istep=1:nstep + + %* Compute the flow = (Density)*(Velocity) + Flow = rho .* (v_max*(1 - rho/rho_max)); + + %* Compute new values of density using FTCS, + % Lax or Lax-Wendroff method. + if( method == 1 ) %%% FTCS method %%% + rho(1:N) = rho(1:N) - coeff*(Flow(ip)-Flow(im)); + elseif( method == 2 ) %%% Lax method %%% + rho(1:N) = .5*(rho(ip)+rho(im)) ... + - coeff*(Flow(ip)-Flow(im)); + else %%% Lax-Wendroff method %%% + cp = v_max*(1 - (rho(ip)+rho(1:N))/rho_max); + cm = v_max*(1 - (rho(1:N)+rho(im))/rho_max); + rho(1:N) = rho(1:N) - coeff*(Flow(ip)-Flow(im)) ... + + coefflw*(cp.*(Flow(ip)-Flow(1:N)) ... + - cm.*(Flow(1:N)-Flow(im))); + end + + %* Record density for plotting. + iplot = iplot+1; + rplot(:,iplot) = rho(:); + tplot(iplot) = tau*istep; + + %* Display snap-shot of density versus position + plot(xplot,rho,'-',xplot,Flow/Flow_max,'--'); + xlabel('x'); ylabel('Density and Flow'); + legend('\rho(x,t)','F(x,t)'); + axis([-L/2, L/2, -0.1, 1.1]); + drawnow; +end + +%% * Graph density versus position and time as wire-mesh plot +figure(1); clf; % Clear figure 1 window and bring forward +mesh(tplot,xplot,rplot) +xlabel('t'); ylabel('x'); zlabel('\rho'); +title('Density versus position and time'); +view([100 30]); % Rotate the plot for better view point +pause(1); % Pause 1 second between plots + +%% * Graph contours of density versus position and time. +figure(2); clf; % Clear figure 2 window and bring forward +% Use rot90 function to graph t vs x since +% contour(rplot) graphs x vs t. +clevels = 0:(0.1):1; % Contour levels +cs = contour(xplot,tplot,flipud(rot90(rplot)),clevels); +clabel(cs); % Put labels on contour levels +xlabel('x'); ylabel('time'); title('Density contours'); + diff --git a/MatlabRevised/tri_ge.m b/MatlabRevised/tri_ge.m new file mode 100644 index 0000000..b4632d2 --- /dev/null +++ b/MatlabRevised/tri_ge.m @@ -0,0 +1,35 @@ +function x = tri_ge(a,b) +% Function to solve b = a*x by Gaussian elimination where +% the matrix a is a packed tridiagonal matrix +% Inputs +% a Packed tridiagonal matrix, N by N unpacked +% b Column vector of length N +% Output +% x Solution of b = a*x; Column vector of length N + +%* Check that dimensions of a and b are compatible +[N,M] = size(a); +[NN,MM] = size(b); +if( N ~= NN || MM ~= 1) + error('Problem in tri_GE, inputs are incompatible'); +end + +%* Unpack diagonals of triangular matrix into vectors +alpha(1:N-1) = a(2:N,1); +beta(1:N) = a(1:N,2); +gamma(1:N-1) = a(1:N-1,3); + +%* Perform forward elimination +for i=2:N + coeff = alpha(i-1)/beta(i-1); + beta(i) = beta(i) - coeff*gamma(i-1); + b(i) = b(i) - coeff*b(i-1); +end + +%* Perform back substitution +x(N) = b(N)/beta(N); +for i=N-1:-1:1 + x(i) = (b(i) - gamma(i)*x(i+1))/beta(i); +end +x = x.'; % Transpose x to a column vector +return; diff --git a/MatlabRevised/zeroj.m b/MatlabRevised/zeroj.m new file mode 100644 index 0000000..38f0b2d --- /dev/null +++ b/MatlabRevised/zeroj.m @@ -0,0 +1,21 @@ +function z = zeroj(m_order,n_zero) +% Zeros of the Bessel function J(x) +% Inputs +% m_order = Order of the Bessel function +% n_zero = Index of the zero (first, second, etc.) +% Output +% z = The "n_zero th" zero of the Bessel function + +%* Use asymtotic formula for initial guess +beta = (n_zero + 0.5*m_order - 0.25)*pi; +mu = 4*m_order^2; +z = beta - (mu-1)/(8*beta) - 4*(mu-1)*(7*mu-31)/(3*(8*beta)^3); + +%* Use Newton's method to locate the root +for i=1:5 + jj = bess(m_order+1,z); + % Use the recursion relation to evaluate derivative + deriv = -jj(m_order+2) + m_order/z * jj(m_order+1); + z = z - jj(m_order+1)/deriv; % Newton's root finding +end +return; diff --git a/Misc/Barrow.txt b/Misc/Barrow.txt new file mode 100644 index 0000000..ec277ab --- /dev/null +++ b/Misc/Barrow.txt @@ -0,0 +1,230 @@ + 3.4420000e+02 + 3.4483000e+02 + 3.4520000e+02 + 3.4537000e+02 + 3.4541000e+02 + 3.4542000e+02 + 3.4552000e+02 + 3.4579000e+02 + 3.4621000e+02 + 3.4656000e+02 + 3.4647000e+02 + 3.4551000e+02 + 3.4342000e+02 + 3.4024000e+02 + 3.3650000e+02 + 3.3306000e+02 + 3.3085000e+02 + 3.3045000e+02 + 3.3184000e+02 + 3.3440000e+02 + 3.3720000e+02 + 3.3952000e+02 + 3.4117000e+02 + 3.4239000e+02 + 3.4349000e+02 + 3.4452000e+02 + 3.4539000e+02 + 3.4595000e+02 + 3.4644000e+02 + 3.4701000e+02 + 3.4757000e+02 + 3.4788000e+02 + 3.4782000e+02 + 3.4762000e+02 + 3.4756000e+02 + 3.4767000e+02 + 3.4760000e+02 + 3.4687000e+02 + 3.4518000e+02 + 3.4259000e+02 + 3.3941000e+02 + 3.3615000e+02 + 3.3346000e+02 + 3.3202000e+02 + 3.3224000e+02 + 3.3401000e+02 + 3.3666000e+02 + 3.3931000e+02 + 3.4139000e+02 + 3.4283000e+02 + 3.4391000e+02 + 3.4491000e+02 + 3.4589000e+02 + 3.4655000e+02 + 3.4689000e+02 + 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The +routines supplement the book, "Numerical Methods for Physics", +2nd Ed. (Prentice Hall). + +Original MATLAB Routines - Tested using MATLAB version 5.2. + +Revised MATLAB Routines - Tested using MATLAB version 7.0.1. + +C++ Routines - Tested using Microsoft Visual C++ version 5.0. + +FORTRAN Routines - Tested using Digital Fortran 77 version 4.0. + +These programs are provided for their instructional value. +Although every effort has been made to ensure that they are error +free, neither the author nor the publisher shall be held +responsible or liable for any damage resulting in connection with +or arising from the use of any of these programs. + +******************************************** +These programs are User Contributed Routines which +are being redistributed by The MathWorks, upon request, on an "as +is" basis. A User Contributed Routine is not a product of The +MathWorks, Inc. and The MathWorks assumes no responsibility for +any errors that may exist in these routines. +******************************************** + +If you have any questions or comments, please contact: + +Alejandro Garcia +Dept. Physics +San Jose State University +San Jose CA 95192 +algarcia@algarcia.org diff --git a/Python/.ipynb_checkpoints/Advect-checkpoint.ipynb b/Python/.ipynb_checkpoints/Advect-checkpoint.ipynb new file mode 100644 index 0000000..3fb6eb9 --- /dev/null +++ b/Python/.ipynb_checkpoints/Advect-checkpoint.ipynb @@ -0,0 +1,171 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# advect - Program to solve the advection equation \n", + "# using the various hyperbolic PDE schemes\n", + "\n", + "# Set up configuration options and special features\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "%matplotlib inline" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Select numerical parameters (time step, grid spacing, etc.).\n", + "method = input('Choose a numerical method, 1) FTCS; 2) Lax; 3) Lax-Wendroff :')\n", + "N = input('Enter number of grid points: ')\n", + "L = 1. # System size\n", + "h = L/N # Grid spacing\n", + "c = 1. # Wave speed\n", + "print 'Time for wave to move one grid spacing is ', h/c \n", + "tau = input('Enter time step: ')\n", + "coeff = -c*tau/(2.*h) # Coefficient used by all schemes\n", + "coefflw = 2*coeff**2 # Coefficient used by L-W scheme\n", + "print 'Wave circles system in ', L/(c*tau), ' steps' \n", + "nStep = input('Enter number of steps: ')" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Set initial and boundary conditions.\n", + "sigma = 0.1 # Width of the Gaussian pulse\n", + "k_wave = np.pi/sigma # Wave number of the cosine\n", + "x = np.arange(N)*h - L/2. # Coordinates of grid points\n", + "# Initial condition is a Gaussian-cosine pulse\n", + "a = np.empty(N)\n", + "for i in range(N) :\n", + " a[i] = np.cos(k_wave*x[i]) * np.exp(-x[i]**2/(2*sigma**2)) \n", + "# Use periodic boundary conditions\n", + "ip = np.arange(N) + 1 \n", + "ip[N-1] = 0 # ip = i+1 with periodic b.c.\n", + "im = np.arange(N) - 1 \n", + "im[0] = N-1 # im = i-1 with periodic b.c.\n", + "\n", + "#* Initialize plotting variables.\n", + "iplot = 1 # Plot counter\n", + "nplots = 50; # Desired number of plots\n", + "aplot = np.empty((N,nplots))\n", + "tplot = np.empty(nplots)\n", + "aplot[:,0] = np.copy(a) # Record the initial state\n", + "tplot[0] = 0 # Record the initial time (t=0)\n", + "plotStep = nStep/nplots+1 # Number of steps between plots" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Loop over desired number of steps.\n", + "for iStep in range(nStep): ## MAIN LOOP ##\n", + "\n", + " #* Compute new values of wave amplitude using FTCS, \n", + " #% Lax or Lax-Wendroff method.\n", + " if method == 1 : ### FTCS method ###\n", + " a[:] = a[:] + coeff*( a[ip] - a[im] ) \n", + " elif method == 2 : ### Lax method ###\n", + " a[:] = .5*( a[ip] + a[im] ) + coeff*( a[ip] - a[im] ) \n", + " else: ### Lax-Wendroff method ###\n", + " a[:] = a[:] + coeff*( a[ip] - a[im] ) + coefflw*(\n", + " a[ip] + a[im] -2*a[:] ) \n", + "\n", + " #* Periodically record a(t) for plotting.\n", + " if (iStep+1) % plotStep < 1 : # Every plot_iter steps record \n", + " aplot[:,iplot] = np.copy(a) # Record a(i) for ploting\n", + " tplot[iplot] = tau*iStep\n", + " iplot += 1\n", + " print iStep, ' out of ', nStep, ' steps completed'" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Plot the initial and final states.\n", + "plt.plot(x,aplot[:,0],'-',x,a,'--');\n", + "plt.legend(['Initial ','Final'])\n", + "plt.xlabel('x') \n", + "plt.ylabel('a(x,t)')" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Plot the wave amplitude versus position and time\n", + "from matplotlib import cm\n", + "from mpl_toolkits.mplot3d import Axes3D\n", + "\n", + "fig = plt.figure()\n", + "ax = fig.gca(projection = '3d')\n", + "Tp, Xp = np.meshgrid(tplot[0:iplot], x)\n", + "ax.plot_surface(Tp, Xp, aplot[:,0:iplot], rstride=1, cstride=1, cmap=cm.gray)\n", + "ax.view_init(elev=30., azim=190.)\n", + "ax.set_ylabel('Position') \n", + "ax.set_xlabel('Time')\n", + "ax.set_zlabel('Amplitude')" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python [default]", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.12" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} diff --git a/Python/.ipynb_checkpoints/Balle-checkpoint.ipynb b/Python/.ipynb_checkpoints/Balle-checkpoint.ipynb new file mode 100644 index 0000000..708fe78 --- /dev/null +++ b/Python/.ipynb_checkpoints/Balle-checkpoint.ipynb @@ -0,0 +1,137 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# balle - Program to compute the trajectory of a baseball\n", + "# using the Euler method.\n", + "\n", + "# Set up configuration options and special features\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "%matplotlib inline" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Set initial position and velocity of the baseball\n", + "y1 = input('Enter initial height (meters): ') \n", + "r1 = np.array([0, y1]) # Initial vector position\n", + "speed = input('Enter initial speed (m/s): ')\n", + "theta = input('Enter initial angle (degrees): ') \n", + "v1 = np.array([speed * np.cos(theta*np.pi/180), \n", + " speed * np.sin(theta*np.pi/180)]) # Initial velocity\n", + "r = r1 # Set initial position \n", + "v = v1 # Set initial velocity\n", + "\n", + "#* Set physical parameters (mass, Cd, etc.)\n", + "Cd = 0.35 # Drag coefficient (dimensionless)\n", + "area = 4.3e-3 # Cross-sectional area of projectile (m^2)\n", + "grav = 9.81 # Gravitational acceleration (m/s^2)\n", + "mass = 0.145 # Mass of projectile (kg)\n", + "airFlag = input('Air resistance? (Yes:1, No:0): ')\n", + "if airFlag == 0 :\n", + " rho = 0 # No air resistance\n", + "else:\n", + " rho = 1.2 # Density of air (kg/m^3)\n", + "air_const = -0.5*Cd*rho*area/mass # Air resistance constant" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Loop until ball hits ground or max steps completed\n", + "tau = input('Enter timestep, tau (sec): ') # (sec)\n", + "maxstep = 1000 # Maximum number of steps\n", + "xplot = np.empty(maxstep); yplot = np.empty(maxstep)\n", + "xNoAir = np.empty(maxstep); yNoAir = np.empty(maxstep)\n", + "for istep in range(maxstep):\n", + "\n", + " #* Record position (computed and theoretical) for plotting\n", + " xplot[istep] = r[0] # Record trajectory for plot\n", + " yplot[istep] = r[1]\n", + " t = istep*tau # Current time\n", + " xNoAir[istep] = r1[0] + v1[0]*t\n", + " yNoAir[istep] = r1[1] + v1[1]*t - 0.5*grav*t**2\n", + " \n", + " #* Calculate the acceleration of the ball \n", + " accel = air_const * np.linalg.norm(v) * v # Air resistance\n", + " accel[1] = accel[1] - grav # Gravity\n", + " \n", + " #* Calculate the new position and velocity using Euler method\n", + " r = r + tau*v # Euler step\n", + " v = v + tau*accel \n", + " \n", + " #* If ball reaches ground (y<0), break out of the loop\n", + " if r[1] < 0 : \n", + " laststep = istep+1\n", + " xplot[laststep] = r[0] # Record last values computed\n", + " yplot[laststep] = r[1]\n", + " break # Break out of the for loop" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Print maximum range and time of flight\n", + "print 'Maximum range is', r[0], 'meters' \n", + "print 'Time of flight is', laststep*tau , ' seconds' \n", + "\n", + "#* Graph the trajectory of the baseball\n", + "# Mark the location of the ground by a straight line\n", + "xground = np.array([0., max(xNoAir[0:laststep])])\n", + "yground = np.array([0., 0.])\n", + "# Plot the computed trajectory and parabolic, no-air curve\n", + "plt.plot(xplot[0:laststep+1],yplot[0:laststep+1],'+',\n", + " xNoAir[0:laststep],yNoAir[0:laststep],'-',xground,yground,'r-')\n", + "plt.legend(['Euler method','Theory (No air) ']);\n", + "plt.xlabel('Range (m)')\n", + "plt.ylabel('Height (m)')\n", + "plt.title('Projectile motion')" + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "kernelspec": { + "display_name": "Python [default]", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.12" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} diff --git a/Python/.ipynb_checkpoints/Bess-checkpoint.ipynb b/Python/.ipynb_checkpoints/Bess-checkpoint.ipynb new file mode 100644 index 0000000..997474d --- /dev/null +++ b/Python/.ipynb_checkpoints/Bess-checkpoint.ipynb @@ -0,0 +1,169 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# Program to test the bess function\n", + "\n", + "# Set up configuration options and special features\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "%matplotlib inline" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def bess(m_max,x) :\n", + " # Bessel function\n", + " # Inputs\n", + " # m_max = Largest desired order\n", + " # x = Value at which Bessel function J(x) is evaluated\n", + " # Output\n", + " # jj = Vector of J(x) for all orders <= m_max\n", + "\n", + " #* Perform downward recursion from initial guess\n", + " eps = 1.0e-15\n", + " m_top = max(m_max,x)+15 # Top value of m for recursion\n", + " m_top = int(2*np.ceil( m_top/2 )) # Round up to an even number\n", + " j = np.empty(m_top+1)\n", + " j[m_top] = 0.\n", + " j[m_top-1] = 1.\n", + " for m in reversed(range(m_top-1)) : # Downward recursion\n", + " j[m] = 2.*(m+1)/(x+eps)*j[m+1] - j[m+2]\n", + "\n", + " #* Normalize using identity and return requested values\n", + " norm = j[0] \n", + " for m in range(2,m_top,2) :\n", + " norm = norm + 2*j[m]\n", + " \n", + " jj = np.empty(m_max+1) # Send back only the values for\n", + " for m in range(m_max+1) : # m=0,...,m_max and discard values\n", + " jj[m] = j[m]/norm # for m=m_max+1,...,m_top\n", + " \n", + " return jj" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def zeroj( m_order, n_zero) :\n", + " # Zeros of the Bessel function J(x)\n", + " # Inputs\n", + " # m_order = Order of the Bessel function\n", + " # n_zero = Index of the zero (first, second, etc.)\n", + " # Output\n", + " # z = The \"n_zero th\" zero of the Bessel function\n", + " \n", + " #* Use asymtotic formula for initial guess\n", + " beta = (n_zero + 0.5*m_order - 0.25)*np.pi;\n", + " mu = 4*m_order**2;\n", + " z = beta - (mu-1.)/(8.*beta) - 4.*(mu-1)*(7.*mu-31.)/(3.*(8.*beta)**3);\n", + "\n", + " #* Use Newton's method to locate the root\n", + " jj = np.empty(m_order+2)\n", + " for i in range(5) :\n", + " jj = bess(m_order+1,z) \n", + " # Use the recursion relation to evaluate derivative\n", + " deriv = -jj[m_order+1] + m_order/z * jj[m_order]\n", + " z = z - jj[m_order]/deriv # Newton's root finding \n", + " \n", + " return z" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Enter m: 3\n" + ] + }, + { + "data": { + "image/png": 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jwbgGaNcO8PZ2PFBZtmwZjEYj5s2bB09PT3VnkyZqXkPH6R9N09BgbAOc+vmU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\nxeja0fYFyFYwm8k77yR9fdcQAN9//32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ONapQ1oZDOinOLmZ0ULTFPbBKZmD0KNVTMqry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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "nplot = 200\n", + "xMax = 20.\n", + "m = input(\"Enter m: \")\n", + "x = np.linspace(0.,xMax,nplot)\n", + "\n", + "jj = np.empty((nplot,m+1))\n", + "for i in range(nplot) :\n", + " jj[i,:] = bess(m,x[i])\n", + " \n", + "jZero = np.empty(20)\n", + "for i in range(20) :\n", + " jZero[i] = zeroj(m,i+1)\n", + " if jZero[i] > xMax :\n", + " break\n", + "nZeros = i # Skip the zero that's > xMax\n", + " \n", + "for mi in range(m+1) :\n", + " plt.plot(x,jj[:,mi],'-',jZero[0:nZeros],np.zeros(nZeros),'*')\n", + " plt.xlabel('x')\n", + " plt.ylabel('J_m(x)')" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + } + ], + "metadata": { + "anaconda-cloud": {}, + "kernelspec": { + "display_name": "Python [default]", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.12" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} diff --git a/Python/.ipynb_checkpoints/Dftcs-checkpoint.ipynb b/Python/.ipynb_checkpoints/Dftcs-checkpoint.ipynb new file mode 100644 index 0000000..dde73db --- /dev/null +++ b/Python/.ipynb_checkpoints/Dftcs-checkpoint.ipynb @@ -0,0 +1,159 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# dftcs - Program to solve the diffusion equation \n", + "# using the Forward Time Centered Space (FTCS) scheme.\n", + "\n", + "# Set up configuration options and special features\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "%matplotlib inline" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Initialize parameters (time step, grid spacing, etc.).\n", + "tau = input('Enter time step: ')\n", + "N = input('Enter the number of grid points: ')\n", + "L = 1. # The system extends from x=-L/2 to x=L/2\n", + "h = L/(N-1) # Grid size\n", + "kappa = 1. # Diffusion coefficient\n", + "coeff = kappa*tau/h**2\n", + "if coeff < 0.5 :\n", + " print 'Solution is expected to be stable'\n", + "else:\n", + " print 'WARNING: Solution is expected to be unstable'" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Set initial and boundary conditions.\n", + "tt = np.zeros(N) # Initialize temperature to zero at all points\n", + "tt[int(N/2)] = 1./h # Initial cond. is delta function in center\n", + "## The boundary conditions are tt[0] = tt[N-1] = 0\n", + "\n", + "#* Set up loop and plot variables.\n", + "xplot = np.arange(N)*h - L/2. # Record the x scale for plots\n", + "iplot = 0 # Counter used to count plots\n", + "nstep = 300 # Maximum number of iterations\n", + "nplots = 50 # Number of snapshots (plots) to take\n", + "plot_step = nstep/nplots # Number of time steps between plots" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Loop over the desired number of time steps.\n", + "ttplot = np.empty((N,nplots))\n", + "tplot = np.empty(nplots)\n", + "for istep in range(nstep): ## MAIN LOOP ##\n", + " \n", + " #* Compute new temperature using FTCS scheme.\n", + " tt[1:(N-1)] = ( tt[1:(N-1)] + \n", + " coeff*( tt[2:N] + tt[0:(N-2)] - 2*tt[1:(N-1)] ) )\n", + " \n", + " #* Periodically record temperature for plotting.\n", + " if (istep+1) % plot_step < 1 : # Every plot_step steps\n", + " ttplot[:,iplot] = np.copy(tt) # record tt(i) for plotting\n", + " tplot[iplot] = istep*tau # Record time for plots\n", + " iplot = iplot+1" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Plot temperature versus x and t as a wire-mesh plot\n", + "\n", + "from matplotlib import cm\n", + "from mpl_toolkits.mplot3d import Axes3D\n", + "\n", + "fig = plt.figure()\n", + "ax = fig.gca(projection = '3d')\n", + "Tp, Xp = np.meshgrid(tplot, xplot)\n", + "ax.plot_surface(Tp, Xp, ttplot, rstride=2, cstride=2, cmap=cm.gray)\n", + "ax.set_xlabel('Time')\n", + "ax.set_ylabel('x')\n", + "ax.set_zlabel('T(x,t)')\n", + "ax.set_title('Diffusion of a delta spike')" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Plot temperature versus x and t as a contour plot\n", + "\n", + "levels = np.linspace(0., 10., num=21) \n", + "ct = plt.contour(tplot, xplot, ttplot, levels) \n", + "plt.clabel(ct, fmt='%1.2f') \n", + "plt.xlabel('Time')\n", + "plt.ylabel('x')\n", + "plt.title('Temperature contour plot')" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + } + ], + "metadata": { + "anaconda-cloud": {}, + "kernelspec": { + "display_name": "Python [default]", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.12" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} diff --git a/Python/.ipynb_checkpoints/Dsmceq-checkpoint.ipynb b/Python/.ipynb_checkpoints/Dsmceq-checkpoint.ipynb new file mode 100644 index 0000000..1fd5da9 --- /dev/null +++ b/Python/.ipynb_checkpoints/Dsmceq-checkpoint.ipynb @@ -0,0 +1,422 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# dsmceq - Dilute gas simulation using DSMC algorithm\n", + "# This version illustrates the approach to equilibrium\n", + "\n", + "# Set up configuration options and special features\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "%matplotlib inline" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "class sortList:\n", + " def __init__(self, ncell_in, npart_in):\n", + " self.ncell = ncell_in\n", + " self.npart = npart_in\n", + " self.cell_n = np.zeros(ncell_in, dtype=int)\n", + " self.index = np.empty(ncell_in, dtype=int)\n", + " self.Xref = np.empty(npart_in, dtype=int)" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def sorter(x,L,sD) :\n", + " # sorter - Function to sort particles into cells\n", + " # Inputs\n", + " # x Positions of particles\n", + " # L System size\n", + " # sD Structure containing sorting lists\n", + " # Output\n", + " # sD Structure containing sorting lists\n", + "\n", + " #* Find the cell address for each particle\n", + " npart = sD.npart\n", + " ncell = sD.ncell\n", + " jx = np.empty(npart,dtype=int)\n", + " for ipart in range(npart) :\n", + " jx[ipart] = int( x[ipart]*ncell/L )\n", + " jx[ipart] = min( jx[ipart], (ncell-1) )\n", + "\n", + " #* Count the number of particles in each cell\n", + " sD.cell_n = np.zeros(ncell)\n", + " for ipart in range(npart) :\n", + " sD.cell_n[ jx[ipart] ] += 1\n", + "\n", + " #* Build index list as cumulative sum of the \n", + " # number of particles in each cell\n", + " m = 0\n", + " for jcell in range(ncell) :\n", + " sD.index[jcell] = m\n", + " m += sD.cell_n[jcell]\n", + "\n", + " #* Build cross-reference list\n", + " temp = np.zeros(ncell) # Temporary array\n", + " for ipart in range(npart) :\n", + " jcell = jx[ipart] # Cell address of ipart\n", + " k = sD.index[jcell] + temp[jcell]\n", + " sD.Xref[k] = ipart\n", + " temp[jcell] += 1\n", + "\n", + " return sD" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def colider(v,crmax,tau,selxtra,coeff,sD) :\n", + " # colide - Function to process collisions in cells\n", + " # Inputs\n", + " # v Velocities of the particles\n", + " # crmax Estimated maximum relative speed in a cell\n", + " # tau Time step\n", + " # selxtra Extra selections carried over from last timestep\n", + " # coeff Coefficient in computing number of selected pairs\n", + " # sD Structure containing sorting lists \n", + " # Outputs\n", + " # v Updated velocities of the particles\n", + " # crmax Updated maximum relative speed\n", + " # selxtra Extra selections carried over to next timestep\n", + " # col Total number of collisions processed\n", + "\n", + " ncell = sD.ncell \n", + " col = 0 # Count number of collisions\n", + " vrel = np.empty(3) # Relative velocity for collision pair\n", + " \n", + " #* Loop over cells, processing collisions in each cell\n", + " for jcell in range(ncell) :\n", + " \n", + " #* Skip cells with only one particle\n", + " number = sD.cell_n[jcell]\n", + " if number > 1 : \n", + " \n", + " #* Determine number of candidate collision pairs \n", + " # to be selected in this cell\n", + " select = coeff*number*(number-1)*crmax[jcell] + selxtra[jcell]\n", + " nsel = int(select) # Number of pairs to be selected\n", + " selxtra[jcell] = select-nsel # Carry over any left-over fraction\n", + " crm = crmax[jcell] # Current maximum relative speed\n", + " \n", + " #* Loop over total number of candidate collision pairs\n", + " for isel in range(nsel) :\n", + " \n", + " #* Pick two particles at random out of this cell\n", + " k = int( np.floor( np.random.uniform(0,number) ) )\n", + " kk = int(np.ceil( k + np.random.uniform(0,number-1) ) ) % number\n", + " ip1 = sD.Xref[ k + sD.index[jcell] ] # First particle\n", + " ip2 = sD.Xref[ kk + sD.index[jcell] ] # Second particle\n", + "\n", + " #* Calculate pair's relative speed\n", + " cr = np.linalg.norm( v[ip1,:] - v[ip2,:] ) # Relative speed \n", + " if cr > crm : # If relative speed larger than crm,\n", + " crm = cr # then reset crm to larger value\n", + "\n", + " #* Accept or reject candidate pair according to relative speed\n", + " if cr/crmax[jcell] > np.random.random() :\n", + " #* If pair accepted, select post-collision velocities\n", + " col += 1 # Collision counter\n", + " vcm = 0.5*( v[ip1,:] + v[ip2,:] ) # Center of mass velocity\n", + " cos_th = 1. - 2.*np.random.random() # Cosine and sine of \n", + " sin_th = np.sqrt(1. - cos_th**2) # collision angle theta\n", + " phi = 2*np.pi*np.random.random() # Collision angle phi\n", + " vrel[0] = cr*cos_th # Compute post-collision \n", + " vrel[1] = cr*sin_th*np.cos(phi) # relative velocity\n", + " vrel[2] = cr*sin_th*np.sin(phi)\n", + " v[ip1,:] = vcm + 0.5*vrel # Update post-collision\n", + " v[ip2,:] = vcm - 0.5*vrel # velocities\n", + "\n", + " crmax[jcell] = crm # Update max relative speed \n", + " \n", + " return [v, crmax, selxtra, col]" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Enter number of simulation particles: 50000\n", + "Each particle represents 536.953242836 atoms\n" + ] + } + ], + "source": [ + "#* Initialize constants (particle mass, diameter, etc.)\n", + "boltz = 1.3806e-23 # Boltzmann's constant (J/K)\n", + "mass = 6.63e-26 # Mass of argon atom (kg)\n", + "diam = 3.66e-10 # Effective diameter of argon atom (m)\n", + "T = 273. # Temperature (K)\n", + "density = 1.78 # Density of argon at STP (kg/m^3)\n", + "L = 1e-6 # System size is one micron\n", + "npart = input('Enter number of simulation particles: ')\n", + "eff_num = density/mass*L**3/npart;\n", + "print 'Each particle represents ', eff_num, ' atoms'" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Assign random positions and velocities to particles\n", + "np.random.seed(0) # Initialize random number generator\n", + "x = np.empty(npart)\n", + "for i in range(npart) :\n", + " x[i] = np.random.uniform(0.,L) # Assign random positions\n", + "v_init = np.sqrt(3*boltz*T/mass) # Initial speed\n", + "v = np.zeros((npart,3)) \n", + "for i in range(npart) : # Only x-component is non-zero\n", + " v[i,0] = v_init * (1 - 2*np.floor(2*np.random.random()))" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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SJHWCoUeSJHWCoUeSJHWCoUeSJHWCoUeSJHWCoUeSJHWCoUeSJHWCoUeSJHWCoUeSJHWC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\npAeXaRN6kpwAvBR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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#* Plot the initial speed distribution\n", + "vmag = np.sqrt( v[:,0]**2 + v[:,1]**2 + v[:,2]**2 )\n", + "plt.hist( vmag, bins=20, range=(0,1000))\n", + "plt.title('Initial speed distribution')\n", + "plt.xlabel('Speed (m/s)')\n", + "plt.ylabel('Number')" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Initialize variables used for evaluating collisions\n", + "ncell = 15 # Number of cells\n", + "tau = 0.2*(L/ncell)/v_init # Set timestep tau\n", + "vrmax = 3*v_init*np.ones(ncell) # Estimated max rel. speed\n", + "selxtra = np.zeros(ncell) # Used by routine \"colider\"\n", + "coeff = 0.5*eff_num*np.pi*diam**2*tau/(L**3/ncell)\n", + "coltot = 0 # Count total collisions\n", + "\n", + "#* Declare sortList object for lists used in sorting\n", + "sortData = sortList(ncell, npart)" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Enter total number of time steps: 50\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "C:\\Users\\Alejandro\\Anaconda2\\lib\\site-packages\\ipykernel\\__main__.py:35: VisibleDeprecationWarning: using a non-integer number instead of an integer will result in an error in the future\n", + "C:\\Users\\Alejandro\\Anaconda2\\lib\\site-packages\\ipykernel\\__main__.py:41: VisibleDeprecationWarning: using a non-integer number instead of an integer will result in an error in the future\n" + ] + }, + { + "data": { + "image/png": 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snyP6tJ+SJGmaTLal553A15I8D7gUuE8rSCnlzRNZWTO2zqgBrJRyJHDkKMvv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\n0CR3Un9hebz77xruf1vzpcD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wf0Q8BhARZ0saTZozZjywCDgoIjYVypgDbAYWkCbWuwE4oWo/R5Im1ruJNLHe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\nPCDpr0hJxWXAUYCAj0bEJqBT0ouBr/V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LgMOAN0raLcd0APsAH42IWyLi18Ac4CBJU5t/hGZmZtYsQ05oJG0h6TpJOze4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\np4CZwAuBAyLiiqqYU4EjgEn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ZZ5uBSwb5nm/q61GKfUsut7fYHxTi5pBWn74/1/EJUlLxYQqrNRfiRRoLs6Sfer40l/mb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\nljSp2ednZmZmzdUWCQ0wCfg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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#* Loop for the desired number of time steps\n", + "nstep = input('Enter total number of time steps: ')\n", + "for istep in range(nstep) :\n", + "\n", + " #* Move all the particles ballistically\n", + " x = x + v[:,0]*tau # Update x position of particle\n", + " x = np.remainder( x+L, L) # Periodic boundary conditions\n", + "\n", + " #* Sort the particles into cells\n", + " sortData = sorter(x,L,sortData);\n", + " \n", + " #* Evaluate collisions among the particles\n", + " [v, vrmax, selxtra, col] = colider(v,vrmax,tau,selxtra,coeff,sortData)\n", + " coltot = coltot + col \n", + " \n", + " #* Periodically display the current progress\n", + " if (istep+1) % 10 < 1 :\n", + " vmag = np.sqrt( v[:,0]**2 + v[:,1]**2 + v[:,2]**2 )\n", + " plt.hist( vmag, bins=20, range=(0,1000))\n", + " plt.title('Done %d of %d steps; %d collisions' % (istep, nstep, coltot))\n", + " plt.xlabel('Speed (m/s)')\n", + " plt.ylabel('Number')\n", + " plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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y66iPVJIkTRpjHWj+DLhnhJ/5GXAK9bHN84CvAlckmQOQ5BTgrcCbqPe/eQBY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\n3JrkV0m+neT3J7pNbZXk3Um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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#* Plot the initial speed distribution\n", + "vmag = np.sqrt( v[:,0]**2 + v[:,1]**2 + v[:,2]**2 )\n", + "plt.hist( vmag, bins=20, range=(0,1000))\n", + "plt.title('Final speed distribution')\n", + "plt.xlabel('Speed (m/s)')\n", + "plt.ylabel('Number')" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + } + ], + "metadata": { + "anaconda-cloud": {}, + "kernelspec": { + "display_name": "Python [default]", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.12" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} diff --git a/Python/.ipynb_checkpoints/Fftpoi-checkpoint.ipynb b/Python/.ipynb_checkpoints/Fftpoi-checkpoint.ipynb new file mode 100644 index 0000000..43e7c5e --- /dev/null +++ b/Python/.ipynb_checkpoints/Fftpoi-checkpoint.ipynb @@ -0,0 +1,223 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# fftpoi - Program to solve the Poisson equation using \n", + "# MFT method (periodic boundary conditions)\n", + "\n", + "# Set up configuration options and special features\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "%matplotlib inline" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "System is a square of length 1.0\n" + ] + } + ], + "source": [ + "#* Initialize parameters (system size, grid spacing, etc.)\n", + "eps0 = 8.8542e-12 # Permittivity (C^2/(N m^2))\n", + "N = 50 # Number of grid points on a side (square grid)\n", + "L = 1. # System size\n", + "h = L/N # Grid spacing for periodic boundary conditions\n", + "x = np.arange(N)*h # Coordinates of grid points\n", + "y = np.copy(x) # Square grid\n", + "print 'System is a square of length ', L" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Enter number of line charges: 2\n", + " For charge # 0\n", + "Enter position [x, y]: [.5, .55]\n", + "Enter charge density: 1\n", + " For charge # 1\n", + "Enter position [x, y]: [.5, .45]\n", + "Enter charge density: -1\n" + ] + } + ], + "source": [ + "#* Set up charge density rho(i,j) \n", + "rho = np.zeros((N,N)); # Initialize charge density to zero\n", + "M = input('Enter number of line charges: ')\n", + "for i in range(M) :\n", + " print ' For charge #', i\n", + " r = input('Enter position [x, y]: ') \n", + " ii=int(r[0]/h + 0.5) # Place charge at nearest\n", + " jj=int(r[1]/h + 0.5) # grid point\n", + " q = input('Enter charge density: ') \n", + " rho[ii,jj] += q/h**2" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Compute matrix P\n", + "cx = np.cos( (2*np.pi/N) * np.arange(N) )\n", + "cy = np.copy(cx)\n", + "numerator = -h**2/(2.*eps0)\n", + "tinyNumber = 1e-20; # Avoids division by zero\n", + "P = np.empty((N,N))\n", + "for i in range(N) :\n", + " for j in range(N) :\n", + " P[i,j] = numerator/(cx[i]+cy[j]-2.+tinyNumber)" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Compute potential using MFT method\n", + "rhoT = np.fft.fft2(rho) # Transform rho into wavenumber domain\n", + "phiT = rhoT * P # Computing phi in the wavenumber domain\n", + "phi = np.fft.ifft2(phiT); # Inv. transf. phi into the coord. domain\n", + "phi = np.real(phi); # Clean up imaginary part due to round-off\n", + "\n", + "#* Compute electric field as E = - grad phi\n", + "[Ex, Ey] = np.gradient(np.flipud(np.rot90(phi))) \n", + "for i in range(N) :\n", + " for j in range(N) :\n", + " magnitude = np.sqrt(Ex[i,j]**2 + Ey[i,j]**2) \n", + " Ex[i,j] /= -magnitude # Normalize components so\n", + " Ey[i,j] /= -magnitude # vectors have equal length" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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ZjaLebXOenZ3ljDPOCGy89773vXzve9/jZz/7GZs3bw5sXCGEtqYF2TTNYnBA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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#* Plot potential\n", + "from matplotlib import cm\n", + "from mpl_toolkits.mplot3d import Axes3D\n", + "\n", + "fig = plt.figure()\n", + "ax = fig.gca(projection = '3d')\n", + "Xp, Yp = np.meshgrid(x, y)\n", + "ax.contour(Xp,Yp,np.flipud(np.rot90(phi)),35)\n", + "ax.set_xlabel('x')\n", + "ax.set_ylabel('y')\n", + "ax.set_zlabel('Phi(x,y)')" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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GjeDt7Q1ZVsY4cXd3R/fu3aHTKQ/6HR0dMXjwYCQkKMMFp6en4/3330dBgfL8Oy0tDb6+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\nKrYM5eXluu1R3f52FV9WViZVSlW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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#* Plot electric field\n", + "plt.quiver(Xp,Yp,Ey,Ex) # Plot E field with vectors\n", + "plt.title('E field (Direction)'); \n", + "plt.xlabel('x')\n", + "plt.ylabel('y');\n", + "plt.axis('square'); \n", + "plt.axis([0., L, 0., L]);" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python [default]", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.12" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} diff --git a/Python/.ipynb_checkpoints/Ftdemo-checkpoint.ipynb b/Python/.ipynb_checkpoints/Ftdemo-checkpoint.ipynb new file mode 100644 index 0000000..48dc376 --- /dev/null +++ b/Python/.ipynb_checkpoints/Ftdemo-checkpoint.ipynb @@ -0,0 +1,147 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# ftdemo - Discrete Fourier transform demonstration program\n", + "\n", + "# Set up configuration options and special features\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "%matplotlib inline" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Initialize the sine wave time series to be transformed.\n", + "N = input('Enter the number of points: ')\n", + "freq = input('Enter frequency of the sine wave: ')\n", + "phase = input('Enter phase of the sine wave: ')\n", + "tau = 1. # Time increment\n", + "t = np.arange(N)*tau # t = [0, tau, 2*tau, ... ]\n", + "y = np.empty(N)\n", + "for i in range(N): # Sine wave time series\n", + " y[i] = np.sin(2*np.pi*t[i]*freq + phase) \n", + "f = np.arange(N)/(N*tau) # f = [0, 1/(N*tau), ... ] " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Compute the transform using desired method: direct summation\n", + "# or fast Fourier transform (FFT) algorithm.\n", + "yt = np.zeros(N,dtype=complex)\n", + "Method = input('Compute transform by: 1) Direct summation; 2) FFT :')\n", + "\n", + "import time\n", + "startTime = time.time()\n", + "if Method == 1 : # Direct summation\n", + " twoPiN = -2. * np.pi * (1j) /N\n", + " for k in range(N):\n", + " for j in range(N):\n", + " expTerm = np.exp( twoPiN*j*k )\n", + " yt[k] += y[j] * expTerm\n", + "else: # Fast Fourier transform\n", + " yt = np.fft.fft(y)\n", + "\n", + "stopTime = time.time()\n", + "\n", + "print 'Elapsed time = ', stopTime - startTime, ' seconds'" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Graph the time series and its transform.\n", + "plt.plot(t,y)\n", + "plt.title('Original time series')\n", + "plt.xlabel('Time')\n", + "plt.ylabel('Amplitude') " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "plt.plot(f,np.real(yt),'-',f,np.imag(yt),'--')\n", + "plt.legend(['Real','Imaginary '])\n", + "plt.title('Fourier transform')\n", + "plt.xlabel('Frequency')\n", + "plt.ylabel('Transform')" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Compute and graph the power spectrum of the time series\n", + "powspec = np.empty(N)\n", + "for i in range(N):\n", + " powspec[i] = abs(yt[i])**2\n", + "plt.semilogy(f,powspec,'-')\n", + "plt.title('Power spectrum (unnormalized)')\n", + "plt.xlabel('Frequency')\n", + "plt.ylabel('Power')" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python [default]", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.12" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} diff --git a/Python/.ipynb_checkpoints/Interp-checkpoint.ipynb b/Python/.ipynb_checkpoints/Interp-checkpoint.ipynb new file mode 100644 index 0000000..0a08b64 --- /dev/null +++ b/Python/.ipynb_checkpoints/Interp-checkpoint.ipynb @@ -0,0 +1,132 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# interp - Program to interpolate data using Lagrange \n", + "# polynomial to fit quadratic to three data points\n", + "\n", + "# Set up configuration options and special features\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "%matplotlib inline" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def intrpf(xi,x,y):\n", + " # Function to interpolate between data points\n", + " # using Lagrange polynomial (quadratic)\n", + " # Inputs\n", + " # x Vector of x coordinates of data points (3 values)\n", + " # y Vector of y coordinates of data points (3 values)\n", + " # xi The x value where interpolation is computed\n", + " # Output\n", + " # yi The interpolation polynomial evaluated at xi\n", + "\n", + " #* Calculate yi = p(xi) using Lagrange polynomial\n", + " yi = ( (xi-x[1])*(xi-x[2])/((x[0]-x[1])*(x[0]-x[2])) * y[0] \n", + " + (xi-x[0])*(xi-x[2])/((x[1]-x[0])*(x[1]-x[2])) * y[1] \n", + " + (xi-x[0])*(xi-x[1])/((x[2]-x[0])*(x[2]-x[1])) * y[2] )\n", + " return yi" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Initialize the data points to be fit by quadratic\n", + "x = np.empty(3)\n", + "y = np.empty(3)\n", + "print 'Enter data points as x,y pairs (e.g., [1, 2])'\n", + "for i in range(3):\n", + " temp = np.array(input('Enter data point: '))\n", + " x[i] = temp[0]\n", + " y[i] = temp[1]" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Establish the range of interpolation (from x_min to x_max)\n", + "xr = np.array(input('Enter range of x values as [x_min, x_max]: '))" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Find yi for the desired interpolation values xi using\n", + "# the function intrpf\n", + "nplot = 100 # Number of points for interpolation curve\n", + "xi = np.empty(nplot)\n", + "yi = np.empty(nplot)\n", + "for i in range(nplot) :\n", + " xi[i] = xr[0] + (xr[1]-xr[0])* i/float(nplot)\n", + " yi[i] = intrpf(xi[i], x, y) # Use intrpf function to interpolate" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Plot the curve given by (xi,yi) and mark original data points\n", + "plt.plot(x,y,'*',xi,yi,'-')\n", + "plt.xlabel('x')\n", + "plt.ylabel('y')\n", + "plt.title('Three point interpolation')\n", + "plt.legend(['Data points','Interpolation '])" + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "kernelspec": { + "display_name": "Python [default]", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.12" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} diff --git a/Python/.ipynb_checkpoints/Legndr-checkpoint.ipynb b/Python/.ipynb_checkpoints/Legndr-checkpoint.ipynb new file mode 100644 index 0000000..51766f1 --- /dev/null +++ b/Python/.ipynb_checkpoints/Legndr-checkpoint.ipynb @@ -0,0 +1,117 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Populating the interactive namespace from numpy and matplotlib\n" + ] + } + ], + "source": [ + "# test_legndr - Program to test the legndr function\n", + "\n", + "# Set up configuration options and special features\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "%matplotlib inline" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def legndr(n,x) :\n", + " # Legendre polynomials function\n", + " # Inputs \n", + " # n = Highest order polynomial returned\n", + " # x = Value at which polynomial is evaluated\n", + " # Output\n", + " # p = Vector containing P(x) for order 0,1,...,n\n", + "\n", + " #* Perform upward recursion\n", + " p = np.empty(n+1)\n", + " p[0] = 1. # P(x) for n=0\n", + " if n == 0 :\n", + " return p\n", + " p[1] = x # P(x) for n=1\n", + " if n == 1 :\n", + " return p\n", + " \n", + " # Use upward recursion to obtain other n's\n", + " for i in range(1,n) :\n", + " p[i+1] = ((2*i+1)*x*p[i] - i*p[i-1])/(i+1)\n", + "\n", + " return p" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Enter x: 3.\n", + "For n=0; Computed = 1.0 Expected = 1\n", + "For n=1; Computed = 3.0 Expected = 3.0\n", + "For n=2; Computed = 13.0 Expected = 13.0\n", + "For n=3; Computed = 63.0 Expected = 63.0\n", + "For n=4; Computed = 321.0 Expected = 321.0\n", + "For n=5; Computed = 1683.0 Expected = 1683.0\n" + ] + } + ], + "source": [ + "x = input(\"Enter x: \")\n", + "n = 5\n", + "\n", + "p = np.empty(n)\n", + "p = legndr(n,x)\n", + "\n", + "print \"For n=0; Computed = \", p[0], \" Expected = 1\"\n", + "print \"For n=1; Computed = \", p[1], \" Expected = \", x\n", + "print \"For n=2; Computed = \", p[2], \" Expected = \", 0.5*(3*x*x-1)\n", + "print \"For n=3; Computed = \", p[3], \" Expected = \", 0.5*(5*x*x*x-3*x)\n", + "print \"For n=4; Computed = \", p[4], \" Expected = \", 0.125*(35*x*x*x*x-30*x*x+3)\n", + "print \"For n=5; Computed = \", p[5], \" Expected = \", 0.125*(63*x*x*x*x*x-70*x*x*x+15*x) " + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python [default]", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.12" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} diff --git a/Python/.ipynb_checkpoints/Lorenz-checkpoint.ipynb b/Python/.ipynb_checkpoints/Lorenz-checkpoint.ipynb new file mode 100644 index 0000000..e77c34a --- /dev/null +++ b/Python/.ipynb_checkpoints/Lorenz-checkpoint.ipynb @@ -0,0 +1,272 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# lorenz - Program to compute the trajectories of the Lorenz \n", + "# equations using the adaptive Runge-Kutta method.\n", + "\n", + "# Set up configuration options and special features\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "%matplotlib inline" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def rk4(x,t,tau,derivsRK,param):\n", + " # Runge-Kutta integrator (4th order)\n", + " # Input arguments -\n", + " # x = current value of dependent variable\n", + " # t = independent variable (usually time)\n", + " # tau = step size (usually timestep)\n", + " # derivsRK = right hand side of the ODE; derivsRK is the\n", + " # name of the function which returns dx/dt\n", + " # Calling format derivsRK (x,t,param).\n", + " # param = extra parameters passed to derivsRK\n", + " # Output arguments -\n", + " # xout = new value of x after a step of size tau\n", + " \n", + " half_tau = 0.5*tau\n", + " F1 = derivsRK(x,t,param) \n", + " t_half = t + half_tau\n", + " xtemp = x + half_tau*F1\n", + " F2 = derivsRK(xtemp,t_half,param) \n", + " xtemp = x + half_tau*F2\n", + " F3 = derivsRK(xtemp,t_half,param)\n", + " t_full = t + tau\n", + " xtemp = x + tau*F3\n", + " F4 = derivsRK(xtemp,t_full,param)\n", + " xout = x + tau/6.*(F1 + F4 + 2.*(F2+F3))\n", + " return xout" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def rka(x,t,tau,err,derivsRK,param):\n", + " # Adaptive Runge-Kutta routine\n", + " # Inputs\n", + " # x Current value of the dependent variable\n", + " # t Independent variable (usually time)\n", + " # tau Step size (usually time step)\n", + " # err Desired fractional local truncation error\n", + " # derivsRK Right hand side of the ODE; derivsRK is the\n", + " # name of the function which returns dx/dt\n", + " # Calling format derivsRK (x,t,param).\n", + " # param Extra parameters passed to derivsRK\n", + " # Outputs\n", + " # xSmall New value of the dependent variable\n", + " # t New value of the independent variable\n", + " # tau Suggested step size for next call to rka\n", + "\n", + " #* Set initial variables\n", + " tSave, xSave = t, x # Save initial values\n", + " safe1, safe2 = 0.9, 4.0 # Safety factors\n", + " eps = 1.e-15\n", + "\n", + " #* Loop over maximum number of attempts to satisfy error bound\n", + " xTemp = np.empty(len(x))\n", + " xSmall = np.empty(len(x)); xBig = np.empty(len(x))\n", + " maxTry = 100\n", + " for iTry in range(maxTry):\n", + "\n", + " #* Take the two small time steps\n", + " half_tau = 0.5 * tau\n", + " xTemp = rk4(xSave,tSave,half_tau,derivsRK,param)\n", + " t = tSave + half_tau\n", + " xSmall = rk4(xTemp,t,half_tau,derivsRK,param)\n", + " \n", + " #* Take the single big time step\n", + " t = tSave + tau\n", + " xBig = rk4(xSave,tSave,tau,derivsRK,param)\n", + " \n", + " #* Compute the estimated truncation error\n", + " scale = err * (abs(xSmall) + abs(xBig))/2.\n", + " xDiff = xSmall - xBig\n", + " errorRatio = np.max( np.absolute(xDiff) / (scale + eps) )\n", + " \n", + " #* Estimate new tau value (including safety factors)\n", + " tau_old = tau\n", + " tau = safe1*tau_old*errorRatio**(-0.20)\n", + " tau = max(tau, tau_old/safe2)\n", + " tau = min(tau, safe2*tau_old)\n", + " \n", + " #* If error is acceptable, return computed values\n", + " if errorRatio < 1 :\n", + " return np.array([xSmall, t, tau]) \n", + "\n", + " #* Issue error message if error bound never satisfied\n", + " print 'ERROR: Adaptive Runge-Kutta routine failed'\n", + " return np.array([xSmall, t, tau])" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def lorzrk(s,t,param):\n", + " # Returns right-hand side of Lorenz model ODEs\n", + " # Inputs\n", + " # s State vector [x y z]\n", + " # t Time (not used)\n", + " # param Parameters [r sigma b]\n", + " # Output\n", + " # deriv Derivatives [dx/dt dy/dt dz/dt]\n", + "\n", + " #* For clarity, unravel input vectors\n", + " x, y, z = s[0], s[1], s[2]\n", + " r = param[0]\n", + " sigma = param[1]\n", + " b = param[2]\n", + "\n", + " #* Return the derivatives [dx/dt dy/dt dz/dt]\n", + " deriv = np.empty(3)\n", + " deriv[0] = sigma*(y-x)\n", + " deriv[1] = r*x - y - x*z\n", + " deriv[2] = x*y - b*z\n", + " return deriv" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Set initial state x,y,z and parameters r,sigma,b\n", + "state = np.array(input('Enter the initial position [x, y, z]: '))\n", + "r = input('Enter the parameter r: ')\n", + "sigma = 10. # Parameter sigma\n", + "b = 8./3. # Parameter b\n", + "param = np.array([r, sigma, b]) # Vector of parameters passed to rka\n", + "tau = 1. # Initial guess for the timestep\n", + "err = 1.e-3 # Error tolerance" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Loop over the desired number of steps\n", + "time = 0.\n", + "nstep = input('Enter number of steps: ')\n", + "tplot = np.empty(nstep)\n", + "tauplot = np.empty(nstep)\n", + "xplot, yplot, zplot = np.empty(nstep), np.empty(nstep), np.empty(nstep)\n", + "for istep in range(nstep):\n", + "\n", + " #* Record values for plotting\n", + " x, y, z = state[0], state[1], state[2]\n", + " tplot[istep] = time\n", + " tauplot[istep] = tau \n", + " xplot[istep] = x \n", + " yplot[istep] = y \n", + " zplot[istep] = z \n", + " if istep % 50 < 1 :\n", + " print 'Finished ',istep, ' steps out of ',nstep\n", + "\n", + " #* Find new state using adaptive Runge-Kutta\n", + " [state, time, tau] = rka(state,time,tau,err,lorzrk,param);" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Print max and min time step returned by rka\n", + "print 'Adaptive time step: Max = ', np.max(tauplot[2:nstep]), \n", + "' Min = ', np.min(tauplot[2:nstep])\n", + "\n", + "#* Graph the time series x(t)\n", + "plt.plot(tplot,xplot,'-')\n", + "plt.xlabel('Time')\n", + "plt.ylabel('x(t)')\n", + "plt.title('Lorenz model time series')" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Graph the x,y,z phase space trajectory\n", + "# Mark the location of the three steady states\n", + "x_ss = np.empty(3); y_ss = np.empty(3); z_ss = np.empty(3)\n", + "x_ss[0] = 0\n", + "y_ss[0] = 0\n", + "z_ss[0] = 0\n", + "x_ss[1] = np.sqrt(b*(r-1))\n", + "y_ss[1] = x_ss[1]\n", + "z_ss[1] = r-1\n", + "x_ss[2] = -np.sqrt(b*(r-1))\n", + "y_ss[2] = x_ss[2]\n", + "z_ss[2] = r-1\n", + "\n", + "from mpl_toolkits.mplot3d import Axes3D\n", + "fig = plt.figure()\n", + "ax = fig.gca(projection='3d')\n", + "ax.plot(xplot,yplot,zplot,'-')\n", + "ax.plot(x_ss,y_ss,z_ss,'*')\n", + "ax.set_xlabel('x')\n", + "ax.set_ylabel('y')\n", + "ax.set_zlabel('z')\n", + "ax.set_title('Lorenz model phase space')" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python [default]", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.12" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} diff --git a/Python/.ipynb_checkpoints/Lsfdemo-checkpoint.ipynb b/Python/.ipynb_checkpoints/Lsfdemo-checkpoint.ipynb new file mode 100644 index 0000000..5943fe7 --- /dev/null +++ b/Python/.ipynb_checkpoints/Lsfdemo-checkpoint.ipynb @@ -0,0 +1,264 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# lsfdemo - Program for demonstrating least squares fit routines\n", + "\n", + "# Set up configuration options and special features\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "%matplotlib inline" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def linreg(x,y,sigma):\n", + " # Function to perform linear regression (fit a line)\n", + " # Inputs\n", + " # x Independent variable\n", + " # y Dependent variable\n", + " # sigma Estimated error in y\n", + " # Outputs\n", + " # a_fit Fit parameters; a(1) is intercept, a(2) is slope\n", + " # sig_a Estimated error in the parameters a()\n", + " # yy Curve fit to the data\n", + " # chisqr Chi squared statistic\n", + "\n", + " #* Evaluate various sigma sums\n", + " s = 0; sx = 0; sy = 0; sxy = 0; sxx = 0\n", + " for i in range(len(x)):\n", + " sigmaTerm = sigma[i]**(-2)\n", + " s += sigmaTerm \n", + " sx += x[i] * sigmaTerm\n", + " sy += y[i] * sigmaTerm\n", + " sxy += x[i] * y[i] * sigmaTerm\n", + " sxx += x[i]**2 * sigmaTerm\n", + " denom = s*sxx - sx**2\n", + "\n", + " #* Compute intercept a_fit(1) and slope a_fit(2)\n", + " a_fit = np.empty(2)\n", + " a_fit[0] = (sxx*sy - sx*sxy)/denom\n", + " a_fit[1] = (s*sxy - sx*sy)/denom\n", + "\n", + " #* Compute error bars for intercept and slope\n", + " sig_a = np.empty(2)\n", + " sig_a[0] = np.sqrt(sxx/denom)\n", + " sig_a[1] = np.sqrt(s/denom)\n", + "\n", + " #* Evaluate curve fit at each data point and compute Chi^2\n", + " yy = np.empty(len(x))\n", + " chisqr = 0.\n", + " for i in range(len(x)):\n", + " yy[i] = a_fit[0]+a_fit[1]*x[i] # Curve fit to the data\n", + " chisqr += ((y[i]-yy[i])/sigma[i])**2 # Chi square\n", + " return [a_fit, sig_a, yy, chisqr]" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def pollsf(x, y, sigma, M):\n", + " # Function to fit a polynomial to data\n", + " # Inputs \n", + " # x Independent variable\n", + " # y Dependent variable\n", + " # sigma Estimate error in y\n", + " # M Number of parameters used to fit data\n", + " # Outputs\n", + " # a_fit Fit parameters; a(1) is intercept, a(2) is slope\n", + " # sig_a Estimated error in the parameters a()\n", + " # yy Curve fit to the data\n", + " # chisqr Chi squared statistic\n", + "\n", + " #* Form the vector b and design matrix A \n", + " N = len(x)\n", + " b = np.empty(N)\n", + " A = np.empty((N,M))\n", + " for i in range(N):\n", + " b[i] = y[i]/sigma[i]\n", + " for j in range(M):\n", + " A[i,j] = x[i]**j / sigma[i] \n", + "\n", + " #* Compute the correlation matrix C \n", + " C = np.linalg.inv( np.dot( np.transpose(A), A) )\n", + "\n", + " #* Compute the least squares polynomial coefficients a_fit\n", + " a_fit = np.dot(C, np.dot( np.transpose(A), np.transpose(b)) )\n", + "\n", + " #* Compute the estimated error bars for the coefficients\n", + " sig_a = np.empty(M)\n", + " for j in range(M):\n", + " sig_a[j] = np.sqrt(C[j,j])\n", + "\n", + " #* Evaluate curve fit at each data point and compute Chi^2\n", + " yy = np.zeros(N)\n", + " chisqr = 0.\n", + " for i in range(N):\n", + " for j in range(M):\n", + " yy[i] += a_fit[j]*x[i]**j # yy is the curve fit\n", + " chisqr += ((y[i]-yy[i]) / sigma[i])**2\n", + " \n", + " return [a_fit, sig_a, yy, chisqr]" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Curve fit data is created using the quadratic\n", + " y(x) = c(0) + c(1)*x + c(2)*x**2\n", + "Enter the coefficients as [c(0) c(1) c(2)]: [2., .5, 0.]\n", + "Enter estimated error bar: 2\n" + ] + } + ], + "source": [ + "#* Initialize data to be fit. Data is quadratic plus random number.\n", + "print 'Curve fit data is created using the quadratic'\n", + "print ' y(x) = c(0) + c(1)*x + c(2)*x**2'\n", + "c = np.array(input('Enter the coefficients as [c(0) c(1) c(2)]: '))\n", + "N = 50; # Number of data points\n", + "x = np.arange(1,N+1) # x = [1, 2, ..., N]\n", + "y = np.empty(N)\n", + "sigma = np.empty(N)\n", + "np.random.seed(0) # Initialize random number generator\n", + "alpha = input('Enter estimated error bar: ')\n", + "for i in range(N):\n", + " r = alpha * np.random.normal() # Gaussian distributed random vector\n", + " y[i] = c[0] + c[1]*x[i] + c[2]*x[i]**2 + r\n", + " sigma[i] = alpha # Constant error bar" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Enter number of fit parameters (=2 for line): 2\n" + ] + } + ], + "source": [ + "#* Fit the data to a straight line or a more general polynomial\n", + "M = input('Enter number of fit parameters (=2 for line): ')\n", + "if M == 2 : \n", + " #* Linear regression (Straight line) fit\n", + " [a_fit, sig_a, yy, chisqr] = linreg(x,y,sigma)\n", + "else: \n", + " #* Polynomial fit\n", + " [a_fit, sig_a, yy, chisqr] = pollsf(x,y,sigma,M)" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Fit parameters:\n", + " a[ 0 ] = 1.52564172087 +/- 0.574278606921\n", + " a[ 1 ] = 0.516601120906 +/- 0.019599838302\n" + ] + }, + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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ResNfRaQz7gdiaODJXuvIEcB6rwUrsPxe3BXaY6o6vJR6LQYuEJEDvSt8xGUWvAp3K2JJ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\n6BAREZFAKHSIiIhIIBQ6JCEKCgrCHkKjozkPnuY8eJrz1JZ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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#* Print out the fit parameters, including their error bars.\n", + "print 'Fit parameters:'\n", + "for i in range(M):\n", + " print ' a[', i, '] = ', a_fit[i], ' +/- ', sig_a[i]\n", + "\n", + "#* Graph the data, with error bars, and fitting function.\n", + "plt.errorbar(x,y,sigma,None,'o') # Graph data with error bars\n", + "plt.plot(x,yy,'-') # Plot the fit on same graph as data\n", + "plt.xlabel('x_i') \n", + "plt.ylabel('y_i and Y(x)') \n", + "plt.title([r\"\\chi^2 = \",chisqr,' N-M = ',N-M])" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python [default]", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.12" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} diff --git a/Python/.ipynb_checkpoints/Neutrn-checkpoint.ipynb b/Python/.ipynb_checkpoints/Neutrn-checkpoint.ipynb new file mode 100644 index 0000000..32480f0 --- /dev/null +++ b/Python/.ipynb_checkpoints/Neutrn-checkpoint.ipynb @@ -0,0 +1,154 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# neutrn - Program to solve the neutron diffusion equation \n", + "# using the Forward Time Centered Space (FTCS) scheme.\n", + "\n", + "# Set up configuration options and special features\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "%matplotlib inline" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Initialize parameters (time step, grid points, etc.).\n", + "tau = input('Enter time step: ')\n", + "N = input('Enter the number of grid points: ')\n", + "L = input('Enter system length: ')\n", + "# The system extends from x=-L/2 to x=L/2\n", + "h = L/float(N-1) # Grid size\n", + "D = 1. # Diffusion coefficient\n", + "C = 1. # Generation rate\n", + "coeff = D*tau/h**2\n", + "coeff2 = C*tau \n", + "if coeff < 0.5 :\n", + " print 'Solution is expected to be stable'\n", + "else:\n", + " print 'WARNING: Solution is expected to be unstable'" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Set initial and boundary conditions.\n", + "nn = np.zeros(N) # Initialize density to zero at all points\n", + "nn_new = np.zeros(N) # Initialize temporary array used by FTCS\n", + "nn[int(N/2.)] = 1/h # Initial cond. is delta function in center\n", + "## The boundary conditions are nn[0] = nn[N-1] = 0\n", + "\n", + "#* Set up loop and plot variables.\n", + "xplot = np.arange(N)*h - L/2. # Record the x scale for plots\n", + "iplot = 0 # Counter used to count plots\n", + "nstep = input('Enter number of time steps: ')\n", + "nplots = 50 # Number of snapshots (plots) to take\n", + "plot_step = nstep/nplots # Number of time steps between plots" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Loop over the desired number of time steps.\n", + "nnplot = np.empty((N,nplots))\n", + "tplot = np.empty(nplots)\n", + "nAve = np.empty(nplots)\n", + "for istep in range(nstep): ## MAIN LOOP ##\n", + "\n", + " #* Compute the new density using FTCS scheme.\n", + " nn[1:(N-1)] = ( nn[1:(N-1)] + \n", + " coeff*( nn[2:N] + nn[0:(N-2)] - 2*nn[1:(N-1)] ) +\n", + " coeff2*nn[1:(N-1)] )\n", + " \n", + " #* Periodically record the density for plotting.\n", + " if (istep+1) % plot_step < 1: # Every plot_step steps\n", + " nnplot[:,iplot] = np.copy(nn) # record nn[i] for plotting\n", + " tplot[iplot] = istep*tau # Record time for plots\n", + " nAve[iplot] = np.mean(nn) # Record average density \n", + " iplot += 1 \n", + " print 'Finished ', istep, ' of ', nstep, ' steps'" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Plot density versus x and t as a 3D-surface plot\n", + "from matplotlib import cm\n", + "from mpl_toolkits.mplot3d import Axes3D\n", + "\n", + "fig = plt.figure()\n", + "ax = fig.gca(projection = '3d')\n", + "Tp, Xp = np.meshgrid(tplot, xplot)\n", + "ax.plot_surface(Tp, Xp, nnplot, rstride=2, cstride=2, cmap=cm.gray)\n", + "ax.set_xlabel('Time')\n", + "ax.set_ylabel('x')\n", + "ax.set_zlabel('n(x,t)');\n", + "ax.set_title('Neutron diffusion');" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Plot average neutron density versus time\n", + "plt.plot(tplot,nAve,'*')\n", + "plt.xlabel('Time')\n", + "plt.ylabel('Average density')\n", + "plt.title(['L = ', L ,' (L_c = pi)'])" + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "kernelspec": { + "display_name": "Python [default]", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.12" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} diff --git a/Python/.ipynb_checkpoints/Newtn-checkpoint.ipynb b/Python/.ipynb_checkpoints/Newtn-checkpoint.ipynb new file mode 100644 index 0000000..302113b --- /dev/null +++ b/Python/.ipynb_checkpoints/Newtn-checkpoint.ipynb @@ -0,0 +1,141 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# newtn - Program to solve a system of nonlinear equations \n", + "# using Newton's method. Equations defined by function fnewt.\n", + "\n", + "# Set up configuration options and special features\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "%matplotlib inline" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def fnewt(x,a):\n", + " # Function used by the N-variable Newton's method\n", + " # Inputs\n", + " # x State vector [x y z]\n", + " # a Parameters [r sigma b]\n", + " # Outputs\n", + " # f Lorenz model r.h.s. [dx/dt dy/dt dz/dt]\n", + " # D Jacobian matrix, D(i,j) = df(j)/dx(i)\n", + "\n", + " # Evaluate f(i)\n", + " f = np.empty(3)\n", + " f[0] = a[1] * (x[1]-x[0])\n", + " f[1] = a[0]*x[0] -x[1] -x[0]*x[2]\n", + " f[2] = x[0]*x[1] -a[2]*x[2]\n", + "\n", + " # Evaluate D(i,j)\n", + " D = np.empty((3,3))\n", + " D[0,0] = -a[1] # df(0)/dx(0)\n", + " D[0,1] = a[0]-x[2] # df(1)/dx(0)\n", + " D[0,2] = x[1] # df(2)/dx(0)\n", + " D[1,0] = a[1] # df(0)/dx(1)\n", + " D[1,1] = -1 # df(1)/dx(1)\n", + " D[1,2] = x[0] # df(2)/dx(1)\n", + " D[2,0] = 0 # df(0)/dx(2)\n", + " D[2,1] = -x[0] # df(1)/dx(2)\n", + " D[2,2] = -a[2] # df(2)/dx(2)\n", + "\n", + " return [f, D]" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Set initial guess and parameters\n", + "x0 = np.array(input('Enter the initial guess (row vector): '))\n", + "x = np.copy(x0) # Copy initial guess\n", + "a = np.array(input('Enter the parameter a: '))" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Loop over desired number of steps \n", + "nStep = 10 # Number of iterations before stopping\n", + "xp = np.empty((len(x), nStep))\n", + "xp[:,0] = np.copy(x[:]) # Record initial guess for plotting\n", + "for iStep in range(nStep):\n", + "\n", + " #* Evaluate function f and its Jacobian matrix D\n", + " [f, D] = fnewt(x,a) # fnewt returns value of f and D\n", + " #* Find dx by Gaussian elimination; transpose D for column vectors\n", + " dx = np.linalg.solve( np.transpose(D), f) \n", + " #* Update the estimate for the root \n", + " x = x - dx # Newton iteration for new x\n", + " xp[:,iStep] = np.copy(x[:]) # Save current estimate for plotting" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Print the final estimate for the root\n", + "print 'After', nStep, ' iterations the root is'\n", + "print x\n", + "\n", + "# %* Plot the iterations from initial guess to final estimate\n", + "from mpl_toolkits.mplot3d import Axes3D\n", + "fig = plt.figure()\n", + "ax = fig.gca(projection='3d')\n", + "ax.plot(xp[0,:],xp[1,:],xp[2,:],'o-')\n", + "ax.plot([x[0]],[x[1]],[x[2]],'*')\n", + "ax.set_xlabel('x')\n", + "ax.set_ylabel('y')\n", + "ax.set_zlabel('z')\n", + "ax.set_title('Steady state of the Lorenz model')" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python [default]", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.12" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} diff --git a/Python/.ipynb_checkpoints/Orbit-checkpoint.ipynb b/Python/.ipynb_checkpoints/Orbit-checkpoint.ipynb new file mode 100644 index 0000000..e9f3683 --- /dev/null +++ b/Python/.ipynb_checkpoints/Orbit-checkpoint.ipynb @@ -0,0 +1,273 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# orbit - Program to compute the orbit of a comet.\n", + "\n", + "# Set up configuration options and special features\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "%matplotlib inline" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def gravrk(s,t,GM):\n", + " # Returns right-hand side of Kepler ODE; used by Runge-Kutta routines\n", + " # Inputs\n", + " # s State vector [r(1) r(2) v(1) v(2)]\n", + " # t Time (not used)\n", + " # GM Parameter G*M (gravitational const. * solar mass)\n", + " # Output\n", + " # deriv Derivatives [dr(1)/dt dr(2)/dt dv(1)/dt dv(2)/dt]\n", + "\n", + " #* Compute acceleration\n", + " r = np.array([s[0], s[1]]) # Unravel the vector s into position and velocity\n", + " v = np.array([s[2], s[3]])\n", + " accel = -GM*r/np.linalg.norm(r)**3 # Gravitational acceleration\n", + "\n", + " #* Return derivatives [dr(1)/dt dr(2)/dt dv(1)/dt dv(2)/dt]\n", + " deriv = np.array([v[0], v[1], accel[0], accel[1]])\n", + " return deriv" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def rk4(x,t,tau,derivsRK,param):\n", + " # Runge-Kutta integrator (4th order)\n", + " # Input arguments -\n", + " # x = current value of dependent variable\n", + " # t = independent variable (usually time)\n", + " # tau = step size (usually timestep)\n", + " # derivsRK = right hand side of the ODE; derivsRK is the\n", + " # name of the function which returns dx/dt\n", + " # Calling format derivsRK (x,t,param).\n", + " # param = extra parameters passed to derivsRK\n", + " # Output arguments -\n", + " # xout = new value of x after a step of size tau\n", + " \n", + " half_tau = 0.5*tau\n", + " F1 = derivsRK(x,t,param) \n", + " t_half = t + half_tau\n", + " xtemp = x + half_tau*F1\n", + " F2 = derivsRK(xtemp,t_half,param) \n", + " xtemp = x + half_tau*F2\n", + " F3 = derivsRK(xtemp,t_half,param)\n", + " t_full = t + tau\n", + " xtemp = x + tau*F3\n", + " F4 = derivsRK(xtemp,t_full,param)\n", + " xout = x + tau/6.*(F1 + F4 + 2.*(F2+F3))\n", + " return xout" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def rka(x,t,tau,err,derivsRK,param):\n", + " # Adaptive Runge-Kutta routine\n", + " # Inputs\n", + " # x Current value of the dependent variable\n", + " # t Independent variable (usually time)\n", + " # tau Step size (usually time step)\n", + " # err Desired fractional local truncation error\n", + " # derivsRK Right hand side of the ODE; derivsRK is the\n", + " # name of the function which returns dx/dt\n", + " # Calling format derivsRK (x,t,param).\n", + " # param Extra parameters passed to derivsRK\n", + " # Outputs\n", + " # xSmall New value of the dependent variable\n", + " # t New value of the independent variable\n", + " # tau Suggested step size for next call to rka\n", + "\n", + " #* Set initial variables\n", + " tSave, xSave = t, x # Save initial values\n", + " safe1, safe2 = 0.9, 4.0 # Safety factors\n", + " eps = 1.e-15\n", + "\n", + " #* Loop over maximum number of attempts to satisfy error bound\n", + " xTemp = np.empty(len(x))\n", + " xSmall = np.empty(len(x)); xBig = np.empty(len(x))\n", + " maxTry = 100\n", + " for iTry in range(maxTry):\n", + "\n", + " #* Take the two small time steps\n", + " half_tau = 0.5 * tau\n", + " xTemp = rk4(xSave,tSave,half_tau,derivsRK,param)\n", + " t = tSave + half_tau\n", + " xSmall = rk4(xTemp,t,half_tau,derivsRK,param)\n", + " \n", + " #* Take the single big time step\n", + " t = tSave + tau\n", + " xBig = rk4(xSave,tSave,tau,derivsRK,param)\n", + " \n", + " #* Compute the estimated truncation error\n", + " scale = err * (abs(xSmall) + abs(xBig))/2.\n", + " xDiff = xSmall - xBig\n", + " errorRatio = max( abs (xDiff) / (scale + eps) )\n", + " \n", + " #* Estimate new tau value (including safety factors)\n", + " tau_old = tau\n", + " tau = safe1*tau_old*errorRatio**(-0.20)\n", + " tau = max(tau,tau_old/safe2)\n", + " tau = min(tau,safe2*tau_old)\n", + " \n", + " #* If error is acceptable, return computed values\n", + " if errorRatio < 1 :\n", + " return np.array([xSmall, t, tau]) \n", + "\n", + " #* Issue error message if error bound never satisfied\n", + " print 'ERROR: Adaptive Runge-Kutta routine failed'\n", + " return np.array([xSmall, t, tau])" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Set initial position and velocity of the comet.\n", + "r0 = input('Enter initial radial distance (AU): ') \n", + "v0 = input('Enter initial tangential velocity (AU/yr): ')\n", + "r = np.array([r0, 0])\n", + "v = np.array([0, v0])\n", + "state = np.array([ r[0], r[1], v[0], v[1] ]) # Used by R-K routines\n", + "\n", + "#* Set physical parameters (mass, G*M)\n", + "GM = 4 * np.pi**2 # Grav. const. * Mass of Sun (au^3/yr^2)\n", + "mass = 1.0 # Mass of comet \n", + "adaptErr = 1.0e-3 # Error parameter used by adaptive Runge-Kutta\n", + "time = 0.0" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Loop over desired number of steps using specified\n", + "# numerical method.\n", + "nStep = input('Enter number of steps: ')\n", + "tau = input('Enter time step (yr): ')\n", + "NumericalMethod = input(\n", + " 'Choose a numerical method: 1) Euler; 2) Euler-Cromer; 3) Runge-Kutta; 4) Adaptive R-K')\n", + "rplot = np.empty(nStep) \n", + "thplot = np.empty(nStep)\n", + "tplot = np.empty(nStep)\n", + "kinetic = np.empty(nStep)\n", + "potential = np.empty(nStep)\n", + "\n", + "for iStep in range(nStep): \n", + "\n", + " #* Record position and energy for plotting.\n", + " rplot[iStep] = np.linalg.norm(r) # Record position for polar plot\n", + " thplot[iStep] = np.arctan2(r[1],r[0])\n", + " tplot[iStep] = time\n", + " kinetic[iStep] = .5*mass*np.linalg.norm(v)**2 # Record energies\n", + " potential[iStep] = - GM*mass/np.linalg.norm(r)\n", + " \n", + " #* Calculate new position and velocity using desired method.\n", + " if NumericalMethod == 1 :\n", + " accel = -GM*r/np.linalg.norm(r)**3 \n", + " r = r + tau*v # Euler step\n", + " v = v + tau*accel \n", + " time = time + tau \n", + " elif NumericalMethod == 2 :\n", + " accel = -GM*r/np.linalg.norm(r)**3 \n", + " v = v + tau*accel \n", + " r = r + tau*v # Euler-Cromer step\n", + " time = time + tau \n", + " elif NumericalMethod == 3 :\n", + " state = rk4(state,time,tau,gravrk,GM)\n", + " r = [state[0], state[1]] # 4th order Runge-Kutta\n", + " v = [state[2], state[3]]\n", + " time = time + tau \n", + " else : \n", + " [state, time, tau] = rka(state,time,tau,adaptErr,gravrk,GM);\n", + " r = [state[0], state[1]] # Adaptive Runge-Kutta\n", + " v = [state[2], state[3]]" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Graph the trajectory of the comet.\n", + "ax = plt.subplot(111, projection='polar') # Use polar plot for graphing orbit\n", + "ax.plot(thplot,rplot,'+') \n", + "ax.set_title('Distance (AU)') \n", + "ax.grid(True)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Graph the energy of the comet versus time.\n", + "totalE = kinetic + potential # Total energy\n", + "plt.plot(tplot,kinetic,'-.',tplot,potential,'--',tplot,totalE,'-')\n", + "plt.legend(['Kinetic','Potential','Total']);\n", + "plt.xlabel('Time (yr)')\n", + "plt.ylabel('Energy (M AU^2/yr^2)')" + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "kernelspec": { + "display_name": "Python [default]", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.12" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} diff --git a/Python/.ipynb_checkpoints/Orthog-checkpoint.ipynb b/Python/.ipynb_checkpoints/Orthog-checkpoint.ipynb new file mode 100644 index 0000000..0476b1c --- /dev/null +++ b/Python/.ipynb_checkpoints/Orthog-checkpoint.ipynb @@ -0,0 +1,84 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# orthog - Program to test if a pair of vectors \n", + "# is orthogonal. Assumes vectors are in 3D space\n", + "\n", + "# Set up configuration options and special features\n", + "import numpy as np" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Initialize the vectors a and b\n", + "a = np.array(input('Enter the first vector: '))\n", + "b = np.array(input('Enter the second vector: '))" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Evaluate the dot product as sum over products of elements\n", + "a_dot_b = 0\n", + "for i in range(3):\n", + " a_dot_b += a[i] * b[i]" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Print dot product and state whether vectors are orthogonal\n", + "if a_dot_b == 0:\n", + " print 'Vectors are orthogonal'\n", + "else:\n", + " print 'Vectors are NOT orthogonal'\n", + " print 'Dot product = ' , a_dot_b" + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "kernelspec": { + "display_name": "Python [default]", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.12" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} diff --git a/Python/.ipynb_checkpoints/Pendul-checkpoint.ipynb b/Python/.ipynb_checkpoints/Pendul-checkpoint.ipynb new file mode 100644 index 0000000..cb041b6 --- /dev/null +++ b/Python/.ipynb_checkpoints/Pendul-checkpoint.ipynb @@ -0,0 +1,134 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# pendul - Program to compute the motion of a simple pendulum\n", + "# using the Euler or Verlet method\n", + "\n", + "# Set up configuration options and special features\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "%matplotlib inline" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Select the numerical method to use: Euler or Verlet\n", + "NumericalMethod = input('Choose a numerical method (1: Euler; 2: Verlet): ')\n", + "\n", + "#* Set initial position and velocity of pendulum\n", + "theta0 = input('Enter initial angle (in degrees): ')\n", + "theta = theta0 * np.pi /180 # Convert angle to radians\n", + "omega = 0.0 # Set the initial velocity\n", + "\n", + "#* Set the physical constants and other variables\n", + "g_over_L = 1.0 # The constant g/L\n", + "time = 0.0 # Initial time\n", + "irev = 0 # Used to count number of reversals\n", + "tau = input('Enter time step: ')\n", + "\n", + "#* Take one backward step to start Verlet\n", + "accel = -g_over_L * np.sin(theta) # Gravitational acceleration\n", + "theta_old = theta - omega*tau + 0.5*accel*tau**2 " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Loop over desired number of steps with given time step\n", + "# and numerical method\n", + "nstep = input('Enter number of time steps: ')\n", + "t_plot = np.empty(nstep)\n", + "th_plot = np.empty(nstep)\n", + "period = np.empty(nstep)\n", + "for istep in range(nstep): \n", + "\n", + " #* Record angle and time for plotting\n", + " t_plot[istep] = time \n", + " th_plot[istep] = theta*180/np.pi # Convert angle to degrees\n", + " time = time + tau\n", + " \n", + " #* Compute new position and velocity using \n", + " # Euler or Verlet method\n", + " accel = -g_over_L * np.sin(theta) # Gravitational acceleration\n", + " if NumericalMethod == 1 :\n", + " theta_old = theta # Save previous angle\n", + " theta = theta + tau*omega # Euler method\n", + " omega = omega + tau*accel \n", + " else: \n", + " theta_new = 2*theta - theta_old + tau**2*accel\n", + " theta_old = theta # Verlet method\n", + " theta = theta_new \n", + " \n", + " #* Test if the pendulum has passed through theta = 0;\n", + " # if yes, use time to estimate period\n", + " if theta*theta_old < 0 : # Test position for sign change\n", + " print 'Turning point at time t = ',time\n", + " if irev == 0 : # If this is the first change,\n", + " time_old = time # just record the time\n", + " else:\n", + " period[irev-1] = 2*(time - time_old)\n", + " time_old = time\n", + " irev = irev + 1 # Increment the number of reversals" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# Estimate period of oscillation, including error bar\n", + "nPeriod = irev-1 # Number of times the period was measured\n", + "AvePeriod = np.mean(period[0:(nPeriod-1)])\n", + "ErrorBar = np.std(period[0:(nPeriod-1)])/np.sqrt(nPeriod)\n", + "print 'Average period = ', AvePeriod, ' +/- ', ErrorBar\n", + "\n", + "# Graph the oscillations as theta versus time\n", + "plt.plot(t_plot,th_plot,'+')\n", + "plt.xlabel('Time')\n", + "plt.ylabel(r'$\\theta$ (degrees)')" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python [default]", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.12" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} diff --git a/Python/.ipynb_checkpoints/Relax-checkpoint.ipynb b/Python/.ipynb_checkpoints/Relax-checkpoint.ipynb new file mode 100644 index 0000000..63e03c4 --- /dev/null +++ b/Python/.ipynb_checkpoints/Relax-checkpoint.ipynb @@ -0,0 +1,280 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# relax - Program to solve the Laplace equation using \n", + "# Jacobi, Gauss-Seidel and SOR methods on a square grid\n", + "\n", + "# Set up configuration options and special features\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "%matplotlib inline" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Choose numerical method, 1) Jacobi; 2) Gauss-Seidel; 3) SOR1\n", + "Enter number of grid points on a side: 50\n" + ] + } + ], + "source": [ + "#* Initialize parameters (system size, grid spacing, etc.)\n", + "method = input('Choose numerical method, 1) Jacobi; 2) Gauss-Seidel; 3) SOR')\n", + "N = input('Enter number of grid points on a side: ')\n", + "L = 1. # System size (length)\n", + "h = L/(N-1) # Grid spacing\n", + "x = np.arange(N)*h # x coordinate\n", + "y = np.arange(N)*h # y coordinate\n", + "\n", + "#* Select over-relaxation factor (SOR only)\n", + "if method == 3 :\n", + " omegaOpt = 2./(1.+np.sin(np.pi/N)) # Theoretical optimum\n", + " print 'Theoretical optimum omega = ', omegaOpt\n", + " omega = input('Enter desired omega: ')" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Potential at y=L equals 1.0\n", + "Potential is zero on all other boundaries\n" + ] + } + ], + "source": [ + "#* Set initial guess as first term in separation of variables soln.\n", + "phi0 = 1. # Potential at y=L\n", + "phi = np.empty((N,N))\n", + "for i in range(N) :\n", + " for j in range(N) :\n", + " phi[i,j] = phi0 * 4/(np.pi*np.sinh(np.pi)\n", + " ) * np.sin(np.pi*x[i]/L)*np.sinh(np.pi*y[j]/L)\n", + "\n", + "#* Set boundary conditions\n", + "phi[0,:] = 0.\n", + "phi[-1,:] = 0.\n", + "phi[:,0] = 0.\n", + "phi[:,-1] = phi0*np.ones(N) \n", + "print 'Potential at y=L equals ', phi0\n", + "print 'Potential is zero on all other boundaries'" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Desired fractional change = 0.0001\n", + "After 1 iterations, fractional change = 0.00319908232239\n", + "After 11 iterations, fractional change = 0.00101431842757\n", + "After 21 iterations, fractional change = 0.000676675910769\n", + "After 31 iterations, fractional change = 0.000518352216807\n", + "After 41 iterations, fractional change = 0.000421260894724\n", + "After 51 iterations, fractional change = 0.000354282266423\n", + "After 61 iterations, fractional change = 0.000304339085997\n", + "After 71 iterations, fractional change = 0.000265130738214\n", + "After 81 iterations, fractional change = 0.00023333363901\n", + "After 91 iterations, fractional change = 0.000206935591989\n", + "After 101 iterations, fractional change = 0.000184631365955\n", + "After 111 iterations, fractional change = 0.000165528254489\n", + "After 121 iterations, fractional change = 0.000148989702437\n", + "After 131 iterations, fractional change = 0.000134587783661\n", + "After 141 iterations, fractional change = 0.000121938312056\n", + "After 151 iterations, fractional change = 0.000110750286041\n", + "After 161 iterations, fractional change = 0.000100786804246\n", + "Desired accuracy achieved after 162 iterations\n", + "Breaking out of main loop\n" + ] + } + ], + "source": [ + "#* Loop until desired fractional change per iteration is obtained\n", + "#flops(0); # Reset the flops counter to zero;\n", + "newphi = np.copy(phi) # Copy of the solution (used only by Jacobi)\n", + "iterMax = N**2 # Set max to avoid excessively long runs\n", + "change = np.empty(iterMax)\n", + "changeDesired = 1.e-4 # Stop when the change is given fraction\n", + "print 'Desired fractional change = ', changeDesired\n", + "for iter in range(iterMax) :\n", + " changeSum = 0\n", + " \n", + " if method == 1 : ## Jacobi method ##\n", + " for i in range(1,N-1) : # Loop over interior points only\n", + " for j in range(1,N-1) : \n", + " newphi[i,j] = .25*( phi[i+1,j] + phi[i-1,j] + \n", + " phi[i,j-1] + phi[i,j+1] )\n", + " changeSum += abs( 1 - phi[i,j]/newphi[i,j] )\n", + " phi = np.copy(newphi) \n", + "\n", + " elif method == 2 : ## G-S method ##\n", + " for i in range(1,N-1) : # Loop over interior points only\n", + " for j in range(1,N-1) : \n", + " temp = .25*( phi[i+1,j] + phi[i-1,j] + \n", + " phi[i,j-1] + phi[i,j+1] )\n", + " changeSum += abs( 1 - phi[i,j]/temp )\n", + " phi[i,j] = temp\n", + "\n", + " else : ## SOR method ## \n", + " for i in range(1,N-1) : # Loop over interior points only\n", + " for j in range(1,N-1) : \n", + " temp = .25*omega*( phi[i+1,j] + phi[i-1,j] + \n", + " phi[i,j-1] + phi[i,j+1] ) + (1-omega)*phi[i,j]\n", + " \n", + " changeSum += abs( 1 - phi[i,j]/temp )\n", + " phi[i,j] = temp\n", + "\n", + " #* Check if fractional change is small enough to halt the iteration\n", + " change[iter] = changeSum/(N-2)**2\n", + " if iter % 10 < 1 :\n", + " print 'After ', iter+1, ' iterations, fractional change = ', change[iter]\n", + "\n", + " if change[iter] < changeDesired : \n", + " print 'Desired accuracy achieved after ', iter+1, ' iterations' \n", + " print 'Breaking out of main loop'\n", + " break" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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+otjbGcIkNLaFrvaJhwoMbLa1xUOVeDEEiS4sAM/nokJ0QY15+mFDwBTKvmVl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\nziyxIZeseA2AYsU0qlaVrrQnn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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#* Plot final estimate of potential as a contour plot\n", + "from matplotlib import cm\n", + "from mpl_toolkits.mplot3d import Axes3D\n", + "\n", + "levels = np.linspace(0., 1., num=11) \n", + "ct = plt.contour(x, y, np.flipud(np.rot90(phi)), levels) \n", + "plt.clabel(ct, fmt='%1.2f') \n", + "plt.xlabel('x')\n", + "plt.ylabel('y')\n", + "plt.title('Potential after %g iterations' % iter)\n" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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VahU55H+IP8oh/9O8iKgdHByeErXcC/8sUcsf82VELSJqAQghC14BsojT09NJSkpS+oXl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\nYMyYMZg8eTI2btyIvXv34m9/+xs6dOiAESNGNIDENwa6d++OixcvonXr1g7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F9yEjI4N2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\nRK5CYII=\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#* Plot final estimate of potential as contour and surface plots\n", + "\n", + "fig = plt.figure()\n", + "ax = fig.gca(projection = '3d')\n", + "Xp, Yp = np.meshgrid(x, y)\n", + "ax.plot_surface(Xp, Yp, np.flipud(np.rot90(phi)), rstride=1, cstride=1, cmap=cm.gray)\n", + "ax.view_init(elev=30., azim=210.)\n", + "ax.set_xlabel('x')\n", + "ax.set_ylabel('y')\n", + "ax.set_zlabel('Phi(x,y)')" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python [default]", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.12" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} diff --git a/Python/.ipynb_checkpoints/Rk4-checkpoint.ipynb b/Python/.ipynb_checkpoints/Rk4-checkpoint.ipynb new file mode 100644 index 0000000..79397fa --- /dev/null +++ b/Python/.ipynb_checkpoints/Rk4-checkpoint.ipynb @@ -0,0 +1,60 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def rk4(x,t,tau,derivsRK,param):\n", + " # Runge-Kutta integrator (4th order)\n", + " # Input arguments -\n", + " # x = current value of dependent variable\n", + " # t = independent variable (usually time)\n", + " # tau = step size (usually timestep)\n", + " # derivsRK = right hand side of the ODE; derivsRK is the\n", + " # name of the function which returns dx/dt\n", + " # Calling format derivsRK (x,t,param).\n", + " # param = extra parameters passed to derivsRK\n", + " # Output arguments -\n", + " # xout = new value of x after a step of size tau\n", + " \n", + " half_tau = 0.5*tau\n", + " F1 = derivsRK(x,t,param) \n", + " t_half = t + half_tau\n", + " xtemp = x + half_tau*F1\n", + " F2 = derivsRK(xtemp,t_half,param) \n", + " xtemp = x + half_tau*F2\n", + " F3 = derivsRK(xtemp,t_half,param)\n", + " t_full = t + tau\n", + " xtemp = x + tau*F3\n", + " F4 = derivsRK(xtemp,t_full,param)\n", + " xout = x + tau/6.*(F1 + F4 + 2.*(F2+F3))\n", + " return xout" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python [default]", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.12" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} diff --git a/Python/.ipynb_checkpoints/Rombf-checkpoint.ipynb b/Python/.ipynb_checkpoints/Rombf-checkpoint.ipynb new file mode 100644 index 0000000..2fd260c --- /dev/null +++ b/Python/.ipynb_checkpoints/Rombf-checkpoint.ipynb @@ -0,0 +1,155 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# Program to test the bess function\n", + "\n", + "# Set up configuration options and special features\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "%matplotlib inline" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def rombf(a,b,N,func,param) :\n", + " # Function to compute integrals by Romberg algorithm\n", + " # R = rombf(a,b,N,func,param)\n", + " # Inputs\n", + " # a,b Lower and upper bound of the integral\n", + " # N Romberg table is N by N\n", + " # func Name of integrand function in a string such as\n", + " # func='errintg'. The calling sequence is func(x,param)\n", + " # param Set of parameters to be passed to function\n", + " # Output \n", + " # R Romberg table; Entry R(N,N) is best estimate of\n", + " # the value of the integral\n", + "\n", + " #* Compute the first term R(1,1)\n", + " h = b - a # This is the coarsest panel size\n", + " npanels = 1 # Current number of panels\n", + " R = np.zeros((N+1,N+1))\n", + " R[1,1] = h/2. * (func(a,param) + func(b,param))\n", + "\n", + " #* Loop over the desired number of rows, i = 2,...,N\n", + " for i in range(2,N+1) :\n", + "\n", + " #* Compute the summation in the recursive trapezoidal rule\n", + " h = h/2. # Use panels half the previous size\n", + " npanels *= 2 # Use twice as many panels\n", + " sumT = 0.\n", + " # This for loop goes k=1,3,5,...,npanels-1\n", + " for k in range(1,npanels,2) : \n", + " sumT += func(a + k*h, param)\n", + " \n", + " #* Compute Romberg table entries R(i,1), R(i,2), ..., R(i,i)\n", + " R[i,1] = 0.5 * R[i-1,1] + h * sumT \n", + " m = 1\n", + " for j in range(2,i+1) :\n", + " m *= 4\n", + " R[i,j] = R[i,j-1] + ( R[i,j-1] - R[i-1,j-1] )/(m-1)\n", + "\n", + " return R" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def errintg(x,param) :\n", + " # Error function integrand\n", + " # Inputs\n", + " # x Value where integrand is evaluated\n", + " # param Parameter list (not used)\n", + " # Output\n", + " # f Integrand of the error function\n", + " \n", + " f = np.exp(-x**2)\n", + " return f" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Error function estimate from rombf routine:\n", + "0.771743332258\n", + "0.439391289468 0.328607275204\n", + "0.425736299643 0.421184636368 0.427356460445\n", + "Expected value = 0.842701\n" + ] + } + ], + "source": [ + "N = 3\n", + "a = 0\n", + "b = 1\n", + "R = np.empty((N+1,N+1))\n", + "param = None\n", + "\n", + "R = rombf(a,b,N,errintg,param)\n", + "\n", + "print \"Error function estimate from rombf routine:\" \n", + "for i in range(1,N+1) :\n", + " for j in range(1,i+1) :\n", + " print 2./np.sqrt(np.pi) * R[i,j],\n", + " print\n", + "print \"Expected value = 0.842701\"\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python [default]", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.12" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} diff --git a/Python/.ipynb_checkpoints/Schro-checkpoint.ipynb b/Python/.ipynb_checkpoints/Schro-checkpoint.ipynb new file mode 100644 index 0000000..d2e4c1b --- /dev/null +++ b/Python/.ipynb_checkpoints/Schro-checkpoint.ipynb @@ -0,0 +1,441 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# schro - Program to solve the Schrodinger equation \n", + "# for a free particle using the Crank-Nicolson scheme\n", + "\n", + "# Set up configuration options and special features\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "%matplotlib inline" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Enter number of grid points: 500\n", + "Enter time step: 1.\n" + ] + } + ], + "source": [ + "#* Initialize parameters (grid spacing, time step, etc.)\n", + "i_imag = 1j # Imaginary i\n", + "N = input('Enter number of grid points: ');\n", + "L = 100. # System extends from -L/2 to L/2\n", + "h = L/(N-1) # Grid size\n", + "x = np.arange(N)*h - L/2. # Coordinates of grid points\n", + "h_bar = 1. # Natural units\n", + "mass = 1. # Natural units\n", + "tau = input('Enter time step: ')" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Set up the Hamiltonian operator matrix\n", + "ham = np.zeros((N,N)) # Set all elements to zero\n", + "coeff = -h_bar**2/(2*mass*h**2)\n", + "for i in range(1,N-1) :\n", + " ham[i,i-1] = coeff\n", + " ham[i,i] = -2*coeff # Set interior rows\n", + " ham[i,i+1] = coeff\n", + "\n", + "# First and last rows for periodic boundary conditions\n", + "ham[0,-1] = coeff; ham[0,0] = -2*coeff; ham[0,1] = coeff\n", + "ham[-1,-2] = coeff; ham[-1,-1] = -2*coeff; ham[-1,0] = coeff\n", + "\n", + "#* Compute the Crank-Nicolson matrix\n", + "dCN = np.dot( np.linalg.inv(np.identity(N) + .5*i_imag*tau/h_bar*ham), \n", + " (np.identity(N) - .5*i_imag*tau/h_bar*ham) )" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Initialize the wavefunction \n", + "x0 = 0. # Location of the center of the wavepacket\n", + "velocity = 0.5 # Average velocity of the packet\n", + "k0 = mass*velocity/h_bar; # Average wavenumber\n", + "sigma0 = L/10. # Standard deviation of the wavefunction\n", + "Norm_psi = 1/(np.sqrt(sigma0*np.sqrt(np.pi))) # Normalization\n", + "psi = np.empty(N,dtype=complex)\n", + "for i in range(N) :\n", + " psi[i] = Norm_psi * np.exp(i_imag*k0*x[i]) * np.exp(-(x[i]-x0)**2/(2*sigma0**2))" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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2VpQTQjQ6yagIIdz6fu/3DGo3yO2xU1qfwop9KwJ2b2egYjWjUn6snN/1+h09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\n4qX1L9G2r+3A/eta1rGmeQ0LqxVURHJJmxKKSMYmT4aCAvj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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#* Plot the initial wavefunction\n", + "plt.plot(x,np.real(psi),'-',x,np.imag(psi),'--')\n", + "plt.xlabel('x'); plt.ylabel('psi(x)')\n", + "plt.legend(('Real ','Imag '))\n", + "plt.title('Initial wave function')" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Initialize loop and plot variables \n", + "max_iter = int(L/(velocity*tau)+.5) # Particle should circle system\n", + "plot_iter = max_iter/20 # Produce 20 curves\n", + "p_plot = np.empty((N,max_iter+1)) # Note that P(x,t) is real\n", + "p_plot[:,0] = np.absolute(psi[:])**2 # Record initial condition\n", + "iplot = 0\n", + "axisV = [-L/2., L/2., 0., max(p_plot[:,0])] # Fix axis min and max" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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WKSdKPEQkduU2Y2mmqiqYOTOszCtS6pR4iEjsynVES0pVFaxaBW+8EXckIm1P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\nStyRiDRPiYeIbJbJk2H33UN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lThQ8RKRk1dTAfvtBu3ahKwmrosIvoqal0yUOFDxEpGSV+8DShIoKWL0aFi8O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\nrxz70kuhK5FSoOAhIrH00kt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meUjrKHiIiGRh+XJ4553KDh4dO8K++yp4SOsoeIiIZCExvFDJwQPC61fwkNZQ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\nU6ZoIbFKoeAhIhVn6lTYdVf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t2zbuSOLVq1f4qeGW4qLEQ0QkYVTfEbRuDV27KvEoNko8REQSZMOGsHBWqdd3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\nxCNpDjkEysth5cq4IxFQ4iE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mhabEQ0SkQsyYoWaWTFqptvCUeIiIVIBFi2DePNhvv9iRFJchQ8JicUuWxI6k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\nOc7jybbzgX+6+1XJ458licn3gXPzcxo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1KfEQEZFmqamB1q2hT5+4Iyks7dvDrrsq8UilxENERJqlpgZ23z0kH7KuRD8P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\namYpLkOHwnvvwdtvxx1J8yj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h6d0bvvkGXn457kjqp2ASDzM738xmm9lyM5tiZnvVUb6nmVWb2bdmNt3MBqbc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\nwUsvhf4dUnwOOADatg3JYy4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UXgDg7h49Rrc0h3WN7k82pprymNl+UawvZRKXiIiULg2jrVm+htXWpsZjF2Av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\nUQeNGkF5OTz2GCxbFnc0IiL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IbHIm8TCzs8zsUzNbaGYTzKx7LeX3NrNKM1tkZtPM7IS0+08ws+Vmtiz6u9zMFjTtsxAR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\n3F6+PHyITpoUOqm+9x48/nhoe66y2mr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C6t+/P02bNl1lX0lJCSW1XKe12WZh5rmHH4bjj6/VhxIRkTw1dixMn55sM0tp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\nKfz008ptzpzwd/Zs+P778H5O/Z0+Pdy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WW7DffvDii3DYYZXfb8KECZSUlACUuPuETOWq2qulkZk1BgxYP3pcujQBjgTm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\ne8LDD8O33yYdjYhIfhowALb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uhLk4KsTdJ0S1JYMJTSbTgePdfXFUpAWwfUr5eWZ2EnAb0I8wlPc8d08d6dIQ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\nkk3/OX9+WIa8Tp2SyxR3ojUreavqMff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d+JJw/vnQrFnDW8W1XTs444yQePTqBRtumHREIiKSS9VqajGzPxNqO54HjgB+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\nyp6vyTZzJtxzT+Xlli8PP5PqbIsXh+S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TpjCzDkBpaWlpbW/YIyIiEquysjKKiooAity9LFM51XiIiIhIbJR4iIiISGyUeIiIiEhs\nlHiIiIhIbJR4iIiISGyUeIiIiEhslHiIiIhIbJR4iIiISGyUeIiIiEhslHiIiIhIbJR4iIiISGyU\neIiIiEhslHiIiIhIbJR4iIiISGyUeIiIiEhslHiIiIhIbJR4iIiISGyUeIiIiEhslHiIiIhIbJR4\niIiISGyUeIiIiEhs8ibxMLMeZjbdzJaY2SQz22MN5TuZWamZLTWzz8zstLTnTzOzFWa2PPq5wsx+\nqtmjEBERkcrkReJhZicANwEDgN2AD4BxZtY8Q/nWwFjgRaAdcAtwt5l1Tiu6AGiZsrSqgfBFRESk\nivIi8QB6A3e6+wPuPhk4F/gJODND+fOAae7e192nuPsI4PFoP6nc3ee4+3fRMqfGjkBERETWKPHE\nw8waAEWE2gsgZAvABKBjhs32jp5PNa6C8o3NbIaZzTSzp81s5xyFLSIiIllIPPEAmgP1gNlp62cT\nbo9UpGWG8k3NrGH0eAqhxuSPwMmEY33DzDbPRdAiIiJSffWTDqCmuPskYFL5YzN7E/gU6EZoSyIi\nIiIxy4fEYy6wHGiRtr4FMCvDNrMylF/o7ssq2sDdfzWz94Bt1xRQ7969adas2SrriouLKS4uXtOm\nIiIiBa+kpISSkpJV1i1YsKBK21poTpEsM5sEvOXuvaLHBswEbnX3oRWUHwx0dfd2KeseBjZ098My\nvMY6wCfAc+5+cYYyHYDS0tJSOnTosLaHJSIiUmeUlZVRVFQEUOTuZZnK5UMbD4BhwDlmdqqZ7QiM\nBBoBowHM7Hozuz+l/EhgazMbYmY7mFl34LhoP0Tb9DezzmbWxsx2A8YAWwF3x3NIIiIiki4fbrXg\n7o9FY3YMItwyeR/oktL9tSWwZUr5GWZ2ODAc6Al8BZzl7qk9XTYC7oq2nQ+UAh2j7roiIiKSgLxI\nPADc/Xbg9gzPnVHBuomEbriZ9tcH6JOzAEVERGSt5cutFhEREakDlHiIiIhIbJR4iIiISGyUeIiI\niEhslHiIiIhIbJR4iIiISGyUeIiIiEhslHiIiIhIbJR4iIiISGyUeIiIiEhslHiIiIhIbJR4iIiI\nSGyUeIiIiEhslHiIiIhIbJR4iIiISGyUeIiIiEhslHiIiIhIbJR4iIiISGyUeIiIiEhslHiIiIhI\nbJR4iIiISGyUeIiIiEhslHiIiIhIbJR4iIiISGyUeIiIiEhslHiIiIhIbJR4iIiISGyUeIiIiEhs\nlHiIiIhIbJR4iIiISGyUeIiIiEhslHiIiIhIbJR4iIiISGyUeIiIiEhslHiIiIhIbJR4iIiISGyU\neIiIiEhslHiIiIhIbJR4iIiISGyUeIiIiEhslHiIiIhIbJR4iIiISGyUeIiIiEhslHiIiIhIbPIm\n8TCzHmY23cyWmNkkM9tjDeU7mVmpmS01s8/M7LRKyp5oZivM7MncRy4iIiJVlReJh5mdANwEDAB2\nAz4AxplZ8wzlWwNjgReBdsAtwN1m1jlD2aHAxNxHLiIiItWRF4kH0Bu4090fcPfJwLnAT8CZGcqf\nB0xz977uPsXdRwCPR/v5HzNbB3gI+BswvcaiFxERkSpJPPEwswZAEaH2AgB3d2AC0DHDZntHz6ca\nV0H5AcBsd78vN9GKiIjI2qifdABAc6AeMDtt/WxghwzbtMxQvqmZNXT3ZWa2L3AG4VaMiIiI5IHE\nazxqgpk1Bh4AznH3+UnHIyIiIkE+1HjMBZYDLdLWtwBmZdhmVobyC6Pajh2BVsCzZmbR8+sAmNnP\nwA7unrHNR+/evWnWrNkq64qLiykuLq7C4YiIiBS2kpISSkpKVlm3YMGCKm1roTlFssxsEvCWu/eK\nHhswE7jV3YdWUH4w0NXd26WsexjY0N0PM7OGwDZpm10LNAZ6AlPd/dcK9tsBKC0tLaVDhw45OjoR\nEZHCV1ZWRlFREUCRu5dlKpcPNR4Aw4DRZlYKvE3ondIIGA1gZtcDm7t7+VgdI4EeZjYEuBc4CDgO\nOAzA3ZcB/0l9ATP7ITzln9b40YiIiEiF8iLxcPfHojE7BhFumbwPdHH3OVGRlsCWKeVnmNnhwHBC\nDcZXwFnunt7TRURERPJIXiQeAO5+O3B7hufOqGDdREI33Kruf7V9iIiISLwKsleLiIiI5CclHiIi\nIhIbJR4iIiISGyUeIiIiEhslHiIiIhIbJR4iIiISGyUeIiIiEhslHiIiIhIbJR4iIiISGyUeIiIi\nEhslHiIiIhIbJR4iIiISGyUeIiIiEhslHiIiIhIbJR4iIiISGyUeIiIiEhslHiIiIhIbJR4iIiIS\nGyUeIiIiEhslHiIiIhIbJR4iIiISGyUeIiIiEhslHiIiIhIbJR4iIiISGyUeIiIiEhslHiIiIhIb\nJR4iIiISGyUeIiIiEhslHiIiIhIbJR4iIiISm/pJByCF75df4JNP4OOP4auvYOFCWGcdaNoUWrWC\nnXcOS716SUcqIiI1TYmH1IilS+Hpp+GRR+Cll2DRorB+442hWTNYsQIWLIAffli5vnNnOPlk6NoV\n6uudKSJSkHSrRXJq/nwYOBA23xyKi+G77+DSS+H110OSMW8eTJsGM2aEsvPmwSuvwPnnw5Qp8Mc/\nwlZbwbBhsHhxwgcjIiI5p8RDcuLXX+Hmm6F1a7jhBjj11JBIvPEGXHEF/P73oaYj3cYbwx/+AFdd\nBe+9F5auXUOyss028MADoXZEREQKgxIPWWsffABFRdCnT7hVMn16SEK23776+2rfHu65B6ZOhU6d\n4LTT4IADQg2JiIjUfko8JGvuIcHYc8/w+zvvwO23Q4sWa7/v1q1D+5AJE+C//4W2bcNjERGp3ZR4\nSFaWLoXTT4fevaFHj5B0FBXl/nUOOijUqBx5ZGgz0q+fbr2IiNRm6jsg1TZ7Nhx9NJSVwZgxcNJJ\nNft6zZrBQw/BbrtB376ha+5DD0GTJjX7uiIiknuq8ZBqmTkzNBSdPh0mTqz5pKOcGVx8MTz7LLz8\nMnTpErrjiohI7aLEQ6ps+vTQA2X5cnjzzdC2I26HHx7GBZk8GQ4+GL7/Pv4YREQke0o8pEq++AL2\n3z8M7DVxYmj8mZTddw/Jx4wZoQ2Ikg8RkdpDiYes0ezZcMgh0KgRvPoqbLll0hGFbrcvvxyGYD/y\nSFiyJOmIRESkKpR4SKUWLYLDDgsX9vHjw4ik+eJ3v4PnnoP334cTTwyDmImISH5T4iEZ/fwzHHMM\nfP45/PvfYUK3fLPnnvD44yEB6dEjjCciIiL5K28SDzPrYWbTzWyJmU0ysz3WUL6TmZWa2VIz+8zM\nTkt7/mgze8fM5pvZj2b2npmdUrNHUVguvDDcWnnmmTCAV77q2hVGjYK77oLbbks6GhERqUzWiYeZ\nNTCzLc1sBzPbeG2CMLMTgJuAAcBuwAfAODNrnqF8a2As8CLQDrgFuNvMOqcUmwdcA+wN7ArcB9yX\nVkYyGDUK7rgjjETaqVPS0azZGWeEIdv79AmTzomISH6qVuJhZk3M7DwzexVYCMwAPgXmmNl/zWzU\nmmoqMugN3OnuD7j7ZOBc4CfgzAzlzwOmuXtfd5/i7iOAx6P9AODuE939mej56e5+K/AhsG8W8dUp\nb7wRblucdx6cfXbS0VTdkCEhSfrzn8Mw6yIikn+qnHiYWR9ConEGMAH4E9Ae2B7oCFxFGAl1vJn9\n28y2q+J+GwBFhNoLANzdo9fomGGzvaPnU42rpDxmdlAU66tViauumj0bjj0W9t47zMNSm9SvD48+\nCo0bh7Ypy5YlHZGIiKSrzpDpewD7u/snGZ5/G7jXzM4DTgf2A6ZWYb/NgXrA7LT1s4EdMmzTMkP5\npmbW0N2XAZhZU+BroCHwK9Dd3V+qQkx10ooVYTp7d3jsMVh33aQjqr5NNoEnngiJ02WXwfDhSUck\nIiKpqpx4uHtxFcstBUZmHVFuLSK0AWkMHAQMN7Np7j4x2bDy0403hi6z48dDy5ZJR5O9Dh3ghhvC\nBHYHHxxGOxURkfyQ1SRxZnYv0MvdF6Wt3wC4zd0ztc2oyFxgOZA+mXoLYFaGbWZlKL+wvLYD/nfL\nZlr08EMz2xm4HKg08ejduzfNmjVbZV1xcTHFxVXKvWqlSZPgiitCLUHnAmh+26sXvPhimEH3gw/y\na/wREZHarqSkhJKSklXWLajiBFrmWQx8YGbLgc3c/bu09c2BWe5erYTGzCYBb7l7r+ixATOBW919\naAXlBwNd3b1dyrqHgQ3d/bBKXuceoI27H5jh+Q5AaWlpKR06dKjOIdRqP/4Yusu2aBGGQ2/QIOmI\ncmPuXGjXDnbZBcaNCxPNiYhIzSgrK6OoqAigyN3LMpWrbq+WpmbWDDCgSfS4fNkIOAz4rvK9VGgY\ncI6ZnWpmOxJu1TQCRkeve72Z3Z9SfiSwtZkNibrzdgeOi/ZTHutlZnawmbUxsx3N7CLgFODBLOIr\naJdeGhqVPvRQ4SQdAM2bw733wgsvhDE+REQkedW91fID4NHyWQXPO2Esjmpx98ei2pJBhFsm7wNd\n3H1OVKQlsGVK+RlmdjgwHOgJfAWc5e6pPV02AEYAWwBLgMnAye7+eHXjK2QvvhjG6rjtNthmm6Sj\nyb0uXeCvf4WLLgrzzbRpk3REIiJ1W7VutZjZHwi1HS8BxwKp84L+DPzX3b/JaYQxqmu3WhYtgl13\nDRfjF1+EdfJmHNvcKj/O1q3DrLaFepwiIkmq6q2WatV4uPurAGbWBpjp2TQQkbxxySWhHcTLLxf2\nxbhJE7jvPjjwQBg5Erp3TzoiEZG6K6vLjbv/N1PSYWZbmVm9tQtLatqECXDnnTB0aN24/XDAAdCt\nG1x+OXxTa+vkRERqv5r4njsD+I+ZHVMD+5YcWLIkXITLL8Z1xfXXw3rrhcnvREQkGTWReBwADAZO\nqIF9Sw5cdx189VWYBK6Qb7Gk22ijMAz8P/4Bzz2XdDQiInVTzi877v6qu9/n7ko88tDkyWEytcsu\ngx0yDUhfwE48MfRu6dEDFi9OOhoRkbonq8QjGmsj03Ndsg9HapJ7mHF2q61CW4e6yCx0H549G666\nKuloRETqnmxrPMrMrEfqCjNraGZ/B55Z+7CkJowZA6+8Ei68662XdDTJ2WYb+NvfYNgw+PjjpKMR\nEalbsk08TgcGmdm/zKyFmbUH3gMOJsxKK3lm/nzo02flrYa67qKLQgLSq1eoCRIRkXhk2532McKs\nrw2AT4A3gVeBDu7+Tu7Ck1wZOBCWLg3f8gXWXReGDw8Dij31VNLRiIjUHWvbuHRdoF60fAssXeuI\nJOf+8x8YMQL694fNNks6mvxx2GFhueiikJSJiEjNy7Zx6YnAR8ACYHvgcOCvwGtmtnXuwpO15R7G\nrWjdGnr2TDqa/DNsWOhafNNNSUciIlI3ZFvjcQ/Qz93/6O5z3P0FYFfga8IEb5Inxo4Ns7MOGwYN\nGyYdTf7ZYYfQzqN8bBMREalZ2SYeHdz9jtQV7j7f3Y8HemTYRmK2bFloUNq5Mxx5ZNLR5K/+/aFx\nY7j00qQjEREpfNk2Lp1SyXMPZh+O5NJtt8H06aERpVnS0eSvZs3g2mvh4Yfh3XeTjkZEpLBVOfEw\ns8vMbP0qlt3LzA7PPixZW3PmwKBBYcCwXXZJOpr8d/rp4Txdcom614qI1KTq1HjsDMw0s9vNrKuZ\n/ab8CTOrb2Ztzay7mb0BPAosynWwUnVXXx3mYRk4MOlIaof69cNQ8q+8As8/n3Q0IiKFq8qJh7uf\nShggrAHwMDDLzH42s0XAMsIAYmcCDwA7uvvEGohXquDzz8MEcJdfDptsknQ0tcdhh0GnTtC3Lyxf\nnnQ0IiKFqX51Crv7B8A5ZtYNaAu0AtYH5gLvu/vc3Ico1dWvH7Rsqe6z1WUGN9wAe+4J998PZ56Z\ndEQiIoWnWo1LzWwdM+sLvAaMAjoCz7j7BCUd+eGtt8K071dfDetXqUWOpNpjjzCsfP/+8NNPSUcj\nIlJ4qtur5QrgOkL7ja+BXsCIXAcl2XEPtwl23RX+8peko6m9rr02NM69+eakIxERKTzVTTxOBbq7\n+6Hu/ifgSOBkM1vbodclB8aOhYkTQyPJevWSjqb22npr6NEDBg8OCYiIiOROdROGrYD/tfl39wmA\nA5vnMiiLk5+OAAAgAElEQVSpvl9/hcsugwMOgEMPTTqa2u/KK0OvoGuuSToSEZHCUt3Eoz6rTwT3\nC6GniyRo9OgwGdwNN2iwsFzYZBO4+GIYORJmzkw6GhGRwlGtXi2AAaPNbFnKuvWAkWa2uHyFux+T\ni+CkapYuhauughNOgN13TzqawtGrF9xyS2ioO2pU0tGIiBSG6tZ43A98R5iVtnx5CPgmbZ3E6O67\n4ZtvQvIhudOkSRgL5b77YOrUpKMRESkM1R3H44yaCkSys2RJmFn1lFPCTKuSW+edBzfdFEaAHTMm\n6WhERGo/9Uap5UaOhO++C+NOSO6tv344tyUl8PHHSUcjIlL7KfGoxRYvDl0+Tz8dtt026WgK15ln\nQuvWSu5ERHJBiUctNmIEzJ8fun5KzVl33XCr5emn4Z13ko5GRKR2U+JRSy1aFLrOnnVW+DYuNevk\nk2GnnZTkiYisLSUetdStt4bko1+/pCOpG+rVg0GDYPz4MDqsiIhkR4lHLfTDD3DjjdCtG2y5ZdLR\n1B3HHAPt24daD/ekoxERqZ2UeNRCN98cBg27/PKkI6lbyodQf+01mDAh6WhERGonJR61zPffw/Dh\n0L07bLZZ0tHUPYcdBnvuGRqbqtZDRKT6lHjUMjfdFCaEu/TSpCOpm8xC0vHGG6r1EBHJhhKPWmTO\nnDB3yAUXwKabJh1N3XXooar1EBHJlhKPWmTo0PCN++KLk46kblOth4hI9pR41BKzZsHf/w4XXgjN\nmycdjRx6KOy1l2o9RESqS4lHLTFkSBhBs0+fpCMRWLXW44UXko5GRKT2UOJRC3z9NdxxR0g6Ntoo\n6WikXJcuqvUQEakuJR61wPXXQ6NG0KtX0pFIqvJajzffVK2HiEhVKfHIczNnwqhRcMkl0KxZ0tFI\nOtV6iIhUjxKPPHfttdC0aehCK/lHtR4iItWjxCOPTZsG994bBgtr3DjpaCSTLl1g771V6yEiUhV5\nk3iYWQ8zm25mS8xskpntsYbyncys1MyWmtlnZnZa2vNnm9lEM/s+Wl5Y0z7zzTXXwCabhOHRJX+p\n1kNEpOryIvEwsxOAm4ABwG7AB8A4M6twxAozaw2MBV4E2gG3AHebWeeUYn8AHgY6AXsDXwLjzaxW\nzHAydSo88ECYCK5Ro6SjkTU55JBQ6zFggGo9REQqkxeJB9AbuNPdH3D3ycC5wE/AmRnKnwdMc/e+\n7j7F3UcAj0f7AcDd/+LuI939Q3f/DDibcLwH1eiR5MigQdCiBXTrlnQkUhXltR6TJsH48UlHIyKS\nvxJPPMysAVBEqL0AwN0dmAB0zLDZ3tHzqcZVUh5gA6AB8H3Wwcbk009hzBi44gpYb72ko5GqKq/1\nUFsPEZHMEk88gOZAPWB22vrZQMsM27TMUL6pmTXMsM0Q4GtWT1jyzlVXwZZbwllnJR2JVIdZ+NtN\nmgTjxiUdjYhIfsqHxKPGmdllwPHAn9z956TjqcxHH8Gjj8KVV0LDTCmU5K3OnaFjR9V6iIhkUj/p\nAIC5wHKgRdr6FsCsDNvMylB+obsvS11pZhcDfYGD3P2TqgTUu3dvmqWN1lVcXExxcXFVNl8rAwdC\nmzZw+uk1/lJSA8rbenTpAv/+N3TtmnREIiK5V1JSQklJySrrFixYUKVtzfPga5mZTQLecvde0WMD\nZgK3uvvQCsoPBrq6e7uUdQ8DG7r7YSnr+gKXA4e4+ztViKMDUFpaWkqHDh3W9rCq7b33oEMHuO8+\nJR61mTvsuy/8+mu47WKWdEQiIjWvrKyMoqIigCJ3L8tULl9utQwDzjGzU81sR2Ak0AgYDWBm15vZ\n/SnlRwJbm9kQM9vBzLoDx0X7IdrmUmAQoWfMTDNrES0bxHNI1TdgAGy3HZxyStKRyNoob+vx9tvw\n/PNJRyMikl/yIvFw98eAiwmJwntAW6CLu8+JirQEtkwpPwM4HDgYeJ/QjfYsd09tOHouoRfL48A3\nKctFNXks2XrnHXj22ZB81M+HG2CyVg46KNR6aFwPEZFV5c0lzt1vB27P8NwZFaybSOiGm2l/bXIX\nXc37299gp53gxBOTjkRyobytx8EHw3PPwRFHJB2RiEh+yIsaj7rujTdCQ8SBA6FevaSjkVw58EDY\nbz/1cBERSaXEIw/87W+w665w3HFJRyK5VN7Wo7QUxo5NOhoRkfygxCNhr74KL74YLlDr6K9RcDp1\ngv33V62HiEg5XeoS5B5qO3bbDf70p6SjkZpQXutRVgb//GfS0YiIJE+JR4JefBEmTgwTwmmsh8LV\nqVNYVOshIqLEIzHuYVj0vfaCww9POhqpaQMHwvvvwzPPJB2JiEiylHgk5Lnn4K234JprVNtRF/zh\nD3DAASEBWbEi6WhERJKjxCMBK1ZA//7hYnTQQUlHI3G56ir44AN4+umkIxERSY4SjwQ8+WSodr/6\natV21CX77RcSTdV6iEhdpsQjZsuXh54sXbqEC5HULQMHwkcfwVNPJR2JiEgylHjE7OGH4dNPQ22H\n1D377huGUVeth4jUVUo8YvTLL+GCc9RRsMceSUcjSbnqKvj4Y3jiiaQjERGJnxKPGI0eDdOnh3E7\npO7aZx845JCQgKjWQ0TqGiUeMVm6NCQcJ5wAbdsmHY0kbeBA+OQTePzxpCMREYmXEo+YjBoF33wT\nLjgiHTuGBsYDBoQGxyIidYUSjxgsXgzXXgunngo77JB0NJIvrrkGJk+Ghx5KOhIRkfgo8YjBiBEw\nb17oRitSbvfd4ZhjQq3HsmVJRyMiEg8lHjXshx9gyBA4+2xo0ybpaCTfXH01fPlluBUnIlIXKPGo\nYTfcEBqWqrZDKrLzzvCXv4TbLosXJx2NiEjNU+JRg77+Gm6+GXr3hs02SzoayVcDBsD338OttyYd\niYhIzVPiUYOuugoaNYJLLkk6EslnbdrAX/8aasfmz086GhGRmqXEo4ZMngz33ANXXgnNmiUdjeS7\nK68MDUxvvDHpSEREapYSjxrSrx9suSWcd17SkUht0LIl9OoVbs3NmpV0NCIiNUeJRw14880w++g1\n10DDhklHI7VF377QoAFcd13SkYiI1BwlHjnmDpdeCu3awUknJR2N1CYbbRSSj5EjYcaMpKMREakZ\nSjxy7Lnn4LXXYPBgWEdnV6qpZ0/YeGPo3z/pSEREaoYujTm0fDlcdhkccECYh0Okuho3Dr2hHnoI\nysqSjkZEJPeUeOTQAw+EGUcHDwazpKOR2uqss2DHHUM3bPekoxERyS0lHjny44+hJ8sJJ8CeeyYd\njdRm9euHYfZfegmefz7paEREckuJR44MGRIGfxoyJOlIpBAceSTsv39obLp8edLRiIjkjhKPHJg5\nMwz81KcPtGqVdDRSCMzCe+qTT2D06KSjERHJHSUeOXD55WF00ssvTzoSKSR77AEnnhh6uGgCOREp\nFEo81tKkSfDww3DttdCkSdLRSKG57jqYOxeGDUs6EhGR3FDisRbcw8yz7dvD6acnHY0UojZt4Pzz\nwwRy336bdDQiImtPicdaeOSRUOMxbBjUq5d0NFKo+vcPQ+/rVp6IFAIlHln66acwWNhRR4UBw0Rq\nykYbhXl/7r8f3n476WhERNaOEo8sDR4cZhEdOjTpSKQuOOecMP9Pz56wYkXS0YiIZE+JRxY+/zyM\n19G3L2y3XdLRSF1Qrx7ccgu89RaMGZN0NCIi2VPiUU3u4VvnZpvpnrvE6w9/gD//Ocx+vGhR0tGI\niGRHiUc1/fOfYRjrm2+GRo2SjkbqmqFDwwi5112XdCQiItlR4lENP/0EvXpB166hUalI3Fq1CjUe\nw4bBF18kHY2ISPUp8aiG668PYynceqtmn5Xk9O0LLVrAhRdq9loRqX2UeFTR1KlhEKdLL4Vtt006\nGqnLGjUKt/rGjoWnn046GhGR6lHiUQXuYfTIzTYLY3eIJO3oo+GII+CCC9TQVERql7xJPMysh5lN\nN7MlZjbJzPZYQ/lOZlZqZkvN7DMzOy3t+Z3N7PFonyvMrGe2sY0ZA+PHw9//rgalkh/Mwvtx/nwY\nMCDpaEREqi4vEg8zOwG4CRgA7AZ8AIwzs+YZyrcGxgIvAu2AW4C7zaxzSrFGwBfApUDWs1zMnRvm\nYznhhPANUyRftGoFAweG8T3eey/paEREqiYvEg+gN3Cnuz/g7pOBc4GfgDMzlD8PmObufd19iruP\nAB6P9gOAu7/r7pe6+2PAz9kG1qcPLF8ePtxF8s2FF8Iuu0C3buF9KiKS7xJPPMysAVBEqL0AwN0d\nmAB0zLDZ3tHzqcZVUj4r48bBgw/CTTeFXgQi+aZBAxg5Et55J/wUEcl3iSceQHOgHjA7bf1soGWG\nbVpmKN/UzBrmIqjFi+Hcc+HAAzXlveS3ffaBv/4V+vWDb75JOhoRkcrlQ+KRl664IkwCd+edGrND\n8t/118P668N552lsDxHJb/WTDgCYCywH0m9mtABmZdhmVobyC9192doGdMYZvfnww2bsskto4wFQ\nXFxMcXHx2u5apEZsvDHccQcccwyUlMBJJyUdkYgUspKSEkpKSlZZt2DBgipta54HX4/MbBLwlrv3\nih4bMBO41d1Xm3jezAYDXd29Xcq6h4EN3f2wCspPB4a7+61riKMDULrZZqVst10HXn4Z1lGdkNQi\nxcWh6/cnn0DLTDcqRURqQFlZGUVFRQBF7l6WqVy+XFaHAeeY2almtiMwktAddjSAmV1vZvenlB8J\nbG1mQ8xsBzPrDhwX7YdomwZm1s7M2gPrAr+NHm+zpmDmz4f77lPSIbXPbbdBvXrQvbtuuYhIfsqL\nS2vU5fViYBDwHtAW6OLuc6IiLYEtU8rPAA4HDgbeJ3SjPcvdU3u6bB7tqzTa/mKgDBi1pnh694at\nt167YxJJQvPm4ZbLU0/BY48lHY2IyOry4lZLvii/1fLuu6UUFXVIOhyRrB1/PLz0Enz8sW65iEg8\natutlryiXixS240YEcb4OP10WLEi6WhEpNCtWBHGvqoKJR4iBeg3vwntlMaNC3O6iIjUpJtvDmMJ\nVYUSD5ECdeih0LMn9O0bbrmIiNSE0tIwc/vJJ1etvBIPkQI2ZAhst10Y12Pp0qSjEZFCs2gRnHgi\ntG0LF1xQtW2UeIgUsPXWgzFjYMqU8I1ERCRX3EPX/Vmz4JFHQruyqlDiIVLg2raFoUPDDMtPPZV0\nNCJSKO66Cx56KEwtsu22Vd9OiYdIHXDBBXDssaGXyxdfJB2NiNR2b78d2pB17179KRqUeIjUAWZw\nzz2w6aZw3HGwZEnSEYlIbTVnTvgc6dABhg+v/vZKPETqiGbN4PHHYfJk6NUr6WhEpDZavnxlY/V/\n/APWXbf6+1DiIVKHtGsXBhcbNQpGj046GhGpba68MoyK/MgjsMUW2e2jfm5DEpF8d+aZ8Oab0K0b\n7LADdOyYdEQiUhs8+CAMHhwaqx94YPb7UY2HSB00YgTstRf86U8wc2bS0YhIvnv9dTj77PDF5aKL\n1m5fSjxE6qB114UnnoD114ejjoLFi5OOSETy1bRpcPTRoXb0jjvWfj4zJR4iddRvfgP//CdMnQqn\nnabJ5ERkdQsWwBFHwIYbhi8r2TQmTafEQ6QOa9s2jGz65JMa2VREVrV0aagR/fZbGDsWNtkkN/tV\n4iFSxx11VJhZcujQ7Prki0jh+fVXKC4OA4WNHRsaoueKerWICD17wjffQJ8+0LJl+MARkbrJHc49\nF559Fp55Bn7/+9zuX4mHiABw/fWhSvW006B5c+jcOemIRCQJl18eRjp+8EE4/PDc71+3WkQECC3V\n774bDjootGD/v/9LOiIRidvAgTBkCAwbBqecUjOvocRDRP6nQYMwrPruu0PXrjBpUtIRiUhcBg6E\nq66C666D3r1r7nWUeIjIKjbYIDQma98eunQJjctEpHC5w4ABIem4/vpwq6UmKfEQkdU0bgzPPQe/\n+x0ccgi8+27SEYlITXCH/v1h0KAwHHoc3eqVeIhIhZo0geefh512CvMyvPJK0hGJSC4tXw7du8O1\n18INN8Cll8bzuko8RCSjpk1h/Pgwr8uhh8LTTycdkYjkwtKlcPzxcNddoVH5JZfE99pKPESkUk2a\nhDYfRx4Jxx4L992XdEQisjZ++CF8kfjXv+Cpp+Css+J9fSUeIrJGDRvCI4/AOeeE2SmvvjrcGxaR\n2uWLL8KAYB9+CBMmwB//GH8MGkBMRKqkXr0wM+Vvfwt/+xv85z9w771hhlsRyX8TJoTbK7/5Dbzx\nBuy4YzJxqMZDRKrMLLSA/8c/wlDK++8fhloXkfzlDrfcEm6v7LknvPVWckkHKPEQkSwcd1wY2XTW\nLNhjD3jttaQjEpGKLFwIJ58MF14YlueeC1PcJ0mJh4hkZbfd4J13YNtt4YADwmiHK1YkHZWIlHv3\nXejQITQOLymBG28Mt0yTpsRDRLLWsiW8+GIY6fDKK0NV7uzZSUclUretWBHmWtlnH9hoI3jvPTjx\nxKSjWkmJh4islfr1Qy+X8eNDS/m2beHJJ5OOSqRumjoVOnWCiy6CCy4It0S32SbpqFalxENEcuLg\ng+H996FjxzDex4knwty5SUclUjcsXw433RQS/6+/hpdfDo/XXTfpyFanxENEcqZlyzAg0cMPwwsv\nwM47h3vLGvNDpOa89VZI+C+5BM49N9Q8duqUdFSZKfEQkZwyg+LiMM7H/vvDSSeFD8EPP0w6MpHC\nMmsWnH467L03/PwzvP46DB8eZpjOZ0o8RKRGtGgBjz8e2n58913oBXP++br9IrK2fvwx9CLbfvvQ\nY2XkSCgtDY1JawMlHiJSozp3DrUdQ4fCAw9AmzZh5NMFC5KOTKR2WbIk1GhsvTUMHAhnnAGffQbd\nuuVHN9mqUuIhIjWuQQPo0wemTYPzzgtJSJs2MHiwEhCRNVm4MHSP3W670I7jqKNC75VbboGNN046\nuupT4iEisWneHG64IUxUVVwcaj623DJ8mH71VdLRieSXb76BSy+FrbYKPw86CD79FEaNglatko4u\ne0o8RCR2m28OI0bAjBnQvXv4IG3TBk45JQy/rl4wUletWAHjxoUu6a1ahYkZzzkHpk+H++8PtR61\nnRIPEUnM5puH2y1ffglDhoRugfvvH7rhDhumUVCl7pgyBQYNCoN9HXpoaLtx003hf2PoUNhii6Qj\nzB0lHiKSuCZNQhuQKVPgpZegfXu47LKQmBx0ENx1l3rDSOGZNi0k3u3bh9lib7wxdD1/883QILtn\nT2jWLOkoc0+Jh4jkjXXWCRPOlZTAt9+GboJmoUFqy5ZwyCFw663h26Bux0ht8/PPYUTRvn1h111D\n7cagQbDDDmGagdmz4b77wrgcZklHW3PM9d/7P2bWASgtLS2lQ4cOSYcjIpHvvoMnngjLa6+FD/A2\nbaBLl9Bd9/e/D+OGiOSTn38OE7S9/jpMnBhq8378MbxXDz0UDjssLI0bJx1pbpSVlVFUVARQ5O5l\nmcrlTY2HmfUws+lmtsTMJpnZHmso38nMSs1sqZl9ZmanVVDmz2b2abTPD8ysa80dQbJKSkqSDqHO\n0TmPz6abhlqPs84qYd48ePZZOPzwMCz7sceG2pBtt4XTTgu3ZcrKYOnSpKMuDHqfV82KFaEm7rHH\nwmzNBxwAG24Yai/69w9dYi+/PAz09c03MHo0HH98xUlHoZ/zvEg8zOwE4CZgALAb8AEwzsyaZyjf\nGhgLvAi0A24B7jazzill9gEeBkYB7YFngKfNbOcaO5AEFfobNR/pnMevpKSExo3hiCPgttvg889D\n47tHHgnfHD/+OPSSKSoKH+i77BKGbB88GP71rzD2wS+/JH0UtYve56tavjy0zfj3v8N7sEePUOPW\ntGm4ZXLCCfDQQ6FtxtVXw6RJYayal1+Gfv2gQ4dwS7EyhX7O6ycdQKQ3cKe7PwBgZucChwNnAjdU\nUP48YJq7940eTzGzfaP9vBCt6wk87+7Dosd/ixKT84HuNXMYIhK3LbYIH/YnnBAeL14MH30UGud9\n8EFYxo6FRYvC8/XqhW6K224bllat4Le/Dcvmm4ef+T7XhdScJUvC7K5ffhmWr75a+fsXX4Sk4+ef\nQ9mGDcN7qH17OPro8LNdO/jNb5I9hnyXeOJhZg2AIuC68nXu7mY2AeiYYbO9gQlp68YBw1MedyTU\noqSXOWqtAhaRvLbBBqF6e++9V65zDxeOzz9fdZk4MaxPHz21WbOQhDRvDptssnJJfbzhhqE3TurS\nqFFhNwqsLdzhp5/C7Y2FC8PfN/X3efNgzpzQU2rOnFWXhQtX3dcmm4TkdostQuPm7bcPY2lsv30Y\n/K42DVWeLxJPPIDmQD0gvcf+bGCHDNu0zFC+qZk1dPdllZRpuXbhikhtYxZGf9xqKzjwwNWf//HH\ncN/9669X/TlvXrg4ffhh+H3evMqHeF9nnXCLpzwRadwY1luv4mX99Vd93LAh1K8fLmRV/VmRTP0F\nKutH4B7aKLiv+vuKFeE8PPpo5ufT163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Hr14xhLbc7b479O0L/frBe+9lHY2ISHFraOJxIHCemT1pZu3NbEPgHWBrYlVa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\n8MgjWUcjIuVKiUeRuOkmePN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d6i88kcV98gnsu2/Mg3HXXdCsIQaFF4GyMnjkkUhAzjor62hEROpHXd+y7wDO\ncvd93X2quz8H/Ab4ili0TaRBzJgBe+0Fyy8P//hH6a9zsvvucNVVMc36gw9mHY2IyJKr7SJxFbq5\n+/jcHe4+HTjQzA5b8rBEFrdgARx2GEyeHBNtrbhi1hGl4+STY26PXr1g/fWjJkREpLGqa+fS8VXc\nd1/dwxEp7KKL4KmnYvG3ddfNOpr0mMVQ4d/8JlbanTw564hEROquxomHmf3FzNrUsOxWZrZX3cMS\nWdTTT8P//R+cfz7suWfW0aSvTZtYxXbePPjzn+OniEhjVJsaj18Dn5vZUDPbw8x+VXGHmbUws65m\n1tfMRgAPAT/Wd7DSNH30UUwMts8+cPbZWUeTnVVXhb/9DUaMiEXwREQaoxonHu5+ODFBWEvgQWCS\nmc01sx+BOcQEYkcD9wIbuPsrDRCvNDGzZ8MBB8R6JvfeW7ojWGpq222jyemSS2KWUxGRxqZWnUvd\nfSxwrJkdD3QF1gDaANOAt919Wv2HKE3ZwIEwfnx0Jm3XLutoisPpp8PLL8c8Jm+/HTUhIiKNRa2+\nP5pZMzM7HfgPcBvQHXjc3Z9X0iH17bHHYOjQmA69a9esoykezZpF7U+rVnDwwervISKNS20rrs8G\nLiH6b3wF9AeG1HdQIhMnxvDRP/0JevfOOpri86tfwV//Cq++ChdckHU0IiI1V9vE43Cgr7vv7u5/\nAPYBDjGzJt7yLvXpl1/im3y7dnDbbTGcVBa33XbRyfTii+H117OORkSkZmqbMKwO/LPihrs/Dziw\nSn0GJU3bhRdGn45hw6B9+6yjKW5nnQVbbhn9PX7UODIRaQRqm3i0YPGF4H4hRrqILLFRo2LExqBB\n0L171tEUvxYt4P77Y1KxAQOyjkZEpHq1nTLdgLvNbE7OvtbAzWb2v8W73X3/+ghOmpaZM2NK9LKy\nWOpeambtteHaa+HYY2HvvWN2UxGRYlXbxOOeSvbdXx+BiJxxBnzxBTz5ZHyTl5rr1Sumkz/mGNh6\na+jUKeuIREQqV9t5PI5qqECkaXvuObjxRrj++lgITWrHLDribrwx9O0Ljz6qTrkiUpw0GkUyN306\nHHUU7LIL9OuXdTSN169+BUOGxJouDz+cdTQiIpVT4iGZO/FE+OknuPNOTYm+pA44ILYTToCpU7OO\nRkRkcXqbl0z94x+xzP0NN0DnzllHUxqGDAH3SD5ERIqNEg/JzPffR3+EvfeOeSikfqy0UiRyDz8c\nfT1ERIrD4wANAAAfwklEQVSJEg/JzGmnRRPLTTepI2R9O+gg2G+/SOymaRUlESkiSjwkEy+8ALff\nDldeCautlnU0pccsErpffoH+/bOORkRkISUekrqff4bjjoMddohJr6RhrLxyTCz24IPwr39lHY2I\nSFDiIak77zz4+uuYd0KjWBrWYYfBzjtHk8vMmVlHIyKixENSNmpUfAu/4AJYd92soyl9FU0uX38N\n55+fdTQiIko8JEVz58bU3pttpgXN0rTuunDuuXD11TB2bNbRiEhTp8RDUnPZZTB+PNxxh9ZiSdtp\np8VU9McfD/PnZx2NiDRlSjwkFR9+CBdfDKefDptsknU0TU+rVnDLLdHUdfPNWUcjIk2ZEg9pcO7R\nuXG11eCcc7KOpunadtsYTXTmmfDVV1lHIyJNlRIPaXDDhsW8HUOGQJs2WUfTtF12GSy9tOb2EJHs\nKPGQBjV9enQkPfBA2H33rKOR9u3huutiKvUnn8w6GhFpipR4SIM66yyYPRsGD846EqlQkQSeeKLm\n9hCR9CnxkAYzcmR0aLz4YlhllayjkQpmsYjcN9/ApZdmHY2INDVKPKRBzJsHvXtDt27Qp0/W0Ui+\nddaBM86AK66Ajz7KOhoRaUqKJvEws35m9qmZzTKzkWa2RTXldzSzcjObbWYfmtkRefcfY2avmNl3\nyfZcdeeU+nP99fDOO1Hj0bx51tFIZc48M2qiTjghRh6JiKShKBIPM+sBXA0MAjYDxgLDzaxDgfJr\nAk8BLwCbANcBt5vZrjnFdgAeBHYEtga+AJ41s5Ub5EnI/3zxRazH0q8flJVlHY0U0qZNJIjPPguP\nPZZ1NCLSVBRF4gEMAG5x93vd/QOgNzATOLpA+T7ABHc/3d3Hu/sQ4JHkPAC4+2HufrO7/9fdPwSO\nIZ7vzg36TIT+/aFtW7jooqwjkerss09sJ58MP/2UdTQi0hRknniYWUugjKi9AMDdHXge6F7gsK2T\n+3MNr6I8wDJAS+C7Ogcr1XrySfj732PIZtu2WUcjNXHddTBtmhJFEUlH5okH0AFoDkzO2z8Z6FTg\nmE4Fyrc1s6UKHHM58BWLJyxST37+OfoL7L47HHBA1tFITa21Vgx7vvpqGDcu62hEpNQVQ+LR4Mzs\nL8CBwB/cfW7W8ZSqiy6CKVNihlKzrKOR2jjtNFhzzeiXo46mItKQimGN0GnAfKBj3v6OwKQCx0wq\nUP4Hd5+Tu9PMTgVOB3Z29/dqEtCAAQNo167dIvt69uxJz549a3J4k/TBB/GN+ZxzoEuXrKOR2mrd\nOub22GMPeOghOOigrCMSkWI2bNgwhg0btsi+GTNm1OhY8yL4emNmI4FR7t4/uW3A58D17n5lJeUv\nA/Zw901y9j0ILO/ue+bsOx04E/i9u79Zgzi6AeXl5eV069ZtSZ9Wk+EOu+wCn30G774bH2LSOP3p\nT/D665FIqo+OiNTG6NGjKYuhjGXuPrpQuWJparkGONbMDjezDYCbgaWBuwHM7FIzuyen/M1AFzO7\n3MzWN7O+wAHJeUiOOQO4gBgZ87mZdUy2ZdJ5Sk3HX/8KL74IN96opKOxGzwYZsyA//u/rCMRkVJV\nFImHuz8MnEokCmOArsBu7j41KdIJ6JxTfiKwF7AL8DYxjLaXu+d2HO1NjGJ5BPg6ZxvYkM+lqfnh\nBxg4ML4paxG4xm/11eHccxdOACciUt+KoqmlWKippfYGDIDbbovREJ07V19eit/cudC1K3TsCC+9\npI7CIlIzja2pRRqh//43OiSed56SjlLSqlX8XV95BR58MOtoRKTUKPGQOlmwIBZ/W2+9mPVSSsuu\nu8Kf/wynnhp9PkRE6osSD6mTe+6BESNg6ND4hiyl55pr4Mcf1dFUROqXEg+pte++g9NPh0MOgR13\nzDoaaSirrRbNaDfcEM1qIiL1QYmH1NrZZ0cHxKuuyjoSaWgnnwzrrqsZTUWk/ijxkFp580245Ra4\n8ELoVGglHSkZrVrF/Cyvvgr33591NCJSCpR4SI3Nnx8dSjfZBPr2zToaScvOO0OPHtHR9Pvvs45G\nRBo7JR5SY7feCuXl0aG0RTGs8iOpufrqWH140KCsIxGRxk6Jh9TIlCmxdHqvXtC9e9bRSNpWXTVG\nt9x4I4wdm3U0ItKYKfGQGjnjDGjWDC67LOtIJCv9+8MGG0RH0wULso5GRBorJR5SrVdfhbvvhksv\nhQ4dso5GstKyZdR4vPYa3Hdf1tGISGOlxEOqNG9edCTdcks45piso5Gs7bQT9OwJp52mjqYiUjdK\nPKRKN9wA774bHUqb6dUixPwts2bFKrYiIrWljxIp6OuvYxRDnz4QCw6KwCqrwPnnRzI6ZkzW0YhI\nY6PEQwoaOBDatIGLLso6Eik2J54IG26ojqYiUntKPKRSzz8Pf/0rXHkltG+fdTRSbFq2hCFD4PXX\nY8FAEZGaUuIhi5k1K5pXdtgBDjss62ikWO2wAxx8cCwYOH161tGISGOhxEMWc8kl8NlncPPNYJZ1\nNFLMrrwS5syBc87JOhIRaSyUeMgixo2Dyy+HM8+MyaJEqlLR0fSmm2I6fRGR6ijxkP9xh969Yc01\nI/EQqYkTToCNNlJHUxGpGSUe8j933w2vvBLfXlu3zjoaaSwqOpqOGgV33ZV1NCJS7JR4CABTp8ay\n54ceGsugi9TG9tvHa+eMM+C777KORkSKmRIPAWIKbPdY/lykLq68En75JVYxFhEpRImH8O9/x1wM\nV1wBK62UdTTSWHXqBBdeCLfeGvN7iIhURolHEzdnTnQo3XZbOProrKORxq5fv5he/7jjYO7crKMR\nkWKkxKOJu+wymDAh5uzQInCypJo3h9tui2HZV12VdTQiUoz0UdOEvfceXHxxzDy50UZZRyOlYtNN\n4ZRT4IIL4KOPso5GRIqNEo8mav586NUL1l5by5tL/Rs0KCYX6907Oi2LiFRQ4tFE3XADvPEG3HGH\n5uyQ+rfMMjEfzIsvwr33Zh2NiBQTJR5N0IQJcPbZsbT5NttkHY2Uqt12i0XkTjkl5okREQElHk2O\nOxx7LPzqV9G/Q6QhDR4cr7mBA7OORESKhRKPJubOO6P6+9ZbYdlls45GSt1KK8WkdPfdB889l3U0\nIlIMlHg0IV9/Hd88jzoKfv/7rKORpuLII2HHHaOj6cyZWUcjIllT4tFEuEPfvtCmjaZFl3SZwS23\nwFdfwXnnZR2NiGRNiUcT8dBD8PjjsYpo+/ZZRyNNzXrrxbwe11yj6dRFmjolHk3AN99EbUePHrD/\n/llHI03VwIGw5ZbR1DdrVtbRiEhWlHiUuIpRLEstFbUdIllp3hzuugsmTlSTi0hTpsSjxN11Fzz9\ndKyfseKKWUcjTd2GG0aTy9VXq8lFpKlS4lHCJk6Ek0+OVWf33jvraESCmlxEmjYlHiVqwYJIONq3\nj0mcRIqFmlxEmjYlHiVqyBD4979jwrC2bbOORmRRanIRabqUeJSg99+HM86Afv1g552zjkakchVN\nLkceqYnFRJoSJR4lZs6cWJhrzTXhiiuyjkaksObN4e674Ysv4LTTso5GRNKixKPEnHkmjBsHw4bB\n0ktnHY1I1TbYAK66CoYOjdFXIlL6iibxMLN+Zvapmc0ys5FmtkU15Xc0s3Izm21mH5rZEXn3/9rM\nHknOucDMTmrYZ5C9f/0rOpJefjlssknW0YjUTJ8+sNde0Rl6ypSsoxGRhlYUiYeZ9QCuBgYBmwFj\ngeFm1qFA+TWBp4AXgE2A64DbzWzXnGJLA58AZwDfNFTsxWLKlGgr3313OKnkUywpJWZwxx0x2d3R\nR8dPESldRZF4AAOAW9z9Xnf/AOgNzASOLlC+DzDB3U939/HuPgR4JDkPAO7+lruf4e4PA3MbOP5M\nucecCAsWRJt5s2L5q4rUUMeOMQLr6afh5puzjkZEGlLmH1Fm1hIoI2ovAHB3B54Huhc4bOvk/lzD\nqyhf0m64AZ55JpKOjh2zjkakbvbeO5pdBg6EDz7IOhoRaSiZJx5AB6A5MDlv/2SgU4FjOhUo39bM\nlqrf8IrbqFFw6qnQvz/suWfW0YgsmauugjXWgIMOgtmzs45GRBpCMSQeUkfffgsHHgjdumnorJSG\npZeGhx6C8eNhwIDqy4tI49Mi6wCAacB8IL+RoCMwqcAxkwqU/8Hd5yxpQAMGDKBdu3aL7OvZsyc9\ne/Zc0lPXmwUL4PDD4aef4OGHoVWrrCMSqR9du8L118Nxx8H220MR/duJSGLYsGEMGzZskX0zZsyo\n0bGZJx7u/ouZlQM7A08AmJklt68vcNjrwB55+36f7F9igwcPplu3bvVxqgZz+eXRr+OZZ2D11bOO\nRqR+HXMMvPxyJB9lZbDeellHJCK5KvsyPnr0aMrKyqo9tliaWq4BjjWzw81sA+BmYjjs3QBmdqmZ\n3ZNT/magi5ldbmbrm1lf4IDkPCTHtDSzTcxsU6AVsGpye+2UnlODeeklOOccOOss2CM//RIpAWYx\numXVVaM5UavYipSOokg8kiGvpwIXAGOArsBu7j41KdIJ6JxTfiKwF7AL8DYxjLaXu+eOdFklOVd5\ncvypwGjgtoZ8Lg3tm2+i6nn77eH887OORqThLLtsNCOqv4dIacm8qaWCuw8Fhha476hK9r1CDMMt\ndL7PKJLEqr7Mng377x/fBocNgxZF89cTaRhdu8KNN0bTy29/C4cdlnVEIrKk9NHVSLjHHAdjxsAr\nr0CnQgONRUrM0UfDiBFw7LGw4Yaw+eZZRyQiS6KkagRK2XXXxQRht90WS4mLNBVmMGQIbLop/PGP\nMDl/Bh8RaVSUeDQCzz0XszkOHKiqZmmaWreGRx+FefPggANgbkkvgiBS2pR4FLmPP4YePWDXXWMI\nrUhTteqqkXyMGgUnn5x1NCJSV0o8itj338O++0KHDtGZtHnzrCMSydY220Szy003RbOjiDQ+6lxa\npObMifbsSZOiY1379llHJFIcjj02Oln36wfrrAM77ZR1RCJSG6rxKELuMXxwxAh4/HHYYIOsIxIp\nLtddBzvuGMn5uHFZRyMitaHEowiddx7cfz/cey9st13W0YgUn5Yt4W9/g86dY1VmjXQRaTyUeBSZ\n226Diy6KjqQ9emQdjUjxatcOnn46JtbbZx+YOTPriESkJpR4FJFHHoHevaFvXzjttKyjESl+q68O\nTz0F770XSwnMm5d1RCJSHSUeRWL4cDj4YDjoILjhhpg0SUSqV1YWzS7PPBN9oxYsyDoiEamKEo8i\nMGJErMGy224xO2kz/VVEamXPPeN/5557orbQPeuIRKQQDafN2Jgx8aa5xRaxEmfLlllHJNI4HXII\nTJ8OJ54Yc9+ceWbWEYlIZZR4ZGjMGNhlF1h3XXjiCWjTJuuIRBq3E06Ab7+Fs86Ctm1jrg8RKS5K\nPDIyZgzsvDOsvXasxdK2bdYRiZSG886DH36IJKRZs1jVWUSKhxKPDFQkHeusA88+C8svn3VEIqXD\nDK66KjqZ9u0bt3v3zjoqEamgxCNlo0bBHnso6RBpSGZwzTXRybRPn6j5OO64rKMSEVDikarnnosp\nnjfdNOYeUNIh0nDMYPDgSD6OPx5mzYL+/bOOSkSUeKTkkUdino5ddonfl14664hESp8ZXHsttG4N\nJ58co14GDdI8OSJZUuKRgltvjereHj1iroFWrbKOSKTpMIslCNq3jyG206dHTYjmyxHJhhKPBrRg\nQQzru/zyGNZ3/fV6sxPJyl/+EslHnz7w3Xdwxx36EiCSBSUeDWTmTDj8cHjssehhf8opqt4Vydrx\nx0ffqsMPhy+/jP/P9u2zjkqkadH37wYwaRLstBP885/xxjZwoJIOkWLRowe88AK88w507w4TJmQd\nkUjTosSjno0cGYtWffEFvPIK/OEPWUckIvm23RZefz2aQ7faCl57LeuIRJoOJR71xB1uugm23x7W\nWAPeeisSEBEpTuuuG8nHr38dNZRDh2pxOZE0KPGoBzNnwlFHxSyJxx0HL70Eq6ySdVQiUp0VV4Tn\nn48Op/36wZFHxnwfItJwlHgsobFjYfPNY2XZe++FG29UT3mRxqRlS7juOrjvPvjb3+C3v4VPPsk6\nKpHSpcSjjhYsiImJttwyEo233oLDDss6KhGpq0MPjaaXH36I2YXvuy/riERKkxKPOvjyS9hrLxgw\nIKpnR42KdmIRadw22SQWcdx//xhye+ihMGNG1lGJlBYlHrXgHrOQbrRRNLH885+xENVSS2UdmYjU\nl+WWg3vugQcegCefjNqPF17IOiqR0qHEo4YmTIh1Vo4/Hv78Z3j/fdh996yjEpGGcvDB8PbbsOaa\n8b9/7LGq/RCpD0o8qjFzJpx3XjSlTJgQK8zefrtWlhVpCtZaK2o7br4ZHnoo3gcef1zDbkWWhBKP\nAtzh0Udhww1jrZWBA+Hdd+Obj4g0Hc2aRU3ne+9Fs8sf/gB77gkffph1ZCKNkxKPSowdCzvuCAcc\nAF27xhvOxRfDMstkHZmIZKVzZ3jqKfj73+GDD2DjjeGMM2IUjIjUnBKPShx9NHz/PTzzTHQuW2ed\nrCMSkWJgFjUe778P55wTK06vvXYMrZ89O+voRBoHJR6VuOiiGFK3xx5ZRyIixahNm+j79eGHkYgM\nHAjrrQd33gm//JJ1dCLpKy+PZLwmlHhUYo89ol1XRKQqnTvDbbdFDcjWW0OvXrEGzI03Rsd0kVK2\nYAE88USsdbT55rHic03o41VEZAmtv34smzB2bEy53r9/DMO96CKYPDnr6ETq188/w5AhsMEGsN9+\n0cz40EMxIKMmlHiIiNSTrl1j4rGPPoI//Sk6pXfuDIccAq+9pmG40ni5x5ICxx0HK68cyfVmm8W+\n11+HAw+EFi1qdi4lHiIi9axLF7jpJvjqK7jsMnjjDdh22xgJc+ml8NlnWUcoUjNffAFXXBFz2Gyz\nDQwfHsuFfPJJ1HJsvXXtz6nEQ0SkgaywApxyCowfH2/Ym24KF14YzTDbbw+33AJTpmQdpciiPvkk\nko2ttoLVV4dBg6Bbt5hA89NP4fzzYY016n7+GlaMiIhIXTVrBr//fWw//gj/+Ec0yfTtC336xBv8\nPvvEtvHGMWxXJC1z50ZT4LPPxhpkY8fGyK3dd4/X6V57Qbt29fd4SjxERFK03HJw2GGxTZkS8wU9\n8QRccgmcfXZ8w/zd72ISw512itsi9emXX2LKiNdeiyUBXnopOoyutFIkx+ecE6M7G2rSTCUeIiIZ\nWWklOPLI2GbPjg+Af/0rft59d5RZa63oH7LFFrFtuim0bp1ZyNIITZ4Mb70FI0ZEsvHGGzBrVryO\nuneHc8+F3XaLztFpTCVRNH08zKyfmX1qZrPMbKSZbVFN+R3NrNzMZpvZh2Z2RCVl/mxm45JzjjWz\nkp0SbNiwYVmH0OTomqevlK9569ZRtX3ttbEq7rRp8NhjsPfeMUX7qafGh8Ryy8VoguOOgxtuiG+s\n33zTcCNmSvmaF6u6XvP582HcOPjrX+Evf4nXU6dOse29dyxwusIK0c/o9ddjteUXX4yp/zfdNL35\nq8yLYHyXmfUA7gGOA94ABgB/BtZz92mVlF8TeBcYCtwB7AJcC+zp7s8lZbYBXgbOAJ4GDkl+38zd\n3y8QRzegvLy8nG7dutXjM2x4++67L0888UTWYTQpuubpa8rXfM6cWKjyzTdjKy+PD5m5c+P+9u1j\n5MGvfx3zinTpErUlXbpA27Z1f9ymfM2zUtU1d4epU2PW3PHj42fF9vHHC18PnTvDJptEQlGxdenS\nsP2HRo8eTVlZGUCZu48uVK5YmloGALe4+70AZtYb2As4GriikvJ9gAnufnpye7yZbZuc57lk30nA\nP939muT2eWa2K3AC0LdhnoaISMNYaikoK4utd+/YN29ejDJ4//1YzPL99yMpefDBaLOvsMIK8aFT\nkYysthqssgqsumpsHTtCy5bZPC9Z1Lx50QwyYgR8/vni28SJUVMBkUSssUZM1/+738Uqyr/5TTSZ\nrLhipk+jSpknHmbWEigDLqnY5+5uZs8D3QsctjXwfN6+4cDgnNvdgasrKbPfEgUsIlIkWrSIKdrX\nXTdmkKxQ8a34009hwoSFPydMiPb9r79e+M0Y4gOsY8dIQlZZJarmO3SI7YsvogNshw7xYdahQ9Sg\naORN9ebPjyRhxoxYePT77+P3776LjsWTJy+6TZkSTWzu8HzyCbf88tHBePXVY1bcnj0j0VhvvVig\nsDH298k88QA6AM2B/ImFJwPrFzimU4Hybc1sKXefU0WZTksWrohIcTOLjqsrrRRDdfO5xwfc11/H\nJGcVW8XtMWPi/mnT4KefYjhlrubNo6/JcsvBsssu/L3iduvW0KpVbC1bLvp7xeyW7gv7pVT20z3W\nAqn4mft7VftqUr7Q4xaKpbL75syJDsG526xZC3//6acYOl1I+/aR7FVsG2208Pfbb4c77ojmkiVp\nJitWxZB4FAUzWxrYAGDcuHEZR1N7M2b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ceOWVaDfRkvXvD08/HW0/+vWDb7/NOiIRaY0a27j0w1q23dX4cESKw6efxoyw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\naaV45LXiisU1yGUxJB5Fwcw6AesCjBk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EVkf3PH265+nTPU9fqd9zrU6bw8zKgIqKioqW3rFHREQkVZWVlfTq1Qugl7tXFiqnGg8R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\nLroovhHedhvsskvW0Yg0vUs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rNU08DBhmZg+Xb0BLYGjePhFpRCZPht69oXv3+LC//354/3045pjoJJqVNm2g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\nMAC42d3vcvcPgb7AL8BRBcr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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#* Loop over desired number of steps (wave circles system once)\n", + "for iter in range(max_iter) :\n", + "\n", + " #* Compute new wave function using the Crank-Nicolson scheme\n", + " psi = np.dot(dCN,psi) \n", + " \n", + " #* Periodically record values for plotting\n", + " if (iter+1) % plot_iter < 1 : \n", + " iplot += 1\n", + " p_plot[:,iplot] = np.absolute(psi[:])**2 \n", + " plt.plot(x,p_plot[:,iplot]); # Display snap-shot of P(x)\n", + " plt.xlabel('x'); plt.ylabel('P(x,t)')\n", + " plt.title('Finished %d of %d iterations' % (iter,max_iter))\n", + " plt.axis(axisV)\n", + " plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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kXET2iMjtLttvFxG7iFRbP+0iUnp2j8JgMHjD8eNw8KDOrg0GSw8vZXCbwUSF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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#* Plot probability versus position at various times\n", + "pFinal = np.empty(N)\n", + "pFinal = np.absolute(psi[:])**2\n", + "for i in range(iplot+1) :\n", + " plt.plot(x,p_plot[:,i])\n", + "plt.xlabel('x'); plt.ylabel('P(x,t)')\n", + "plt.title('Probability density at various times')" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + } + ], + "metadata": { + "anaconda-cloud": {}, + "kernelspec": { + "display_name": "Python [default]", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.12" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} diff --git a/Python/.ipynb_checkpoints/Schro_T-checkpoint.ipynb b/Python/.ipynb_checkpoints/Schro_T-checkpoint.ipynb new file mode 100644 index 0000000..ac33b06 --- /dev/null +++ b/Python/.ipynb_checkpoints/Schro_T-checkpoint.ipynb @@ -0,0 +1,299 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Populating the interactive namespace from numpy and matplotlib\n" + ] + } + ], + "source": [ + "# schro_T - Program to solve the Schrodinger equation \n", + "# for a free particle using the Crank-Nicolson scheme\n", + "# Tridiagonal matrix version\n", + "\n", + "# Set up configuration options and special features\n", + "%pylab inline \n", + "\n", + "############## NOT WORKING ######################" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def tri_ge(a,b) :\n", + " # Function to solve b = a*x by Gaussian elimination where\n", + " # the matrix a is a packed tridiagonal matrix\n", + " # Inputs\n", + " # a Packed tridiagonal matrix, N by N unpacked\n", + " # b Column vector of length N\n", + " # Output \n", + " # x Solution of b = a*x; Column vector of length N\n", + "\n", + " #* Check that dimensions of a and b are compatible\n", + " N_a = shape(a)\n", + " N = len(b)\n", + " if N_a[0] != N or N_a[1] != 3 :\n", + " print 'Problem in tri_GE, inputs are incompatible'\n", + " return None\n", + "\n", + " #* Unpack diagonals of triangular matrix into vectors\n", + " alpha = empty(N-1,dtype=complex)\n", + " beta = empty(N,dtype=complex)\n", + " gamma = empty(N-1,dtype=complex)\n", + " alpha = a[1:N,0]\n", + " beta = a[:,1]\n", + " gamma = a[0:(N-1),2]\n", + "\n", + " #* Perform forward elimination\n", + " for i in range(1,N) :\n", + " coeff = alpha[i-1]/beta[i-1]\n", + " beta[i] = beta[i] - coeff*gamma[i-1]\n", + " b[i] = b[i] - coeff*b[i-1]\n", + "\n", + " #* Perform back substitution\n", + " x = empty(N,dtype=complex)\n", + " x[-1] = b[-1]/beta[-1]\n", + " for i in reversed(range(N-1)) :\n", + " x[i] = (b[i] - gamma[i] * x[i+1])/beta[i]\n", + "\n", + " return x" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Enter number of grid points: 100\n", + "Enter time step: 1\n" + ] + } + ], + "source": [ + "#* Initialize parameters (grid spacing, time step, etc.)\n", + "i_imag = 1j # Imaginary i\n", + "N = input('Enter number of grid points: ');\n", + "L = 100. # System extends from -L/2 to L/2\n", + "h = L/(N-1) # Grid size\n", + "x = arange(N)*h - L/2. # Coordinates of grid points\n", + "h_bar = 1. # Natural units\n", + "mass = 1. # Natural units\n", + "tau = input('Enter time step: ')" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Set up the Hamiltonian operator matrix\n", + "ham = zeros((N,3)) # Set all elements to zero\n", + "coeff = -h_bar**2/(2*mass*h**2)\n", + "for i in range(1,N-1) :\n", + " ham[i,0] = coeff\n", + " ham[i,1] = -2*coeff # Set interior rows\n", + " ham[i,2] = coeff\n", + "\n", + "# First and last rows for periodic boundary conditions\n", + "ham[0,0] = 0.; ham[0,1] = 0.; ham[0,2] = 0.\n", + "ham[-1,0] = 0.; ham[-1,1] = 0.; ham[-1,2] = 0.\n", + "\n", + "#* Compute the Q matrix\n", + "tri_eye = zeros((N,3))\n", + "tri_eye[:,1] = 1.\n", + "Q = 0.5 * (tri_eye + 0.5*i_imag*tau/h_bar*ham) " + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Initialize the wavefunction \n", + "x0 = 0. # Location of the center of the wavepacket\n", + "velocity = 0.5 # Average velocity of the packet\n", + "k0 = mass*velocity/h_bar; # Average wavenumber\n", + "sigma0 = L/10. # Standard deviation of the wavefunction\n", + "Norm_psi = 1/(sqrt(sigma0*sqrt(pi))) # Normalization\n", + "psi = empty(N,dtype=complex)\n", + "for i in range(N) :\n", + " psi[i] = Norm_psi * exp(i_imag*k0*x[i]) * exp(-(x[i]-x0)**2/(2*sigma0**2))" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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pFuu79ajYnaNywVsXMO3baQG0UghRHyRQEULY1rtFbwDW5a4LyfVdS5OVsli/\nRo9Kfr7Z88eK3Yd2szFvY4AtFUKEmgQqQgjbumd0J1pF8+P+0MxTsZtDJb84nyaxTYiPiSc9HSoq\n4PBha+fKfj9ChDcJVIQQtsXHxNM9oztrc0MzT8VuoFKpK+nYrCMQwMaESZnkHs2110AhRL2RQEUI\nUc2RsiO8s/4dv/NPpv5qKud0PickbcjLs55DBeDOwXey7g9mGMp1ntUJtS2atJAeFSHCmAQqQohq\n/vfL/7jk3Uv45fAvPutd2/9aLuh+QUjaEEj6fJdAelQOHJVARYhwJYGKEKKa7/d8T3JcMt3SuzVY\nG+o1UGmSSUFpAeWV5YHdUAgRUhKoCCGq+W7Pd/Rv1Z/oqOgGa0NdApWkJEhIsB6otGjSAoC8Ykm+\nIkQ4kkBFCFHNd79812A7JoNZsVNYaG+OSk0ZGdbnqPTK7MWDZz1IfEx84DcUQoRMTEM3QAgRPgpL\nC9lRtIP+rfo3WBsOHjRfA+1RcZ1rtUclOy2bB85+IPCbCSFCKiJ7VJRSNyqlcpRSJUqp5Uoprx//\nlFJZSqk3lFKblFKVSqmn67OtQkSSbQXbAOjSvEuDtcHuPj+eyH4/QjQeEdejopS6FHgKmAL8D5gK\nfKyU6qq19tTZGw/kAg876wpxQvvwQ/j6azM0kpdnhlkeeQQGDz4eqHRK69Rg7WusgcoNN8D27WZY\nKiMDWrY0ZXX5OYU4EURij8pU4AWt9b+01huB3wHFwGRPlbXWO7TWU7XWrwOH6rGdQoSdY8fgsstg\n9mxYs8Y8X7sWXn/dHD987DBtm7aleWJzS9c7dOwQCzYtCOqeP665JVbnqGzM28iglwexOX9zVZmd\nOSr1Yd8+ePFFOHoUfvkFliyBBx6AWbMaumVChL+IClSUUrHAAGCJq0xrrYFPgUEN1S4hIsWXX5o3\ny8WL4X//g4UL4cILYdkyc/yaftewa+oulMVNdnYV7WL8W+NZf2B90Nro6glJS7NWf8/hPSzfvZwo\ndfzPWbj1qHz1lfk6bx58/jmsWwfjxsGiRQ3aLCEiQkQFKkAGEA3sr1G+H8iq/+YIEVkWLYI2baB3\n7+NlQ4aYN86CAvvXy0o2/+32HdkXpBaaAKNZM4ixODBdtXNy4vExlHAMVLKzzWvvMmYMfPttYK+7\nECeSSAtUhBB1sHAhjB5dfVfiM880X7/5xv710hLTiI2KDXqgYmtDwpJ8olQUqQmpVWXp6VBcDKWl\nQWtWnXyNx5vFAAAgAElEQVT11fHX2WX0aHA4TO+WEMK7SJtMmwdUAi1rlLcEgveX0mnq1KmkpqZW\nK5s4cSITJ04M9q2ECLlt22DTJnjsserl2dnQqpV5Mx071t41o1QULZNbsvfw3qC1Mz/fXg6V/OJ8\nmic2rzb04zo/P796L4Y3uUdz2X1od0iWZR8+DKtXm4mz7tq2NT1bCxfCpZcG/bZC1Iu5c+cyd+7c\namVFRcGbswYRFqhorcuVUiuBEcB8AGUG00cA04N9v2nTptG/f8PlkxAimBYtgthYGDGierlSZvjH\nNY/CrqzkrKD2qOTl2e9RcR/2gePn5+VZC1Rmr57N37/+Owf/dNBGS61ZscL0nAwZUvvYmDFmYrPD\nAVHSvy0ikKcP76tWrWLAgAFBu0ck/td4GrheKXWVUqo7MAtIAl4FUEo9ppSa436CUuoUpVRfIBnI\ndD7vUc/tFqJBLVxo3iybNq19bMgQM7k2kKGSVsmt2He0YYd+0pM8ByrhsN/PsmWmPd271z42ejTk\n5sKqVUG/rRCNRsQFKlrrt4E7gYeA1UAfYJTW2rX9aRbQrsZpq4GVQH/gcmAV8FG9NFiIMFBSAp99\nZj7BezJkCJSVwfff2792sHtUbAcqxd57VOzsoAyh2e/nq6/gjDOqzwtyGTzYBI6y+kcI7yIuUAHQ\nWs/QWnfUWidqrQdprb93O3aN1np4jfpRWuvoGo+Gy2glRD374gsTrHgLVPr0geTkwIZ/spKzqlbe\nBIPdOSrndzufCT0nVCtLTYXoaHs9KgAHig/4qWlPeTksX+552AfMUNw555jeLiGEZxEZqAgh7Fm4\nENq3hx5eBjxjYqDZb3/PzF2/t33t+4bex9ZbttaxhYbW9ntUrh9wPVeecmW1MqXMNawmfXP1qBw4\nGtxA5YcfzOojb4EKmOGfFSvCK0GdEOFEAhUhTgCLFpneFF953HSrVezLLcPhsHftuOg4ywni/Ckq\ngsrK4KSVt5NLpUWTFkDwe1S++goSEsDXvMJzzzUBmixTFsIzCVSEaOS2bIGffzaf3H05EruNsv2d\nWB+8JLO2BWOfHxc7gUpyXDLx0fHkHs2t+43dLFsGAwdCXJz3Oq1bQ79+MvwjhDcSqAjRyC1aZN4o\nhw/3XufQsUMUlecRdahTwMuUg8EVWNiZo+JNRob1QEUpRWaTzKAO/WhtelR8Dfu4jB4NH39sepOE\nENVJoCJEI7doEQwdaibLepNTkANA9xYNG6i45mkEq0fFzryPb6/9lj8P+XPdb+y0ZQscOGAtUBkz\nxrR15cqg3V6IRkMCFSEaMa3NRM2hQ33X21awDYChfcKjR6W+h34A2jZtS5O4JnW/sdNXX5k5QYMs\nbJd6+umm12vFiqDdXohGQwIVIRqxnTvNpnf9+vmut61gG8lxyfx6cAY7d5rzGkJ+PiQlmQmoddXQ\nGxMuW2aWfdfYhcOj2Fg4+WSTal8IUZ0EKkI0Yq43PiuBSqe0TgwZYlbvLF8e4oZ5Ecg+P1sPel4a\nnZEBhYVQURGkxtm0YoVJ9GZVv34SqAjhiQQqQjRiq1dDZqZZWeLLxT0v5p4h99CihcmUmpNj7z7P\nLn+WOz6+I/CGOtnNoTJnzRxOmXWKx2Ou6xQU1LlZtmltXsMuXayf068frF9vMgQLIY6TQEWIRmz1\navMG6C/NybDsYVx6stnCt0MH2LHD3n22FWzj460fB9jK42xvSFicT0aS5y4Y940J61turtk3qUMH\n6+f062cy2dZcHr5m3xqWbFvitedIiMZOAhUhGjFXoGJHIIFKsPb7OXiw7hsSutjd7yeYXK+fnUCl\nTx8TUNYc/nnimycY+dpIuv+jOz/s+yF4jRQiQkigIkQjdeAA7N5df4FKfkk+ZZV1G7c4eBDS0qzX\nzy+pvSGhi+s6DTH0E0igkpwMXbvW3kn5+THP8/PNP9M6pTXPLH8meI0UIkJIoCJEI+X6ZN6/v73z\nOnY0b7RaWz8nKzkLoM6ZXQsKbAYqxd57VOwGKnnFefz+w9/z04GfrDfAix07TODRvLm98/r3r92j\n0iyhGZ2bd+bm029m7rq5Qd2pWohIIIGKEI3U6tWQkgKdO9s7r0MHOHLEXk+EK1Cp65uo7UDFR49K\nfDwkJlr/ORzawayVs9iUv8l6A7zYscO8jna3QOrXD9as8Zyh9rr+1xEbFcuM72bUuX1CRBIJVIRo\npFavhlNOgSib/8tdwxV2hn9cgcrew3vt3cxNZaXZlNBOL0R+sfdABcy1rAYqzRObV12zrlyBil39\n+sHRo2ZvppqaJTRjcr/JzPx+JiXlJXVuoxCRQgIVIRqpQCbSQmCBSmaTTBSqTj0qRUXmq+0eFS9D\nP65rWQ1UYqJiaJbQjLziui8TqkugAt7zqdw68Fbyi/N5c+2bgTdOiAgjgYoQjdCRI2avGSuByoeb\nP2Rj3saq5y1amMywdgKVmKgYbjr9JjqldQqgtYYroLAaqGitWfO7NVze+3KvdewEKgAZSRnklzRc\nj8ry/I9Ivvg2Vq72vDth5+ad+eCyD7ik1yV1bKEQkUMCFSEaoTVrzGRYK4HK5P9M5u31b1c9Vwra\nt7e/8mf66OmM6DTCZkuPsxuoKKXomt7Vax4V17XsBCrpiel17lEpKjKPQAKVl1a/REz2N6xZHe21\nzvhu40mJT6lDC4WILBKoCNEIrV5t9o/p2dN3vSNlRzhQfKBWT0ggS5Tr6uBB89XO0I8/aWnHr2tF\nMHpUAlmaDHDo2CEWbVnEaUmXsnq1vVVXQjRmEqgI0QitXm02uYuL810vp8Dkys9ull2tvCECFbs9\nKlbY7lFJqnuPSqCByn82/odjlce4pNcl5OXBL7/UqRlCNBoSqAjRCFmdSJtT6AxU0sIjUImONkuq\ng8VuoHJqq1M5paXnvYOs2rHDBIhZWfbOm7d+HoPbDeacge0A2aBQCBcJVIRoZMrKYN06a4necgpy\niI+Or1pe7NKhg9kj5+jREDXSg4ICaNbMfu4RX+wGKjcPvJkZY+uWp2THDmjXzt6y8EPHDrF462Iu\n7XUp7dqZ9P8SqAhhSKAiRCOzYYPZ3M5qj0rHZh2JUtX/FLiGLXbuDEEDvbCb7M2KtDQ4dgxK6jHt\nSCArfn7c/yPljnKGdRyGUuZ3J4GKEIYEKkI0MqtWmV6JPn38180pzKk17AOB5VKpq1AFKq5r15dA\nApX1ueuJiYqhW0Y3wAQqNff88URrTXF5cQCtFCJySKAiRCOzerXZ3C452X/dw8cO06lZ7dwnbdqY\n+SJ2AhWHdrDn8B6OlB2x0drjCgrsZaX9z8b/8NyK53zWcV0v3AOVwe0G848x/yAu2sx+7tfP9Gb5\n2/l57JtjuWnhTQG2VIjIIIGKEI2MnYy0Syct5bkxtd/sY2JMsGInUDlSdoQ2T7fho80fWT/Jjd0e\nlQ83f8hrP77ms05996iUlsL+/fYDld4tezNlwJSq567f3w8/+D6vT8s+fLj5QyodnhPECdEYSKAi\nRCPicJhkb3ZS59ecn+Jid+VPSlwKiTGJAafRtxuoFB4rJC3R9wn1Hai45vQEkuzNXZcukJTkf57K\n+G7jOVB8gBW/rKjbDYUIYxKoCNGI/PyzSZ9vZcWPP3YDFaUUWclZ9RaoFJQU0Cyhmc869R2oBJpD\npaboaOjb13+gMrDNQDKTMlmwaUHdbihEGJNARYhGxDUBM5DNCGsKJJdKVnIW+44GFqgcPGizR6W0\nkGbxvgOVuDjTM2EnOy2YSaqB2LHDTGRu2zag06uxMqE2OiqasV3HMn/z/LrfUIgwJYGKEI3I6tVU\n5eGoqw4dYM8es9TZqkB7VCor4dAhmz0qpQV+h37Afi6VPjP7cPeSu62f4GbHDmjd2n9GYCv69YNN\nm/znshnfdTwbDmxg68Gtdb+pEGFIAhUhGpHVq4Mz7AMmUHE4YPdu6+cEGqgUFpqvtntU/Az9uK5p\nJ1BJiEkgvziw/X4C3TXZk/79zX4/P/7ou96vO/+auOg4FmyW4R/RONkOVJRSzZRS1yilXlFKLVFK\nfauUmq+U+otSanAoGimE8E9rM1QQjGEfCCyXSqCBit19frTWIQtU0pPSySsJbL+fYAYqvXqZjSX9\nDf8kxyUzInsES3OWBufGQoQZy4GKUqq1UuolYC9wH5AI/AAsAXYDw4BPlFIblFKXhqKxQgjvdu82\neTeCFai0b2++2g1Uco/m2l4uazdQKa0o5dTWp9I+tb3funYDlYykjHrrUdFaM+v7WWwv3F7rWFyc\nCVasZKidff5s3r/0fes3FiKCxNiouxqYAwzQWm/wVEEplQhcANymlGqntX4yCG0UQljgekOzEqhU\nOio57Z+n8fCwhxnbdazHOomJ0KKFvUDlwu4XMqjtIJTNDXvsBiqJsYmsuM7akty0NNiyxXpb0hPT\nWblnpfUTnCoqTLBoJ1DZe2Qvv//o93xw6Qd0bNax1nGrqfRbJre0flMhIoydQKWn1trnxwytdQkw\nF5irlArCdD4hGpf5m+Yz6/tZJMcl88Svn6BDsyCNE2De0DIyrK042XN4D6v3rfYbUNhd+ZPZJJPM\nJpnWT3CyG6jYEVCPSon9HpU9e8ykYDuByrrcdQCc3OJkj8f794c33jAbTQZjgq4Qkcjy0I+/IMVF\nOf/yWa0vxIkkJiqGhJgEvt39Lee8fg4Hjh4I2rVd81OsdGbkFOYAkN2s9j4/7gJZohyIggKTOyQl\nJfjXbt7c5hyVxHTyi/NtL1EOJIfK+tz1JMYketxvCczvs6zMbDQpxIkqoFU/SqlXlVJNPJR3BL6s\nY5uEaLTGdBnD+5e+z+eTPqeotIjRb4zm8LHDQbm2ndT5OQUmUPE03OCuPgOVtDRrQZZdgfSoVOpK\nio4V2bpPIIHKutx19Mzs6TU78CmnmNdEdlIWJ7JAlyefAvyolBrkKlBKTQLWAIFNlxfiBNK5eWf+\ne8V/2XJwCxfMu4DSitI6XS8vD3btsr40Oacwh6zkLBJjE33W69DBpIV3OOrUPL9CsXOyS1oaHDsG\nJSXW6g9qN4h5F88jPjre1n127DD5a5rU+gjn3foD6+nVopfX48nJZoNJCVTEiSzQQOV04H3gc6XU\no0qpt4HngTu11hcGrXVCRJg9h/fwza5vLNXtm9WXBRMX8M2ub7ji/Stw6MCjATsTacEEKp3Sau+a\nXFOHDmboYV9gyWYtC3Wg4rqHFW2btuWSXpf4DeJq2r7d/oqf9QfWc3Km5/kpLlYy1ArRmAUUqGit\ny7XWfwT+BvwZs9LnHK31P4PZOCEiyd7Dexk2ZxjXzr/W8vLcoR2G8vqFr7Nq7yp2Fe0K+N6rV5tP\n3yedZK1+TkGO3/kpEFgulUDYTZ9vh+u6dtPo27Vzp71AZWfRTo6UHfHZowImUFmzxnqvVlllGYWl\nhdYbIkSYs7Pqp4pSKhYTpNwIPAYMAd5XSl2rtV4YxPYJEVYKC+Hdd+Gtt473MigFjqR97B8zjPjk\no3x5zRdER0VbvuZFPS7igu4X2DqnptWrzSZ2URY/emwr2MZZHc7yW8+1gmjPnoCbZklBAbQM0Qrb\n+tqY8JdfYPhw6/UPFB+gU1onryt+XPr3NxtN/vyzGQbyp++svow+aTRPjXrKemN8WLEC7r8f9u41\nSQW1NhOfzzoLrrgCTjstNHOLhHAJdOjne2A8cLbW+l7gbOAZTLAyI0ht80opdaNSKkcpVaKUWq6U\nOs1P/bOVUiuVUqVKqc3O+TRCWKI1LFwIF19s3kxvuMH8YR45EkaMgFNH7OKXkcPIP3wYPftzVi3p\njJ0FI0qpOgUpYD8j7R2D7mBMlzF+66WlmeyodoZ+3t3wLnN+mGP9BOwP/dy08CYmvDPBUt36ClT2\n7YOsLOv1T219Kltv2eo3aZ3r92p1+OesDmfx743/DnhjRZe9e+Hqq+FXv4L9++Hss00gNnIkDBxo\nAvaBA6FbN3joIVNHiFCoS6DSV2u9HEAbfwcGAUOD1ThPnFlvnwIeAPphJvB+rJTK8FK/I/AhJoPu\nKcCzwEtKqV+Hsp0i8jkc8N575hPt2LGwbRv87W8mqdcnn8Azz8Af/m8TSzqcQbPMEj65/HNO7XQS\nl1xi/qDvCnwkx5YjR0xCMzuBytRBUxnUbpDfelFRJjizE6jM3zSfl1e/bP0E7Acquw7toqTc2uzY\n+ghUyspMVmA7gYpV6elmo0mrE2ov6H4BOYU5rM1dG/A9Z8wwvTcffggvvAArV8L06fDss+bf/Ysv\nmn/fn3wCZ5wBTzwBHTvCrbfa2xtKCCsCGvrRWl/rpXy1UmpA3Zrk11TgBa31vwCUUr8DxgKTgcc9\n1P89sE1rfZfz+Sal1BDndT4JcVtFBDp2DObNg7//3eSvGDECPv8chg6t3sW9cs9Kzn3jXFo0acHi\nKxbTpmkbRs6Hjz+G666D88+Hr782GV5Dac0a0+sTrNT5NbVqZT5dW5WemM73e763dQ+7gUphaaGl\n9PlgEqUlJYU2UHH1JrRqFZrrW81QCzAsexhN45vywcYP6NOyj+17vfUW3Hij6Tl87DHvv5foaNO7\nMnIkPP00PPecCWJmzTI9MSdPeJ/FB2bj0A7iouPo0rwLPTJ60COzBz0ze9I0vqnttokTk529fiwt\nutNaH7NT3w7n3JgBmN4R1/008CmmN8eTXzmPu/vYR31xgtq3Dx580EyInDTJfEL85hv49FMzHl9z\nHH7e+nl0TuvMl1d/SZumbarKR42CBQtg40aYMgVbw0CBWL3avBn37Bma62dl2etRsZvZtbISDh2y\nF6gUlBTQLN7/hoQudnOp2OV6fULRowKmV2/1amv/luKi4xjbZSzvbnjX9vDPmjUweTL89rcwc6b1\n30lampnHsmOHGQb64AO45Rb43/IoCvJiKS4v4Z0N7zB5/mQGvTyI1L+lMvJfI221TZy47PSo/KyU\nehaYo7X2+PnKmZV2JHA7JvHbY3VvYjUZQDRQczR0P9DNyzlZXuo3VUrFuwKrSLF1Kyzf4Xuwuk1S\nNk3jvP+FOVxewC/FOV6PKwU9mvWv9tzFNZluz9GdHK04BCjQyrkiQYEGrRUJKoX0uDZUVlLt4XCY\nR2WlZt3hL6nQZZTrY1RSRrnjGI6oY1SqUipVKUNajKVbZheSk6l6pKQcnzC6dv9a3l7/Nk3jm5IS\nn0KzhGa0a9qODs060Cq5laV5H7t2waJFZg7KwoVmPsbVV8PNN0P37r7P/dvIv1FaUUpSbFKtY337\nwksvmT/4p51m/miHynffwcknhy7FelaWveWx6UnHM7ta2fOn0LlApXlz6/ewunOyi93stCv3rGTf\nkX1e90GqqT4Clbw8Ewh07Oi//qRTJnHuG+fy1c6vOLPDmZbucfAgXHihmXPy4ouBTZBNSYE//Qlu\nuw3mzbuIZ5+9iG+nm9VoF18Aw0cVk95tEz/l/0hZZZnf663YvYLWKa3JSs4iNjrWY51jx6CoCI4e\nNcOgR45AaSmUl0NZmaa47BhljlLKHeZvTLk+hoMKHKocpRx0Tj6F6GjTQxQVRbXvo6Jg+9ENHK44\nSJRSKKVQiqrvo5SiWXwG7ZM7V7WnZmxY6XCwqeiHqufu/ydcddskdSIlNtXr61BYls/e4tpL7zIS\nWnFm31Yk1f4T1KjYCVTOBh4FHlRKrcHMU9kDlAJpQE9ML0UFJkB5IagtFQBMnQoLBvgZXXv7bdjg\nY6Jhz0/hkkt8X+NBP5/EJtwBvd71fnz9xfDOO37ucbbn8soYqEhg5mMdYWOXaoeiosynt/R0UN23\ns/PkOVTGHKZcHUKr4+s3o1UMbZt04t3h64gmFq2huBhyco4/Vq6EtWvNNQcPNkM911wDzSy+/0Wp\nKI9Bisvll8P338Ptt5sMo2f5X2Rjm9bw2Wdmom+otGplv0fFldnVSjARyD4/BaUFpCVaP8Fuj8q/\n1vyLpduX2gpUoqLMJo6hcMYZJnD47DPzb9SfczqfQ/eM7jyz4hlLgUplpfn3WlQES5bg943vpwM/\n8cHGD7j7zLs9Ho+Ph6uugiuvNMOfr7wCr78OTz6ZREpKP846qx9dusBz30B2tgnwoqPNz6iUCTL2\n55cybvmvqq4ZrROIqUwhqrwpjvJ4Kish+uPnObZxmPeG9p0DF/h4wcoT4BE/c50m/gm6fej9+Jor\n4d//8n485hjc5+dv9pvzYfN53o+f8hFc6GENyOcPsPKpBy0neoxUlgMVrfUm4DdKqfbABOBMYDCQ\niMlGuxq4Hliktba3x7t1eUAlUHMhY0vA25/SfV7qH/LXmzJ16lRSU6tHuRMnTmTixImWGxxs06bB\npTuq7+xa81Nr61Edaerj0/WhspHsKTEfkWtG/66u4u7feT9fKdhx5BEOV9xh6kdpQDs/gWmioxXp\nY9I56ZHjn1Bqf1JRbCvaTFx0LHHR8cRHxxMbFU+0jkdXxphPQ5NMNlHXp6RDh8ybzcGDZuJifv55\nnLTmPHJzYX+uJrfwMKVxu6DZdiqb7WBHQgGn3Vn7U1hmpvnjOGAA3PrnfC48tznNm9f++Ki1RqO9\npje34vHHTZf9hAnwww/QurX/cz7L+Yy317/NzHEz/dbdutX0CtlZFmtXVpaZg+FwWFv+nJ5o9iPN\nK84LSaBS4ajgSNkRWz0qdgOV9KR08oqtJ9neu9f8u4qu2+Itr5o3N/NUli61Fqgopbh14K38c9U/\nKassIy7ad3fbgw+aibH//a/5v+HL/E3zueSdS2if2p4/nPYHUhO89wQoBUOGmIfDYf4PLFwIX30F\nH31kkuSVeetYUbGQsQ6VtoOkzFxS0g+T2OwQcU0PEZ9URkKy5qzrMjg503y4cPW6NmkCCQmmd/SX\nkjP5Ie81EmLij/+diY4jRsUSRQzRKpaT/+Dq5a3+1fX9niMzKa54gkqHdvYom78LDof5u9dkeCpZ\n93h/vRw6ni2Hfe/G3fbcTqR47jACoLBsLHuLa18j49et/Pb8htrcuXOZO3dutbKiInvbT/hjezKt\n1nonZtVNcBbp27t3uVJqJTACmA9Vw00jgOleTvsWGF2j7BxnuU/Tpk2jf5iFqp07Q+fOdW1TmvMR\nuAFYSOjgR0ZGF/+VLFNAU44d60VhYS8KCuCwcwsd16e0hAQz/yQ5+fhZ2c+eym0v5NE9ozutU1pX\n/RFyZQ39+8i/c0kvP71PPsTEmIm5vXrBvffC7Nn+zzlYcpBZK2cxddBUuqb7fp2XLDFvjkNDuNYu\nKwsqKkxwmGlhY+SMJLMAL784n5Oa+89AZzdQKSo1fwTtBiqbN1uububZ2Bi+srs02ep13Y0YYXol\ntLY2LHN9/+u5YcANfu+zebNZzXb//fBrP2shX/3hVa6bfx0X9riQ1y58jYSYBMvtj4oyQ1juf1Id\nDhPk7d9/fFhZaxNkpKVF06xZL1JSelnOD1RTezozqFtn/xV96IWF7ch9iuJ06vo3O935CD+ePryv\nWrWKAf56/m0IaNVPA3saeNUZsPwPs3onCXgVQCn1GNBaa+3qJ5sF3KiU+jvwCiaouRjwn0RCRJz4\neLOc1mrysH+M+Qfrc9fzU95P5B7NdY47R6GUYlyXcX4DBStatIC//AVuusks3+zb13f90V1GkxiT\nyAcbP+CuM+7yWXfpUjMHpqnFBRSFpYUs372cM9ufSZM4a/PdXStZ9u2zFqi0aNKC3i16o7E2kdOV\nMdZqoBIfE89zo5+jX5b1ZU5pafYy06YnplPuKOdw2WFLq1P27bO34ue6+ddRUFrA+5e+b/mc4cPN\nMuBNm/zPnwIs5+b5059MT99dvv+p8fS3T3PH4juY0n8KM8bOqHPuHzDBS5s25iGEN5YDFaXU08D/\naa2POr/3Smt9e51b5v3abztzpjyEGcL5ARiltT7grJIFtHOrv10pNRaYBtwC7Aau1VrXXAkkTkBj\nuoyxlPisrq6/3uShuOMOs4rI14fcpNgkRp00ym+g4nCYQOWGG6y3Y/nu5Yx+YzTbbtlGdpz/FPpw\nvKdg717o3dt//ZbJLfnx9z9ablNBgekVcu/p8iU5LpmbTr/J8vUhsB2UwfQKWQlU9u61Fjy4bDm4\nhXap7fxXdHPmmaanYckSe/fy5csvzQqd11/3voxea819S+/j0a8e5e4hd/PI8Eds9wYJURd2OtT6\nAbFu33t7+Pm8WHda6xla645a60St9SCt9fdux67RWg+vUf9LrfUAZ/0uWuvXQt1GIdzFxppPw0uX\nmjF6fy7odgHLdy9n72HvCUzWrjUrQUaMsN6OdbnrSIpNokMz65vSuAKVUG1M6MqhEsr3PlegYnW1\nbnrS8Xk2Vtgd+skptLbXkrsmTUyW2CVL/Ne1wuEwgfOpp4KvaXcPfP4Aj371KE/8+gkeHfGoBCmi\n3tmZTDvM0/dCCGvGjYNhw+CPfzS5VmJ8/O8b13UcSikWbF7AlAFTPNZZutTMuxlkIyPQ+gPr6ZXZ\ny9YE4YQEM1kx1IFKKKWlmUmbJSX+V7SAW4+KhXwwWtsb+jlWcYxfDv1iO1ABM/wzfbqZ5FnXibtz\n55pVaV984XuS9PDs4bRo0sJ2L5YQwRL4cgY3SqmmSqkLlFINPP9YiPClFDz5pEkE99JLvuumJ6Uz\ntMNQ/r3x317rLFlilq0mWJ/PyLrcdX536/UkK8tedlo76itQcd3LivTEdOKi4zhSdsRv3aIik7fD\nao/KzqKdaDTZafYDlREjzM/www/+6/pSUgL33AMXXOB/IvbZHc+WIEU0qIACFaXU20qpm5zfJ2Jy\nqrwNrFVK/SaI7ROiUenf3+SWuP9+s9zalwu6XcCSbUs4dKx2xfJy80nYzrJkh3aw4cAGTs70vVuv\nJ3az09oRjoFKYmwipfeWcnFP/wlq7CZ721awDSCgHpWBA02PUKDDP7sP7abCUcH06WZH7L//PbDr\nCFGfAu1RGQosc35/IWZtaDPMZNX7gtAuIRqtRx4xQcq0ab7rXdzzYmaOnUm0qt3H//33JreMnfkp\n2zEn+3UAACAASURBVAu3U1xezMkt7AcqdpO+2VFQYC8rbSBc17czodbqXAzX62J16CenMIdoFW17\nMi2Y7MNnnmmG/ewqKS9h8MuDmfTeFB59TPO735mNB4UId4EGKqmAa7HfucB7Wuti4CMgmMkxhGh0\n2rY1m7499ZSZDOtNm6ZtuLb/tR6XES9ZYpYk20lVsD53PYAM/QSZ63Wx2qOSU5BDu9R2xEQFlh1i\nxAhYtsxHojQvEmMTeWzEY7y5YTbFg//MffKRUkSIQAOVXcAg58aD5wKLneVpmJT6Qggf7r7bTML8\n298CO3/pUpOS39eE3Jr2HN5DRlIGbVLsJ60Ip6Gf1XtXsy53na17hDJQ2bfPDMdYXV59ee/LmX6u\nt/yU/g0fbraDWLHC/rkjWvyW2CXPUDHwca5cfA4XzruQ8986n5H/GsmP+60vKReiPgUaqDwDvIHJ\nSbIX+NxZPhRYW/dmCdG4ZWSYpaHPPw+7d9s7t6TE7OpsZ9gH4IZTb2DfHfsCWl7aqpWZNFriZ1sU\nl7lr59JuWjtLu/faDVTuWXoPD3z+gPUTMMvDmzQJXaDSqpX15dWnZJ3Ced187OviR9++5vUKZJ7K\nI49Ak7W38rezphMTFUNZZRmVjkoSYxPZlLcp4DYJEUoB9T1qrWcopVYA7YFPoSoF5TZkjooQltx+\nOzz3HPz1rzBrlvXzvv7a7BgbyP4+gWYTdc+l4m8vGDAbNu4+tJtDxw753AumosLM17ETqBSWFtI6\n2cKmSTXYzU5r1d69ods12ZPoaDj7bBOoPPig9fO2b4cXXjBZkv909s38iZtD1EIhgqsuy5P7Ag9j\nNgosVUqtA1pprb8OSsuEaOSaNjVDQC+/DD//bP28f//bpOU/2f6c2IDZTfpmNQ9JYaH5ajdQsbNz\nsovd7LRW2U32FgwjR8Ly5WbljlV/+Yt5DW65JXTtEiIUAl2e/BDwLLAAs5PyBOf305zHhBAW3Hij\nCToesDiSsX27ycFy662hzeRak/t+P1ZYzexqd0NCgIKSAlsbErqEMlCxs89PMPz2tybQfcjiX9sN\nG+Bf/4L77jNDYEJEkkB7VH4PXK+1vltrPd/5uBuYAvwheM0TonFLTIT/+z+TJfSLL/zXv/9+s9T2\n1ltD3zZ3zZubibtWV/6475XjSyCBSmFpYb0EKt/v+Z6zXz3bb7BV30M/AKmpJmHbSy/53xXa4TC9\nKG3bwhTPSY6FCGuBBiqxmCRvNa0kMndkFqLBXH+9WcFz+eVw4IDnOu9teI9zX7qM1183wUp9fyqO\nijI7UlvuUUkMTY9KSXkJxyqPkZYQ+qGfSkclX+z4gj2HvY+vlJebJeb1HaiA6Y1r3Rq/y4wfe8ys\nEnv5ZbO7uBCRJtBA5TVMr0pNUzCrgYQQFkVHwxtvmDe9q64yn4BrqtSVfPzLPNr32cF119V/G8Fe\n0rfE2ESSYpP8zlGxG6gUlppJLfXRo5KVbKKPfUe8/9C5ueZrfQ/9gNk64S9/gXfeMQkAPVm2zAS2\n995r5rUIEYnqMpn2WqXUOqXUS87HWuB6wKGUetr1CFI7hWjUWreG116D//7X7AdUU0ruKKiMYdjv\nFhAbW/t4fbCb9C09Md1Sj0p0tPUcJPUZqLRMbgn4DlTsJnt7b8N7fLXzK+uN8OOqq6BnT/jzn2sf\ny8szuyIPGWJ9DpQQ4SjQQOVkYBVwAOjsfOQ5y04G+jkffYPQRiFOCKNGmTece+4xeVJctIaH700l\n5eDZ/NJkge3rllWW0enZTizYZP9cd3aTvj087GHGdBnjs44rfb7VicHdMrpR+KdCTm9zuvWGODVv\nbu5nIbULAAkxCTRLaOYzULG7z88Dnz/AvHXzrFW2IDoaHn3ULFX+5JPj5Q4HTJpklrG/+aa9xIBC\nhJtA86gMC3ZDhBDw8MOmu/7cc6FdO7O3C5jdcv/wu/H8c/sdHDp2iKbxTS1fc3P+ZnIKc3zmM7HC\nbqAyqe8kv3XsJnuLUlEB/xxpaSbtfEmJySRrRVZylt9ARSmzcssfrTU5hTlMTptsscXWjB8Pgweb\nlUDt25uf8ehR2LYNFi6ENvYTEQsRViTOFiKMxMTAu++ajLVHj5o3nbIys+PyRePPY8azt7B462JL\nu/q6VO3xk2l/jx93rjkqDoeZXBsM9bHPj4t7Gv1gBSp790JmprUei9yjuRSXFwe0a7IvSsErr8DT\nT5vv4+JMJt6BA2H06KDeSogGIYGKEGEmK8tkq62tI71b9Gb+pvm2ApV1uetoldyqKrdJXdpVUWGy\nu2Zk1OlSVfLzQ79zsovrPvn51nsZspKz2HvE+8QcO8necgpzAMhOC26gAtCtm8k6K0RjFKTPRUKI\n+jC+23gWbllIhaPC8jnrD6wPaMfkmuxmp7UiL8/0SNQH13187Vhd0/iu4xnfdbzX47YClQJnoBLk\nHhUhGjvpUREiglzT9xrOaHeG5foVjgqW7VzGdf3qvqbZtQR3797gpe8/cABOtz8vNiCuXiBvuWo8\nmdh7os/je/dC167WrpVTmENaQlqd5woJcaKRQEWICNK5eWc6N+9suf7SnKXkFefZGirypqVZrRux\nPSopKWb+hp0eFX/27YOhQ63VzSnIoVNap+DdXIgThAz9CNGIzVs3j85pnenfqn+dr5WUZPaXCVag\nUlkZ3Pku/ihl7mWnR8UXre0N/Sil6N2yd3BuLsQJRHpUhGjE7ht6H5MOTUIFaQdDO9lpi8uL+WbX\nN/Rv1Z/mibVnzB48aN7s7fSoPPLlI2QlZ3Ft/2utn+QmMzN4PSqHD5ulzlaz0r543ovBubEQJxjp\nURGiEctOy2ZoB4tjExbYyU574OgBfv3ar/nul+88H3f2bNjpUXl/4/t8v8dLvngLgtmjYjcrrRAi\nMBKoCCEss5P0rWoHZS/7/bh6Nuz0qAS6c7JLMHtU7GalFUIERgIVIYRldoZ+kmKTiI+O97rfTyA9\nKgdLDpKWGHiGuGD2qLheh4bYkFCIE4kEKkJEsOLyYg4dO1Rv97Mz9KOUIiMpg/xi7z0q0dHQzGIH\nSYWjgsLSQtITA09cF0iPSu7RXHYV7apVvncvJCaa1URCiNCRQEWICFXhqKDXjF48+Y2H7ZZDJCsL\nCguhtNRa/fQk7zsoHzgA6enW0/EXlBRUXTNQGRkmULG6MSHA1R9czc2Lbq5V7lrxE6R5ykIILyRQ\nESJCxUTFcF7X85j5/UxKykvq5Z6uYY79+63Vz0jK8DlHxc78FNd16tqjUl4Oh2x0Qnnb72ffPhn2\nEaI+SKAiRAS7ZeAt/H97dx5d51Wfe/z7kyzZlmVboyV5SGzLk0wGYsdJAyldqQskDcO60IJNKBRy\nadI2KcsECNDVBZfbroShAQIplymBe5OIFG6BhoYVkjCkJQN2nMSByI5s2Y4TybJsDY4kW5bl3T/2\nOco5ms55z6D3PdbzWeusSO+7z3v22ZF1Hu13D8cGj3HH9js41HeI3pO9DJ0eytvrxT+Y29vTK189\nd+oelSDjU+K3kLLtUYm/droayhsmDCodHRpIKzIdFFRECtiqqlW8c/07+dhDH+OcL59D5ecqmfNP\nc7j+p9fn5fUSl9FPRy57VMpKynjLmrdQN68u/SeNkcl+P/EeFTfmflF7OyxenN411t+xnrueviv9\nFxWRUVrwTaTA3fOOe/jwpR+m/1Q//af6eWXoFS5demleXqu6GkpK0u9R+cIbv0BJccmE57q6YGWA\nFeUvariI+7fen/4TJpBJj0p9eT1DI0P0DfUlTY1ON6j0neyj5WgLc0vmBqytiICCikjBKy0u5fJz\nLp+W1zLzH87pBpV5pfMmPTed+/zEVVe/+trpqi/393cO9x8eDSonT/qVddMJKvt7/a7J2udHJDO6\n9SMigTQ0pH/rZzLOBR+jkgslJX46dNAeFSBpnEqQNVTaetoAWFGxIv0XFZFRCioiEkiQHpXJDA76\nXonpDirw6hTldE0UVOLvP50elbaeNspLy0dX6hWRYHTrR0QCWbwYfvWr7K4R79GY7ls/8dcM0qNS\nXlrOrut3Jd26CRpUVlauzNnGkCIzjYKKiASyeHH2t37iPRqF0KNiZpxfd37SsY4OmD0bKtNYzT8e\nVEQkM7r1IyKBNDTAsWMwlMVyLYXUozKR9nbfDul0krT1tLGyQkFFJFPqURGRQOK3Ozo6YPnyzK6R\nSY/K8MjwpFOdgwjaozKRIGuofPaKz6pHRSQL6lERkUASg0o6PvXIp/jOzu8kHevqgvJymDMnvWs4\n55h/y3y+vv3rAWo6sVz0qHR0pB9Utpy3hUuWXJLdC4rMYAoqIhJI0GX0Hz34KL8++OukY0ePButN\nGRgeYGhkKGnBtUzV1Pi9fk6dyvwa8Vs/IpJ/BRVUzKzSzO4xsz4z6zGzb5vZ5CtK+ef8DzN70MyO\nmtkZM7tguuorcjaqqoLS0vSDSu28WroGk7swuroCbkiYg31+RuuTwTL6YwW59SMi2SmooALcCzQB\nm4GrgTcA30jxnHnAfwIfBwJs7i4iEwm6Ou2iskV0DSQHlaA9KvGNDbPZOTku/rqZBpUTJ6CnR0FF\nZLoUTFAxs3XAm4FrnXM7nHOPATcCW8xs0j1MnXN3O+f+EXgE0EIGIjkQZHXa2nm1HBk4knQscI/K\nidz3qAQZp9LZ38lND97E/p79gValFZHsFUxQAS4DepxzTyccexjfS5KfHdhEZEJBelRqy/ytn8Td\nh4P2qIze+gmpR2X4zDC3PXEbu4/uDrTYm4hkr5CCSj2Q9GeZc24E6I6dE5FpEiiozKvl5OmTDAwP\njB7LpEelpKiE8tLygDUdb/58P8YmSI/KonmLAL+MvoKKyPQKfR0VM7sFuHmKIg4/LmXabdu2jYUL\nFyYd27p1K1u3bg2jOiKREWR12toyn0i6BrooLy3n9Gk/xiNoj0p1WXVOlqE3C76WSmlxKdVzqznc\nf5h5HX5adUWKCUiDw4P88PkfcuWqK0eDjsjZprm5mebm5qRjfX19OX2N0IMK8EXgrhRl2oDDQNK/\ndjMrBqpi53LuS1/6Ehs2bMjHpUUKWkMDdHf7jQVTrYWyonIF737Nuyky34Hb3e13Tw7So5LrtUgy\nWUulYX4Dh/sPMzfNVWn3du/l/T9+P4998DEFFTlrTfTH+86dO9m4cWPOXiP0oOKcOwYcS1XOzB4H\nKszsooRxKpvxA2SfTPflMquliCRKXPRtxYqpy66qWsX3/+z7o99nsirt2pq1rK1ZG7CWk8tkddr6\n8noODxxmdppTk9t62gC0Kq1IlgpmjIpzbjfwIPAtM9tkZq8Hvgo0O+dGe1TMbLeZvT3h+0ozuxB4\nDT7UrDOzC82sbprfgshZI/5Bne44lURh7vMTl0mPSn15PR2vdKS9hkpbTxtlJWXqTRHJUsEElZj3\nALvxs31+CjwKXDemzGogcWDJ24CngfvxPSrNwM4JniciaYpPzc1kF+Uwd06Oy6RHZUXFClq7W+no\nSG9qcnzX5FyMqxGZyUK/9ROEc64XeG+KMsVjvv8e8L181ktkpqmshNmzM+9RKS5OPRg1nzLpUbls\n6WVsb9/O450nWbw49SZF8aAiItkptB4VEYmAoKvTJjp6FKqroSjE3z7xHhUXYNTaVauv4t/e8TP6\njs1J69ZPa3crKysUVESypaAiIhkJMkU5UVdXuLd9wL/+6dMQdBZl/P2mCip9J/vY272X19a/NrMK\nisgoBRURyUhDQ+Y9KmEOpIXMNyaMv99UY1QO9B6gtqyWTUs2Ba+ciCRRUBGRjAS59eOco++k774I\n2qNydPAodz595+gy+rkQf/2g41TSXZX2wvoL6fxoJ001oaxVKXJWUVARkYwECSq3P3k79f9cj3Mu\ncI9KS1cL1/77teM2NsxGNj0qc+fCmAWrJ2RmmvEjkgMKKiKSkYYG6O2FEydSl03c7ydoj0oud06O\nq45dKmiPSnxqsvKHyPRRUBGRjCSuTptKfL+fI/1dgXtU4rd8quZWBa3ipEpK/PToTHpUtBmhyPRS\nUBGRjARZnbZ2nk8mLx7r4uTJ4D0qC2cvZFZRbpd9qqnJbIxK3eJTdA0EfKKIZExBRUQyEmR12vgy\n8m2d/gM+aI9KLm/7xNXWBu9R6eiA7avfynU/1cLWItNFQUVEMlJR4XdOTqdHpabMd6EcOOIHxAbt\nUamem/ugkmmPyjlzXsNzR57LeX1EZGIKKiKSkSCr05YWl7Jw9kJe6s2gR+VENHpUBgf9AnFNVeez\nr3sfA6cGJiw3PDKcoxqKCCioiEgWgqxOu2jeIg4f90El6Mq0DeVp7AIYUNAelfj7vGjJ+Tgcv+/6\n/bgyLx9/mfm3zOeX+3+Zo1qKSEFtSigi0RJkddo7334nD/xrPf9Z7m8ZpetH7/5RZpVLIWiPSvx9\nXrpyPUXPFrGrcxeXLLkkqcyO9h0MjQyxunp1DmsqMrOpR0VEMhZk0bfLz7kcd2xV6Pv8xNXUwPHj\nMDSUXvn4+2w8p4xVVat4rnP8OJXt7dupm1fHkvlLclhTkZlNQUVEMhZ0B+WDB2Hp0vzVJ4h4PV58\nMb3y7e1QVgYLFsD5i85n15Fd48rsaN/BpiWbtCKtSA4pqIhIxhoa/ADTwcH0yre2wpo1+a1TuuL1\naG1Nr3ziqrQX1F3Ac53P4ZwbPe+cY3v7di5uuDgPtRWZuRRURCRjy5f7/7a1pS7rnA8FqyMyfGPp\nUj9WJt2gsm/fq+/3uo3X8cz1zySdP9B7gO4T3doxWSTHFFREJGNNsc2BW1pSl+3q8r0vUQkqRUXQ\n2AgvvJBe+ZaWV99vXXkdSxcsTbrFs719OwAbGzbmuqoiM5qCiohkrKbGP9IJKvGei6jc+gFfl3R6\nVIaHfbl4UJnI9pe3s2zBMurK63JXQRFRUBGR7DQ1pRdU4j0XjY35rU8Qq1en16Oybx+cPj11ULnp\ndTfxgz//Qe4qJyKAgoqIZCndoNLSepKKN32NQ4N70r72fb+7jyvvvjKL2k1t9Wo/6+fkyanLxd/f\nVEGlvryeS5demrvKiQigoCIiWWpqgj17YGRk6nL79hbR+7obefylx9O+9u6ju9nVOX4acK6sWeMH\n+aYaDNzS4vc2qtNdHZFpp6AiIllpavI9EgcPTl1u755SSs8spGsg/XXr87XPT1x8YG+q2z/xgbRa\nHkVk+imoiEhW0pn54xzs3QsLims5MnAk7Wvna+fkuPp6KC9PPaA2ccaPiEwvBRURycqyZTBv3tRB\npb3dLwpXU1ZL12CAHpXB/PaomPlelamCypkzsHu3gopIWBRURCQrZrBu3dRBJX5rZfHCgEElzz0q\nkHrmz0svwcCAgopIWBRURCRrqWb+tLb6BdaW1y4KdOvnUN+hvG/wl2otlXRm/IhI/iioiEjW4kEl\nYeubJK2tfvn5ZRVLONR3KK1rDpwaoHOgk5WVK3NX0QmsXu1vTfX3T3y+pcUvtX/uuXmthohMQkFF\nRLLW1AS9vdDZOfH5F17wgWBdzToq5lRwauRUymsOnxnm5tffzMWL87vJX3zmz969E59vaYG1a6G4\nOK/VEJFJKKiISNZSzfyJ75q85bwt7L5hN6XFpSmvWTGnglv/5FaaavN7zyXVLsqa8SMSLgUVEcla\nYyPMmjVxUBkZ8UvQR2UzwrGqq6GyUkFFJKoUVEQkayUlPohMFFRefBFOnYpuUIHJZ/50dcHRowoq\nImFSUBGRnGhqguefH388irsmjzXZzB/N+BEJn4KKiOTE+vUT96i88ILvcTnnnOmvU7om61FpafGD\naKPcGyRytlNQEZGcaGqCjg7o60s+3toKK1f6MSxRtXq1v8XT25t8vKXFj7+ZPTuceomIgoqI5Mhk\nM3/iM36ibLKZPxpIKxI+BRURyYm1a/1y+mODSnwNlSCODR5jZ8dOTp85nbsKTmGyXZQVVETCp6Ai\nIjlRVuZXb00MKsPDcOBAco9KZ38n5375XB7a99Ck1/r5vp+z8ZsbGTg1kL8KJ1iwAOrqkntU+vvh\n0CEFFZGwKaiISM6M3fNn/36/jkpij0p1WTXtr7TT2j35BjttPW1Uza1i4ZyFeaxtsrG7KO/e7f+r\noCISLgUVEcmZpiZ47jnYswd6el69lZIYVGYVzWJ5xXL2de+b9Dr7e/fnfY+fseIzf06d8jsmP/KI\nP75u3bRWQ0TGKKigYmaVZnaPmfWZWY+ZfdvM5k1RfpaZfc7MdplZv5m9bGbfM7OG6ay3yExx8cVw\n8KD/cK+qgre9DebOhSVjNkBurGxkX8/UQWVFxYo81zbZmjWwY4ef4bNsGXziE/7Y/PnTWg0RGSPC\nEwYndC9QB2wGSoHvAt8A3jtJ+TLgtcD/AnYBlcDtwE+AS/JcV5EZZ8sWH1Y6OvwGhZ2d/kO/aMyf\nRI2VjTz64qOTXqetp41NizflubbJPvABKC31AWvRIj9mZdWqaa2CiEygYIKKma0D3gxsdM49HTt2\nI/AfZvZR59zhsc9xzh2PPSfxOjcAT5rZUufcS9NQdZEZw8zfQkk1y6exqpHvPvtdnHOYWdK54ZFh\nDvUdmvYelbo6+MhHpvUlRSQNhXTr5zKgJx5SYh4GHHBpgOtUxJ7Tm6qgiORHY2Ujg8ODHO4f9/cF\nh44fYsSNTPsYFRGJpkIKKvXAkcQDzrkRoDt2LiUzmw3cCtzrnOvPeQ1FJC2NVY0A7O3eO+7cgd4D\nAKyonN4eFRGJptCDipndYmZnpniMmFnW61qa2SzgB/jelL/JuuIikrHGyka++ZZvjgaWRFcsv4Ku\nj3VN+60fEYmmKIxR+SJwV4oybcBhYFHiQTMrBqpi5yaVEFKWAX+cbm/Ktm3bWLgweR2HrVu3snXr\n1nSeLiKTmFsylw9t/NCE58yMmrKaaa6RiGSiubmZ5ubmpGN9Yzf8ypI553J6wXyJDab9PXBxwmDa\nNwEPAEsnGkwbKxMPKSuBK5xz3Wm81gbgqaeeeooNGzbk6i2IiIic9Xbu3MnGjRvBT37Zme31Qr/1\nky7n3G7gQeBbZrbJzF4PfBVoTgwpZrbbzN4e+3oW8P+BDfgpzCVmVhd7lEz/uxAREZEgonDrJ4j3\nAF/Dz/Y5A/wQ+PCYMquB+P2aJcBbYl8/E/uv4cepXAFMvpCDiIiIhK6ggopzrpfJF3eLlylO+Pog\nUDxFcREREYmwgrn1IyIiIjOPgoqIiIhEloKKiITm/j3388RLT4x+f9/v7uPan1wbYo1EJGoKaoyK\niJxdPvPrz7C+dj1NNU2Ul5bzm0O/4cmXnwy7WiISIQoqIhKa9bXruXvX3dy9624AiqyIq1dfHXKt\nRCRKFFREJDRfufIrXHP+Nbwy9ArHh45zfOg4m1duDrtaIhIhCioiEpqquVVcuerKsKshIhGmwbQi\nIiISWQoqIiIiElkKKiIiIhJZCioiIiISWQoqIiIiElkKKiIiIhJZCioiIiISWQoqIiIiElkKKiIi\nIhJZCioiIiISWQoqIiIiElkKKiIiIhJZCioiIiISWQoqIiIiElkKKiIiIhJZCioiIiISWQoqIiIi\nElkKKiIiIhJZCioiIiISWQoqIiIiElkKKiIiIhJZCioiIiISWQoqIiIiElkKKiIiIhJZCioiIiIS\nWQoqIiIiElkKKiIiIhJZCioiIiISWQoqIiIiElkKKiIiIhJZCioiIiISWQoqIiIiElkKKiIiIhJZ\nCioiIiISWQUVVMys0szuMbM+M+sxs2+b2bwUz/m0mbWYWb+ZdZvZQ2Z2yXTVeaZpbm4OuwoFR22W\nGbVbcGqzzKjdwlVQQQW4F2gCNgNXA28AvpHiOXuAvwXOA14PHAB+bmbV+avmzKV/0MGpzTKjdgtO\nbZYZtVu4CiaomNk64M3Atc65Hc65x4AbgS1mVj/Z85xz33fO/cI5d8A51wJ8BFgAXDAtFRcREZGM\nFUxQAS4DepxzTyccexhwwKXpXMDMSoDrgF7g2ZzXUERERHJqVtgVCKAeOJJ4wDk3YmbdsXOTMrOr\nge8DZUA78EbnXHe+KioiIiK5EXpQMbNbgJunKOLw41Ky8QvgQqAG+BDwAzO7xDl3dJLycwBaWlqy\nfNmZp6+vj507d4ZdjYKiNsuM2i04tVlm1G7BJHx2zsnF9cw5l4vrZF4BP6g11cDWNuAvgC8650bL\nmlkxcBL4M+fcTwK85gvAd5xzn5vk/HuAe9K9noiIiIxzjXPu3mwvEnqPinPuGHAsVTkzexyoMLOL\nEsapbAYMeDLgyxYBs6c4/yBwDX6G0MmA1xYREZnJ5gDL8Z+lWQu9RyUIM3sAWAT8NVAK3An81jn3\nFwlldgM3O+d+YmZlwN8D/w504G/93ABsATbGZgGJiIhIRIXeoxLQe4Cv4Wf7nAF+CHx4TJnVwMLY\n1yPAOuB9+JByDNgOXK6QIiIiEn0F1aMiIiIiM0shraMiIiIiM4yCioiIiESWgsoEzOxqM3vCzAZj\nGxn+25jzy8zsP8xswMwOm9nnzUxtCZhZqZk9Y2ZnzOyCMefUbjFmdm5sU8222M9Zq5l9JrZ6cmI5\ntdkYZva3ZrbfzE7E/p1uCrtOUWFmnzSz35rZcTPrNLMfmdmaCcp91szaYz97D5nZqjDqG1Vm9onY\n77DbxhxXuyUws8Vm9v/M7GisTZ41sw1jymTdZjP6F95EzOydwP8FvgOcD7wOvxli/HwR8AB+IPIf\nAO8H/hL47HTXNaI+D7yEX6hvlNptnHX4qfUfAtYD24DrgX+KF1CbjWdm7wb+Gfg0cBF+K4wHzawm\n1IpFxx8CX8VvK/InQAl+E9a58QJmdjN+9uNfAZcAA/g2LJ3+6kZPLPj+FWO2WVG7JTOzCuA3wBB+\nH74m4CagJ6FMbtrMOadH7AEUA4eAv5yizFXAMFCTcOy62P+cWWG/h5Db7yrg9/gP4TPABWq3QO33\nUWCv2mzKNnoC+ErC94YPxh8Pu25RfOBnO57Bz3SMH2sHtiV8vwA4Abwr7PqG/QDKgT3AHwO/LRHL\nbAAABT1JREFUBG5Tu03aVrcCv05RJidtph6VZBuAxQBmtjPWXfWAmb0mocwfAM+55OX3H8RPiU4s\nN6OYWR3wTeC9+B/EsdRuqVUAiXtQqc0SxG6LbQQeiR9z/rffw/hNS2W8CnzvZjeAma3A742W2IbH\n8Ytmqg3hDuB+59wvEg+q3Sb0VmCHmf1r7DbjTjP7n/GTuWwzBZVkK/F/oX0a371+Nf6v11/FurnA\nN3znmOd1Jpybqe4C/sUl726dSO02hdh92xuA/5NwWG2WrAbf6zlRm8zE9piSmRnwZeC/nHPPxw7X\n44OL2nAMM9sCvBb45ASn1W7jrcQvvroHeBPwdeB2M4svwJqzNpsRQcXMbokNjJrsMRIbcBZvj390\nzv049qH7AXxj/3lobyAk6babmf0dvss0vneShVjtUAX4WUt8zhLgZ8B9zrk7w6m5nIX+BT/+aUvY\nFYk6M1uKD3XXOOeGw65PgSgCnnLO/YNz7lnn3LeAb+HH2uVUoa1Mm6kv4v/in0obsds+wOiqtc65\nU2bWBpwTO3QYGDvLoC7h3NkknXbbD1yB78ob8n/EjdphZvc45z7AzGm3dH/WAD9qHr+79385564b\nU26mtFm6juJXm64bc7yOmdkekzKzrwF/Cvyhc64j4dRh/B8SdST/pVsHTNYbOhNsBGqBnfbqL7Fi\n4A1mdgOvDn5Xu72qg4TPypgW4B2xr3P2szYjgopLf+PDp/AjmNcCj8WOleA3VzoYK/Y48Ckzq0kY\nO/AmoA94nrNIgHa7Eb+nUtxi/FiKdwG/jR2bEe2WbpvBaE/KL/DbOnxwgiIzos3S5Zwbjv0b3Yzf\nvyt+e2MzcHuYdYuSWEh5O/BHzrkXE8855/ab2WF8m+2KlV+AnyV0x3TXNUIexs/yTPRd/Afvrc65\nNrXbOL/Bf1YmWkvsszKnP2thjxyO2gP4EvAi8EZgDfBtfHJcGDtfhJ+29jPgAvy0rE7gf4dd96g8\ngHMZP+tH7ZbcRouBVuDnsa/r4g+12ZTt9i5gEL9/1zrgG/hgWBt23aLwwN/u6cFPU65LeMxJKPPx\nWJu9Ff/h/OPYz2Jp2PWP0oPxs37UbsntczH+D/tPAo34vfheAbbkus1Cf7NRe+C7+z4fCye9+J6B\npjFllgE/BfpjHxyfA4rCrntUHrGgMpIYVNRu49ro/bE2SnycAUbUZin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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#* Plot the initial wavefunction\n", + "plot(x,real(psi),'-',x,imag(psi),'--')\n", + "xlabel('x'); ylabel('psi(x)')\n", + "legend(('Real ','Imag '))\n", + "title('Initial wave function')" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Initialize loop and plot variables \n", + "max_iter = int(L/(velocity*tau)+.5) # Particle should circle system\n", + "plot_iter = max_iter/20 # Produce 20 curves\n", + "p_plot = empty((N,max_iter+1)) # Note that P(x,t) is real\n", + "p_plot[:,0] = absolute(psi[:])**2 # Record initial condition\n", + "iplot = 0\n", + "axisV = [-L/2., L/2., 0., max(p_plot[:,0])] # Fix axis min and max" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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hRWQssFct9UYSxhv1aOzrzPK8tU2n7U5IEBZHj6VPU29PWNNiZvSa5kW/2xcDFRnX6cIs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\nk45CpHjorUakjC1bFrpaNL6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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#* Loop over desired number of steps (wave circles system once)\n", + "for iter in range(max_iter) :\n", + "\n", + " #* Use Gaussian Elimination for the Crank-Nicolson scheme\n", + " chi = tri_ge(Q,psi)\n", + " psi = chi - psi \n", + " \n", + " #* Periodically record values for plotting\n", + " if iter % plot_iter < 1 : \n", + " iplot += 1\n", + " p_plot[:,iplot] = absolute(psi[:])**2 \n", + " plot(x,p_plot[:,iplot]); # Display snap-shot of P(x)\n", + " xlabel('x'); ylabel('P(x,t)')\n", + " title(('Finished ', iter, ' of ', max_iter, ' iterations'))\n", + " axis(axisV)" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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24Llsb5a2XQy8pek+mmNbW1M8x/pZjxxEnUr+IriNPNhujxleYy/yjIwbqvWPB7bqWHdP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\nqScGEZIkqScGEZIkqScGEZIkqSf/H/eKEE0x4IqEAAAAAElFTkSuQmCC\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#* Plot probability versus position at various times\n", + "pFinal = empty(N)\n", + "pFinal = absolute(psi[:])**2\n", + "#plot(x,p_plot(:,1:3:iplot),x,pFinal)\n", + "plot(x,pFinal)\n", + "xlabel('x'); ylabel('P(x,t)')\n", + "title('Probability density at various times')" + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "kernelspec": { + "display_name": "Python [default]", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.12" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} diff --git a/Python/.ipynb_checkpoints/Sprfft-checkpoint.ipynb b/Python/.ipynb_checkpoints/Sprfft-checkpoint.ipynb new file mode 100644 index 0000000..287131e --- /dev/null +++ b/Python/.ipynb_checkpoints/Sprfft-checkpoint.ipynb @@ -0,0 +1,222 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# sprfft - Program to compute the power spectrum of a \n", + "# coupled mass-spring system.\n", + "\n", + "# Set up configuration options and special features\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "%matplotlib inline" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def rk4(x,t,tau,derivsRK,param):\n", + " # Runge-Kutta integrator (4th order)\n", + " # Input arguments -\n", + " # x = current value of dependent variable\n", + " # t = independent variable (usually time)\n", + " # tau = step size (usually timestep)\n", + " # derivsRK = right hand side of the ODE; derivsRK is the\n", + " # name of the function which returns dx/dt\n", + " # Calling format derivsRK (x,t,param).\n", + " # param = extra parameters passed to derivsRK\n", + " # Output arguments -\n", + " # xout = new value of x after a step of size tau\n", + " \n", + " half_tau = 0.5*tau\n", + " F1 = derivsRK(x,t,param) \n", + " t_half = t + half_tau\n", + " xtemp = x + half_tau*F1\n", + " F2 = derivsRK(xtemp,t_half,param) \n", + " xtemp = x + half_tau*F2\n", + " F3 = derivsRK(xtemp,t_half,param)\n", + " t_full = t + tau\n", + " xtemp = x + tau*F3\n", + " F4 = derivsRK(xtemp,t_full,param)\n", + " xout = x + tau/6.*(F1 + F4 + 2.*(F2+F3))\n", + " return xout" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def sprrk(s,t,param):\n", + " # Returns right-hand side of 3 mass-spring system\n", + " # equations of motion\n", + " # Inputs\n", + " # s State vector [x(1) x(2) ... v(3)]\n", + " # t Time (not used)\n", + " # param (Spring constant)/(Block mass)\n", + " # Output\n", + " # deriv [dx(1)/dt dx(2)/dt ... dv(3)/dt]\n", + " deriv = np.empty(6)\n", + " deriv[0] = s[3]\n", + " deriv[1] = s[4]\n", + " deriv[2] = s[5]\n", + " param2 = -2.*param\n", + " deriv[3] = param2*s[0] + param*s[1]\n", + " deriv[4] = param2*s[1] + param*(s[0]+s[2])\n", + " deriv[5] = param2*s[2] + param*s[1]\n", + " return deriv" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Set parameters for the system (initial positions, etc.).\n", + "x = np.array(input('Enter initial displacement [x0, x1, x2]: ')) \n", + "v = np.array([0, 0, 0]) # Masses are initially at rest\n", + "# Positions and velocities; used by rk4\n", + "state = np.array([x[0], x[1], x[2], v[0], v[1], v[2]]) \n", + "tau = input('Enter timestep: ') \n", + "k_over_m = 1 # Ratio of spring const. over mass" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Loop over the desired number of time steps.\n", + "time = 0. # Set initial time\n", + "nstep = 256 # Number of steps in the main loop\n", + "nprint = nstep/8 # Number of steps between printing progress\n", + "tplot = np.empty(nstep)\n", + "xplot = np.empty((nstep,3))\n", + "for istep in range(nstep): ### MAIN LOOP ###\n", + "\n", + " #* Use Runge-Kutta to find new displacements of the masses.\n", + " state = rk4(state,time,tau,sprrk,k_over_m) \n", + " time = time + tau\n", + " \n", + " #* Record the positions for graphing and to compute spectra.\n", + " xplot[istep,:] = np.copy(state[0:3]) # Record positions\n", + " tplot[istep] = time\n", + " if istep % nprint < 1 :\n", + " print 'Finished ', istep, ' out of ', nstep, ' steps'" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Graph the displacements of the three masses.\n", + "plt.plot(tplot,xplot[:,0],'-',tplot,xplot[:,1],'-.',tplot,xplot[:,2],'--')\n", + "plt.legend(['Mass #1 ','Mass #2 ','Mass #3 '])\n", + "plt.title('Displacement of masses (relative to rest positions)')\n", + "plt.xlabel('Time') \n", + "plt.ylabel('Displacement')" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Calculate the power spectrum of the time series for mass #1\n", + "f = np.arange(nstep)/(tau*nstep) # Frequency\n", + "x1 = xplot[:,0] # Displacement of mass 1\n", + "\n", + "x1fft = np.fft.fft(x1) # Fourier transform of displacement\n", + "\n", + "spect = np.empty(len(x1fft)) # Power spectrum of displacement\n", + "for i in range(len(x1fft)):\n", + " spect[i] = abs(x1fft[i])**2" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Apply the Hanning window to the time series and calculate\n", + "# the resulting power spectrum\n", + "x1w = np.empty(len(x1))\n", + "for i in range(len(x1)):\n", + " window = 0.5 * (1. - np.cos(2*np.pi*float(i)/nstep)) # Hanning window\n", + " x1w[i] = x1[i] * window # Windowed time series\n", + " \n", + "x1wfft = np.fft.fft(x1w) # Fourier transf. (windowed data)\n", + "\n", + "spectw = np.empty(len(x1wfft)) # Power spectrum (windowed data)\n", + "for i in range(len(x1wfft)):\n", + " spectw[i] = abs(x1wfft[i])**2" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Graph the power spectra for original and windowed data\n", + "plt.semilogy(f[0:(nstep/2)],spect[0:(nstep/2)],'-', f[0:(nstep/2)],spectw[0:(nstep/2)],'--');\n", + "plt.title('Power spectrum (dashed is windowed data)')\n", + "plt.xlabel('Frequency')\n", + "plt.ylabel('Power')" + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "kernelspec": { + "display_name": "Python [default]", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.12" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} diff --git a/Python/.ipynb_checkpoints/Test_bess-checkpoint.ipynb b/Python/.ipynb_checkpoints/Test_bess-checkpoint.ipynb new file mode 100644 index 0000000..67e5b75 --- /dev/null +++ b/Python/.ipynb_checkpoints/Test_bess-checkpoint.ipynb @@ -0,0 +1,115 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Populating the interactive namespace from numpy and matplotlib\n" + ] + } + ], + "source": [ + "# test_legndr - Program to test the legndr function\n", + "\n", + "# Set up configuration options and special features\n", + "%pylab inline " + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def legndr(n,x) :\n", + " # Legendre polynomials function\n", + " # Inputs \n", + " # n = Highest order polynomial returned\n", + " # x = Value at which polynomial is evaluated\n", + " # Output\n", + " # p = Vector containing P(x) for order 0,1,...,n\n", + "\n", + " #* Perform upward recursion\n", + " p = empty(n+1)\n", + " p[0] = 1. # P(x) for n=0\n", + " if n == 0 :\n", + " return p\n", + " p[1] = x # P(x) for n=1\n", + " if n == 1 :\n", + " return p\n", + " \n", + " # Use upward recursion to obtain other n's\n", + " for i in range(1,n) :\n", + " p[i+1] = ((2*i+1)*x*p[i] - i*p[i-1])/(i+1)\n", + "\n", + " return p" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Enter x: 3.\n", + "For n=0; Computed = 1.0 Expected = 1\n", + "For n=1; Computed = 3.0 Expected = 3.0\n", + "For n=2; Computed = 13.0 Expected = 13.0\n", + "For n=3; Computed = 63.0 Expected = 63.0\n", + "For n=4; Computed = 321.0 Expected = 321.0\n", + "For n=5; Computed = 1683.0 Expected = 1683.0\n" + ] + } + ], + "source": [ + "x = input(\"Enter x: \")\n", + "n = 5\n", + "\n", + "p = empty(n)\n", + "p = legndr(n,x)\n", + "\n", + "print \"For n=0; Computed = \", p[0], \" Expected = 1\"\n", + "print \"For n=1; Computed = \", p[1], \" Expected = \", x\n", + "print \"For n=2; Computed = \", p[2], \" Expected = \", 0.5*(3*x*x-1)\n", + "print \"For n=3; Computed = \", p[3], \" Expected = \", 0.5*(5*x*x*x-3*x)\n", + "print \"For n=4; Computed = \", p[4], \" Expected = \", 0.125*(35*x*x*x*x-30*x*x+3)\n", + "print \"For n=5; Computed = \", p[5], \" Expected = \", 0.125*(63*x*x*x*x*x-70*x*x*x+15*x) " + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python [default]", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.12" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} diff --git a/Python/.ipynb_checkpoints/Test_legndr-checkpoint.ipynb b/Python/.ipynb_checkpoints/Test_legndr-checkpoint.ipynb new file mode 100644 index 0000000..67e5b75 --- /dev/null +++ b/Python/.ipynb_checkpoints/Test_legndr-checkpoint.ipynb @@ -0,0 +1,115 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Populating the interactive namespace from numpy and matplotlib\n" + ] + } + ], + "source": [ + "# test_legndr - Program to test the legndr function\n", + "\n", + "# Set up configuration options and special features\n", + "%pylab inline " + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def legndr(n,x) :\n", + " # Legendre polynomials function\n", + " # Inputs \n", + " # n = Highest order polynomial returned\n", + " # x = Value at which polynomial is evaluated\n", + " # Output\n", + " # p = Vector containing P(x) for order 0,1,...,n\n", + "\n", + " #* Perform upward recursion\n", + " p = empty(n+1)\n", + " p[0] = 1. # P(x) for n=0\n", + " if n == 0 :\n", + " return p\n", + " p[1] = x # P(x) for n=1\n", + " if n == 1 :\n", + " return p\n", + " \n", + " # Use upward recursion to obtain other n's\n", + " for i in range(1,n) :\n", + " p[i+1] = ((2*i+1)*x*p[i] - i*p[i-1])/(i+1)\n", + "\n", + " return p" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Enter x: 3.\n", + "For n=0; Computed = 1.0 Expected = 1\n", + "For n=1; Computed = 3.0 Expected = 3.0\n", + "For n=2; Computed = 13.0 Expected = 13.0\n", + "For n=3; Computed = 63.0 Expected = 63.0\n", + "For n=4; Computed = 321.0 Expected = 321.0\n", + "For n=5; Computed = 1683.0 Expected = 1683.0\n" + ] + } + ], + "source": [ + "x = input(\"Enter x: \")\n", + "n = 5\n", + "\n", + "p = empty(n)\n", + "p = legndr(n,x)\n", + "\n", + "print \"For n=0; Computed = \", p[0], \" Expected = 1\"\n", + "print \"For n=1; Computed = \", p[1], \" Expected = \", x\n", + "print \"For n=2; Computed = \", p[2], \" Expected = \", 0.5*(3*x*x-1)\n", + "print \"For n=3; Computed = \", p[3], \" Expected = \", 0.5*(5*x*x*x-3*x)\n", + "print \"For n=4; Computed = \", p[4], \" Expected = \", 0.125*(35*x*x*x*x-30*x*x+3)\n", + "print \"For n=5; Computed = \", p[5], \" Expected = \", 0.125*(63*x*x*x*x*x-70*x*x*x+15*x) " + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python [default]", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.12" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} diff --git a/Python/.ipynb_checkpoints/Traffic-checkpoint.ipynb b/Python/.ipynb_checkpoints/Traffic-checkpoint.ipynb new file mode 100644 index 0000000..bc17eea --- /dev/null +++ b/Python/.ipynb_checkpoints/Traffic-checkpoint.ipynb @@ -0,0 +1,228 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# traffic - Program to solve the generalized Burger \n", + "# equation for the traffic at a stop light problem\n", + "\n", + "# Set up configuration options and special features\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "%matplotlib inline" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Choose a numerical method, 1) FTCS; 2) Lax; 3) Lax-Wendroff :3\n", + "Enter the number of grid points: 80\n", + "Suggested timestep is 0.2\n", + "Enter time step (tau): .2\n", + "Last car starts moving after 20.0 steps\n", + "Enter number of steps: 100\n" + ] + } + ], + "source": [ + "#* Select numerical parameters (time step, grid spacing, etc.).\n", + "method = input('Choose a numerical method, 1) FTCS; 2) Lax; 3) Lax-Wendroff :')\n", + "N = input('Enter the number of grid points: ')\n", + "L = 400 # System size (meters)\n", + "h = L/N # Grid spacing for periodic boundary conditions\n", + "v_max = 25. # Maximum car speed (m/s)\n", + "print 'Suggested timestep is ', h/v_max\n", + "tau = input('Enter time step (tau): ')\n", + "print 'Last car starts moving after ', (L/4)/(v_max*tau), 'steps'\n", + "nstep = input('Enter number of steps: ')\n", + "coeff = tau/(2*h) # Coefficient used by all schemes\n", + "coefflw = tau**2/(2*h**2) # Coefficient used by Lax-Wendroff" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Set initial and boundary conditions\n", + "rho_max = 1.0 # Maximum density\n", + "Flow_max = 0.25*rho_max*v_max # Maximum Flow\n", + "Flow = np.empty(N)\n", + "cp = np.empty(N); cm = np.empty(N)\n", + "# Initial condition is a square pulse from x = -L/4 to x = 0\n", + "rho = np.zeros(N)\n", + "for i in range(int(N/4),int(N/2)) :\n", + " rho[i] = rho_max # Max density in the square pulse\n", + "\n", + "rho[int(N/2)] = rho_max/2 # Try running without this line\n", + "\n", + "# Use periodic boundary conditions\n", + "ip = np.arange(N) + 1 \n", + "ip[N-1] = 0 # ip = i+1 with periodic b.c.\n", + "im = np.arange(N) - 1 \n", + "im[0] = N-1 # im = i-1 with periodic b.c.\n", + "\n", + "#* Initialize plotting variables.\n", + "iplot = 1\n", + "xplot = (np.arange(N)-1/2.)*h - L/2. # Record x scale for plot\n", + "rplot = np.empty((N,nstep+1))\n", + "tplot = np.empty(nstep+1)\n", + "rplot[:,0] = np.copy(rho) # Record the initial state\n", + "tplot[0] = 0 # Record the initial time (t=0)" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Loop over desired number of steps.\n", + "for istep in range(nstep) :\n", + "\n", + " #* Compute the flow = (Density)*(Velocity)\n", + " Flow[:] = rho[:] * (v_max*(1 - rho[:]/rho_max))\n", + " \n", + " #* Compute new values of density using \n", + " # FTCS, Lax or Lax-Wendroff method.\n", + " if method == 1 : ### FTCS method ###\n", + " rho[:] = rho[:] - coeff*( Flow[ip] - Flow[im] )\n", + " elif method == 2 : ### Lax method ###\n", + " rho[:] = .5*( rho[ip] + rho[im] ) - coeff*( Flow[ip] - Flow[im] )\n", + " else : ### Lax-Wendroff method ###\n", + " cp[:] = v_max*(1 - (rho[ip]+rho[:])/rho_max);\n", + " cm[:] = v_max*(1 - (rho[:]+rho[im])/rho_max);\n", + " rho[:] = rho[:] - coeff*( Flow[ip] - Flow[im] ) + coefflw*(\n", + " cp[:]*(Flow[ip]-Flow[:]) - cm[:]*(Flow[:]-Flow[im]) )\n", + "\n", + " #* Record density for plotting.\n", + " rplot[:,iplot] = np.copy(rho)\n", + " tplot[iplot] = tau*istep\n", + " iplot += 1" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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Y7XZlBTscDuLi4nA6nTidTux2e5O3b1IbU5BNgMDSmNJCDje4QTDt+eHXHJx5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TPmz5+PdevWqXKOREl0kJVbUCYYDCIcDsPlcsWIiFYV4gg1NTVs4KSaFeK40A7mIml73KhxbqlM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\ngLeJSEGNb71hAF7kOG5e546OwWB0Vf4/Cksgz/uG9+oAAAAASUVORK5CYII=\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# %* Graph density versus position and time as wire-mesh plot\n", + "\n", + "from matplotlib import cm\n", + "from mpl_toolkits.mplot3d import Axes3D\n", + "\n", + "fig = plt.figure()\n", + "ax = fig.gca(projection = '3d')\n", + "Tp, Xp = np.meshgrid(tplot[0:iplot], xplot)\n", + "ax.plot_surface(Tp, Xp, rplot[:,0:iplot], rstride=1, cstride=1, cmap=cm.gray)\n", + "ax.view_init(elev=30., azim=10.)\n", + "ax.set_xlabel('t')\n", + "ax.set_ylabel('x')\n", + "ax.set_zlabel('rho')\n", + "ax.set_title('Density versus position and time')" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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IASOXwa6T2n56vbbOwMVQ7X6bmrBnkkogXG3jRhuff25h5EivTJVAHDkSSrt2\nKzl9OvzutmzZvGnfvhx16xZmyzFPVuyEIq9AzgAzV3LfopdzsSiVQDy6/BgIwosZ3OQMxrtTXif1\nKjnZRWyKjylpK7EOoogPzA52dTQalUS4OSm1wsibkfe21S0L/Vpqi2uNXwXXndfpz1bAqxPgzHVt\nzoiqJV0Ts3JP69YenDnjz8iRXnh6Zo6m5LNn79CkyXf89NMpFi8+9J/HF/4Or02DPO3hiF0SXP0K\n2YUHb5PXBdFmbDoE75APbwQfcpnvCeM6ZhKwA2DBwQHiKITh7iyWiuv0PwYXnXUQfukkV04nYSip\nxdcLShaAI5egRRVtngfQZpnsUBfGroT957UZKQNzQrnCkCeba2N2V/HxEm9v0Osf/WIshKBYscxz\n8Q4NjePFF5eSK5cvRYoEcO5cBAD//GPDw1Ow9KCeGdsh2+tg9oGB9UPZ7BXPN5RUazk8oRL48CXF\nmM8tZhPKF9zkefwIxMAuYsmBB5+oUS4ut+QqLL4G3zwP5dLR0i+qJcLN5c+hzUb5+U+w8+S/H+vY\nAHwMsHqPdr9Pc/hukDYqQ3m2Bg0y8corCbRsmcBvv1mJiNCahh0O1UScKC7OQsuW32M229m4sTM1\nagRy7lwEq1ZZadA4gZf/B18eBJ/XIV92WPRCLJv9Q3mXfFRVUzI/ldx48jEF+YNyjKcI2fEgAQft\nycl4ClNB1UO41MlY6HsMehSC7umgDiIp1RKRCQx9TWtt6D4DfhoGVUvcK6IsW0irj0ikU2nlMxUT\nI2nbNoGICEmfPgZ++83GkCFmata0sXixDzqdtmy1cNUg73Tk1KkwDh0KxdfXk+HD/2D9+nMEBOSn\nUycjRVr5cMNfh3cLqJXPRq3KNxmlD6cq/rxNPleH7jb80NOMbDRDNUemF/HOOogg3/RTB5GU+sjI\nJJZ+AKULQofJMG8THLoAW4/AhgNQXF2DU83p0w5u3JAsX+5D374G1q/3ZeBAA3v22PnkExOgZgFN\nVK1aIOfPD+Djj+tx7Nht4uOt5MjxIrmK67lg96DUa4KA7Ebiq55koz6CwRRgPsXVsEPFbUkJfY/C\n5QRYVRV80+HXfpVEZBIGT9gyFhoFw4JN0Hw09JoJfVtq3RhK6oiNldy86cDb+94HXceOnnTr5slX\nX1k5cMB+tzUiMzKZbCxceJCQkFgAihfPwYgR9Th27F2WLRvK4cM++NXyoUglwWEhKV/tGjmEB+sp\nS0/yYlA6yRtWAAAgAElEQVSXMMWNfXMNvr0OcytAmSyujiZl6TCvUVLTooFwMwJCo7R6iDKFXB2R\nexMCChfWceCAnaAg7QMvWzbBa695sHu3nYkTzaxc6ZspuzPi4y20bv0DW7deolu3indX4wTYtMlG\nn3fM5HvJl/MGQZaqULNsONe94vmGEuTG04WRK0rqOxED/Y5pa2J0TcfXaZXGZzJCQIGcULm4SiCe\npT17bAwaZOL0aW1onN2utSw0auSBlxesWmXl9m3H3f1LldJTp46ekBBJSIgjxed0Z/HxFlq1Ws4/\n/1ynTJlcHDp0E9Bmp5w82UyLtkao7cedYD36loIq+c2Yi4bwBrmoTjr9SqYoz0icsw6iuC/MLO/q\naB5MJRGK8pSmTjXTqFECS5ZY+PFHGzabRK8XWCxaIjFpkjcrVthYu9ZGfPy9boty5XTs3Wt32cI5\nrhIXZ6FFi+/Zvz+ETZu60K9fNU6fDic62kanTkaGTrDh08Ife0Md1lqCPkGSwMpXyCk8GEwBV4ev\nKKkqsQ7iqlGbDyI91kEkpZIIN+FwwJDFsH6/qyPJXE6ftrNunY0pU7zp1MmTTZts/PqrDQCDQeBw\nSBo18qBvX0+mTrWwcqX17rFXrkgaNtSTJUvmyiKmTdvDX39dpU6dQuTK5UuePH5YrQ7eeCOetVsc\neNb3JaCpIKGkYEwlE7bgCxwU8YyjsJoLIhVcxMQ5jK4OQ3FafA2+c9ZBlM4AjW7pPMdRHoXJog3f\n/HEXlMjv6mgyl6JFdQwYYKBZMw9MJg/atzfy449WypfXUbKkHrtdGzY7a5YPXbsamTDBwoIFVkqU\n0LFypZVJk7zw989cSUTfvtUwGq0sXHiI0qVnA1CqVAU2bhSU7+3LneyC0AKSDvVusir7bfLiyWyK\nqW6MVDKXUE6QwG+UQaiRLi51LAb6HYU3C0OXDNLdLNyxKlwIURk4cODAASpXruzqcFJVZBy0GQd7\nz8GywdC2lqsjytxWrbIyfryZNm08GTHCgIeHwGqVeHoKYmIkBw7Y2bjRRlSUpHdvA9WqZZ5v1leu\nRJEnjx8+PlpRpNlsY9Wqk1y/HsuyZeWIy+LFxVw+FOoDOUvfxlz8Bv3Ix5vkVUt6p5JY7DTgGO+S\njz5qvg2XirNB1T/BIOCf+uDjwkvDwYMHqVKlCkAVKeXBB+2r/jIzsGthUG8YHL8KW/6nEghXSpx5\nsl07T+rV8+D332389pvWreHpqXVrZM0qeOEFDyZO9GbePJ9Mk0BIKZkyZTdBQV/QocOqu9u9vDzo\n1CkYi6UqRy96EFXYm4JtINzbjCwWQidy0Y/8KoFIRZuIxIKkNTkevrOSaqSEd4/CdSP8WM21CcTj\nUn+dGdTRS1BzCMSbYNdEqFPW1RG5r7Nn7Vy75iAu7l6rXfIWPJ1O3E0khg0zYDDAypVWzp93sGWL\njU8/NadpzOmFwyEZPPh3hgzZjF4v+P33C9jt2miUmBhJ+/ZGRn5hw9DCD0sTQWhOSaM62lwQg1QR\nZapbSwS1yUJeDK4OJVNbdBWWXof5FaFUBpvBXSURGdDWI1BvOOTNBnsmazNRKqnjzTeN1KmTQLNm\nCdSsGc/69VYcDm2a6uTrXiQmEvnza3USJ086aN1aO9ZicdEJuJDZbKNz59XMmPE3s2a1YPPmrpjN\nds6cucPRo3aqVI3nt5M6dE19Mbwq0OeD8Q2iuOgdy6cUUkWUqewyJg4ST1tyujqUTO1oNAw4Bm8V\ngU4Z8FqukogMZtkOeHEM1CwFO8ZrCxEpz57DIRk50sShQ3Z+/tmHb7/1oWhRHSNHmpk5U8sIdLr/\nFqElbvPzExw96sDHBw4c8GPyZO80jd/VHA7Ja6+tZPXqU6xc2Z5+/aoTHKwt1b1yZSQ1asQTGeiF\nuYI3vq8LsueA2Q1i+CXrdZoSwAsEuPgM3N8aIsiCnkbqvXaZWBu8fgCe84cZ6Xw+iPtRSUQGISV8\nvgo6T4VO9eG3TyGLr6ujcl8OB6xfb6NVKw9q1/agWjU9S5b4UKeOB4sWWfnzT63eIXEuiKR+/tnK\niy8mMHSogQMH/KlUKfN9o54zZx/r1p1jzZoOtGun9bVt23YJgNWrc1O4sid3snhSpjME5DTTvPFF\nxvldoBjefEIGKUvPwOxIfiGClmTHS30MuISU8M4RuOGcDyIj1UEkpYZ4ZgB2OwxcAHPWw8g3YHRH\nMt0ERWktLg6yZhX4+Nx7o3PkEHTv7snFiw6mTrVQu7Yeg0Fgt0uOH3dQsaJ2FXjlFU9OnNBRpkwG\nvSo8pXPn7jB06Gb69q1KyZI5WLbsGPv23WDVqlMEB9fg2DE9y37yZKkdNvuYKV/3NOd0eqYQRAuy\nqWGGaeBvYrmFlbaqoNJlFl6FZTdgWWWtJSKjUiloOmc0w+uTYO5GmN8PxnRSCURayJZN4O0t+Osv\nOzEx91obKlfW89JLHty86WDzZq01YuJEC+3bGzl2zH53v8yaQBw4EEKlSvMwGm0sWHCQ556bRefO\nq/nll7NUrx6ExVKTunX1lG6kZ5uvpEqtK+TSefALpWlJdpVApJG1RFAMb4JRzZmucMRZB/F2EeiY\nAesgklJJRDp2JwaajtSW614zXK22mdb+9z8vNm60sWGD7V/bO3b05Pp1SUSEdr9kSR316unJmTNz\nfwCuXHmCevUWk5CgzcrZq1clNm3qQnj4EH7/vT9XrjQlJERH74neNN4jeK54BNF+2kyUWVWjaJqJ\nwcYWomhDDpW0uUCMVVsXo0wGroNISiUR6dTlW1DnIzhzA7Z+Bq1ruDqizKdqVT19+njy4Ycmjh+/\n18oQECDImlVw5Yo2VLF9e08WLfKhQIHM+efkcEhGj95Ohw6raNu2DGFhQxACatQIpFmz4mzY4EGl\nSnFERkpm/O7HgCg9pQPsZC0VQguyUU3NRJmmNhKFVc0N4RJSwltHINSs1UF4u0GDZea86qVzhy5A\nraFgtcPuSVCztKsjyrxmz/YmSxbB+++bWL3aitksWbfOitUqadpUfXt2OCSdOv3EmDE7GDeuEUuX\ntiVnTl+KFcvOsWNh9OxppGtXE23aeDJhsz8D7uipkk3SuGYIscLOYAJdfQqZzloiqENW8qjl1NPc\nvCuwIgQWPQ8lMnAdRFLqKpjObDoI7SZC6UBtBEZeNYTTpTw8BL/84suwYSa6dTMSHKzn0CE7w4Zl\nrimr7+ebbw6zYsUJ+k54k4g8BVn4OxTJ7SA21sKFCzn45RcrX3/tTdk2BuruhIbF4vAte43VwsQw\nAimgJjlKU5cwcZh4phLk6lAynUPR8P5xeDcI2rvRPGoqiUhHlvwBvWfBi5XhhyHgl7mmFki3SpTQ\nsXixD6dPO7hyxUGFCjqee04lEDExZoYP/4OCbfvwx5UC5IyAX/eB2Wjldp4GnDlTnMaN9bTuaKDK\nX5JylW9wIzCMYHxZQSnKq6K+NLeGCLKquSHSXIwVXt8PZbPAtHKujubZUklEOiAlTPgRPl4KfZrB\nnHfBQ31GpStZsgiqVdOr1genyEgjvXv/SpRfCbJ65eb13PsgPoJr8bDjrA8eBapwJtqLGR9Bn6Ng\nyR+OJTCMYQTSmdzokxT0neUMhSmCNyprTk2Jc0O8pOaGSFOJdRC3zLChhnvUQSSlfpNczGaHvl9p\nCcTojjCvn0og0tK2bTZ277Y9fEflriNHQqlSZT5bt16ic49qxN+5w/zpW1i37hw3LtygqD4B/RnI\nmkswcKsHP9+0kqdsCB3JRTfy/CuBAFjKt/zMGhedTeaxh1huY6WNKqhMU3Mva3UQCyu6Tx1EUiqJ\ncKEEM7w6ARb8DosGwCg1iVSaiYuT9OtnpFGjBObNs7o6nAxj6dKj1Kq1iIAAbw4efIsmtXNiFP68\nN6Y9x4/3o0WLzhzcV5sqhaDZ6zrOhUCdXJF46wT9H7DUdAwxaXgWmdMa7lACb9WNlIYORsH7J6Bf\nELzupjXEqjvDRcJjoNX/tGW8f/0UWlRxdUSZx7ZtNnr1MnL7tuTLL73p109VqT+Mzebggw82MXPm\nXrp1q8jcuS/h4+PJ5p0XIN6TfbcKU6luAif3aUWnJXp70euYILefg2N7PZhUJw8rWUg4YWQjO9mc\n/wWQDQCJw8Vn6N6isfEH0Qwkv5obIo1EO+sgymeBqW5WB5GUSiJc4MJNaDEGouNh+zioWtLVEWUO\ncXGSoUNNfPWVlfr19WzZ4kPx4qox7lF89dU+Zs/ex+zZLXn77aro9doH0bG9Z8gTbWXL8db4eutY\nsgb2B3nQ65jkpYp3OHhLYpCC5hIWiusUpRi5yEU00VziEtFEARBEMVeentvbQBR2JC+rrow0ISX0\nPgxhFthUC7zcuIs6XSQRQoh6wBCgCpAfaCOl/CXJ44uB7skO2yilbJl2UT4b+85pLRABftoy3sXu\n38KrPENbt9p4802t9WHWLG/efdczxVU4lf8ymWx8/vkuunSpQFSuarz2OeTwhxerSH759TzPl6rJ\n77vj8Wzux+htgkuFrFRrdpOjERYithbj854OzonteONNF7rhmWR+AolkFJ+QUy1HnarWcoe6ZCW3\nmhsiTcy5DKtuwqqqUNzP1dGkrvTyNcwPOAz0Bf67LKJmA5AXyOe8dUyb0J6d9fuh4Qgtcdg9SSUQ\naSE2VvLuu0YaN04gKEjHsWP+9OtnUAnEI4qJMfP++xsJDY3jUp6W/LIXAnNqM6mOXWbjaoQnZ8+W\noFl1wdfjBZeEA+8bVvZ/UgjvJUXp31THe830HOMIZSn3rwQCUE3raeACJo6SoAoq08iBKPjgBAwo\nCq+50XwQ95MuWiKklBuBjQBC3Le00CylDEu7qJ6thb/DO3PgpaqwfAj4erk6Ive3ZYuN3r2NhIdL\nZs/25p13VOvD4zhyJJS2bVcQGhpH4769CDEa2D4ecmWFM2fCqTRIh654ay4f9mDyYi/eOQfBn1zC\n12Hlf5ElKJpVYMx7jPnsJIIIXqGtq08pU1rLHQLQ84KaGyLVRTnrIIKzwOSyro4mbaSXlohH0VAI\ncUsIcVoIMUcIkSHSailh1DLoMwveag4/DVcJRGqLiZG8/baRpk0TKF5ca33o21e1PjyOH344fncU\nxuad/fDNV5DBbSCLl42Ro/8kOHgB8ko0Ds88fDbRi6l6DzyzJmDJEcNHubLhX3IvP+edzkp+wICB\nrnSnqKp7SHO2JHNDGDLU5T7jSayDuGOBlVXduw4iqXTREvEINgA/AZeA4sAEYL0QopaU8n7dHy5n\ns8Pbs+HrLTC+Kwxrp4ZwprYtW7Tah4gIyVdfefP2257cv3FLSc5mczB8+BamTNlD587BzJ//Mkab\nJ0XygCMqhEqV1nDmjC8BAW8SE+NPgYp6rjf35OA1eLXZTUJuZCEicB2HuEx5gulIJ/KTCdp006nd\nxBCGjVdVzUmqm30ZfroJP1WFYm5eB5FUhkgipJQrk9w9IYQ4BlwAGgLbXBLUQ8QZocNk+P0QfDsI\nur7g6ojcW0yMZMgQE/PnW2nUSM+iRT4EBalvXo/r44//YPr0v5k+vTnvvVcDIQS+QOvnbtCk4UKe\ne646DkcdypfX8/oHXgz5Qcfccw66NL3J5s0Gcu3OxZmPb9De9xWqUNXVp5PprSGCknhTBh9Xh+LW\n9kfB4BMwsCi8msly5gyRRCQnpbwkhAgHSvCAJGLQoEEEBPy7H7Bjx4507Ji6NZm3IqHVWDh9A9aN\nhGaVUvXlMr1Nm2z06WMkMlIyZ47W+qC6Lh6fyWRjwYKDfPBBLd5/v+a/Htu2+Qw5c/ri6VmPJk0E\nq9b5UnOdwOLpoMbLp9h11Ifb84vy1sg9+PrqKU+wi85CSRSFja1EM4gCqoA1FUVaoP1+qJgVJmXA\nOojly5ezfPnyf22Ljo5+5OMzZBIhhCgI5ARuPmi/6dOnU7ly5bQJyunsDW0OiAQz/DkeKhVP05fP\nVKKjJYMHm1i0yEqTJnoWLvShSBHV+vAkYmPNjBjxB5GRJnr3/u/fzI4dVyhevAZ79zqYu8CXTgcF\nUYG38MyeFZ/D2Qmdkp/P+xgxVtlIHZrghSr8cbUNROJA0gq1FHBqkRJ6HtYKKrfVzph1ECl9sT54\n8CBVqjzaDIjpIokQQvihtSokpsvFhBAVgQjnbRRaTUSoc7+JwFlgU9pHe397TkPrz7Tq9T/GQlBe\nV0fkvpK2Psyb502fPqr24Unt3n2N9u1/JCLCyOefN+a55/7df37yZDj//BNOQMDLvPiinl+yerDb\nFEGuoDAibuZhx/j8vNkmioBWP+DAi+rUcNGZKEmtJYL6ZCWXmhsi1cy8BD+HwppqEJRJZxNPF0kE\nUBWtW0I6b1Od25egzR1RAegGZANC0JKHkVLKdLPowdq/oeMUqFIcfv4YcmZ1dUTuSbU+PFtff32I\nd975jZo1C7J7dy92Xc7GmOXgkFC1qJXta3Yyc8Y/6D3a4XAY6DDOm54XJDVeDKW8yZfdgSbyljlH\n/p4rcFCADnRUrRDpwDmMHCOBGRR1dShua28kfHgC3i8GbfK7OhrXSRdJhJRyBw8ebvpiWsXyJOZu\ngH7z4NWa8N0H4G1wdUTuaeNGrfUhOloyf743vXur1ocnZbM5GDx4E19+uZe3367Cl1+2YORyPYu3\nQJUSkr2nrESHR2OPDiJb3mAskQa+/9WP3uF6aj0XSZTBTF3DSXTv3aR2UT/q0ZNiFFd97+nEz0SQ\nDT0NUd9mUkOkBTocgEoBMDED1kE8S+or3FOQEj5ZCu9+Bf1fgh+GqAQiNURFSd5800iLFgmULavj\n+HF/+vQxqATiKbRrt5I5c/YzZ05L5s5txdErepZshZ+GS2y7lnJnxQQComxIj0LYgrMzYakf04Qe\ns8HM7SNW7DOLcsV6mg5FS9ODXhSnhEog0ol7c0PkUHNDpAIpoZezDmJFVTBk8rc4k5/+k7PaoOcX\nMG4lTOoBM3qDPgMW1aR3GzZYKV8+jh9/tDJ/vjcbN/pSuLD6tX1SUkq+/fYIP/98hiVL2vDuu9UA\niIoHgwfYYiLYvPkiH3zwBncO+NG3uSS4qo4Pt+g4khBB/hpnMEfq8QiRmCyCymoYZ7qzixjCsdFW\nTXOdKr64CGtD4ZvnM28dRFLqavwEYhPgpf/Bsj/h+8Ew5FU1idSzFhUl6dXLSMuWRsqVU60Pz8LJ\nk2E0afId3buv5bXXyvD66/fWJy6YCzz1sGxjNDqdjvXrC9CggZ4uAz04VNgGJisiIYHXfLKzq7s3\nrwz9hjp+wWRXlf/pzhoiKKXmhkgV/0TCkJPwQTF4JRPXQSSVLmoiMpKbEVoCcSEUNo2GFyq4OiL3\ns2GDlT59TMTGShYu9KZXL1X78DRsNgcjR25j8uTdBAVlY926TrRs+e/15wvlgucCYdXBbOQt1owz\nZySfL/Hm5QN2inU+S5Q9H16/56dvEws7fdbj7RNFfRq65oSU+4rCxjai+UDNDfHMRVigw36omg0+\nz+R1EEmpJOIxnL4OL47WprP+awJUUIXPz1RUlGTQIBPffGOleXM9Cxb4UKiQaix7GlFRJt54YxVb\ntlxk9OiGDBlSGy+v//7ZW00mSif8zYaYihBYldcaWJlh1pO9aCge3lZ6BfqwISSS2fp56LDQnBfJ\nqor20p31RCLV3BDPnJTQ4xDE2GBHFfBUl6W7VBLxiHadhNbjIH922DAKCuV2dUTuZd06K2+9ZSIu\nTrJokTc9e6rWh6e1d+8NunVbw61b8Wzc2IUmTf67AFZCgpWZM/9h4sRdJCRkwde7Ah61YGOcF/E7\nHTzXzEj1i3Zm/2qkVLVz1DJUpjZ1yUIWF5yR8jBruEN9Asip5oZ4pqZdgF9vwS/VoYiqg/gXlUQ8\ngjV7oNNUqPEcrB0B2fxdHZH7iIzUWh+WLLHy4ota60PBgirNfxpxcRaGD9/C7Nn7eP75fOzd25uS\nJf+7ANPq1afo3389t2+bKVXqNc6cyU/hPDp+XCCoNU/gf83G+cmFicvrT9Gi0WzuXQE/MtHKQhnM\nWYycwMjb5HN1KG5lTwQMOwUfFoeX1Vv7HyqJeIiZv8F7C6B9HW0hLS+V4D8zv/xi5Z13TCQkSL7+\n2psePVTrw9Pas+caXbuu4ebNOKZNa07//tXx8Eg5KRswYANlyuSmRYvWfP+9jilTvAh81UDjk5L8\nva8jvKNparGh0/3Be4EvqQQinVtLBNnxoL7qZnpmIpzzQVTLBuPLuDqa9El95bsPhwOGLIaB8+GD\nV2D5hyqBeFYiIiRduxp55RUjlSvrOXHCn5491ciLp2G12vn0063UrbuYXLl8OXLkHd5/v+Z9E4iQ\nkFhCQmJ54YU6LF6sY9w4L2JaeNH1gomCdc+QpXA4Y/LmoU6hI5QJ1FOCkik+j5I+WJH8SgStyK7m\nhnhGpITuhyDeBj+oOoj7Ui0RKbBYoeeXsPxPbf6H91q7OiL38euvWu2D0Sj55htvunVTrQ9Pa/fu\nawwYsIEjR0IZPboBw4fXu2/ykOjAgRDAg4ULc1G7tp74lwxMiY2kRIMrBAkvJotS+HKHeZzhVdqh\nUx9M6douYrij5oZ4pqZegN9uwW81oLCqg7gvlUQkEx0Pr06AnSe1GShfr+vqiNzDnTsO3nvPzPff\nW2nZ0oP5870JDFQfTE8jNDSOjz7awrffHqFSpXzs2fMm1aoFPvQ4h0MyY8Y/+Ps35fZtwZRfvHnj\nkp2yza/SVBfAMLKxh00c5AC5yEUwahxzereGO5TCh9KoT7tnYbezDmJIcXhJLaT4QCqJSOLGHWg5\nBq6Gwe//gwblXR2Re1i7Vqt9MJslS5Z407Wran14GlarnVmz9jJq1HYMBj3z57eiV69K6PUPTspM\nJhtLlx5l2rQ9nDqVFSjN3HnezIjRU7r0TbyEhVocYQ4H8cKLJjSjOjXQo6ZiTc8isbGNGIZQwNWh\nuIVwszYfRK3sME7VQTyUSiKcTlyFFqO1f++cCOUKuzQctxARIRk40MT331t5+WUP5s3zJn9+1frw\nNLZtu8SAARs4eTKMd96pymefNSJHjgfPTBgba2b69L+ZPXsfYWHx1KtXnRshtchb34fYah7sDrFT\nuXYYL4nznOYsDWlETWqp1TgziHVEApKX1NwQT83hrIMwOWC5qoN4JCqJALYfgzbjoXAu2DAaAv87\nGk55TD//fK/14bvvvOncWbU+PI0jR0IZMWIr69efo1atguzf/xaVKz/avLsjR27jq6/206tXJYKD\nazHgfQ/8a/twLsiTMWFWKta7hENnQc9ZalGHBmomygxlrXNuiBxqboinNvUCrL8N62tAQTVr+CPJ\n9EnEir+g23SoVw5+GgYBahTbU7lzx8HAgSaWLbPx8ssezJ3rTYECKp1/UhcuRDBy5HaWLz9GiRI5\nWLmyHa+9Vhad7tETsj17rtO+fTnatGlOq7YJBLTwI6a6Dp/6cRStfoksnvA+Fo5gpYpaUCtDOYOR\nkxh5V80N8dR23YHhp2BYCWih6iAeWaZOIqathcFfQ5eGsGgAGFQi/1TWrNFaH2w2WLrUh06dPFTr\nwxMKDY1j7NgdzJ9/kNy5fZk7txU9ez6Pp+fj1SfY7Q6OHr1F1arVeOV1I15N/YltBgH1w8hb7gaV\n8GeKCOJnFlOM4mQjW+qckJIq1nKHHHhQnwBXh5KhhZvhjQNaHcTY0q6OJmPJlEmEwwEfLobpP8NH\nr8H4rqBTX5afWHi4gwEDTPzwg41XXtFaH/LlU2/ok4iONjF58m6mT/8bg0HPZ5+9wIABNfD1fbIM\n96+/rmI0evLNkiJ4NvDF3kiQrc4dcpW/QQ/y0ANvdrCGq1yhPR2e8dkoqUmbGyKSVmTHUy229cQc\nErodAqOzDuIho6OVZDJdEmGyaN0Xq3bDzLegfytXR5SxrV5t5d13TVitqvbhaZhMNmbP3sv48Tsx\nGq28914Nhg6tQ/bsT94xm5BgZciQzeTO3YT47F7E5tCjL+6gTLmbNMaHchxmDv/giy+teYXyBD/D\nM1JS21/EEIGNtqgirqcx6TxsuA0baqo6iCeRqZKIyDhoMw72ntPqH9rWcnVEGVd4uIP+/U2sWGGj\ndWut9UGNvHh8NpuDb789wqhR27l5M5bevSszcmQDChR4sgWuTCYbGzacY+XKk/z66xmMxqxIXXGy\nNvAmf3Pwf+42vvow/NnJIaAhjahFbQwYnu2J/Z+9846Oou7C8DO7m2w2vZNAAgRC7733jgRQOtK7\nFAErTVBQUETpHyIgIiIKSkKRHnqR3kuogSSkkd6T3Z3vjyEQFSSEJFsyzzk5sGV27raZd+/v3vfK\nFDj+xFAJDRWQz3x55WgMzLgJU8tBR3dDR2OaFBkRERItjfGOiIfAOdBY7v/NM9nZB60WNmzQ0K+f\nXPvwqoiiSEDATaZPP8CNG4/p06cKc+a0eu6grNySnq6lUqXlBAfHU716Md59txXbd1Qm2MGapLKQ\n5pFOsbJRtBKCcMaJIQyT52GYKLFkcZgEPuTl5mIyzyc6A/qdg8ZOMLuCoaMxXYqEiLh8Hzp9BpYq\nOP4VVPQydESmSXS0VPvw229aundXsWKFXPuQFw4evM+UKYGcPh1G+/ZlWb/+TerUeX2joCNHHhAc\nHM/Bg4OxtfWmW49Uoktp0LZToqinpUrTu3gJWiCMBnSTBYQJI3lDCHSRba7zhF6EgechQ66DeG3M\n/qU7cAmaTYVijnDya1lA5JXff8+iSpUU9u3T8csvGrZs0cgC4hU5fz6cDh1+pnXrnwAIDBzEnj0D\n8kVAAOzadRsvL3sePixO4/ZpxFS3QeyhhFoiTVrew8ZSz0QhC4CKyKk4U8afWFphj1PR+B2Y73x1\nB/ZGw4baUEJeDXotzPossOscdPwMGlaAw3PBQzZ0e2WiovT07p1Kr15pNG2q5Pp1G/r1k4snX4Xb\nt2Po2/d36tT5nocPE/jjj9789ddwWrf2ybd9iKLIzp138PZuzuCxmYjNbVD0EFBXy6Bju7skW6Xz\npZ0HKggAACAASURBVGDPTU7jTUlssc23fcsULjdI5SZpckFlHjkSAzNuwLRy0F6ug3htzFrGzlgP\ng9+CVePBwqyfaf4jiiKbNmkZNy4dgF9+0dC3r1z78Co8epTE7NmHWb36PJ6edqxe7cfgwTVfOmEz\nL5w6FcatW/E4OJSlVEcNSTUhrWwKZZreQRRExhHMPs7jiCN+dMv3/csUHgHE4oKKJtgbOhSTI+pJ\nHURTF/hUroPIF8z61DqiPXw/EeTz3qsRFaVn7Nh0/vhDS8+eKpYvt8Ld3ayTVvlKXFwaX311nCVL\nTqHRWPDVV20ZN64+VlYF93Vbs+Y8Tk61iUNFgkKJdU09leo9pI4QShku84gsWtOWxjRBZd5fe7Mm\nEz07iKMbzrI3RB4QRWjqDAurynUQ+YVZH03e6SwLiFchO/swfryUffjtNw29e8s2nrklNTWLpUtP\n8eWXx8nM1PH++4344IPGODhYFdg+RVFk0aK/WL36Ko7OI3BuqkHXBuwrRFJMfQsPzlCOmrSjA/by\nL1eT5wiJxKHlTbmgMk8Us4LfZGf3fMWsRYRM7omIkLIP/v5y9uFVycrS8cMPF/jss8NER6cyalRt\nPvmkBR4eBVt3EB+fzpAhAWzdGoKr+wDiyzihr6NAWTYDb99IGgrhlMKXHvQq0DhkCo8AYqmChnKy\nN4SMkSCLiCKOKIr8+quUfVAqYfNmDT17ytmH3KDXi/z++3VmzDjAnTux9O9fjdmzW1GmTMFX8F64\nEE7PnpuJiPDE1mEkSb426Jur0NcUaNsoFJ0AIuFUoGOBxyJTOMSQxRESmILcYiZjPMg/NYswkZF6\nevZMo3//NNq1kzovZAHxckRRZO/eu9Srt4o+fX6nXDkXLlwYzc8/v1UoAmLLlhs0bLiG+PjmpNIR\nobk9umYqxEYCfWvHEGKTyGCS0aHDl/IFHo9M4bCDOAQEOiO3mckYD3ImogiSnX2YMCEdhULOPrwK\np06FMnVqIAcPBtO4sTeHDw+hefNShRrD558foUqVuly4UAbfwTboLAVa9dJyp2wo1xyj6U4Qt7lJ\nOcrjIrcBmgUiIv7E0AoHHOXDtkwBc+By7u8rfxqLGOHhet55J52tW7X07atiyRIr3NzkhNTLuHEj\nmunTD+Dvf5OqVd3Ztq0vXbqUL/SW1/j4dC5ejKBq1a54N7HkTqyCX+ens6TibVwJoy0XEMikPX7U\npT6CXMFvFtwgjVukM5n8MSYzd0RRLqrPC6IIX/0BU3/I/TayiCgiiKLIxo1axo9Pw8JC4I8/NLz1\nlpx9eBkPHybw6aeHWLfuEiVLOvDTT93p378aSqVhhNfRow8QRWeuBNli3UXNgFZ6fql4l5qcxIUH\n+FABP7rigKNB4pMpGGRviBcTlQHBqWCnApUA5WwlAaEXQSELiVyj08HEVbB8J4zsAKuO5m47WUQU\nAXJmH/r0UbFsmRWurnL24b94/DiVefOOsnz5Gezt1Sxa1IFRo+qgVhvuK3P06APeey8QK80b0ECD\nrTU0GvGYAIJx4QHdeYta1JazD2aG5A0RS3dcUMnv7d8ISoY+Z+FxJqTooIItNHOGr6tIAkIWErkj\nLQPe/ga2noaVY6GuO6yakbttZRFhxoiiyC+/aJkwQc4+5Jbk5EwWLjzJ11+fAGDatGZMntwQOzu1\nwWIKCnrMlCmBBATcxsXFj0yf4mCvZMOHMM8qiobE4IIrtaljsBhlCo4jJBKPTvaGeA7dT0NzF3i/\nrJSR2B8Nmx7BgcfSXIyKdoaO0PiJSQS/z+HiPdg6HbrUg/Pnc7+9LCLMlPBwPWPGpLNtm5Z+/aTa\nBzn78GIyM3V8//055sw5Qnx8OuPG1WPq1Ka4uRlu0mVSUgZTpuxn5cpzODpVx9V1LLEqK/Rlrfji\nbUitHks4mdgQSkVqGyxOmYLFnxiqYi17Q/yDiwlgqYCPfaGMDZS3hZoO0NgZFt6DvudgWTXJ4lrm\n+dyPkOZLxSbBoblQPw/NXPJZxcwQRZGff86kSpVk/vpLx5YtGn75xVoWEC9Arxf5+efLVKy4jIkT\nd9O5czlu3RrPt992MKiAEEVY9L+zrFlzgZGj/Ih53BrfRtZYNNLwRj2R8j1j+JSHdCKYdFKoQhWD\nxSpTcDwmiyMk0l3OQvwLayXcTIbjsc+us1VJQ7VmlAM3S/g1zHDxGTvn70Kjj6RaiJPz8yYgQBYR\nZkV4uJ5u3dIYODCdTp1UXL9uw5tvyssXz0MURf788xa1aq1k4EB/atTw4PLlMaxd241SpQxflPj+\nNVjmXA71NyP4w74Kpd+04KqVmqa19VSY+oCZiod0IQEbztGSVnjhbeiQZQqA7cSikL0hnks5Gxjg\nBVvC4XLC329r4gL9veD7B3A72TDxGTN7zkOLaVDKHU5+Db6v0fQjiwgzQBRF1q/PpHLlZE6f1uHv\nr2HDBmtcXOS393kcO/aQ5s1/pEuXjTg5WXHixDD8/ftQpYpxzAXufVZa21Vduod1rJJoewUPelnh\n3lKPetotDqsSmClaYcFBqlCVlrQ2dMgyBYCISACxtJa9IZ6LIEDv4nAxEabdhDNxkKF7dntzF6hs\nB2m6Fz9GUeTHQOgyB1pUgQOfg5vD6z2efJYxccLC9HTtmsagQel07qzi2jUbuneXsw/P4/LlSPz8\nNtKs2VqSkzPZvfttDh4cTKNGxvMr/mICnI2Hb0okEf39ERLnK7G+o8AtRuCRD1wPcuB9grkl/Iob\nbrxJDxTy19gsuUYat0mXlzJycC8FTsbC8Rjpcgd32F4fbiRJI75XPoBLCVKR5cpgSNBCVbkrFpCW\nSOf8CkMXw9A2EDAdbPJhNqAsb00UURT58ccsJk9Ox9paICBAQ7dusnh4HvfvxzFz5iE2bLhMmTJO\nbNzYg969q6Awwt4vEXicrueT2UexsGiEtriGrBiBNX7pTM6KIjXEis02Au+WbEFDGmOJpaFDlikg\nAojBTfaGeMpPIbAiGK4mQhV7eLsEjCktiYS7bWHYBUlEzL8jtXVqFPBbHbnFE0Crg3dWwOq9MLs/\nzOiTf2ZcsogwQcLC9Iwalc7OnVoGDbJg0SIrnJzkb8o/iYxM5osvjvLdd2dxcbFm+fLOjBhRGwsL\npaFD+xfx8els3HiF1RuukeTXmos2xclS+2Bd1Yq+TQWulYqiceYlbsb5kBDWiZYlZcFozmSi50/i\n6CV7QwBwPQneuQxLqkINB1h6D3ZHwYQykKIFGxX8UAtOx0GW/plnRClrQ0dueFLSoc982HMBfpwI\ng9vk7+PLIsKE+Gf2Yds2DX5+8snknyQmZrBgwQm+/fYkKpWC2bNbMWFCfWxsjPNXu14vUrfu9wQH\nx9OxUzm6lrRmdzEvVCo96dHQY3ASM4ihp+UNfL0d+f2qBZHpUCwfUpEyxskhEklARzd59gkAQy7A\n2NIw/MmYmg984cNr0hJGph6cLWBVTagv15/+jegE8JsDVx/CnzOhfa3834csIkyEkBA9o0alsXu3\njkGDLFi40ApnZ/kXSk7S07WsWHGGL744SkpKFu++W5+PP26Ks7Nx99f/dTOOu4l6fvAfQN3Spejc\nNRXtYNC3VdLWOYspFmG0IhYtCXhpK6OU33azJ4AYqmNNWWSleC5e6sR4O8cE9NlBEJQC3ezA1VJa\n6ph4BRZUAaUgL2EA3A2Hjp9CYiocngt1fAtmP7KIMHKysw+TJqVjZyewY4eGN96Qsw850Wr1rF9/\niVmzDvHoURLDhtVi1qwWlChh/GvJ82/D2iBLWDCS/2nVXB2dgVjBGtsbAl06ZrEpXoHbVW/Oq5U4\na3rwV7ALU8vJWQhzJposjpLIdLltF5CWJT70lf4F2PIIdkbByaZQ/UlnwaN0OBknzc6QB2/Bmdvw\nxmxwtJFaOMt4FNy+ZBFhxISGSrUPu3ZpGTJEyj44OsrfkGxEUWTr1iCmTQvkxo3H9OpVmTlzWlGh\ngquhQ8sVPz6EeXegwfU7hF/I4GyLuihbaigVDR9/GccPLqG0jrPB7pGSC4ngIpZhVgV4t4yhI5cp\nSLYTixKBTvIQNUAykKph/0wcvFUcytpIAiJ7NkZ9RwhNg0QtOBTx31h/noHe86GGD2ybAa4F/FtK\nFhFGiCiK/PBDFu+9l46trcD27Rq6dCni34x/cOhQMFOm7OfUqTDatSvDTz+9Sd26pjMm+WYSTLkB\nK6qJTHnnEM6KrmjLiKQ7QNe3s5gVl4qfJoXyTntIckxmtNCEVmJZVLKGNGuyvSHa4ICDfHh+SraA\n0InSckWNJxkIhSC1Lm4IBV8bWUCs2gNjVkDX+rDhfbAuhJE/8qfUyHj4UM/IkWns3atj6FALvv1W\nzj7k5Pz5cKZNC2TPnrvUrVuc/fsH0qaN6f00PxoL3T2gWHgEDx5oESxcoJoSZ2v46bEeK6WSzcEV\n+Kh+FO/aN8EFV+QiffPnGmncIZ0PKWHoUIySf9YDxWXC3NtwKwX2NjJMTMaAKMKsX2DObzCuMywe\nCcpCakKTRYSRkDP7YG8vsHOnhk6diriszsGdO7HMmHGA3367RoUKLvz+ey/eeqsSgokugHZ0hzo2\nWha8ewIrq/pkTLVF1MOHzePZ53KMssn32X1mFHYx3XAx/tIOmXwigBjcsaAx8vjJbETx+XUOwamw\n5qHU6ulfr+jWQmRpYcz/4If98OVg+Oitwn0tZBFhBOTMPsi1D3/n0aMk5sw5zOrVF/DwsGX1aj8G\nD66JSmXaLo1hl0IZPnwbN2+6onerC+EKxpQT2eMWRkPC8Lax5YbaClGU7v+iA6mM+ZCBnh3E0RsX\nlEU07RSbCXdT4E4KVLGD4lbg+iQlrxelZFz296C0NTRzhm4eULuIlo8kp0Gvr2D/JfhpMgxsVfgx\nyCLCgIiiyJo1cvbhecTFpTF//nEWLz6FRmPBl1+2YezYemg0pv36JCdnMn16IEuWXMHZuRN6Ox9U\n9TV0LwUN+zzmJGmoeYRHZhcStFDsyQFUFhDmz0ESSERH9yLsDdHhL2n+RVAKlNRIQmJ4SfDz+Hvb\n5oUEqOUgTewsqkTGwRtz4FYY7JwJ7QrAAyI3yCLCQOTMPgwbJtU+ODjIZ4rU1CyWLj3Fl18eJzNT\nx3vvNeLDDxvj4GD6PY3BwfG0bPkj4eF2WFuPIMPFCnUVDdXLwBeTMxmmiKQrj0nJsmDZxZoUt4Le\n8tJ4kcGfWGpgTZki6g0x+DxYKWBjbfC1hR8ewp4o+Pg6XEqEGU9GVW8Mhak34JPyz8yniiJ9F8Cj\nWDgyD2oasCxMFhGFjCiKrFqVxQcfpOPgILBrlzUdO8pvQ1aWjrVrL/LZZ4eJikph9Og6zJjRHA8P\nW0OHlm8EBNwkMjKFGjWGkiiqeFhKQ5e60HNyLAPUwdTiMveiRcJCBxCdbsnlloaOWKawiCKL4yTy\nSRH1hkjIgvAMKevg++QrP6wkNHSSjKS2RUgC4wNf8LGGVq7Q0jQ6uQuMFe+AxlIa521I5LNXIfLg\ngZ4RI9LYv1/HiBEWLFggZx/0epHff7/OjBkHuHMnlv79q/HZZy0pW9Z8Jhf+GSlN5zwSp8S9UV3O\nHBIoM1iDlxWU/yCEJao7tBfPYSmk4EIf4m1KM6Si7LpXlNhOLBZF2BvCwUIaKb01AgZ6P+vCqGwH\n75WV/B9WPYDB3tDQGWo6gJXxjcApVCp6vfw+hYEsIgoBURT5/nsp++DoKLB7tzUdOhTtl14URfbt\nu8fUqYGcPx9Op06+bN7cixo1CtBazQD0OANXEsFSAUGVq6F00mNZz5IHtwVmfB3FX4pztOM8Vhk+\njLAajJubOxnOoC7iB8iihIiIP7G0xRH7InhIzi4a7lkcFtyFHRHQ1UO6ThTBXQ3Lq0GxPeAfDqNK\nywLCmDDtEncT4P59PW3bpjJmTDp9+lhw9aptkRcQp0+H0bbtejp0+BkrKxWHDw9h5863zU5ArHsI\nf8XB9gbwm3sUuvc3kXFFSWYFJb6DRPxtI6mvuIxXel1OXBrCF1elvKSl/K0sUlwmlXuk0w3zyb69\nCtlFwyNKQW0H6HceVj+EVO2z20SkrESa3mBhFjiJqZCW8exydmeWsVO0z2YFiF4vsnJlFh9+mI6r\nq8Devda0a1e0X+4bN6KZMeMgW7bcoEoVN7Zt60uXLuVN1uvhZYSlg4+QwZKP97N+/WU0um4I9xUo\nSoBYTkvMDUdSK6toKDbngEqBw5OPh5m+HDIvIIBYPLCgkewNwS914JObMOYSBEbDIG9pwFZQMpyK\nkzIS5kZKutSmmZwGkQkwoh30bAw+HqDXg8LIf1QYeXimSXCwnnbtUhk7Np0BAyy4csW2SAuIkJAE\nhg/fStWqKzh37hHr1nXn0qUx+PlVMFsBERh4j3ULj3I8OI3fTkTRqVN7UhUlSbNTMbseqLxiSIx2\nxirRA1fNRubW+I1PKiYYOmyZQiYDPbuIww/nIusN8U/mVIRDTeB6Eky5Di1PwJL7sKgqVDEz47X4\nZKj/vlT/9K4ftKoGf5yA/t9AWIwkIPRGnn0pume2AkCvF1mxIouPP07HxUVg3z5r2rYtui9xTEwq\n8+YdY9my09jbq1m4sAOjR9dBrTbv10QURfr0+R23OqXw7FCfmp8NYtv4NKxaWuNVXCT0jYc4KIJJ\nflSKsw/LEuY6HqUK1ERQnImGDl+mEDnw1BuiaC5lvIhmLnC5leQHIYrgYgmlrA0dVf5z5QGoLWDN\nBCjmBD2bwO5z8NUW8JsDx76S5l8Ys9mceR/NC5F79/QMG5bG4cM6xoyx4KuvrLC3N9J3vYBJTs5k\n0aK/+PrrE+j1IlOnNuW99xphZ1cI02CMgMjIFGJi0vh+dHUOJylYYqNAmGSDT6hI27kP2KOIZxj3\n+MPOAVt9BsUYgJ4k4tmNJ+8iyL9Iiwz+xFATG3yKqDfEy6jlYOgICpb4FLj2ENIyn13XsQ5YqODj\ndTBqGfz8vvEKCJCXM14bvV7kf//LpHr1ZB480BMYaM2KFZoiKSAyM3UsW3aasmWXMGfOEYYNq8m9\ne+8ya1bLIiMgQKr9ADh4sBhLPsxCsQtUJSG+i5Yd0QK9Hjty4bGeS6HVqeF8FaVgiRMdyeABadw0\ncPQyhUUkmZwgiTflLESRpZQbVC0Fey5AZtaz65tVhqFtJIFx0sgPCbKIeA3u3dPTpk0q48alM3Cg\nBZcv29K6ddFL7uj1Ihs2XKZixWVMnLibTp18CQoaz8KFHXFzszF0eIXO+fPhWFh4s+x7C1QNNHTz\ngcF+wejsUhDuuvD5KS8OXevK0JIiXUtuRIkDdjREgTVJnDB0+DKFxHbisECgI06GDkWmkIhPhpjE\nZ5er+0BZD/huF1wKfna9pQX0bwEPouFGSKGH+UoUvTNePqDXiyxfnsWUKem4uQns329NmzZF96Vc\ns+Y8o0btoFu3Cmzf3o8qVYqwoT2wd+893N3rkVLCkgwLGD4pkbnqe3xc7yKhSUoq62vRUtUAb5uT\n3CUVe5oiYIElHmQRZejwZQoBEZEAYmiLI3YUXdODNB1oisjTn7hKyixcCYZhbaFXU6hdVhqcVXU8\nfLgWFgyFuuWk+ztYQ2VvUBn565OnM58gCGWBoUBZYKIoilGCIHQCHoqieC0/AzQ27t3TM3RoGkeO\n6Bg71oIvv7TCzs58li6uX4+mWDEbXFxyX8U0YEB1qlUrRsOGRmKhZkDS0rI4fDgUFG+gqm/JwPYi\ny6yDacEpHLFnqF0PPPAE4CH7sMQbK6ShACrcyOKxIcOXKSQkb4gMplF0vzPbI+Cdy3CyGXhrDB1N\nweI3B0Iew9Se0sCsDYelbEON0mBlCYfmQvOpMG09dG8I7WvCrvOS6Chf3NDR/zevLCIEQWgB7AKO\nA82B6UAUUAMYDvTMzwCNBan2Qeq8KFZM4OBBa1q2NJ/sw7FjDxk79k+SkjJRqRQMGlSdIUNq4u3t\ngF4vovgPD2aNxuJfAiIw8B7378c/vVy7tie1a3sWWPzGQEpKJlOnBpKRURl8NWTqwLf3YyIJwpJ0\nejMCNaE84jcSOUwaQRRj9NNCSks8SOU6IqJcXGnmZHtDNCii3hAPU2HIBWjqAl5mXFMqijB3s1RA\nuX0GeLtJ11tawNIdkqgQBPByhV2z4Ms/YM5vsGQ7JKXB6gnQsKJhn8PLyMtZ8EtghiiK3wqCkJTj\n+gPA+PwJy7i4e1fP8OFS58XYsVLnha2t+RzkIyKSmTJlP61alWbkyDps2xbEhg1XuHIlik2bev2n\ngHgeN28+pm3b9f+6XhRn5VPExoUoivj732Ty5D2Eh9ujcOmFWEnNhz1gl2MUjYmkNpmE0Q0dCShx\nxJ5muDMCJ9o/fRwnOhPLVlI4jy11DPiMZAqSdPTsJI7+uBZJb4gsPfQ5B3YqWFvTuDsPXpfUDIhL\nhl5NoLgz6HSgVEp+EOsOQJZWykTodFDBC74bC48TJdHhZAPFTWAqfF5ERDWg/3OujwLMaq5aztqH\nYsUEDhywplUr88k+iKKIIAicOhXKhQsRbN7cC09PO6pWdcfb254vvjjKggUn+OCDxi/NRuSkYkVX\n9u8f+K9MhDly61YMEybsYu/eMLy9O5MllETdwIaa5aDh23HsIRklkXhxEyt8KMHHWFMV4Tnr4HY0\nQU0Zolkviwgz5gAJJKErsjbXU2/AuXg42hScLQ0dTcFiYwUDW4GvpyQesq2sRVESCpla6bLyyeFA\nbQElXKQ/UyEvZ8R4wBO4/4/rawFhrx2RkXDnjpR9OHJEx/jxFsybZx7Zh9TULHQ6PXZ26qdukenp\nWsqXdyEjQ/f0fl26lOfq1SgWLfqLsWPrYW1t8Ur7adPm+QPuzWmZIyoqhVq1VuLqao+r6ygSkpV4\n97IlupzAgKHpLFWG0pZbgIiSMBwYjQ01Xvh4AgrcGUAIn5PJIywx8sVQmTzhTwy1sKF0EfSG2BYB\n39yFhVWgQRFpSqnhI/2b08I6MRUEJD8IkCyv/f+CAS1NLzOTlxbPX4GvBEHwQJqLohAEoQmwAPgp\nL0EIgtBMEIRtgiCECYKgFwSh63PuM1sQhEeCIKQKgrBPEATfvOzrZej1IosXZ1C9ejIhIXoOHrRm\n6VKNyQuIzEwd48fvpGbN7/Dz28jixX8RGir1GqnVKhIS0rl581lRn5OTBj+/Cjg7a/juu7OAlLl4\nHbKXOUaO3P70r06d71/rMQ1JUNBjUlOzePvtfsTGKan/jh3hNRVYvhHPaq/rVOMkNtziDZqgJwUr\nyr30MZ3wQ4GaWLYVwjOQKWwiirA3RHAqDL4A3Txg4vN/Y5g1OWdgKBTg4QT21hAcCVUnwL6Lpicg\nIG8iYhpwEwgBbIHrwBHgBPB5HuOwAS4CY5GEyd8QBOFjpHqLUUB9IAXYIwhCvibDbt/W0aJFKpMm\nZTBihCVXrtiaRfGkVqtn2LCtnDwZyvz57ahWzZ1Vq84zevQOALp3r4hCIfDHH9dJSEh/ul3lym6U\nK+dCUNBjtFr9a8+5yF7mWLXK7+nfuXOjXusxDUlkZAqgYP16Cyp017DfQsChcwQ+dYPoojiGC+H0\n420qIhn+W1H2pY+pxAZH2hNLAOK/vwoyJs42YlEXQW+ITD30PQeOFuZbB5GSLmUYcvLP313Zl6Pi\nwdkW/roJ9T+AxhWlVk9T5JXPkKIoZgIjBUGYA1RFEhIXRFG8ndcgRFHcDewGEJ5/ppoIzBFFcceT\n+wwCIoHuwKa87jcbnU5kyZJMpk/PwNNT4NAha1q0MH3xkM3Nm4/Zv/8eGzf2oFUrH7p3r0hAwE1G\nj97B3LlHmTatGTNmNGf8+J10716RN96QWg6dnTUkJ2diaalEpcofX7IXLXOYIiEhCSiVlQjVqsDT\nAttOCVSofI12nEGDngGMwBUIZQkCVrlennCmu1xgaYZI3hCxtMMR2yLmDTH1OpyPh2NNwckM6yBG\nL4egMAiOkpwmO9aGBhUksZRz7kX2vzFJEHgZDl2FSV3h66GGi/11yfOZQRTFh6Io7hRFcdPrCIiX\nIQiCD+ABBObYdyJwCmj0uo8fFKSjWbNU3n9fyj5cvmxrVgICQKkUyMrS4+r6zPuhQ4eyjBtXj7lz\nj5KWlsWQITWpW7c4ixefIjDwHgDx8elkZemoV09em38eGzdexda2Hg511Ng3gjKVImkiXsUZNcPo\njo5VXKczqVylJJ8i5PLrZks9LClBLAEF/AxkCpMLpBBMBt0xoaq5fGBrOHx7D76uAvXNMAHT80s4\nfgOGtJFMpH47BlN+gu2npdsFQeq+yIlSIf398K5pCwjIm0+EgOQF0Qpw5x9CRBTFt/IntKdk115E\n/uP6yCe35QmdTmTxYin74OWl4MgRa5o2NS/xkE1CQgY+Po4cPx5CtWrFAMnboX//aqxZc4G5c48y\nZ05rvvmmPQsWnKRTpw28/XZ1Tp4MQaEQ6Nq1goGfgXERHBzP1q03OXNGBw4u4K7EqkQqtvYh2BNC\nS3SE0RcldhRnMm70RUHu3XQEFDjTjSjW4cW0V9pWxnjZSiyeWNAAW0OHUmgEp8KQi/CmB7zrY+ho\n8p97EXAnXJrC2eDJYbJ1dfjfTvhkg7Rk0aSy1H2h1cHDaCjjIRlK1Sv3zJ3SlMlLJmIRsB7wAZKB\nhH/8GT1BQVLtwwcfZDBmjCWXLtmYtIC4fj2aW7diSErKeO7tDRt6YWen5sSJEMLCnhm3e3ra0qNH\nJQ4cCCYzU0edOsVZs6Yrq1d3xcPDhpEja3P9+jh8fYteEdjz2LnzNmXKLMbHZzGTJ+/Bw7MFmupq\nrOuJeJePorp4j9rcQs9hPJhAZfZSjKF5EgHOdENPCvHsK4BnIlPYpKNnF3F0wxlFEfGGyNRDn7Pg\nZAE/1DLPOghRhAdREB737LqmlWH8G1DaHeb+DqFP6tXn/AZvzYOgUPB0Ng8BAXlr8RwIvCWK4s78\nDuYFRCB1wxTj79mIYsCF/9pw8uTJODg8myUrimBn1xN//+54eSk4fNiaZs1MVzyEhSUydOhW3sNp\n1wAAIABJREFUTp8Ow9vbAYVCYO3abn9rmdTp9CiVCoYPr8XMmQcJDLzPoEFSm6GNjSUWFgrUaiVa\nrR4LCwXW1hZPb5d5RkaGljFjdlCqlCPz53fg0CEvlv+phEYWWFVJwcozCndCKEYCrvTBg5GvtT81\n3thSl1i24sy/mpVkTIxA4klGT7citJTx4TW4mAjHm0oFleaIxhLKFYfLwdCpjuTzANC4EvRpCnM2\nwdk7kiOllwtULQnFHA0a8r/YuHEjGzdu/Nt1CQm5zwfk5QyaANzLw3Z5QhTF+4IgRABtgMsAgiDY\nAw2A5f+17cKFC6lduzYAN2/qGDIknT//1DF5siVz5qixtjZdaSyKIl99dRwLCyUnTw4nJSWLyZP3\nMGHCLqZMaYKfXwX0ehGlUko2DRhQnc2br/PTT5coU8aJpk1LAhATk4azs+aVfSCKGt99d5awsCTW\nrh3I9OkazjwSEDpbQWORGnVDqUwUoEVBLGpK5cs+nenOQz6RPSPMAH9iqYMNpVAbOpRC4Y9HsOQ+\nLKsGdY3spJmfFHeBno1h1kZoUgna5Pj91a8FLAiALSel5YuRHWB4u7+3ehoD/fr1o1+/fn+77vz5\n89Spk7ui7rw8nU+BWYIg5NtCrSAINoIg1BAEoeaTq8o8uez95PIiYIYgCH6CIFRD8qMIBba+7LF1\nOpFvvsmgVq0UYmNFjh2z5ptvrExaQIBU5+Dvf5O2bX2oVMmNunWLs3ZtN0qUsGPRolOkp2tRKAT0\nehGtVg/ArFktcHbW0LHjz0ydup9Bg/zZsuUGgwfLmYf/IjU1iy++OErHjs3p0cOS6woL9M2tsewA\n9WtEkWydRDUeUB4XQIca75c+Zm5wpAMKrIh9+cdcxogJJ5OTJBWZgsr7KTD8IvT0hLGlDR1NwfNR\nD/CrB4MXwamgvxdRVvaW7K6zMTYBkR/k5SltApyAKEEQrgiCcD7nXx7jqIu0NHEOqYjyG+A88BmA\nKIrzgaXASqSuDA3Q6Um76Qu5f19H06apfPihVPtw8aINjRub7vJFTqKjU3Bx0eDp+WyAj6+vM2+9\nVYmYmFRWrToHgEIhPG3PrF3bk3XrujN1alPCw5NJTMzg0KEh+PnJhZP/xdWrUURHpxIbWx3XShYk\nFbPEs5+O0o0eQOkb9OAwSURRkzgUaLCmcr7sV/KM6ECM7Blh0mwjFisUdMSMf5I/IfPJXAxnS1ht\npn4Qz+Pn96BCCejzNXy/By7chYOXYdc5yfLanMnLGXUdUAf4GalG4bWPbqIoHuYlgkYUxU+RsiC5\npl+/NEqXFjl61JomTcxDPGRTrpwLqalZnDoVSq9elZ8uW7Rp48OePXcJDLzPsGG1sLGx5PDhYPR6\nkVatfNBoLJg+vTlarT7fvB/MnfDwJEDNmbMqPHurcW8hYlE7mErFLlCdy7jhypv0IJpBFGMEqnw0\nEpI8IwJkzwgTRUTEn1ja44hNEfCG+Og6XEqEE03BoQitkFpaQODnMGyxJCJmbQRrNYztDCPav3x7\nUyYvZ9Y3gA6iKB7L72Dym759LVi50gaNxjzl8IQJ9Zk16xDjx9enbFkpZ+bmZkPlyq78+us1EhMz\nSEzMYM6cIyQmZnD8+DAsLKQDmSwgcs+jR0kolWXRFVMR6q7AqVEUzTxPUpkb1KchbWjCIz5DiR3u\n5G/Tty11saQEMfjLIsIEuUAKD8ngs3xa4jJm/MNh8T1YWg3qmH/S5bmseRfCYyEiXiq6rGT+b3ue\nljNCgMSX3ssImDRJbbYCAmDEiNrY2lry7bcn/9beWbWqO1euRGJpqcTT046BA6szZ06rpwJC5tXY\nufMOlupaaGpaoWmmp1SlECqLt2hBZWpwmSDak8BBSvARSmzydd/ZnhHx7EZH6ss3kDEqAoilOJbU\nM3NviHspMPSCVAcxrrShozEcgiAVW9YuWzQEBORNRLwPzBcEoXT+hiLzqmg0Fixc2IF16y7xww8X\niI+X5l7s3XuXbt0qPu24GDy4Jh06FMi8MrPm7t1YPv30EDt2JJNm7UlaKQUq7wSKqULwFEJwZi5x\n7MKdwVRlP874FUgcznRHTyoJ7C+Qx5cpGNKKiDdEhg56nwWXIlYHISORl+WMnwFr4K4gCKlAVs4b\nRVGUnYkKkR49KnPhQgRLl57mp58uY2Wl4urVKFav9kOjKUKLkvmEKIqsXn2etWsvcvJkKLa2lpQs\n2YeYsmoUtUV8dTa0IopKRGJNdcrxI4oCbttT44Ut9YnBX/aMMCH2EU8KerqZ+cTOD67DlSTzr4NI\nywBN0ejQRavNfaljXkTEpDxsI1OAzJrVgj59qnDkyAMSEjLYu3cANjZmOOWmENi9+w6jRu2gUydf\nfvmlBzdulGHOWgFqqMANxnqnEkow9oTgRN8CFxDZSJ4R08ggDDUlCmWfMq9HADHUxZaSZuwN8fsj\nWPbED8Kc6yAu3gO/z2HVOOho5qVJJ09q6d8/Ldf3z8sUz3Wvuo3Mq5OSksmmTdcYMqTmS0dwW1go\nqVat2NO5GDJ5588/b1O6tCObN/dj2LB0Nh0GhZ8VtBQZ6CVQqvhpkslAQIeGioUWlyPtCeVzYtmK\nJ2MLbb8yeSOMTE6RzOeUNHQoBcbdJ34QvYubtx/E3gvQ40uoWAJqmc8Q4n+RliYyc2YG336bSaVK\nud8uVzURTxwin/7/v/5ePXSZnGRm6vjf/85QtuwSxoz5k5s3Hxs6pCKDKIr8+edtmjevTLPmqfhf\nUUAHa1SdBJq6CPyvZhbnhDNUxxUAKwqvzkSJNY50IJYARPSFtl+ZvLH9iTdEezP1hsiug3CzhFU1\nzLcO4qcD8MZsaFYZDn4BxcxwCilI2YdatVJYujSTefPU/PBD7r0kc1tYGScIgvuT/8cDcc/5y75e\nJg/o9SK//HKFSpWWM378Tjp29CUoaDyVKrkZOrQiQ2hoIsHB8Vy/XoMHGUqyKllh+yZUdIIf68fz\nq2IdWpLw4CIWeGBRyGvdLrxJJqEkc65Q9yvzakjeEDF0MGNviPevwdUk2FwP7M2wDkIU4YtNkgvl\noFawdTrYmuEw3dRUkffeS6dJk1QcHODCBRs++kiNSpV7VZjb5YzWQOyT/w9FavP8x4R0FGDGubsC\nQhRFdu26w9SpgVy+HEnXrhXYurUvVau6v3xjmXwlLCwJUHL1qhr3t9RYtYBEC1jU5BIbLbdhjUBX\nbpFFKL6sKvT4bKiDJd7E4o8d9Qp9/zK54xwphJDJ52ZaULkpDJYHw4rqUMvhpXc3ObQ6GPedZBr1\nWX/4pI95ZlqOHdMydGg6oaF65s9XM2mS5SuJh2xyJSKeOEpm8wPgKYpiVM77CILgAuxHcrSUyQUn\nToQwZcp+jh59SLNmJTl+fBiNGxeR5mIjJCIiGShOukbFQ42A4AHz6p/hoGUANShPZXaQxSN8WYMN\n1Qo9PgEBF7oTyWq8mJ7vnhQy+UMAMXhhSR0z9Ia4kwwjLkGf4jA6f+bMGRWpGdD3a8mueu1EGNLG\n0BHlP6mpIjNmZLBoUSYNGyrZscOGChXynjHLS3eGwPOtrm2B9DxHUoS4ejWKadMC2b79FjVqFGPn\nzv507Oj70gJKmYIhEz0hZHIsNgab1hXQalUITaGaUyZa1x20JhpnDpKFHl9+yLfZGHnBma6Es5R4\n9uFCd4PFIfN8UtGxh3gG42523hDpOuh1FjzU8L0Z1kE8ToSun8Ol+7B9hnl2YRw7pmXYsHQePtTz\n9ddS9kGpfL03MtciQhCEb5/8VwTmPPGIyEaJNJr74mtFY+YEB8cza9Yh1q+/hI+PExs2vEXfvlVR\nKMzs22hifEYIp7VJhPZVU6yeFaL9PeITXRlVIgKlcAsHruLMANx4GzVeBo3VkhLY0oBYtsoiwgjZ\nT4LZekNMvAo3kuGvZuZXB3EvAjp+CvEpcGgu1Ctn6Ijyl5QUkWnTMli6VMo+bNtmQ8WK+VOv8yqZ\niFpP/hWAakDOCZqZwCVgQb5EZWZERaUwd+5RVqw4i5OTFcuWdWbEiNpYWppn0ZWpkJqaxcxr19nj\nk8GDt8+iDfHBskMdNP0zcKsayW9WSfTCAVvq4sXHhg73KZJnxFQyCDW4qJH5O/7EUA9bvM3MG2Jj\nKHz/QMpA1DSzOoizt6UODAcbODkfyprZ1M2jR7UMHZrGo0ci336rZsKE188+5CTXIkIUxVYAgiCs\nBSaKomgS8zMMSVJSBt98c5JvvjmJQiEwc2ZzJk1q+C8jqMDAe9y/H//0cu3antSubWafZCMjJiaV\nKlX+h+X66rhuyWJqy4Ys+74cMeE2ZEbqaeWuIaZUMHtpRkMjq7B3pB2hzCGWADwZb+hwZJ6Q7Q3x\nhZnVl99OhtGXoX8JGGFeT42dZ6H3fKhaErZ/Am5mJJBSU0WmT89g8eJMGjVSsmuXFeXK5f+xLC9m\nU/k7ptAMycjQ8t13Z/n886MkJWUwfnx9pk5tiouL9b/ue/PmY9q2Xf+v60VxVmGEWmTZufM2kZEp\njK9TivAGCpZV8SC6nAaxrYC9UsWw4nc5zEmO0Jxf8KC6oQPOgeQZ0ZFYtuHBWIQ8jcCRyW+2EYvG\nzLwhctZBfGdmdRCr98Lo/0GXurDxQ2l0t7lw5IiWYcPSCAsT86324UXkpbBS5gXodHp+/vkyM2ce\nIjQ0kWHDajJzZgu8vV8sbytWdGX//oH/ykTIFCx//nmbunWL43nZjV1ejxCnpUKmFaK7wJb6Ipcs\nTtGIVOzZxS3GkYLOqHr+XehOLFtI5pzJt3tOYCK22Bk6jNdCRCTADL0hJl+FoCd1EHZmcrYQRZj9\nK3y6EcZ2hiUjQWkmb1lKisjUqVLtQ5MmSnbutKJ8+YJ9cmbysTAsoiiyffstpk0L5Nq1aHr2rMye\nPQOoWNE1V9u3afN8L1V5maNg0OtF9uy9S/MWHZjhp6DELw7Yvh2NPiaT0ZYuiC7XiSSC5sRznqpE\noTW6E4M5eUa4YfqeKNneEF/gYuhQ8o1fw+C7J3UQNcwkza/VwdgVsGovzB0IU3qaT3YlO/vw6JHI\nokVqxo8vuOxDTmQR8ZocOfKAKVP2c/JkKG3a+LB2bTfq1Xv9AUnyMkfBkZCQTnxcOvfvFqdcEw13\n/nDA0csG72ph7FFGcI5gKlCatdhyihbMwMPQIf8L2TPCuPB/4g1R20zeh1vJMPIi9DOjOoiUdOgz\nH/ZcgB8nwmAz8YDI7rxYskTKPhRU7cOLkEVEHrl4MYJp0wLZtesOdep4sm/fQNq2zb/pLPIyR8Gx\nWP8I+wElubFJjV1FS5w7CXgkaRitPMoxwZZM3AkmE2sq8TFl6IRxGuZLnhHLiGcvLrxp6HCKLCno\n2E08w83EGyLtSR1EcStYaSZ1EFHxUgfGzTD4cya0r/XybUyBnNmHhQvzv/MiN8gi4hW5cyeWmTMP\nsnHjVcqXd2Hz5l706FGpQIyinrfM8c8lDpCXOV6Fm6Sy2TkR12kVyRoaSexdgRSNPbMb7CBBeMQn\nZJLELjyYTHGaojTik8Izzwh/WUQYkP3Ek2ZG3hCTrkqZiFNmUgdx55HkAZGSAUfmQq2yho7o9clZ\n+9C0aeFnH3JiBh+RwiE8PIk5c46watV53N1tWLmyC8OG1UKlKrzK+BctcYC8zJFbSqLGKVrPvQMK\nVOVVePYNwT3TihD1dc5Tj2qsox4f4sJAoxYQ2bjQnQdMIYMQ1MiW6YbAn1gaYEsJM/CG+OWJH8Sq\nGlDdDOogTt+CLnPA2VbygChdzNARvT6HDknZh4gIKfvw7ruWBjUslEXES4iPT+frr4+zaNEp1Gol\nc+e2Zvz4+mg0hW/Z9rwlDpCXOV4FjaggZUsEYlp5IrZ6YecZT4UKIeylDVosqMQPuJtQi54j7Qh5\n6hkxwdDhFDlCyeA0yXyJ6Q+SCEqG0ZdggBcMN4M6iB1noPdXUKsMbJsBLvaGjuj1SE4WmTIlneXL\ns2jWTMnevRp8fQ3f3i2LiBeQlpbFsmWnmTfvGOnpWiZNashHHzXB0dHKoHHltpMD5GWOnGzYcJmf\nfrrMmTNhpHoVp/imTBQHtGQEu1OzykECxLKUzIriI1UwTRXujMMTFVIBozGjQIMTnYhlKx6Mkz0j\nCpmtxGKNgraY9s/2NB30PgslNNJ0TlOvg/h+N7zzHXStD7+8DxoTTxIdPKhl+HAp+7B4sdR5YSzj\nEmQR8Q+0Wj0//niRTz89RGRkCiNG1GLmzBZ4ehpvH7u8zPHfnDv3iEGDAmjevBRjxzbmj4DKxJzN\nxKltLN2ytFwUVFTRXmPSrf8R6NyScx4DEBSeRi8gsnGmOzH8TjKnsKORocMpMugRCSCWjjhibWQt\nwK/KxCd1EKebg60JnxVEEWb8DHM3w7jOsNjEPSCSkkQ++iid774zruxDTkz445K/iKLIH3/cYPr0\nA9y6FUO/flWZPbsVvr7GXywlL3O8GK1Wz8iR26levRjz5vVn0KB07tuosRCz8HQNo4z9I45Tkvlp\nH9Mo4TSVUm6THPsXqooBoDLOrox/YkMt1JQihq2yiChEzpJMGJm8aeLeEBtCYdUDWFMTqplwyj9L\nC8OXwvqDMH8IfPCmaWdUAgOl7MPjxyLLllnxzjsWRpN9yIksIoD9++8xZcp+zp0Lp1MnX379tQe1\naj07AZvCUoG8zPF8Fi36i0uXIpk06R2aNk/DuZkGbRkLtA6W1LRQ86NKRQOuUzkjCgDHyrtxvN4J\nbnSHKvtBYfzjCgUEnOlGJKvQ8YnsGVFIBBCLt4l7Q9xMkuogBnrBUBOuy01Og55fwoErsPED6Nvc\n0BHlnaQkkY8/TmfFiixatVJy8KAGHx/jyj7kpEiLiDNnwpg6NZDAwPs0bOjFoUODadGi9N/uY8pL\nBaYce36xbt0lunevz7ffqmk8UMNJUYWNH9RwEhlse4t1RNGLrVjrSwHXwLoauA2E8GWQFQ3q4oZ+\nCrnCmW6Es5R4duNCD0OHY/akoGMP8YygmMkse/2TVC30PAveGvifCddBRMbBG3PgVhjsmgVtahg6\noryzb5+WkSPTiI427uxDToqkiAgKesyMGQf5/ffrVK7sRkBAH7p2rfBcrwdTXiow5djzi4iIZDyL\nl8bKSeBCphKXXuBgLfJe412cFY7zEdZYch1b5TvATkg+DRH/A68pJiMgACzxxI6GxBBg9CIiiihO\ncZIQQkgmCQBb7PDGmwY0wt0EbLD3Ek86erqasDfEuCtwLxXONDPdOoigUOj0GaRnwZF5UDP//P4K\nlcREkQ8+SGfVKtPIPuTERD86eSM0NJHPPjvE2rUXKVHCnh9/7MaAAdVRKv/7zTLlpQJTjv11ycrS\n8fhxKlevuuDcyoq4JgpS1CLzm+3govIvutAeaz7Fjs5oFOWkjYJ6g1U58P7EsMHnAWfe5AEfkcED\n1EbacniLIDayAU+KU5FK2GILQDLJ3OUO37GcfgygHOUMHOl/E/DUG8LS0KHkiZ9C4McQ+LEmVDHR\nOoiTN8FvDrg7wqG5UNLN0BHljcBAyfchNlZkxQorRo0y/uxDToqEiIiJSeXLL4+xdOlp7OzULFjQ\nnjFj6mJllfenb8pLBaYc+6sQkBBF8Y0NUTjGkqXMwNJVw+clHnNffZJuuGHFZ+ynKnqGMSY9EGuA\nrCjwWQQK0+sJc6QNIdgSw1aK866hw3ku+9hLU5rThrb/uq01bThAIHvZZdQiIoQMzpiwN8SNJHjn\nMgz2hsEm6gex5QS8/S3U84WtM8DJ1tARvTqJiVLnxcqVWbRsqeTwYQ2lS5tG9iEnZi0i0tKy+OKL\nI8yffwK9XmTKlKa8914j7O1f/wRhyksFphx7btlBLN/YR4KoRp+uwrJqOnZuyeywj6QzSSgJQE17\n4hjFOVHH4EcLsXYfAgmHIOEAuPUz9FN4ZXJ6Rngy3ig9I2J4TA1evGhdneoc40ghRvTqbCUWGxP1\nhkjVSn4QpTSwvJqho8kby3bAu6ugVxNYNwmsTDAZtHevlhEjpOzD8uVWjBljWtmHnJi1iOjadSNJ\nSS68805dpk9vjrt7/lZRv2ipwBQw5dhzw1LCqXdB5FR/LepmJbH4UKSdzUP0Do/YR3McGcggsTaT\nsqIIjVyBS1Y0lJoHESvg0ULwWQxKa0M/jVdG8ozYTDKnsaOhocP5F444EUQQrjw/9xxEEI5G7Biq\nR2QrsXTEySS9Id69KtVBnG4GNiZ29BdFmL4e5v0O73WDr4eCwvh08n+SmCjy/vvprF6dRdu2Slat\nMp7sw/Xr0RQrZoOLy6sd90zsY/RqNGrkzbJlwyldunAPSqZeb/DP+E0pdoAosnBCRdTlCFRWPmjL\nqMgQBdo4XMVNv4nz8Q35wdaRuterUjklSJrRWXoBWHqA2yAI+RzujgHfNSbR4pkTG2o+8YzwN0oR\n0Zo2/M4mgrlPWcpi86QmIoVk7nGX29ymJ70NHOWLyfaGMMVhW+tDYM1DWGuCdRCZWTBimeQB8c0w\neK+7oSN6dfbte5Z9WLnSipEjLQpkcOOrcuzYQ8aO/ZOkpExUKgWDBlWnTp3cSwOzFhGzZ7cqdAFh\n6vUGL4rfFGLPJvZmAiGpjwn1USJWckfnC84q0GpuUC3lEr1vBPBW3f0c8v2Gyhk6UJcAm9rSxpqy\nUP5nuD1YavGsuBmUprPgKnlGdCeClU88I4wr9qpUwx57/uIkxzn+r+6MoYygJMa7UB9ALCVRU8fE\nvCFuJMGYyzDEG4YY78v7XBJTocc8OHINfv0Q+jQzdESvRs7Oi9atlaxZYzzZh4iIZKZM2U+rVqUZ\nObIO27YFsWHDFY4ckUWEwTD1eoPnxW8qsZ8794h5846xZcsNvHuXxGZBbTzmxRCvt6C/TwqCcB/r\nlHREBGpZ+HBLLYCtz78fyK0fWLjDzTfhaiuo9CdYGn/bYTbOdCWcJcSzxyjbPUtSipImWJSY7Q0x\n0sS8IVK00OsslLaGZSZWB/EoBjrPhuAo2PMZtDSx+LNrH+LipM6L0aONI/sgiiKCIHDqVCgXLkSw\neXMvPD3tqFrVHW9vez75ZF+uH0sWEQVAbtsqjXWZwBTrJQ4fDqZly3WULevEd9/5sXdvBXa/l4Ln\nyig0mtuIijR0qEjMcOGWYwX2K1KYyH/4QDi2gaqH4XonuNYaqp0ElfHOT8mJ5BnRiBj8jVJEmCp7\nTNQbYvwVuJ8KZ5qbVh3EjRDJA0Knh2NfQlUT0p0JCVL2YfXqLNq0UbJ6teGzD6mpWeh0euzs1E+F\nTEaGjvLlXcjI0D29X5cu5QkMvMK6dbl7XBP6SJk25rBMYMwcPfoQJycrbtwYxzvvZOK/T4fdm248\nOOxKg7oRHC0RxmV6sMOzG6piAnWx5a2XzTywrQVVD8Hl+nBnGFTYZDK2fs50N0rPiGSSn3pDAITz\niJOcIIYY7LCjAQ3xwThFbACx/2fvvKOjqr42/NwpSSa90iEQCITQm0hVeoeEDtK7NLsCFhAUqaKA\ngNKLdCSBgIJSpArSu9RQEgLpdWYy5X5/XAL4k09JMi1wH1bWIhPuOXtIcmfPPu9+N6/iQbEC5A2x\n4o7kB7GyBoQWjBwYgMOXoMMXUNxPcqEs4W/viJ6fXbuk6kNKisiiRZLvgz2rD9nZJt59dxe7d9+g\nWDEPwsND6NIllBIlPHFyUpKaquPKlYTHR/8+PhoaNSr83EmEYxzMvATkHBMsXtzh8cfJk8PsHdYL\nw5UrCYSEBDBhgoGlm0y4tXHD8LqAv4uC2YVTCBO20INNvPtgE7NiNjH5ec/dXUMgeAUkbobY2dZ8\nChbFm+YoHnlGOBIzmUYGGQDc4TY/sIgUUihFIHr0rGQ50dyyc5T/5A56TpBBWAGqQlxMg5HnYVAp\n6FeA5mJsPQrNP4NqZeDgVwUrgfj4Yx2tW2cREqLgwgV3hg93smsCYTSaGTQokqNH7zFjRguqVCnE\n4sWnGD48CoCwsBAUCoEtWy6Rmqp7fF1Q0PNnnHIlwoYU9GMOR+bKlQTc3asya64B13buKJsLGP1h\n9StZ/KneQ1WyCeIAVZPdUTqVhdy05/l1huIfQfRH4F4HvF6z2vOwFApcHnlGRFCUUQgO2I64j71U\nozphdH782E52sI+9DGSwHSP7J5Ek4Y6C5g7cfvo0mUbofhKCXGFeZXtH8/zMi4K3FkP3hpIHhHPB\nao6iQQOlQ3VeXLmSwG+/3WTdui40aVKGsLAQIiKuMHx4FFOnHmTChEZ88kljRo/eSVhYCO3alQfA\ny+v5q21yEmFn5GMOyxAbm46PT1FKN3TiXmGBrEKwsmYal31XoOY6QfyONy1R6DaDZ4vcbxD4hTRX\n46+eUP0MOBW2/JOwMH50JpFNpPMHnjSwdzj/4CEPaEqzvz1Wm9osY4mdIno2ZkS2kkgbfNAUkOLt\nqPMQnQUnGoNrAbjLm83wwXL4OhLeC5NGeRc0DwiAtm0dK+tRKgUMBjP+/k+8H1q1KsuoUXWYOvUg\n77zzKgMGVGfFijN8++0xXFxUNGsWRHq64bn3KIDfphcL+Zgj/4iiSHx8Fvdi3EnzVeP1Orzik01y\n0aWouUtdDuNBHQKNExCyY8C1Uu43EVRQfi0gwtXeIJr+8xJ740pVnAkiiQh7h/I3stGjQ4fq0Z+n\nUaHCwPPfwGzBMTKIw0D4f2loHIQVd2DlXVhYFSoWAB2E3gC9ZsGcbTBvGMwa5BgJRGamiMkk2juM\nfJGaqqdMGW8OH777+DGNRk3v3lXw83Nl6tSDAMye3RI/P1fatPmRgQMjGTDg0HPvUQBy1Bcf+Zgj\nf6Sl6TEa3UnDGQopQANf1fwdhPO8wmVcKE8Z0zQUsd9JF7jmsb7rVATKr4OLzeHuZCj1ueWehBWQ\nPCM6EccCTKSjxDFeUb5lzuO/xxBD0ae6ZB7yEA8cywkpkkQCcaYaju9geqGA6SBSMyF8Khy5Aps/\ngs717R2RxNixOi5dMiEIMHasEw0aqPD1FTCbRYeyp750KR6VSkHRou54ePxznMOrr5axkmu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4wj0x3HRAqgTh0lQ4eqef99HRcuPKkyeHkJeHgI3L5tBqBbNzVLlmisPkRLFEV27bpO7do/0LPn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\nqb+AMsCv6GM/CpH+N/ZCwJ7737u76jzZx3YeCFJK5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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# %* Graph contours of density versus position and time.\n", + "\n", + "levels = np.linspace(0., 1., num=11) \n", + "ct = plt.contour(xplot, tplot, np.flipud(np.rot90(rplot)), levels) \n", + "plt.clabel(ct, fmt='%1.2f') \n", + "plt.xlabel('x')\n", + "plt.ylabel('time')\n", + "plt.title('Density contours')" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python [default]", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.12" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} diff --git a/Python/.ipynb_checkpoints/Untitled-checkpoint.ipynb b/Python/.ipynb_checkpoints/Untitled-checkpoint.ipynb new file mode 100644 index 0000000..59ce53d --- /dev/null +++ b/Python/.ipynb_checkpoints/Untitled-checkpoint.ipynb @@ -0,0 +1,6 @@ +{ + "cells": [], + "metadata": {}, + "nbformat": 4, + "nbformat_minor": 1 +} diff --git a/Python/.ipynb_checkpoints/Zeroj-checkpoint.ipynb b/Python/.ipynb_checkpoints/Zeroj-checkpoint.ipynb new file mode 100644 index 0000000..59ce53d --- /dev/null +++ b/Python/.ipynb_checkpoints/Zeroj-checkpoint.ipynb @@ -0,0 +1,6 @@ +{ + "cells": [], + "metadata": {}, + "nbformat": 4, + "nbformat_minor": 1 +} diff --git a/Python/Advect.ipynb b/Python/Advect.ipynb new file mode 100644 index 0000000..3fb6eb9 --- /dev/null +++ b/Python/Advect.ipynb @@ -0,0 +1,171 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# advect - Program to solve the advection equation \n", + "# using the various hyperbolic PDE schemes\n", + "\n", + "# Set up configuration options and special features\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "%matplotlib inline" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Select numerical parameters (time step, grid spacing, etc.).\n", + "method = input('Choose a numerical method, 1) FTCS; 2) Lax; 3) Lax-Wendroff :')\n", + "N = input('Enter number of grid points: ')\n", + "L = 1. # System size\n", + "h = L/N # Grid spacing\n", + "c = 1. # Wave speed\n", + "print 'Time for wave to move one grid spacing is ', h/c \n", + "tau = input('Enter time step: ')\n", + "coeff = -c*tau/(2.*h) # Coefficient used by all schemes\n", + "coefflw = 2*coeff**2 # Coefficient used by L-W scheme\n", + "print 'Wave circles system in ', L/(c*tau), ' steps' \n", + "nStep = input('Enter number of steps: ')" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Set initial and boundary conditions.\n", + "sigma = 0.1 # Width of the Gaussian pulse\n", + "k_wave = np.pi/sigma # Wave number of the cosine\n", + "x = np.arange(N)*h - L/2. # Coordinates of grid points\n", + "# Initial condition is a Gaussian-cosine pulse\n", + "a = np.empty(N)\n", + "for i in range(N) :\n", + " a[i] = np.cos(k_wave*x[i]) * np.exp(-x[i]**2/(2*sigma**2)) \n", + "# Use periodic boundary conditions\n", + "ip = np.arange(N) + 1 \n", + "ip[N-1] = 0 # ip = i+1 with periodic b.c.\n", + "im = np.arange(N) - 1 \n", + "im[0] = N-1 # im = i-1 with periodic b.c.\n", + "\n", + "#* Initialize plotting variables.\n", + "iplot = 1 # Plot counter\n", + "nplots = 50; # Desired number of plots\n", + "aplot = np.empty((N,nplots))\n", + "tplot = np.empty(nplots)\n", + "aplot[:,0] = np.copy(a) # Record the initial state\n", + "tplot[0] = 0 # Record the initial time (t=0)\n", + "plotStep = nStep/nplots+1 # Number of steps between plots" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Loop over desired number of steps.\n", + "for iStep in range(nStep): ## MAIN LOOP ##\n", + "\n", + " #* Compute new values of wave amplitude using FTCS, \n", + " #% Lax or Lax-Wendroff method.\n", + " if method == 1 : ### FTCS method ###\n", + " a[:] = a[:] + coeff*( a[ip] - a[im] ) \n", + " elif method == 2 : ### Lax method ###\n", + " a[:] = .5*( a[ip] + a[im] ) + coeff*( a[ip] - a[im] ) \n", + " else: ### Lax-Wendroff method ###\n", + " a[:] = a[:] + coeff*( a[ip] - a[im] ) + coefflw*(\n", + " a[ip] + a[im] -2*a[:] ) \n", + "\n", + " #* Periodically record a(t) for plotting.\n", + " if (iStep+1) % plotStep < 1 : # Every plot_iter steps record \n", + " aplot[:,iplot] = np.copy(a) # Record a(i) for ploting\n", + " tplot[iplot] = tau*iStep\n", + " iplot += 1\n", + " print iStep, ' out of ', nStep, ' steps completed'" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Plot the initial and final states.\n", + "plt.plot(x,aplot[:,0],'-',x,a,'--');\n", + "plt.legend(['Initial ','Final'])\n", + "plt.xlabel('x') \n", + "plt.ylabel('a(x,t)')" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Plot the wave amplitude versus position and time\n", + "from matplotlib import cm\n", + "from mpl_toolkits.mplot3d import Axes3D\n", + "\n", + "fig = plt.figure()\n", + "ax = fig.gca(projection = '3d')\n", + "Tp, Xp = np.meshgrid(tplot[0:iplot], x)\n", + "ax.plot_surface(Tp, Xp, aplot[:,0:iplot], rstride=1, cstride=1, cmap=cm.gray)\n", + "ax.view_init(elev=30., azim=190.)\n", + "ax.set_ylabel('Position') \n", + "ax.set_xlabel('Time')\n", + "ax.set_zlabel('Amplitude')" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python [default]", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.12" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} diff --git a/Python/Balle.ipynb b/Python/Balle.ipynb new file mode 100644 index 0000000..708fe78 --- /dev/null +++ b/Python/Balle.ipynb @@ -0,0 +1,137 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# balle - Program to compute the trajectory of a baseball\n", + "# using the Euler method.\n", + "\n", + "# Set up configuration options and special features\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "%matplotlib inline" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Set initial position and velocity of the baseball\n", + "y1 = input('Enter initial height (meters): ') \n", + "r1 = np.array([0, y1]) # Initial vector position\n", + "speed = input('Enter initial speed (m/s): ')\n", + "theta = input('Enter initial angle (degrees): ') \n", + "v1 = np.array([speed * np.cos(theta*np.pi/180), \n", + " speed * np.sin(theta*np.pi/180)]) # Initial velocity\n", + "r = r1 # Set initial position \n", + "v = v1 # Set initial velocity\n", + "\n", + "#* Set physical parameters (mass, Cd, etc.)\n", + "Cd = 0.35 # Drag coefficient (dimensionless)\n", + "area = 4.3e-3 # Cross-sectional area of projectile (m^2)\n", + "grav = 9.81 # Gravitational acceleration (m/s^2)\n", + "mass = 0.145 # Mass of projectile (kg)\n", + "airFlag = input('Air resistance? (Yes:1, No:0): ')\n", + "if airFlag == 0 :\n", + " rho = 0 # No air resistance\n", + "else:\n", + " rho = 1.2 # Density of air (kg/m^3)\n", + "air_const = -0.5*Cd*rho*area/mass # Air resistance constant" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Loop until ball hits ground or max steps completed\n", + "tau = input('Enter timestep, tau (sec): ') # (sec)\n", + "maxstep = 1000 # Maximum number of steps\n", + "xplot = np.empty(maxstep); yplot = np.empty(maxstep)\n", + "xNoAir = np.empty(maxstep); yNoAir = np.empty(maxstep)\n", + "for istep in range(maxstep):\n", + "\n", + " #* Record position (computed and theoretical) for plotting\n", + " xplot[istep] = r[0] # Record trajectory for plot\n", + " yplot[istep] = r[1]\n", + " t = istep*tau # Current time\n", + " xNoAir[istep] = r1[0] + v1[0]*t\n", + " yNoAir[istep] = r1[1] + v1[1]*t - 0.5*grav*t**2\n", + " \n", + " #* Calculate the acceleration of the ball \n", + " accel = air_const * np.linalg.norm(v) * v # Air resistance\n", + " accel[1] = accel[1] - grav # Gravity\n", + " \n", + " #* Calculate the new position and velocity using Euler method\n", + " r = r + tau*v # Euler step\n", + " v = v + tau*accel \n", + " \n", + " #* If ball reaches ground (y<0), break out of the loop\n", + " if r[1] < 0 : \n", + " laststep = istep+1\n", + " xplot[laststep] = r[0] # Record last values computed\n", + " yplot[laststep] = r[1]\n", + " break # Break out of the for loop" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Print maximum range and time of flight\n", + "print 'Maximum range is', r[0], 'meters' \n", + "print 'Time of flight is', laststep*tau , ' seconds' \n", + "\n", + "#* Graph the trajectory of the baseball\n", + "# Mark the location of the ground by a straight line\n", + "xground = np.array([0., max(xNoAir[0:laststep])])\n", + "yground = np.array([0., 0.])\n", + "# Plot the computed trajectory and parabolic, no-air curve\n", + "plt.plot(xplot[0:laststep+1],yplot[0:laststep+1],'+',\n", + " xNoAir[0:laststep],yNoAir[0:laststep],'-',xground,yground,'r-')\n", + "plt.legend(['Euler method','Theory (No air) ']);\n", + "plt.xlabel('Range (m)')\n", + "plt.ylabel('Height (m)')\n", + "plt.title('Projectile motion')" + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "kernelspec": { + "display_name": "Python [default]", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.12" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} diff --git a/Python/Bess.ipynb b/Python/Bess.ipynb new file mode 100644 index 0000000..b969548 --- /dev/null +++ b/Python/Bess.ipynb @@ -0,0 +1,169 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# Program to test the bess function\n", + "\n", + "# Set up configuration options and special features\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "%matplotlib inline" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def bess(m_max,x) :\n", + " # Bessel function\n", + " # Inputs\n", + " # m_max = Largest desired order\n", + " # x = Value at which Bessel function J(x) is evaluated\n", + " # Output\n", + " # jj = Vector of J(x) for all orders <= m_max\n", + "\n", + " #* Perform downward recursion from initial guess\n", + " eps = 1.0e-15\n", + " m_top = max(m_max,x)+15 # Top value of m for recursion\n", + " m_top = int(2*np.ceil( m_top/2 )) # Round up to an even number\n", + " j = np.empty(m_top+1)\n", + " j[m_top] = 0.\n", + " j[m_top-1] = 1.\n", + " for m in reversed(range(m_top-1)) : # Downward recursion\n", + " j[m] = 2.*(m+1)/(x+eps)*j[m+1] - j[m+2]\n", + "\n", + " #* Normalize using identity and return requested values\n", + " norm = j[0] \n", + " for m in range(2,m_top,2) :\n", + " norm = norm + 2*j[m]\n", + " \n", + " jj = np.empty(m_max+1) # Send back only the values for\n", + " for m in range(m_max+1) : # m=0,...,m_max and discard values\n", + " jj[m] = j[m]/norm # for m=m_max+1,...,m_top\n", + " \n", + " return jj" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def zeroj( m_order, n_zero) :\n", + " # Zeros of the Bessel function J(x)\n", + " # Inputs\n", + " # m_order = Order of the Bessel function\n", + " # n_zero = Index of the zero (first, second, etc.)\n", + " # Output\n", + " # z = The \"n_zero th\" zero of the Bessel function\n", + " \n", + " #* Use asymtotic formula for initial guess\n", + " beta = (n_zero + 0.5*m_order - 0.25)*np.pi;\n", + " mu = 4*m_order**2;\n", + " z = beta - (mu-1.)/(8.*beta) - 4.*(mu-1)*(7.*mu-31.)/(3.*(8.*beta)**3);\n", + "\n", + " #* Use Newton's method to locate the root\n", + " jj = np.empty(m_order+2)\n", + " for i in range(5) :\n", + " jj = bess(m_order+1,z) \n", + " # Use the recursion relation to evaluate derivative\n", + " deriv = -jj[m_order+1] + m_order/z * jj[m_order]\n", + " z = z - jj[m_order]/deriv # Newton's root finding \n", + " \n", + " return z" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Enter m: 2\n" + ] + }, + { + "data": { + "image/png": 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yTubRjt47KKBOAJ3+7rSu72XKbykUVD+IwjuG07k953Rrx0ihoXzN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\nqFCtTJyoO85++KHTIzlu927gxrRnIc2bo+ljf9e2o4HywgvazOuDD4D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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "nplot = 200\n", + "xMax = 20.\n", + "m = input(\"Enter m: \")\n", + "x = np.linspace(0.,xMax,nplot)\n", + "\n", + "jj = np.empty((nplot,m+1))\n", + "for i in range(nplot) :\n", + " jj[i,:] = bess(m,x[i])\n", + " \n", + "jZero = np.empty(20)\n", + "for i in range(20) :\n", + " jZero[i] = zeroj(m,i+1)\n", + " if jZero[i] > xMax :\n", + " break\n", + "nZeros = i # Skip the zero that's > xMax\n", + " \n", + "for mi in range(m+1) :\n", + " plt.plot(x,jj[:,mi],'-',jZero[0:nZeros],np.zeros(nZeros),'*')\n", + " plt.xlabel('x')\n", + " plt.ylabel('J_m(x)')" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + } + ], + "metadata": { + "anaconda-cloud": {}, + "kernelspec": { + "display_name": "Python [default]", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.12" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} diff --git a/Python/Dftcs.ipynb b/Python/Dftcs.ipynb new file mode 100644 index 0000000..dde73db --- /dev/null +++ b/Python/Dftcs.ipynb @@ -0,0 +1,159 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# dftcs - Program to solve the diffusion equation \n", + "# using the Forward Time Centered Space (FTCS) scheme.\n", + "\n", + "# Set up configuration options and special features\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "%matplotlib inline" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Initialize parameters (time step, grid spacing, etc.).\n", + "tau = input('Enter time step: ')\n", + "N = input('Enter the number of grid points: ')\n", + "L = 1. # The system extends from x=-L/2 to x=L/2\n", + "h = L/(N-1) # Grid size\n", + "kappa = 1. # Diffusion coefficient\n", + "coeff = kappa*tau/h**2\n", + "if coeff < 0.5 :\n", + " print 'Solution is expected to be stable'\n", + "else:\n", + " print 'WARNING: Solution is expected to be unstable'" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Set initial and boundary conditions.\n", + "tt = np.zeros(N) # Initialize temperature to zero at all points\n", + "tt[int(N/2)] = 1./h # Initial cond. is delta function in center\n", + "## The boundary conditions are tt[0] = tt[N-1] = 0\n", + "\n", + "#* Set up loop and plot variables.\n", + "xplot = np.arange(N)*h - L/2. # Record the x scale for plots\n", + "iplot = 0 # Counter used to count plots\n", + "nstep = 300 # Maximum number of iterations\n", + "nplots = 50 # Number of snapshots (plots) to take\n", + "plot_step = nstep/nplots # Number of time steps between plots" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Loop over the desired number of time steps.\n", + "ttplot = np.empty((N,nplots))\n", + "tplot = np.empty(nplots)\n", + "for istep in range(nstep): ## MAIN LOOP ##\n", + " \n", + " #* Compute new temperature using FTCS scheme.\n", + " tt[1:(N-1)] = ( tt[1:(N-1)] + \n", + " coeff*( tt[2:N] + tt[0:(N-2)] - 2*tt[1:(N-1)] ) )\n", + " \n", + " #* Periodically record temperature for plotting.\n", + " if (istep+1) % plot_step < 1 : # Every plot_step steps\n", + " ttplot[:,iplot] = np.copy(tt) # record tt(i) for plotting\n", + " tplot[iplot] = istep*tau # Record time for plots\n", + " iplot = iplot+1" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Plot temperature versus x and t as a wire-mesh plot\n", + "\n", + "from matplotlib import cm\n", + "from mpl_toolkits.mplot3d import Axes3D\n", + "\n", + "fig = plt.figure()\n", + "ax = fig.gca(projection = '3d')\n", + "Tp, Xp = np.meshgrid(tplot, xplot)\n", + "ax.plot_surface(Tp, Xp, ttplot, rstride=2, cstride=2, cmap=cm.gray)\n", + "ax.set_xlabel('Time')\n", + "ax.set_ylabel('x')\n", + "ax.set_zlabel('T(x,t)')\n", + "ax.set_title('Diffusion of a delta spike')" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Plot temperature versus x and t as a contour plot\n", + "\n", + "levels = np.linspace(0., 10., num=21) \n", + "ct = plt.contour(tplot, xplot, ttplot, levels) \n", + "plt.clabel(ct, fmt='%1.2f') \n", + "plt.xlabel('Time')\n", + "plt.ylabel('x')\n", + "plt.title('Temperature contour plot')" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + } + ], + "metadata": { + "anaconda-cloud": {}, + "kernelspec": { + "display_name": "Python [default]", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.12" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} diff --git a/Python/Dsmceq.ipynb b/Python/Dsmceq.ipynb new file mode 100644 index 0000000..1fd5da9 --- /dev/null +++ b/Python/Dsmceq.ipynb @@ -0,0 +1,422 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# dsmceq - Dilute gas simulation using DSMC algorithm\n", + "# This version illustrates the approach to equilibrium\n", + "\n", + "# Set up configuration options and special features\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "%matplotlib inline" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "class sortList:\n", + " def __init__(self, ncell_in, npart_in):\n", + " self.ncell = ncell_in\n", + " self.npart = npart_in\n", + " self.cell_n = np.zeros(ncell_in, dtype=int)\n", + " self.index = np.empty(ncell_in, dtype=int)\n", + " self.Xref = np.empty(npart_in, dtype=int)" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def sorter(x,L,sD) :\n", + " # sorter - Function to sort particles into cells\n", + " # Inputs\n", + " # x Positions of particles\n", + " # L System size\n", + " # sD Structure containing sorting lists\n", + " # Output\n", + " # sD Structure containing sorting lists\n", + "\n", + " #* Find the cell address for each particle\n", + " npart = sD.npart\n", + " ncell = sD.ncell\n", + " jx = np.empty(npart,dtype=int)\n", + " for ipart in range(npart) :\n", + " jx[ipart] = int( x[ipart]*ncell/L )\n", + " jx[ipart] = min( jx[ipart], (ncell-1) )\n", + "\n", + " #* Count the number of particles in each cell\n", + " sD.cell_n = np.zeros(ncell)\n", + " for ipart in range(npart) :\n", + " sD.cell_n[ jx[ipart] ] += 1\n", + "\n", + " #* Build index list as cumulative sum of the \n", + " # number of particles in each cell\n", + " m = 0\n", + " for jcell in range(ncell) :\n", + " sD.index[jcell] = m\n", + " m += sD.cell_n[jcell]\n", + "\n", + " #* Build cross-reference list\n", + " temp = np.zeros(ncell) # Temporary array\n", + " for ipart in range(npart) :\n", + " jcell = jx[ipart] # Cell address of ipart\n", + " k = sD.index[jcell] + temp[jcell]\n", + " sD.Xref[k] = ipart\n", + " temp[jcell] += 1\n", + "\n", + " return sD" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def colider(v,crmax,tau,selxtra,coeff,sD) :\n", + " # colide - Function to process collisions in cells\n", + " # Inputs\n", + " # v Velocities of the particles\n", + " # crmax Estimated maximum relative speed in a cell\n", + " # tau Time step\n", + " # selxtra Extra selections carried over from last timestep\n", + " # coeff Coefficient in computing number of selected pairs\n", + " # sD Structure containing sorting lists \n", + " # Outputs\n", + " # v Updated velocities of the particles\n", + " # crmax Updated maximum relative speed\n", + " # selxtra Extra selections carried over to next timestep\n", + " # col Total number of collisions processed\n", + "\n", + " ncell = sD.ncell \n", + " col = 0 # Count number of collisions\n", + " vrel = np.empty(3) # Relative velocity for collision pair\n", + " \n", + " #* Loop over cells, processing collisions in each cell\n", + " for jcell in range(ncell) :\n", + " \n", + " #* Skip cells with only one particle\n", + " number = sD.cell_n[jcell]\n", + " if number > 1 : \n", + " \n", + " #* Determine number of candidate collision pairs \n", + " # to be selected in this cell\n", + " select = coeff*number*(number-1)*crmax[jcell] + selxtra[jcell]\n", + " nsel = int(select) # Number of pairs to be selected\n", + " selxtra[jcell] = select-nsel # Carry over any left-over fraction\n", + " crm = crmax[jcell] # Current maximum relative speed\n", + " \n", + " #* Loop over total number of candidate collision pairs\n", + " for isel in range(nsel) :\n", + " \n", + " #* Pick two particles at random out of this cell\n", + " k = int( np.floor( np.random.uniform(0,number) ) )\n", + " kk = int(np.ceil( k + np.random.uniform(0,number-1) ) ) % number\n", + " ip1 = sD.Xref[ k + sD.index[jcell] ] # First particle\n", + " ip2 = sD.Xref[ kk + sD.index[jcell] ] # Second particle\n", + "\n", + " #* Calculate pair's relative speed\n", + " cr = np.linalg.norm( v[ip1,:] - v[ip2,:] ) # Relative speed \n", + " if cr > crm : # If relative speed larger than crm,\n", + " crm = cr # then reset crm to larger value\n", + "\n", + " #* Accept or reject candidate pair according to relative speed\n", + " if cr/crmax[jcell] > np.random.random() :\n", + " #* If pair accepted, select post-collision velocities\n", + " col += 1 # Collision counter\n", + " vcm = 0.5*( v[ip1,:] + v[ip2,:] ) # Center of mass velocity\n", + " cos_th = 1. - 2.*np.random.random() # Cosine and sine of \n", + " sin_th = np.sqrt(1. - cos_th**2) # collision angle theta\n", + " phi = 2*np.pi*np.random.random() # Collision angle phi\n", + " vrel[0] = cr*cos_th # Compute post-collision \n", + " vrel[1] = cr*sin_th*np.cos(phi) # relative velocity\n", + " vrel[2] = cr*sin_th*np.sin(phi)\n", + " v[ip1,:] = vcm + 0.5*vrel # Update post-collision\n", + " v[ip2,:] = vcm - 0.5*vrel # velocities\n", + "\n", + " crmax[jcell] = crm # Update max relative speed \n", + " \n", + " return [v, crmax, selxtra, col]" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Enter number of simulation particles: 50000\n", + "Each particle represents 536.953242836 atoms\n" + ] + } + ], + "source": [ + "#* Initialize constants (particle mass, diameter, etc.)\n", + "boltz = 1.3806e-23 # Boltzmann's constant (J/K)\n", + "mass = 6.63e-26 # Mass of argon atom (kg)\n", + "diam = 3.66e-10 # Effective diameter of argon atom (m)\n", + "T = 273. # Temperature (K)\n", + "density = 1.78 # Density of argon at STP (kg/m^3)\n", + "L = 1e-6 # System size is one micron\n", + "npart = input('Enter number of simulation particles: ')\n", + "eff_num = density/mass*L**3/npart;\n", + "print 'Each particle represents ', eff_num, ' atoms'" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Assign random positions and velocities to particles\n", + "np.random.seed(0) # Initialize random number generator\n", + "x = np.empty(npart)\n", + "for i in range(npart) :\n", + " x[i] = np.random.uniform(0.,L) # Assign random positions\n", + "v_init = np.sqrt(3*boltz*T/mass) # Initial speed\n", + "v = np.zeros((npart,3)) \n", + "for i in range(npart) : # Only x-component is non-zero\n", + " v[i,0] = v_init * (1 - 2*np.floor(2*np.random.random()))" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#* Plot the initial speed distribution\n", + "vmag = np.sqrt( v[:,0]**2 + v[:,1]**2 + v[:,2]**2 )\n", + "plt.hist( vmag, bins=20, range=(0,1000))\n", + "plt.title('Initial speed distribution')\n", + "plt.xlabel('Speed (m/s)')\n", + "plt.ylabel('Number')" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Initialize variables used for evaluating collisions\n", + "ncell = 15 # Number of cells\n", + "tau = 0.2*(L/ncell)/v_init # Set timestep tau\n", + "vrmax = 3*v_init*np.ones(ncell) # Estimated max rel. speed\n", + "selxtra = np.zeros(ncell) # Used by routine \"colider\"\n", + "coeff = 0.5*eff_num*np.pi*diam**2*tau/(L**3/ncell)\n", + "coltot = 0 # Count total collisions\n", + "\n", + "#* Declare sortList object for lists used in sorting\n", + "sortData = sortList(ncell, npart)" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Enter total number of time steps: 50\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "C:\\Users\\Alejandro\\Anaconda2\\lib\\site-packages\\ipykernel\\__main__.py:35: VisibleDeprecationWarning: using a non-integer number instead of an integer will result in an error in the future\n", + "C:\\Users\\Alejandro\\Anaconda2\\lib\\site-packages\\ipykernel\\__main__.py:41: VisibleDeprecationWarning: using a non-integer number instead of an integer will result in an error in the future\n" + ] + }, + { + "data": { + "image/png": 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snyP6tJ+SJGmaTLal553A15I8D7gUuE8rSCnlzRNZWTO2zqgBrJRyJHDkKMvv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\n0CR3Un9hebz77xruf1vzpcD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wf0Q8BhARZ0saTZozZjywCDgoIjYVypgDbAYWkCbWuwE4oWo/R5Im1ruJNLHe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\nPCDpr0hJxWXAUYCAj0bEJqBT0ouBr/V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LgMOAN0raLcd0APsAH42IWyLi18Ac4CBJU5t/hGZmZtYsQ05oJG0h6TpJOze4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\np4CZwAuBAyLiiqqYU4EjgEn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ZZ5uBSwb5nm/q61GKfUsut7fYHxTi5pBWn74/1/EJUlLxYQqrNRfiRRoLs6Sfer40l/mb\nfG3WktaVObaf15yar+GT+doeUcfvwi7553FFPof/y+/Z2FKdvkEaXL+OtC7NO0vl7JqvT3na9jOl\nuPuAiwrPP5HLe4z09+JX+Xy2GaCcwf6u3Qdc3cfPw4311MOP1j6U3ygzs7Yg6YfACyPidQ0o6yBS\ni8vrYphdH2bW3lo+hkZpOere7hr7xULMGZIeUloC/fryOgCSxks6X2kp6rWSFpWnQ0raQdKlktYo\nLaH/ZfW/ZLiZVd9bSYvNOZkx28q1PKEh9T9PLzz+nNR/fAWApFNJ4yuOI92ddh2wuDQo7hzSQkmH\nk5bk3pnnD3C8jDTQbm6O3Y/nL9hmZluRiDglIv524Egzq7q263LKA9gOiohX5ucPAf8WEQvz88mk\nAYDvjYgr8vNHSX3CV+WYmaTBa/tExJI8WPVXwJzIK15KOoA00n2XaM46E2Y2BLnLaceIeH2r62Jm\n1dEOLTTPylMzj+K5abK7kVptnr3pX6RR9bfx3F1i9yTNrCnGLCcNSqzF7AOsii2X776B1BJUvpGd\nmbVQRLzNyYyZ1autEhrSdMIpPHdn3OmkpGNlKW4lz61+OQ3YmBOdvmKmk2ZCPCvS1M/H6X0VTTMz\nM6uQdluH5hjg++3SBZQXxTqANN1vQ//RZmZmVjCBNKV/caQ1v5qqbRKavFDV/qR1KmpWkNZlmMaW\nrTTTSGuB1GLGSZpcaqWZlvfVYsqznrYh3fOkv+TpAPpYrdPMzMwG5Sjquy/ZkLRNQkNqnVlJWkEW\ngIi4P68EOpe0GFRtUPDewPk57A7S0t5zSYuz1QYFzyAtgkT+d3tJexTG0cwlJUu39VOnBwAuueQS\nZs2a1U+YNdKCBQtYuHBhq6sxqviajzxf85Hnaz6yurq6mDdvHhTuv9ZMbZHQ5PvKvA/4akRsLu0+\nBzhN0r08t9Lj70jLtxMRT+Tl88+WtIq0aua5wC2R78USEfdIWgxcKOkE0k0Ev0han6K/FpoNALNm\nzWL27P5uZWKNNGXKFF/vEeZrPvJ8zUeer3nLjMiQjbZIaEhdTS8hLa+9hYg4K9/V9ALSDe9uBg6M\nLe8NtIC0pPYi0o3CasvuFx0JnEea3bQ5x57c2NMwMzOzVmiLhCYirge26Wf/6aT7zfS1/ylgfn70\nFbOadNM3MzMz28q027RtMzMzs7o5obG209HR0eoqjDq+5iPP13zk+Zpv3dru1gftRNJs4I477rjD\nA8nMzMzqsHTpUubMmQPptkNLm308t9CYmZlZ5TmhMTMzs8pzQmNmZmaV54TGzMzMKs8JjZmZmVWe\nExozMzOrPCc0ZmZmVnlOaMzMzKzynNCYmZlZ5TmhMTMzs8pzQmNmZmaV54TGzMzMKs8JjZmZmVWe\nExozMzOrPCc0ZmZmVnlOaMzMzKzynNCYmZlZ5TmhMTMzs8pzQmNmZmaV54TGzMzMKs8JjZmZmVWe\nExozMzOrPCc0ZmZmVnlOaMzMzKzynNCYmZlZ5TmhMTMzs8pzQmNmZmaV54TGzMzMKs8JjZmZmVWe\nExozMzOrvLZIaCTtLOliST2S1ku6U9LsUswZkh7K+6+XtHtp/3hJ5+cy1kpaJGmnUswOki6VtEbS\nKklfljRpJM7RzMzMmqflCY2k7YFbgKeAA4BZwEeBVYWYU4GTgOOAvYB1wGJJ4wpFnQMcDBwO7Afs\nDFxZOtxlufy5OXY/4IKGn5SZmZmNqLGtrgDwcaA7Io4tbHuwFHMycGZEfBdA0tHASuBQ4ApJk4Fj\ngCMi4qYc836gS9JeEbFE0ixSwjQnIpblmPnA9yR9LCJWNPEcbZTo7u6mp6enKWVPnTqVGTNmNKVs\nM7Oqa4eE5l3AdZKuAN4C/B74UkR8GUDSbsB04MbaCyLiCUm3AfsCVwB7ks6lGLNcUneOWQLsA6yq\nJTPZDUAAewNXN+0MbVTo7u5m5sxZbNiwvinlT5gwkeXLu5zUmJn1oh0SmpcBJwD/DnyG1KV0rqSn\nIuJiUjITpBaZopV5H8A0YGNEPNFPzHTgkeLOiNgk6fFCjNmQ9fT05GTmElLPZiN1sWHDPHp6epzQ\nmJn1oh0SmjHAkoj4ZH5+p6TXAMcDF7euWmZDNQuYPWCUmZk1TjskNA8DXaVtXcBf5f+vAERqhSm2\n0kwDlhVixkmaXGqlmZb31WLKs562AXYsxPRqwYIFTJkyZYttHR0ddHR09Pcys4br6ir/qjSGx+eY\n2XB0dnbS2dm5xbY1a9aMaB3aIaG5BZhZ2jaTPDA4Iu6XtII0M+kugDwIeG/g/Bx/B/BMjrkqx8wE\nZgC35phbge0l7VEYRzOXlCzd1l8FFy5cyOzZ/sZtrfQwMIZ58+Y1pXSPzzGz4ejtS/7SpUuZM2fO\niNWhHRKahcAtkj5BGuC7N3As8MFCzDnAaZLuBR4AzgR+Rx7ImwcJXwScLWkVsBY4F7glIpbkmHsk\nLQYulHQCMA74ItDpGU7W/lYDm/H4HDOz3rU8oYmI2yUdBnwO+CRwP3ByRFxeiDlL0kTSmjHbAzcD\nB0bExkJRC4BNwCJgPHAdcGLpcEcC55FmN23OsSc347zMmsPjc8zMetPyhAYgIq4Frh0g5nTg9H72\nPwXMz4++YlYDzWmzNzMzs5Zp+UrBZmZmZsPlhMbMzMwqzwmNmZmZVZ4TGjMzM6s8JzRmZmZWeU5o\nzMzMrPLaYtq22Ujp7u6mp6enKWU367YEZmY2MCc0Nmp0d3czc+asfEdsMzPbmjihsVGjp6cnJzPN\nuH0ApLUhPzlglJmZNZ4TGhuFmnX7AHc5mZm1igcFm5mZWeU5oTEzM7PKc0JjZmZmleeExszMzCrP\ng4LNDGjeOjpTp05lxowZTSnbzKzGCY3ZqPcwMIZ58+Y1pfQJEyayfHmXkxozayonNGaj3mpgM81Z\nn6eLDRvm0dPT44TGzJrKCY2ZZc1an8fMrPk8KNjMzMwqzwmNmZmZVZ4TGjMzM6s8JzRmZmZWeU5o\nzMzMrPKc0JiZmVnlOaExMzOzynNCY2ZmZpXnhMbMzMwqzwmNmZmZVZ4TGjMzM6s8JzRmZmZWeU5o\nzMzMrPKc0JiZmVnlOaExMzOzynNCY2ZmZpXX8oRG0qckbS497i7FnCHpIUnrJV0vaffS/vGSzpfU\nI2mtpEWSdirF7CDpUklrJK2S9GVJk0biHM3MzKy5Wp7QZL8EpgHT8+PPajsknQqcBBwH7AWsAxZL\nGld4/TnAwcDhwH7AzsCVpWNcBswC5ubY/YALmnAuZmZmNsLGtroC2TMR8Wgf+04GzoyI7wJIOhpY\nCRwKXCFpMnAMcERE3JRj3g90SdorIpZImgUcAMyJiGU5Zj7wPUkfi4gVTT07MzMza6p2aaF5haTf\nS/qNpEskvQRA0m6kFpsba4ER8QRwG7Bv3rQnKTErxiwHugsx+wCraslMdgMQwN7NOSUzMzMbKe2Q\n0PwMeB+pBeV4YDfgx3l8y3RS0rGy9JqVeR+krqqNOdHpK2Y68EhxZ0RsAh4vxJiZmVlFtbzLKSIW\nF57+UtIS4EHgPcA9ranVlhYsWMCUKVO22NbR0UFHR0eLamRmZtY+Ojs76ezs3GLbmjVrRrQOLU9o\nyiJijaRfA7sDPwJEaoUpttJMA2rdRyuAcZIml1pppuV9tZjyrKdtgB0LMX1auHAhs2fPrv9kzMzM\nRoHevuQvXbqUOXPmjFgd2qHLaQuSXkBKZh6KiPtJCcfcwv7JpHEvP82b7gCeKcXMBGYAt+ZNtwLb\nS9qjcKi5pGTptuaciZmZmY2UlrfQSPo34DukbqY/Bj4NPA1cnkPOAU6TdC/wAHAm8DvgakiDhCVd\nBJwtaRWwFjgXuCUiluSYeyQtBi6UdAIwDvgi0OkZTmZmZtXX8oQG2IW0RswLgUeBnwD7RMRjABFx\nlqSJpDVjtgduBg6MiI2FMhYAm4BFwHjgOuDE0nGOBM4jzW7anGNPbtI5mZmZ2QhqeUITEQOOrI2I\n04HT+9n/FDA/P/qKWQ3Mq7+GZmZm1u7abgyNmZmZWb2c0JiZmVnlOaExMzOzymv5GBqzsu7ubnp6\nehpebldXV8PLNDOz9uCExtpKd3c3M2fOYsOG9a2uipmZVYgTGmsrPT09OZm5BJjV4NKvBT7Z4DLN\nzKwdOKGxNjULaPTtJtzlZGa2tfKgYDMzM6s8t9CYWdM1c0D21KlTmTFjRtPKN7NqcEJjZk30MDCG\nefOat0j3hAkTWb68y0mN2SjnhMbMmmg16dZpzRjkDdDFhg3z6OnpcUJjNso5oTGzEdCMQd5mZs/x\noGAzMzOrPCc0ZmZmVnlOaMzMzKzynNCYmZlZ5TmhMTMzs8pzQmNmZmaV54TGzMzMKs8JjZmZmVWe\nExozMzOrPCc0ZmZmVnlOaMzMzKzynNCYmZlZ5TmhMTMzs8pzQmNmZmaV54TGzMzMKs8JjZmZmVWe\nExozMzOrPCc0ZmZmVnlOaMzMzKzynNCYmZlZ5TmhMTMzs8pru4RG0sclbZZ0dmn7GZIekrRe0vWS\ndi/tHy/pfEk9ktZKWiRpp1LMDpIulbRG0ipJX5Y0aSTOy8zMzJqnrRIaSW8EjgPuLG0/FTgp79sL\nWAcsljSuEHYOcDBwOLAfsDNwZekQlwGzgLk5dj/ggoafiJmZmY2otkloJL0AuAQ4Flhd2n0ycGZE\nfDcifgkcTUpYDs2vnQwcAyyIiJsiYhnwfuBNkvbKMbOAA4APRMTtEfFTYD5whKTpzT9DMzMza5a6\nExpJ20q6UdIrGlyX84HvRMQPSsfbDZgO3FjbFhFPALcB++ZNewJjSzHLge5CzD7Aqpzs1NwABLB3\nQ8/EzMzMRtTYel8QEU9Lel0jKyHpCOANpMSkbDop6VhZ2r4y7wOYBmzMiU5fMdOBR4o7I2KTpMcL\nMWZmZlZBdSc02SXAB4CPD7cCknYhjX/ZPyKeHm55zbBgwQKmTJmyxbaOjg46OjpaVCMzM7P20dnZ\nSWdn5xbb1qxZM6J1GGpCMxY4RtL+wB2kQbrPioiP1FHWHOBFwFJJytu2AfaTdBLwKkCkVphiK800\noNZ9tAIYJ2lyqZVmWt5XiynPetoG2LEQ06uFCxcye/bsOk7JzMxs9OjtS/7SpUuZM2fOiNVhqAnN\na4Cl+f+vLO2LOsu6AXhtadtXgS7gcxFxn6QVpJlJd8Gzg4D3Jo27gZRUPZNjrsoxM4EZwK055lZg\ne0l7FMbRzCUlS7fVWWczMzNrI0NKaCLibY2qQESsA+4ubpO0DngsIrrypnOA0yTdCzwAnAn8Drg6\nl/GEpIuAsyWtAtYC5wK3RMSSHHOPpMXAhZJOAMYBXwQ6I6LfFhozMzNrb0NtoQEgL273cuDHEfGk\nJEVEvS00vdmijIg4S9JE0pox2wM3AwdGxMZC2AJgE7AIGA9cB5xYKvdI4DxSq9DmHHtyA+prZmZm\nLTSkhEbSC4ErgLeRko9XAPcBF0laFREfHU6lIuLtvWw7HTi9n9c8RVpXZn4/MauBecOpm5mZmbWf\noS6stxB4mjRGZX1h+zeAdw63UmZmZmb1GGqX0zuAAyLid89NTALg/4Bdh10rMzMzszoMtYVmElu2\nzNTsCDw19OqYmZmZ1W+oCc3NpPsp1YSkMcApwA+HXSszMzOzOgy1y+kU4EZJe5KmP58F/AmpheZN\nDaqbmZmZ2aAMqYUm3/H6lcBPSGvBTAK+BewREb9pXPXMzMzMBjbkdWgiYg3wmQbWxczMzGxIhpzQ\nSNqBdIPKWXnT3cBXIuLxRlTMzMzMbLCG1OUkaT/SLQg+DOyQHx8G7s/7zMzMzEbMUFtozictondC\nRGyCZ+9c/aW8r3yzSTMzM7OmGWpCszvw7loyAxARmySdzZbTuc3Mmq6rq2vgoCGYOnUqM2bMaErZ\nZtZYQ01olpLGziwvbZ8F3DmsGpmZDdrDwBjmzWvOLdomTJjI8uVdTmrMKmDQCY2k1xWengt8Id9t\n+2d52z6ku1t/vHHVMzPrz2pgM3AJz81PaJQuNmyYR09PjxMaswqop4Xm56Q7axdv3nRWL3GXkcbX\nmJmNkFnA7FZXwsxaqJ6EZrem1cLMzMxsGAad0ETEg82siJmZmdlQDWdhvZ2BPwN2orSeTUScO8x6\nmZmZmQ21hQF7AAAaCElEQVTakBIaSe8DLgA2Ao+RxtbUBGnQsJmZmdmIGGoLzZnAGcC/RsTmBtbH\nzMzMrG5DTWgmApc7mRm9uru76enpaXi5zVogzczMtm5DTWguAv4a+FwD62IV0d3dzcyZs9iwYX2r\nq2JmZgYMPaH5BPBdSe8EfgE8XdwZER8ZbsWsffX09ORkphmLmV0LfLLBZZqZ2dZuOAnNATx364Py\noGAbFZqxmJm7nMzMrH5DTWg+ChwTEV9tYF3MzMzMhmTMwCG9egq4pZEVMTMzMxuqoSY0XwDmN7Ii\nZmZmZkM11C6nvYC3S/oL4Fc8f1DwXw23YmZmZmaDNdSEZjXwrUZWxMzMzGyohpTQRMT7G10RMzMz\ns6Ea6hgaMzMzs7Yx1JtT3k8/681ExMuGXCMzMzOzOg11DM05pefbAnsA7wT+bVg1MjMzM6vTUMfQ\nfKG37ZJOBPYcVo3MzMzM6tToMTTfBw6v5wWSjpd0p6Q1+fHTfI+oYswZkh6StF7S9ZJ2L+0fL+l8\nST2S1kpaJGmnUswOki7Nx1gl6cuSJg35TM3MzKxtNDqheTfweJ2v+S1wKummQHOAHwBXS5oFIOlU\n4CTgONL6N+uAxZLGFco4BziYlEztB+wMXFk6zmWkmw/NzbH7ARfUWVczMzNrQ0MdFLyMLQcFC5gO\nvAj4UD1lRcT3SptOk3QCsA/pToUnA2dGxHfzsY8GVgKHAldImgwcAxwRETflmPcDXZL2ioglOTk6\nAJgTEctyzHzge5I+FhEr6qmzmZmZtZehDgq+mi0Tms3Ao8CPIuKeoVZG0hjgPcBE4KeSdiMlSjfW\nYiLiCUm3AfsCV5DG7IwtxSyX1J1jlpCSo1W1ZCa7IZ/D3vl8zMzMrKKGOij49EZWQtJrgFuBCcBa\n4LCclOxLSjpWll6ykpToAEwDNkbEE/3ETAceKe6MiE2SHi/EmJmZWUXVldBI2kw/689kERH1Jkr3\nAK8HppDG4Xxd0n51lmFmZmajVL2Jx2H97NsX+DBDGGgcEc8A9+WnyyTtRRo7cxZpfM40tmylmQbU\nuo9WAOMkTS610kzL+2ox5VlP2wA7FmL6tGDBAqZMmbLFto6ODjo6OgY+OTMzs61cZ2cnnZ2dW2xb\ns2bNiNahroQmIp431kTSTOBzwLuAS4F/bkC9xgDjI+J+SStIM5PuysebTBr3cn6OvQN4JsdcVajT\nDFI3Fvnf7SXtURhHM5eULN02UGUWLlzI7NmzG3BaZmZmW5/evuQvXbqUOXPmjFgdhjooGEk7A58G\n3gssBt4QEb8cQjmfJa1f0w38EXAU8BbgHTnkHNLMp3uBB4Azgd+RB/LmQcIXAWdLWkUag3MucEtE\nLMkx90haDFyYZ1CNA74IdHqGk5mZWfXVndBImgL8IzAf+DkwNyJuHkYddgK+BrwYWENqiXlHRPwA\nICLOkjSRtGbM9sDNwIERsbFQxgJgE7AIGA9cB5xYOs6RwHmk2U2bc+zJw6i3mZmZtYl6BwWfQloE\nbwXQ0VsXVL0i4thBxJwOnN7P/qdICdb8fmJWA/Pqr6GZmZm1u3pbaD4HPAncC7xX0nt7C4qIvxpu\nxczMzMwGq96E5usMPG3bzMzMbETVO8vpfU2qh5mZmdmQNfrmlGZmZmYjzgmNmZmZVZ4TGjMzM6s8\nJzRmZmZWeU5ozMzMrPKGfOsDM7PRoKurqynlTp06lRkzZjSlbLPRyAmNmVmvHgbGMG9ecxYYnzBh\nIsuXdzmpMWsQJzRmZr1aTbrt2yXArAaX3cWGDfPo6elxQmPWIE5ozMz6NQuY3epKmNkAPCjYzMzM\nKs8JjZmZmVWeExozMzOrPCc0ZmZmVnlOaMzMzKzynNCYmZlZ5TmhMTMzs8pzQmNmZmaV54TGzMzM\nKs8JjZmZmVWeExozMzOrPCc0ZmZmVnlOaMzMzKzynNCYmZlZ5TmhMTMzs8pzQmNmZmaV54TGzMzM\nKs8JjZmZmVWeExozMzOrPCc0ZmZmVnlOaMzMzKzyWp7QSPqEpCWSnpC0UtJVkl7ZS9wZkh6StF7S\n9ZJ2L+0fL+l8ST2S1kpaJGmnUswOki6VtEbSKklfljSp2edoZmZmzdXyhAZ4M/BFYG9gf2Bb4H8k\nbVcLkHQqcBJwHLAXsA5YLGlcoZxzgIOBw4H9gJ2BK0vHugyYBczNsfsBFzT+lMzMzGwkjW11BSLi\noOJzSe8DHgHmAD/Jm08GzoyI7+aYo4GVwKHAFZImA8cAR0TETTnm/UCXpL0iYomkWcABwJyIWJZj\n5gPfk/SxiFjR5FM1MzOzJmmHFpqy7YEAHgeQtBswHbixFhARTwC3AfvmTXuSkrNizHKguxCzD7Cq\nlsxkN+Rj7d2MEzEzM7OR0VYJjSSRuo5+EhF3583TSUnHylL4yrwPYBqwMSc6fcVMJ7X8PCsiNpES\np+mYmZlZZbW8y6nkS8CrgTe1uiJmZmZWHW2T0Eg6DzgIeHNEPFzYtQIQqRWm2EozDVhWiBknaXKp\nlWZa3leLKc962gbYsRDTqwULFjBlypQttnV0dNDR0TGIMzMzM9u6dXZ20tnZucW2NWvWjGgd2iKh\nycnMXwJviYju4r6IuF/SCtLMpLty/GTSuJfzc9gdwDM55qocMxOYAdyaY24Ftpe0R2EczVxSsnRb\nf/VbuHAhs2fPHtY5mpmZba16+5K/dOlS5syZM2J1aHlCI+lLQAdwCLBO0rS8a01EbMj/Pwc4TdK9\nwAPAmcDvgKshDRKWdBFwtqRVwFrgXOCWiFiSY+6RtBi4UNIJwDjSdPHOrXWGU3d3Nz09PQ0vt6ur\nq+FlmpmZDUfLExrgeNKg3x+Vtr8f+DpARJwlaSJpzZjtgZuBAyNiYyF+AbAJWASMB64DTiyVeSRw\nHml20+Yce3IDz6VtdHd3M3PmLDZsWN/qqpiZmTVdyxOaiBjUTKuIOB04vZ/9TwHz86OvmNXAvPpq\nWE09PT05mbmEtJZgI10LfLLBZZqZmQ1dyxMaa7ZZQKPH/7jLyczM2ktbrUNjZmZmNhRuoTEza5Fm\nDbCfOnUqM2bMaErZZu3KCY2Z2Yh7GBjDvHnNGdI3YcJEli/vclJjo4oTGjOzEbeaNNGyGYP2u9iw\nYR49PT1OaGxUcUJjZtYyzRi0bzY6eVCwmZmZVZ4TGjMzM6s8JzRmZmZWeU5ozMzMrPKc0JiZmVnl\nOaExMzOzynNCY2ZmZpXnhMbMzMwqzwmNmZmZVZ4TGjMzM6s8JzRmZmZWeU5ozMzMrPKc0JiZmVnl\nOaExMzOzynNCY2ZmZpXnhMbMzMwqzwmNmZmZVZ4TGjMzM6s8JzRmZmZWeU5ozMzMrPKc0JiZmVnl\nOaExMzOzynNCY2ZmZpU3ttUVMDOzxuvq6mpa2VOnTmXGjBlNK99sKJzQmJltVR4GxjBv3rymHWHC\nhIksX97lpMbaihMaM7OtympgM3AJMKsJ5XexYcM8enp6nNBYW3FCY2a2VZoFzG51JcxGjAcFm5mZ\nWeW1RUIj6c2SrpH0e0mbJR3SS8wZkh6StF7S9ZJ2L+0fL+l8ST2S1kpaJGmnUswOki6VtEbSKklf\nljSp2ednZmZmzdUWCQ0wCfg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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#* Loop for the desired number of time steps\n", + "nstep = input('Enter total number of time steps: ')\n", + "for istep in range(nstep) :\n", + "\n", + " #* Move all the particles ballistically\n", + " x = x + v[:,0]*tau # Update x position of particle\n", + " x = np.remainder( x+L, L) # Periodic boundary conditions\n", + "\n", + " #* Sort the particles into cells\n", + " sortData = sorter(x,L,sortData);\n", + " \n", + " #* Evaluate collisions among the particles\n", + " [v, vrmax, selxtra, col] = colider(v,vrmax,tau,selxtra,coeff,sortData)\n", + " coltot = coltot + col \n", + " \n", + " #* Periodically display the current progress\n", + " if (istep+1) % 10 < 1 :\n", + " vmag = np.sqrt( v[:,0]**2 + v[:,1]**2 + v[:,2]**2 )\n", + " plt.hist( vmag, bins=20, range=(0,1000))\n", + " plt.title('Done %d of %d steps; %d collisions' % (istep, nstep, coltot))\n", + " plt.xlabel('Speed (m/s)')\n", + " plt.ylabel('Number')\n", + " plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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y66iPVJIkTRpjHWj+DLhnhJ/5GXAK9bHN84CvAlckmQOQ5BTgrcCbqPe/eQBY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\n3JrkV0m+neT3J7pNbZXk3Um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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#* Plot the initial speed distribution\n", + "vmag = np.sqrt( v[:,0]**2 + v[:,1]**2 + v[:,2]**2 )\n", + "plt.hist( vmag, bins=20, range=(0,1000))\n", + "plt.title('Final speed distribution')\n", + "plt.xlabel('Speed (m/s)')\n", + "plt.ylabel('Number')" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + } + ], + "metadata": { + "anaconda-cloud": {}, + "kernelspec": { + "display_name": "Python [default]", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.12" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} diff --git a/Python/Fftpoi.ipynb b/Python/Fftpoi.ipynb new file mode 100644 index 0000000..43e7c5e --- /dev/null +++ b/Python/Fftpoi.ipynb @@ -0,0 +1,223 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# fftpoi - Program to solve the Poisson equation using \n", + "# MFT method (periodic boundary conditions)\n", + "\n", + "# Set up configuration options and special features\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "%matplotlib inline" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "System is a square of length 1.0\n" + ] + } + ], + "source": [ + "#* Initialize parameters (system size, grid spacing, etc.)\n", + "eps0 = 8.8542e-12 # Permittivity (C^2/(N m^2))\n", + "N = 50 # Number of grid points on a side (square grid)\n", + "L = 1. # System size\n", + "h = L/N # Grid spacing for periodic boundary conditions\n", + "x = np.arange(N)*h # Coordinates of grid points\n", + "y = np.copy(x) # Square grid\n", + "print 'System is a square of length ', L" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Enter number of line charges: 2\n", + " For charge # 0\n", + "Enter position [x, y]: [.5, .55]\n", + "Enter charge density: 1\n", + " For charge # 1\n", + "Enter position [x, y]: [.5, .45]\n", + "Enter charge density: -1\n" + ] + } + ], + "source": [ + "#* Set up charge density rho(i,j) \n", + "rho = np.zeros((N,N)); # Initialize charge density to zero\n", + "M = input('Enter number of line charges: ')\n", + "for i in range(M) :\n", + " print ' For charge #', i\n", + " r = input('Enter position [x, y]: ') \n", + " ii=int(r[0]/h + 0.5) # Place charge at nearest\n", + " jj=int(r[1]/h + 0.5) # grid point\n", + " q = input('Enter charge density: ') \n", + " rho[ii,jj] += q/h**2" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Compute matrix P\n", + "cx = np.cos( (2*np.pi/N) * np.arange(N) )\n", + "cy = np.copy(cx)\n", + "numerator = -h**2/(2.*eps0)\n", + "tinyNumber = 1e-20; # Avoids division by zero\n", + "P = np.empty((N,N))\n", + "for i in range(N) :\n", + " for j in range(N) :\n", + " P[i,j] = numerator/(cx[i]+cy[j]-2.+tinyNumber)" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Compute potential using MFT method\n", + "rhoT = np.fft.fft2(rho) # Transform rho into wavenumber domain\n", + "phiT = rhoT * P # Computing phi in the wavenumber domain\n", + "phi = np.fft.ifft2(phiT); # Inv. transf. phi into the coord. domain\n", + "phi = np.real(phi); # Clean up imaginary part due to round-off\n", + "\n", + "#* Compute electric field as E = - grad phi\n", + "[Ex, Ey] = np.gradient(np.flipud(np.rot90(phi))) \n", + "for i in range(N) :\n", + " for j in range(N) :\n", + " magnitude = np.sqrt(Ex[i,j]**2 + Ey[i,j]**2) \n", + " Ex[i,j] /= -magnitude # Normalize components so\n", + " Ey[i,j] /= -magnitude # vectors have equal length" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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ZjaLebXOenZ3ljDPOCGy89773vXzve9/jZz/7GZs3bw5sXCGEtqYF2TTNYnBA\n0EU6vDGhfiGpp6dv0BbyclTa51bpSy1ECLIn/x9CB08hdPDTmNNfwem7CBmKorkz4B4F6QIaQgqw\nc2Bn0DKTOPGzsYdeF8AUGxeMWopW1NvGstseALttvh7z8/OB1bG+6qqr+OpXv8r1119PPB5ncrLw\nANrX19fSaPrFSGtXrXyLaJoW+AVbryD7hVjTtKqEuNPwW/WV3OvVEpSFXBrU1ZVIiW79Aj1xP3Jz\nAu3IYbTZ74K9mNcoFq1MAQgBuga6gGgebeBxwgsfJh/7A6TefBdiUGVW621jWSrS3UYrgkeDIMhO\nT9deey1CCC699NIlP/+3f/s33vKWt7RkTCGELqV0hBAfWtOC7L842+HKrVVI6ulJXG7MoDwB5fbI\n67Hq202pS91bkL2FvFsWOj13C+GFj6Db9+MYZ2H1/j7uwHZcYxuuvg20oYqvFc5hzPRnCWW+gJn+\nP2QGbsAJXRzg7FtHtdZ0uYYKlmUVq/2t1b3pViJlsJ2egvaSesMufl/be8h+OtllXSrEjeThtsNl\n7aWzNPowsRKtOC6vqpkXKOdVlPIWaSgUQGnGfmSrCaWvRbfvJ9P3/7DDr0UKcLCwRIa8yGDxFJZI\nY4s8kMElh0sYV4A0XYi8DMN5EadO/QH53KeZjH4IDQNTRgnJKCZRTBlFXyXlDZazph3HKebFN1Kn\nOUi65cGxlNXeC1kev3j+YXXcOXXSbgvZo9K4juOQzWabWhCjHcfpCXGrinq0YpEpteR7enrQdZ1c\nLldcoHO5HJZlFZu9O46zZD+yXHnIIBdmmxwL2hGOhJ8nF05C9Nc4Z+JW5vJ/yR39P6ZXf54+jhIm\nR1jmCJOjh8J3AwcAF0Ge0OJPw2TNMHPhHH3Zn3BrbLjsuLo0CcsEEdlL1O0rfJe9xNxBEnKYhDtM\nVPYh6D63r/f5CSHI5XLFPtPVWNOlLm9lTVdHMpkMpJphu5Gq29Nx2uWyLjduaWWqbutJDIVj8Od3\nd8sxuK5LOp0ua8m7rnvCQxywZO+7lmYLzUzByZPhqP4Mx7TnOKY/zzHtOea1KRAS4qBJg/WuxcGR\nU9gy9QCvffYp8gmNTGIMy9wADIIcRpMjCDmCIwcRMoJggphzkLh7CCGnCC08iJ5Lkus3+Z38YSzn\nt8i6l2GJLBaLlrZIkxULZMQcWW2OI9rTZMQcOW3++DmQBnF3iF53nD53Hb3uODFnmIhoXUWkVuB9\nbrXWafbO+DanAAAgAElEQVRoRRvLSnSjhew4TqBBXe1mzQuyJ4jtspD949ZamarR8VpBaVEPoKGA\nrWpp9LhKz329lrx/P7K02UJpDefSFJxykb2VxndxOaY9w2FjPxPGfo5oTyOFiyFD9DsbGXd2clr+\nZfS647Cg0Z+4Fj3yHxAdITX+OkLzeczULwjPHwYOI4kitQhShJGAwEJz5hAstfIcfT0LA59CxubR\n+S566P8jkv8Awv7TFc+NTZ6UdpSUmGFBm2FBm2ZOm+Ap804y2hxEQUidfncDg85mBt0tDDlb6HPX\ndZw1Xc21Vs3edNBtLLtNkOfn5xFCkEgk2j2VlrPm0578eAt60E+RnuWVTqfJZrMATe9JXDpeKwS5\nXFGPUCjE/Pz8yi9uI6XzjkQiRKPRpl8DYrE8ZOnYy7k5y7m85/UpnjJ/wdPmXWS1JKaMMmafynnW\nGxh1TibhjqL5xEvi4vT9Orp5P+T/Gmm/hax+P7MD92EPrke39mFYzyFIobkSzc0iACkEtt6PbejY\n+uKXYeAKAeJjIE2QA/TKU+kLfZy0mMa0PoRJT8VzYBCizx2nj3EWPeJF8qSZcZ7lqPYcC9HDzOhP\n8KR5O1JIQjLOiL2dUecURp1T6Hc3IsrX6e8K/NZ0kG0su9FC9prGdGNUe62otCeWWshB492E3r5j\nK4XYo5nVwbz38QKfSot6eEFPQaWz1FoVzB85XU9VsEbP30puTm9htmyLafMAj0Vu4Wj4KUw3yqbs\neWyyz2XY3YqhLRelfvznE+ZtWJH/C8LGlSYWBnZIYDOEzRgOOlL2IGQfhoyjy0LepcQFIRHSQcgM\ngnkQSYRYICtsDBklZn6BZ8M3kaUf2zmDsDyFuHMSPc7pxN2taCs440LEGLK30mdvIi4KtQEsshzV\nn2VKf4xp/THuD38PV9hE3T7W22ey3t7FmHMqBqFl37uVNGvdWM6zUmsby+U8K90myF4v5G6bd60I\nIcLAH695QfbwPnDXdVtex7rUKtM0reueAru5qIc/cto0zWLAVidQujAf1Z5lb/g7TBmPMWhv4YL5\nNzOePQPhFh54cuTJkS/r8s5pExyJ/B3oR1gnBQnxc56VJ+G6pxFxdxJ1NxF1NxB2hwnJIUzZi6C2\n8+AwD5HLsDEJuZegGb9E6neQl0/xrGHgCIkmwyScHfQ7uxi2XkxUrq/qvU0ijDk7GHN2LI5lMaM/\nyUHjQQ4ZD/JE6HYMGWaTfQ4nWRcx6pwcmGs7yEyF5SK9K+VNl2u80Y059O2qY90GeoD3df7q2WI8\nIfbEsNX7q6VuXcdxlozfapphIXs1s1cq6hFUwQ5vrJXGqXbetdIKD4tE8pj5M/aGv0OPO8aL0u9m\nvXNmwVUbOT5uqcvbsi0WQg9yJPJjYpEfomOTc7Ywbb2EUfPbnCYfQzi7wT4f3EvqFjDJPBhfQjM+\nC2IKLXsT6+UuJDnmzW+QDH2BDeRJZD5MWqRJ6vt5PnQdz4a/QsI5mWHrJYxal53g4l7uPOqYjDmn\nMuacyjm5K0hqkzxn3MdT5l08Zf6CmDvIydYetuf3ECaY9nztsNyW25teLk4BKP6/W9pYeilPnTzH\nJnEUeM+aF2SPVorHcrWaFxYWiqIcBI0cZzcW9YAT87g7fd4SyV2Rf+dp8y525C9ld+61ZXN7S62n\njDjEM5FrmTP2MuiCgaT32OcxcjsBSIv3Y0a/hhH9OlrkK0h3A9K+FMEgMACyD+gH2QuYFLo+HQUx\nufg1sfh9CsQTQB6cK8B6D0KeVpgTYXqtN5OwfpuJ2FuwzB+yIfOPbLBei0OOY8bdTBu38kz4izwX\n/iob8q9lff416ERrOkcCUdiPzv8mZ+QvZ0Z/kieNO3ko9J88HLqRbdYlnJr/NeKyNVHbnWhtrhSn\n4GU9dGIby0qsFQt5sePTdUqQF2mFIJcKcTn3aNAXfj3HuVxRDxubbxvfZEyOMS7XMeaO008/AhGo\nhVyOZkVOB83DoR/xtHkXF2feykn2hVW9ZsK8kSfDnyckBzgt/SEykY8g5QD95vks5BYwTRNd34Br\n/zHW3PtA+yVa+Ftoxv0ILYkQc4v7wmU+K2mAHAU5VvhyzwH5GnDegJDlO+Fo9NCXfydHoteQ1x4h\n5O5EJ8ywvYdhew95McvzoW/xXOjrHDZ/wPbce4hnz67rfAkEI852Rpzt7M7/Fo+ZP+Ox0K08Yd7O\n6flXsDP/MnRaG+Xfqfi3MnK5HKFQCNM0O6qN5XJ4vZBXM0IIIaWUQojYmhdkfx4hNEc8atlfbVe6\nVTVjluZDlxO0DBkkkr36XlLi5wBEZIQxOcaYO04i2sNGsYkNbFgS/dts/OexNPWqW3KgAVLiKA+G\nfsAZucurFuMZ4+c8Ef4/jFmvYGvuf6ATZiH3bo5GP0LK+BHwwjLW00uQ7otxs36Xt4Ur5xBiHoSN\nEA6CQTQxjKYZNRc20WQhVcUVyRN+F5L9bMu9g/X51/BU+F95JPI3bLHexWDmJVW9dyUisodd+Vex\nM/8yHgrdyL7QDTxl3sWF2Tcy6pzS0HuXoxuuqXJ0SxvLIMtmtgMhhCaldIUQFwKfW/OC7NEMQS4V\nYsMw6O3tXTbQKWhBrubmqSUfuocefs/+7wDMM8+kNsGEmGBSTHBAf5TZ/lkADGkwKkcZk+sYd8cZ\nl+OMyjGMJqbC+/fo642croVWLERT+mMgJDvyL63q7x2yPBb5e4btF7E99+7innDcfjVZ63aORD5M\npOcNGPk3AaNLXntiwFAYKeMnpt84LlLmiq+rZlHOafs4FvlbwvY5hJ0LKs4/IkfZmf0AT4Sv5Zme\nawnZ48Q4p6pjXw6TCGfnf5ut9kXcHf4qP43+Exdm31T1Q85KdKLLejm8+S53zVZT3KRVbSwrsVZc\n1sAW4MCaF+TSykv13mj1di8KOv95uQePUsuy1jSsHnrocXs4meOWyOTcJLPRY8xGZ5kUEzwvnmOv\ncR9SSIQUDMsRxuU4Y3KccbfwPUJtbc688+c9zXda5HQtpLVjaNIgVOWeqityuCLPsL1nSYCWQDCY\n/Qh6eB3zsW+Qi3+LhPV6EtZrMNxtFfN4Gylsoukarvkkmch3SYe/jenuYDD74RVzhgU623PvJqk9\nwlTsB4xajQuyR5+7jssyf8Tdka/wi+gXSeeOcXr+FU17/9VONcVNGm1juRxzc3OsX19dVH6X4i3E\nNwE3rHlB9lOPIPuF2Kt5bBhG1RdeJ+whl4v+bpZlGZZhNtmbOdXZWfyZhcW0mCpY0osW9X7tYWyj\nsMD3y4GiOI/LccbccXoqFJzwIqcdx0EIUTz/QdLMh6l+ZwOusMmIJDG5sqtOSBOkxhHjDgbti5aI\nn0aMgdzV6Ed/B6v3OyxEv8l86EsY7iai9kuI2i/CcDejyyHECnuspS5vicSRc9hMkdceI2vcQd68\nC1c/Am6MWPK9RDJXYGshXC23Yo6sQCdhnUrSvB+sE37dEBo6F2bfRMwd4IHw9Qw4m1jnnN6U9+4W\nl3U1FnItVGtNV9PGcjlrejW7rIUQYbnoepJSzgohhBJkH17VrGpoVsRxswt1VIt381Qq6tEsyj3k\nmJislxtYLzcUG4+5uBwRM0V394Q2wV3anWRFoXpZXMaLVvS4XMeIPUo4HcbKW0sWhm7Ig16OPnc9\nQmo8HLqR83JvWNG6NIixPfdunoj8C2F3jC35N57wN5rspyfzbgacd5LT7yZj/Iy0cSPzoS8f/xu3\nH12OoMthhAwDBgITgQHSRCBwxDEcbQZHTOOIIyCOW0Smcwpx51VEshcTsncjXRPHqL6WN0KSNB8g\nYTVHKEsRCM7Mv5JJ/VEeCF/PePq0hqp9dZvLOgiqtaarabzh/WyVd3r6lBBiB/CnUsq9UkrZ3atX\nE/CLYDXJ834hbkYbwaAjkb3xHMchmUwGUtSjmmPT0BiRo4zIUXZxFjgFK2yOWSZ8+9IP6A9wh7gd\nTAiFQ4y6Y6xjHQOZQYasYRIk0GssbtFJJOQQ5+d+j7sjX2HEOZkt9vkrvmbc+g1skeKZ8BexRZKN\n+d8lLE/sbawRIeq8iKjzImTuGiztSRwxgSNmlgitFHkgi4uNFBZgI3HQ5QCmu4WIez66HC58uSMY\ncgO6HPEPBBpVu7wlNs/1f5acPsmmuXdha3ZLmiwIBLvyr+a/Yv/AlH6AMefUpr5/J9NsC7kWqrGm\nSxtvvPKVrySVSpFIJLjpppvo7+9n9+7drFu3rqXH8M///M988pOfZGJigt27d/NP//RPXHBB5RiI\nBvlfwLuBfxdCHAH+S9QgBKvykdBfunJhYQHXdcuG2Zem/kSj0ab087Vtu1ivNQjrzhsPCgtmNBpt\naeOHZDJZzP1tBG9/O5PJkNEzzMXmOBY+wqQ2yYR2mGPiGAC61BmVYz5ruhA8ZjYh7cXbJ/OEwrZt\nstkssVis6eJxe+RfOWw8zDm5K9hmXVKVNXfI/B7Phr+GS55x6+VsyF9BWA6zsLBAKBQiFGpficly\nSCmZE4/wTOT/kTIOsHn2PfRnLy7+vtaykNVgk+dbPX/MCzJvq+phpxL5fB7LsojHgylA0ijetRqP\nxzvaze6J9Je//GXuu+8+br75ZmZmZkin0wAMDw9z7733snnz5qaP/fWvf523vvWtfO5zn+PCCy/k\n05/+NN/85jc5cOAAw8PlW43WyAknXgiRAM4BXgPsWvOCDBQT5lOpFLZtL3GRlApxJBJpai6r4zjM\nzc21vCOS37IHilZxq29Or7lET0/lpgPLUe3+9tH0USaYYKFnvuDyFhPMiGlc4SKkYEgOnxA8Fq2x\nGEWpIHvXRisE2SLDfeFv81ToTsbt07gg+0bicuWesDYpDod+wKHQ97BJ0+/spmfhYkacS4iGOsP1\nJ5HMa49wMHQdR81fEHM2sy33LkILJxeDCUvrN5e6vOsNFkqJI3w/8WEuybydzfZ5dR9DLpfDtu2u\nEWTLssjlch0vyH6klOzYsYObbrqJRCLB/fffzwMPPMA111zTEuPl4osv5qKLLuIf/uEfiuNv2rSJ\n973vffzZn/1ZM4ZYcuK9lKfFf4eAU5UgU3jalVIW++D29/eX7UnciqISrusyOztLIpFoiQVTzrJP\np9OEQqFAFpN6BbnW/e1yD1M2djF4bEKbYFIcZlJMYouCq7RP9pcNHqtkjbquW3ygEUK0VJA9DukP\ncXfkK9giy+7cb7PVekHZql2l2KSZMW9j2vgZSWMfmgzR5+ymzz6TPucs4u5JNdetbgSJQ0p7mhnj\n58yYt5HTpgi7Y2zO/XdG7Bcj0MlkMgBEoyc+KJUrZOGP96i2E9I94a/yrPErXp36K8wao/n9KEFu\nPVJKxsfHefzxx1seaW1ZFrFYjG9/+9u85jWvKf78yiuvZG5ujuuuu64Zw5Q98UIIXUrpgOqHvAQv\nqCuVSi0R4lYWlWjVHvJyRT28No9BUEugnEdpClk1+9vlgscMDNbJ9ayT65cEjx0VRwoiLQ4zqU3w\nS+0XxeCxmIwxLscZd9ctWtPrGGCgKNLlgu9auf+/3jmDy1N/wa8i3+aeyNd4KHQjO/KXst3as2xq\nlEGMcesVjFuv4Gj6aeYTv2Q+/CDPhv8DV/wbuoyTcLYRcdcRkeNE3MKXKQcwZQ9aHR2UJC4OaSyR\nxBJzpPSnSWlPktKfJK09gyvyGG4PQ/YLGbFfTK9z2gkPBZXus2oKWSzXvlLXdR6P3MrjoZ9zdvZ1\nDYnxSnPtRNq5h1wvnmcsiCjrmZkZHMdhbGxsyc/HxsZ49NFHWzKmEOIzwF9LKSeEEFdTqImngKXW\nTy6XC7y6U7MWdSklmUxm2aIeQRcjqXYsx3FIp9MtrZWtoTEsRxiWI5zJrmLwWJI5Di9a0RNigge9\n4DEgJEOMyXHG3DGG5DBj7jjDsil7SlURIsZF2Tdzav7XeDR0Mw+Gv89D4f9ks3U+26yLGXK3LrvH\nHHKHWZf9bba4v4uLxbx+gDn9QdLaMyzoTzCj3Y4jUkteo8kwhuzBlD3oMopAR2AUvksDgYHExhZJ\nLDFf/I44/vAlpE7U3UTc3cqI9WLi7nZ6nJ0VWzHWmmmwUrCQ5/LO2RkeifyIJ6O3sm3hxWxKXUxO\nzzWUH9uNUdbdJMZQiD/xaiGsUjZxvDP4q4GIEmQgk8kUgwYA+vr6Aisq4QWpNHqD11LUI0hBrrYy\nmGfNNxK5Xu8xCQR99NPn9rOT4/nSKVLFFKwJcZgntCe4J3Y3UAgeG3KGGQwNsZ71hVQsd4RQC3vz\n9rvruSj7Zs4Sr+Zx8+c8Zf6CJ0O30+uMscW+kE3WOfTKsWXfQ8OkzzmDPueM4s8kEpt5stoklpjD\nLgrsAraYxxEZJA5yMdpaCguHDBoGYTlK3D0ZU/YuCngvhkxgyl6i7oa6LO1G8Kfe6IbOYf1h7ot8\ng7SYZVf6NZycuxSpFSK+KzVYWM7l3a104wOEV8c6iM9heHgYXdeZnJxc8vPJyUnGx8dbNeyVUspj\ni//+YyChBJmCIEQiEXRdJ5VKteVGrPeGKW1gUU1Rj3rcyPWynPhXY83XMk6ziRNnm9zONmc7UAiM\nm8vOcdQ8wow5w6Q2waQ5wQHjkWLw2IA7yJg7xqgzVvxea/DYSkRlP7vyr+KM/G8ypR/gKfNOHg79\niAfD36fPWccGezfjzk6GnK1V7TcLBCa9mO7qKOLvYPOscQ+PhG5mTj/EiH0KL85eVXhY8T0flKbd\n1NJgIei6Ac2g2+YbZA6yaZqcd9553HzzzcU9ZCklN998M+973/taMqZPjJFSPgBqDxkoBBz5n5hd\n1w2sPzHUZ7EGUdSjVZRGTtdaojNoljw4IBjKDzPEMDvFaYWF2YDZ8BwzxjRTxhRT+iSPG49hicL1\n1Ov2LhHoMXeMhKwcPFYtGhrjzk7GnZ3Y5Jkw9vO8sZfHQ7fxsLgRXYYYcbbTL09iXO5ghK2rtuuR\ni8u0/jjPGb/ieeNXZLV51ttnck76CsacU8uea7/L28tw8Fze/gjvcg0WvPvVcZyOaldYCWUhr8z7\n3/9+rrzySs4777xi2lM6nebKK69s+dhCiB7gLUqQfXiCEPTFW8sF59Vs9spF1lPUI2iXtb8LU6se\nIlpxTOUeHLzFeEkxAxv67D766GM7JxeOR4OkMcdMaIZpfYopfYr7zHvJhBcjid0oo+4YY06hK9ao\nM8aAHKhbpA1CbLR3s9HejYvLrPY8U/oBJo1HeSxxM49o/4kmDQbcTQw7Wxl0ttDnrqPHHe0oka72\nXpC4JLUJZvSnmNafYEJ/mKw2T8wdYIt9AdusF9Dn1h6ZW6naVKXmCl5keKe7vLvRog+69eLv/u7v\nMjMzw4c//GEmJyc5++yz+dGPfsTIyMjKL24AIcQg8LfArytB9hF01Sz/uNWM6QlxrQ0s6h2vmXhC\nHERlsEYp9+AQi8UQQpDP55dYVrZtEw6H0XV9qfvTdolbCeKZBFs4qbBQ6xopI8WMMc20Oc20Nsl+\ncz+/1O4CwJQhRp1RRt1RxpwxRt1xht3hmiuPaWgMupsZdDez03oZyYU50tFpkpHnmdGf4nnjfh4N\n3QKAkIKEHKHXGaNHjhJ3h0m4IyTcIWJysCqXd6vJkyGpHWZWP8i8NlUUYktkEFLQ725ki30hm61z\nGHRPatjzUI7SKO90Oo0QglAoVJfLW7Ey7ahjfdVVV3HVVVcFMpYQhT7IwJnAK4F3t/9u6wC8G6RT\nBbnZ0cdBCrLnApyfny8232hFAZRm1QQvfejxPzhUOmf+hddPqevTsR3CVpgNbGQDG4uvyRs5ZswZ\npo1ppvRJntGf5lfmfSBAkxrD7siiQC9+OaM1BY9p6Aw6mxm3TmaHdSkAOVIk9QmSWuFrTjvM8/r9\npMRR5GKktJCCqOwnInuJur1EZOErJOOEZIyQjGISIyRjmDKMTghdmuiEyva+lri4OMUvKRwcHCyR\nJi1mmY1MkjcWcMwMOZEiK+ZZ0KZJa8cW56ORkMP0uKPszP8aw842Bp0tTUlhqodGXN6NdkGqFSll\nx24JVWKV17EGMIE8sBF4Xkr5XSXIZWiHIJcLsiot6tFo3ewg8UdOAx0/d9d1i4VhvFKfjaZciZIO\nScASd7e3YGtZndHsGKOMcabYVbC8NbsYPDalTzKpT/KQuQ9XuCBhQA4WRdr7HpOxqucWJs6Is52R\nxYC14nnAIS2OsaDNkNKOkBJHyYokWS3JUe05siJJXqRwxPItmTRpoGMiC32hFutir3BfSUFYJojK\nXsIyQUT2MGRtoc9dT5+7nl53rOPd67W4vMs13OhUl3c7WO29kKWUXneWbwGnCyF+SwkySy3kdrhz\nS8dcrqhHK8ZrJq7rFtOvPJdePp9vuRjXayGXRno3+1yXm2e53NnSAhfYMJgfYpAhThU7Cwu8DsfM\nY4XgMb0QPPZE6Amsxa5LPW7PEoEec8bokbXtwWnoJOQwCWf4eIZkGRws8iKNJTLkSWOJLI6wcLBw\nyBf/DQINvfAldTQMNHRE8f8apowSlQO4CzohI0w4HK7n1AZKrffPSoVNWu3y7tY95BamHLUVIcQ7\ngI8DB4AMsB14pxLkEtopyM1MA1ppPGjuTVopctq27WJp0k5aEJoR6d3MB6RKBS6WuLzzDr35Xnrp\nZbs4ubBAa2JJ8NikPsmvzPvIaMeDxwZDQ4y5Y6xnA6PuGAPuQFmXci3omERlH1HZPAsmRWrlP1pF\ndJPLux0kk0l27ty58h92J48CX6bgstaAe4ARJcgltEOQ4XhN6yDSgJopyPXkQbcbb76O43Rsulg5\n12e5KlSO7RCz4mzOxNnMlmLwWFpPM2NOM21Mc5hDPBZ6jPv0ewEwpclIMXCsYEkPucMYHRDA1U3C\n0oq5tsrl3WkPxNWwyveQ75BS3iaEOBN4A4WqXfvbfwd2AO0qK+mJmbfP6olDJ4uZn9LI6Z6enhOE\nLahAuWrGKQ3YalbLyyBTyLzFerlew47tELJCrM9uYD0b2M3ZaJqGE7IXg8cKaVjP6s+w1/wVUkg0\nqTHkDpcUNRklROe7j9tB0A/tjbq8/a/pFmGen58PPMo6CBajqx0hxFnAtRTc1YeBVylBLiGIKlal\naTW6ruM4TjG1ptU0KpL+Vo7VRk63szBBaWnORgK22uVBWY6VgseKWwZZjZHsKCOMcsaiu9TRnBOC\nx/YbD+MIZzF4bIAxZ3wxursg1LUEj9VCp53XTqdal7fn7s7n88WgxU53eUspV3NQl6DQPfF9wALw\nNuAp4DVKkFlqIWuatuQps9mUy8d1XZeFhYXAnl7rFeTSqO9qhC2oG73cMXn1vTOZTMsDtgpdpNLM\nixwpkWNeZElqWWZFmlmRYV7LYvuTfoS7+H+Ju/hvF4mBhil1THRMqRPCICwNYtIkSoiYDBGTJjEZ\npkdG6JMRet0IvTJK2Ody9i/W+Xwe0zQxTfOE4DFpSwbygwwwyA5xajF4bNacXQwem2RKn+TJ0BPk\nF4PHEm4PY+4ooz6Xd6/sa0n+byfSyZ2Tyrm8vQwC717tlijvVe6yBrgE+JSU8obF/yuXtYe/Pm0r\nntSXK+rhPcEG3fCh2vFKI6drEbZ25HZ7WwHpdLrpe/ISyZQ2z4SeZFIkec44wlQoxaQ+jyWWhiXH\nZYg+N0q/jDHm9mJI3YsvxpBe7LFAR0eXAg0NBxdL2ORxsIRDHoecsEmLPEmRJE2etMiTEnnckjSi\nuAwx5CYYduMMuwmGZYIRN0GvZjCAWVPwWE++hx562Ca2F4PH5s15ZszjEd73m3tJa4WmLBEZWSxq\nMl7cmx50BxsOHlM0D13XT9jqCCrKux6SySQDAwOBjNUmhoAH/D9QglxCswW5mqIe7SpIstJ45TpI\nRaPRtj85l8Obk2VZpFKppgVsWTg8KaZ5QpvmCTHNk6FpFrTCnn9YGoxZCTba/Vxkb2Xc7aVPRonL\nMAkZwqixwlYtSCRp8iS1LEmRZU5kOKqlOCJSzGgLPGUeYVakkQKIQdwNsc7tY9ztY5PbzzZnmHG3\nD62G4LGoFWUTm9nE5mLwWEbPLAaPFfalHzMe5Z7QL4FC8Ji/qMmYM8awO9IRwWNrkdL7tpOjvD2X\n9WrcQ/YRBv5ICLEPyAET6s4owZ+C1MhFVktRj6AFeaXjambkdFDH5jgF6zSTyTQcsJXDYp92iHu1\nZ3hQO0hWWESkyVZ3iBdZJ7PVHmKjHKBXRkgtpAiHwy2pPrYcAkGcMHE3zDrKu/UsHI5oCzyVn+JI\nOM2UmeJJfZo7zCdwhSQiTU5yBtnujLDDGWOrM4SOtsTt6T+HpZG+ju1gWibrsutZx/ri4mwZFjPm\nDDPGFJP6FM/pz3G/udcXPDa0JF961BkjvBg81okPe5XolrnWcu+tFN1fTZS335qul4WFBVzXDbSW\ndVBIKb0gpVuBcWAdhapdmhLkRfwu60ZopKhHu13WXrCZlxJUKXK6HlpZiMRfEawRK/6gOMZP9P38\nUnuKvHDY6A7wCucMznI3slH2I6TAsqwTrpNODUYy0Rl3+0hkdUJuiJBTKLeZxeJZ/ShP6jM8pR/h\nltCj/FDsIyQNTnZG2GmPcaa9nrGSoiLLRfr6LSqRFYxkRxhhhDO0XYUIb83hqHnU5/Ke4BFjfyF4\nDOh3+xk0hhiX61jPekbdMeIyHsyJqpFO/bwr0eied6VUrGpd3n5rulqX99zcHIlEouPSEZvM6wCd\nghiHgIgS5BKaVfGplqIe7XrS9i8szWpcUUqrjq00YCsSiZDNZjEMo+YxHxaHuMHYx6PaBP0yyuXO\nLi50TmKUpYIk6a6FuBIRTHY4Y+xwxoBCQNpz2jEeNSZ5VJ/k++EH+U5kL+udPs62N3GevZnxCr2S\nV6o85i3UheCxAQYYWBI8NmfMFhpt6FMc1g5xj/lL8loheCzuJhgrsaT7Oih4rFss5FZRrcs7n88v\neV2pu7ucNe0FdK3mcyyltAGbgrsaUHvIRbwPvlYXazMrPrXDQq4ncroemnVsldzpANlstqb3OsIC\n3wIHz4gAACAASURBVDDu4T79Wba6w7zD2sN57kkYKwQiBZnLaeMyL2ySwiIpbLI4i4FgAhMNXQoM\nBGE0EtKgR5roNQqWhsYWd4gt+SFezunksdlvTPAr4zluCT3KDeF9bHWGeIG1jXOtzURXqCdd7ULt\n5B0S+R4Si8FjUspCUZNweklv6QfM+0lphSpeYRleEt096o4x5A4FGjy21izkWqjG5V1sW1rG5T07\nO8uBAwfI5/Ntc1c/88wzfPSjH+WWW25hYmKCDRs28MY3vpG/+Iu/aPnWlBLkEryL1ssPrkQ37rOW\n4s2/lSlBzXy/5QqReOeu2nN4v/YcnzduI4LJO6w9XOhubYvlJZFMixxP6ime1Apfx7R8UYTTYpmC\n0hWIS50eadInTcbcMEPobBAxNmoJNjlRelYQ1BAGu+2N7LY3YuGwzzjEneaTfDV8D98M38dF1kn8\nWn4no7Kn6jlVU3nMsixcxyWSjrCRTWxkU9HlmdHTTC/uS0/pUzxuHODe0N0AGNJgxB3xCfU4Iyp4\nrGNYyeXtf0j76U9/yjvf+U4Aenp6uOKKKzj77LM5++yzOf/881m/vvYe17XyyCOPIKXk85//PNu3\nb2ffvn284x3vIJ1O84lPfKKlY4saRKC7HgtrxLbt4oUxOztLIpEgFDqxxV1pUY9mlV48duxYcf+z\nlfhdvUDL6mX7afTYSiPVY7HYCU+qUkqOHTtGPB5fsTnBT7VH+YrxS852N/E2+xKiVbYy9D5713WL\ni0sqlcI0zbLXSiUWsLnDPMIdxgwH9AUWRGHfrc812ebGGXHD9EiDXmkWv/cufg+j4VKwnG0hsZE4\nSLLCYUHYJIXNvLCYx2ZWs5gQWQ6JNLP68b29rU6cs5w+zrL7OMPpJValcM2KNHeaT/Iz8zEWRI6z\n7I38Rv50NruDVR97JaSUpFKponfphHzpMtaUZVgc8bWtnNImOaIdQQqJkIIhd9jXW7rg8o40oVWj\n51WKxWJdUVXPKwiSSCTaPZUVyefzPProo3znO9/h+uuvZ/Pmzezdu5cjR47wB3/wB/zLv/xLW+b1\nyU9+kmuvvZbHH3+8kbdZcZFVj5CLVOOyLlfUoxmlF71xW2khl+bmCiEwTbPlDwD+8WultMJWNS0c\nVxrncTHFf5h38VLnVH7PviAwV6dEco9+jB+Zk9xnHMNBcqbTx2vy69nuxNnmxhmUodqs9CpP6cLC\nAm5I52jE5UktxQPGHLcbM3wvdAhDCi60B7nMGuVcp39Zd32/jHF5/kxelj+NX5pPc7P5CJ+I3cSv\n53fym/kzMZuU5lVL8NhwdoRhRjhDO7Mg5MXgsZliUZMDxqPYxYeevsWKY8fzpROyNqHqNpd1NxEK\nhdi1axd33nkn5557Ll/72teQUnLw4MGWV1BcjtnZWQYHG3/wXAklyBWoFPBUbanIWmmVIJdGTnsW\n/cLCQtPHqkSt1rc//xmqs+KrGcPF5cvGLzjJHWqqGK/0ud2vz/Ll8LM8qs9zipPgytxJ7LGHGZTV\nW9WNEkHnJDfKSW6cy+xRJJLDIstdxlF+ak7z17H99LoGv26N8VprA72y8vVtovNCazsXW1u5KbSf\nG0IP8YBxkLdkL2KLO1TX/FY6h9UGj7m2pD8/QD8DnCJ2FAKGdMGsMXs8X1qb5O7QXeREIZYm5sZP\nCB7rl/0dEzzWKN1Uv9rDXzZTCMHGjRvbNpfHH3+cz3zmM3zqU59q+VhKkBfxW8ieOFZT1KOZ4zdb\nkJdrphDkDVrtsTVzX74cEyLJQW2Wq/MvC8QytnD5TORx/suc5hQnwV+lz+BspzMKHQgE62WU11ob\neK21gae0FDebk/wwdJgbQod5VX49v51fv+x+s47Gb+TP4Cx7A/8euYu/jf2Ey/On88r8rmCOoULw\n2AmdkfI2iXyCBAm2im3FymMpc4Fp43hRkwfNB0lpdwIQkmHGnNElNbyH3OEl1003iVw3zRUKFmmz\ny2Z+8IMf5OMf/3jF3wsh2L9/Pzt27Cj+7ODBg1x++eW84Q1v4O1vf3tT51MOJcgV8ITB7ypt5QNz\nMwW52upgneR6q6Zz1EqsdExHF/vtjsv6oje99/fvIVcig8P/ju7nIT3JH2VO4TJ7pCkWVx7JjHCY\nFg7TmsOMcHApJDKaixHXhaRGwYCrMyp1IsgVd8m3unHekdvG6/ObuM48yPWhQ9xoTvCxzC42u8s3\nk1jv9vMn6V/nxtBD3BB+iHVuH+famxs+1npYrjxoaeWxsFUueCxTLGoypU/xhPE494buAUCXOiPu\nCMPWKIPaIJv0TYy4o5grBMm1m066z6tlfn6esbGxpr7nn/zJn/C2t71t2b/Ztm1b8d+HDh3isssu\nY8+ePXz2s59t6lwqoQR5Ea/oupe+5HVf8kceHxaH+Yr574zLcda561kn17POXUcfjbu3vPEboZY9\n12aMVy3LCWXpw0MrtgM8IosL54xYYKiOfUO/1eXPrSwn0teHDrFfn+cvM2ewy6nvSX8WhzuNLLcb\nGQ5oFtPCYVZb+pmZEnQEFhKn0iWYgH5XMCYNzncivNSOcrYTLpse1SdNrsyfxG9Z6/lI9CE+En2I\nj6d3MSqXD4bS0fjN/Jkc1pL8R+RuRtI9bHI7ow5xNZXHvFQcwzIYz44zznhxL9s2bI4YM0ybheCx\nCeMwD4f34QoXIQWD7lBJ28rmBI81k26zkFvRWGJoaIihoeq2VA4ePMhll13GBRdcwBe+8IWmzmM5\nlCAvYts2s7OzS6rLRCJLb6q4jHGR8wIOi0Ps0/dxp7gDgKiMMi7Xsc5dtyjS6+mltyaRbsRiLS2S\nUW3kdDufnOsJ2FqJlc7hdjnCiExwh/4Ep9rjVb1naQ6l1wXHS9Pxfr+kQ5gm+HF8ghdZQzWLsYXk\na+Y8N5lp9ml5pIBTHJNznDCjUmfE1RmR+uK/DXoQxevMRWIvvkdOSI4uWtLP5dPMhgSHDcmPjTT/\nEZpnwNV4qR3lTVYvW90TH4AGZIj/mTmDP489yIdjD/G3qbNWTJcSCN6UvZC/j93CVyJ384H0y2s6\ndghWOKoNHiMLQwwzxDCna2cAkHfzpBOport7skLwmJcvPeaOEZeJ9qTWdaGF3M7Wi4cOHeLSSy9l\n69atfOITn2Bqaqr4u2Zb7aUoQV5E13Wi0SjhcJhUKlX2b3rpY4/zouL/F1jgsHaICXGYw+IwD+j3\nc4e4HYCYjLHOXV8Q6kVLumdx+SxHPYLcSFGSdu0hl845iLSr4jwQ7HFO4fv6/VwitnOqrCzK3nz9\nKTeaphXFN5/PFyuEGYZRqEa1KM5paTOt5dmZTxQtae9BzzvOcp/RfXqWvw4f5VnN5qV2lCvyg7zA\niTAqq7tNNQQhCu7quIRBqXMysCvjEHJChEIh3Jxkn5bnv4w0N5hpvmumuNyO8fu5PraUBHINyhAf\nyJzKH8fv5yEjycX2ytZFBJOLra1cF96Lg4veZd2eqgkecxwHA4PehT566eNkX/DY3GLw2JQx/f+z\n9+bhUZV3///rnFkyWQkJIRurbCqKYAigVuuOfUq1rY9L7QJWBcWK4lKtTx+kP1rrWrWKolRQqaAW\nv9rWB2qtS1VAArKpIGJBEUhCEsg6mfXcvz+GezgzTJKZyew5r+vK5eUwk7lPzsz9uT/b+8NBtZ6P\nrRtwKL7ixBwtJ0DQpNRbSqHonxAjnW4ecjIHS7z11lvs3r2b3bt3M3jwYOBoYZzUzI8XhkE+gqqq\n/hagcP/weeQxShvNKI4WAbTRRq16gFqlllrlAJtNH7NG+QCAXJF31IsW5ZRrFeSR53/PSNTBetsL\nncgcsvx7yrareBRsyffp6Zou8J7ITrWOxy3vcLP7PEaJY0+8MmUhDaxco8vlwul0+g8/eo9e/7e3\naBbKNRtbslo531MaoFIVvF5ppN8zd3JbThMne60st5cxWotPBbaKwjgti3GuLG5wFfK6pZ1nra2s\nzq3lf5xF/NAdGMov03xRIjfhpzcqtUI8isZe9RDDtQFhvSaVvbjg4jHZ15udnX1M8ViuK49c8him\nKx6zWzp8vdLmgzSY6vnM8hnr1Y8AsArrkbGV0lCXUawVY4rhpLB0q7IWQtDS0pI0gzx9+nSmT5+e\nlPc2DLIOuaGrqhoYgoyAfPLJ18YwmjGAr/+0jVYOqLXUKQeoVWvZqNbQqfiEOfJFPuVaBSW2Evpp\n/bFiJZeuRfVlC5OsnI62FzqRBll6Fu3t7THv344UCyZmu8/hccvbPGZ5m597zuBUbShw1BPS54RV\nVcXtduNwONA0DYvF0mMUQlVVrnQP4ZGsLxibU8glnkp/vl5u3noj7UTwUF4zp7msPNJehElR0Y7k\niuMpPGFF4XJ3Ppe48/i97RAPZB3mFK+VEbrDwMtZ36AKqNDC71f34Dt45IruBVrSFWngwi0es7qz\nqGQQlQzy6zg7TI4jbVi+vPQe8242WT8GfMVj+rGVA72llGglWMMUsAlFOhlkSG7IOpkYBjkEsTRW\nCgoF9KNA68fxHA9en5FuoYU61edFH1APsDFrA06bk1VAgeiny0f7/mv1WmNe/BRvgywVjeThJp4F\nW5GQhZlfuM/lWfOHPGX5N5O9w7nCNZFszeITnDjiuWqahsPh8PefRzJ95jxvKXvddp6x/ocmxcmV\n7iHkYD7GwGqaxqdKJ7UmL7+090NFOZq7PIK+KKlWwOeKQh1QJwj4b4PwaYVYgTygUIFCIM9spQiV\nsZrguwrkBm3OWSjc5ejPR7kO7rY1scJehhfBK9ZveN16gOscwxmhhV8Et8W8H5swMyDCwrl0J5Li\nMZPbRKmjjFLKUNVTfBOxTF6f8pjFl5euNdXyqeUTNEXjNOfpfMt1VlTrSuXoQ1f0gVnIITEMcgji\n7T0qKBRSSKFWyPGcAF5wOB3UOmqxF3b4DLVayzp1DU6zT7wg31PAQHWg76StDiJLZPWq3SLaqVbh\nIA2ZnHwlc6zxNsaR3DcbFm5wf5uPvHt4yVLDjqxaprrHcqZnJBZUHA6HP0+ck5MT8RQpBYWr3cPJ\nEWZetuzlHfNBpruGca63NKC6WVVVTiGH/kJlg83DeaZ+fg9aHzb/TNNYqCn8FcVfTV2EoBzfQNUT\nFYVS1deZ5wbagGYBzcDXikoLKgu9PkP9A0XwExVOVY5+DmyoHKdZ+Fx18bnaziLbl+xV7VzlHMI0\nd3nY173NtJ8PrV9ymeNU1AwR1ghFJJ+FrorH9IVjciJWkbOYIoo5QR17RHlMo9naTA7dt551R7qF\nrN1uNx0dHfTvnxpV+onE0LLWIXWKnU6n/wORqA+yy+Wivb2dwsJCf/GQvdNOvbuORmsjh7KbOGg5\nSL1Sh0vxFQr114p8uegj+egyUe4f9N4T8bjGrgq25DSpeJ94W1tb/ROrwlmrNHiH6ODvWZ9QY/6K\nAmHjrPbjqLYPpsCaG5OBGwcVB0ste3jf3ECxZuU8bynne0qpFEc32ccth1hsaWGho5Qzg/p+b3F7\ned4rGATMVgQXIhgoBGYRmNeVHlqwmH97eztWq5Vai4UVGqzQYD9wmgIPm2CUAqvN7dxr288Y4aBB\n7WCYN4ebHaMi8ow/Mu9hhW0DYz3lXOf4VkTFSumkDy3TFzk50RvJUIRUHguKlATPFw7nbyXvfyR6\n68mksbGRMWPG0NnZmWnzkHv8QhgGWYc0yMHGMVHv3dbWRkFBAR6Pp8vKaQ2NQ0rTkaKxWmrVA9Qr\ndbgVNwDFWnFA0VipKAuZe4rlNYYqMtNvrHa7HafTGfcTb1tbG+ALjXe31uA8saIoeDwe9roaeCtn\nJ1uzD2DFxCTPcM7yjGKQiM269yjtrDLX8m9zAx2KhzHefMZrhZzsLaRSy+U+62H+ZbbzbU8Ot7mL\nGCYs/NOrcYVbY4FZZZZJwaI7HOivQ/5XXqNEURScTidmsxmr1eoLjQrBWwLmCwfWrCZKsppwqHZM\naJzoKWCau5wpnqIex1BKOnHzRtYnvGf9gtNdx3G5sypiXWuPx4PD4ejTBjkUwf3v0lBLpJHWG2p5\nIJOv7+joICsrKyXSReGwe/duzjvvPA4ePJjyn4UIMQxyJMiJT9I49uvXL2EnNPmeMuwabNS6Q0Oj\nSWnkgHLAn5euV+p9PZECBogSv4EuF+WUijJwE5NrDJbnlOFdPZ2dnTgcjqQa5OB+YrlpBeeJbTYb\nrRYnH5q/ZI3pP7SonQzxFnGqdwgTvIMpjVLlS48LjfWmJj4wNfCJqYVWxY1JKIzU8rCQxTZFo1lR\nGaPlsdOZi+rJ5gOTDVUJ47OgM87ys2wXbpotGrVWF/8x2fnEYudrcwcuxY0AvMLKmZ7+/NhV0aMq\nlx4vGmstu3nD+glOxcPFznGc4x4dVRtPuhlkGQFKBqGKx+R9l+i9aKfTmVYe8ubNm7n66qv58ssv\n0yrUHgaGQY4EaZA9Hg+tra0B2s/xRC8baTKZyM3N7fX7amg0KAePeNG+Cu96pR6v4kURCgO0ARQ7\nBzDYPIRKKikVZRHNj5UhRpfL5e/h7krn2+FwYLfb4z4tpb29HU3TAgabh+onlmvU54ltNtsx6/ei\nsc20nw2mr/jUtB+X4qVSK2Sct5ITvOUcpw3A3Mv2FIFgr2LnE1MLO9QW9qp29iudOBXp7YKmqCBM\nZGMi98goxnxM5AkVEwoeoeDUoFNTaMdLp+LGqbpxq248qttfse27JhUPZnI0G8e789nkKOJjbx6f\n4KUkRLg7FM1KJ2ss/2Gt5T80q51Mdg/je85x9BfRe4zpZJD1o0tTiVCedKixlXpjnYoG77333mPe\nvHls3rw52UuJNcb4xUgIHsEYb2lJGZqWldPg+5LH4hCgolIqyigVZYzXJgDgxctB5SB1Si372cd+\ny36+MO9EUzRUoVIiBgZ40iVi4DFGWgjh93hlwVO4edZEF5eE00+clZXV5fpNqEzwDmaCdzAuPHxm\nOsAm017eN3/JastnWIWJUVopo70DOU4rYahWhDXCr5SCwlCRy1BPLtPwDV/XEDQqTvYpdvYonSzC\nTqfJSbbqm3fcoDjRFBH0e8SR16r+H6+w4PHm4HRm4XBkk+PK4zyzlZ9mWdmtqTziFWwXggcVwQBB\nQNgbAnPSraqD7dY6PjHv5zNTLWZMVLuH8m33KCq1vlcNm4qEyinLg7PcUzRNC2jp1Oei9SHvZNJX\nK6zBMMghkR/qeFVa671LWYRkNptpbm6Oa3W3CZO/CGyc9xRaWlrIzs/msPWQ35M+oBxgq3kLQhGo\nQmWgKPW3XxU7isnpyEUVKjabjezs7LC+vIk2wl31E8sDULj9xHqsmJngHcIE7xA0BPuUw+ww1bLD\nVMcqy6c4FQ+qUBik9We4VswgrYhBopByrZ9fQztcVBQGChsDhY1TgbOE4Kd2L+8JGAw4W800tJr4\nYaGLQVZBkUlQqHrJ1ZwU4CHXrFJmyaEQC60ehX2awhYP/LlTYZFJ4xm8oAhOUuBNq5nx6tEDqPyb\ntdDJ16YmvjIdYoeljn3mZhQBwz3F/KDzFCa5hpGjWGPuzSbbGIRLuqxTYrFY/If+UMVjeiMte6z1\nxjqRUYvm5uaAKFdfwjDI3RBr4xjcDhTKu0ykehb4RAgqRCUVohIpxuTGzUGlngPKAWrVA3zD12wx\nb0LkC0x5JgaKUiqOaHaXi3IGiJKEjDMMF7nJdNVP3NuUgIrCEFHEEE8RUz1j8aJRq7Sw29TIbrWR\nnaZ63jd/iVAEioABIp9yrR8DRR4DRT4lWj4lIp/+IicsackSRWGV1cQaTTC7VeFgngcKPLyKr8+4\nWECRUChSbAhV5RAKjW5oFBr+qddmsBTA6SjsPWyls93Ma8NdZKtOvlLbaVTaOGhuY696mK/VJg6r\ndgDytCyO95Zynn0Mx7tLydGsR/W7CfS0wgl3ZwLp1kYEgQeIcMZWytSd/jXdFY/Fkr4qCgKGQQ4g\n1EzkWCCHP8hikK68y1QZiWjBQqUYRKm7jDH24/F4PAizoC2vlQbLQQ4oB/ha+YqPzRtBAbMwU+qf\ngOUTMikWxX4jHc+eZ/l7JV6vl7a2Nv+GIzcWOXQjHvOsTagMEv0Z5OnPWYwCwI2XWqWFfeph9qvN\n1KmtbFX306S0+8PNilAoEDYKRTb9RA6FIpt8bOQIK7nCSjZWcoSVbGHBqpg5STXxU83Kw19bWTzS\nSaOmUe920wS0mFWaVTArXkYrGpMVFwWqh1zFRbbiIkt1k6e4cCouavPsrHV38D+2NhTT0alVucLK\nIK0/1d5hDHUXM0wrokjkHi3SOuLoB1d366MSeiIx0qnwuc9Ewv27hqs85vF4cLvd/ufoPWk5eKW3\n3694THpKFwyD3AWxMI5CCP9c5XD0mxOtLy3XGIymadjt9oCQusVioVgpZph3uP95TpzUK3XUHqns\n3q3+h41qDQAWYfGPqSyxDCTfVECBKIi5J63PE8uwnDTCwfKnsq1Nbjzx9OQsmHxetLcIdBLWXjQO\nKR0cVNo4pNhpVu20KJ00K3b2qI204sCuuHArXWipD4YfDIZVQQ+bADn6wQs0Hvnx/7tQsQkrmtdK\nvTOXxs4B5NuHcX1BNiVaHiUin5wwpRnl302/eUtjrM/Z99ZIpzLp7CFH8ppg5bHgbgX5XYtl8Vhr\na2vcC0BTFcMg6wgO6/TGOOorpy0WC/n5+T22FyXbIEdasJVFFkPEUIZ4h/ofc+DwTb9Sa6lTatll\n+oIa83qw+YT0A8ZUinL6i6Ko2mRC5YnNZjMejwen04mmaZjNZrKysvwTmrxeL06nM+BvII1zIow0\n+LzpEuELWQMBxlqPGy+duLArbjoVFy48uIQHu9vBx52C/9eZRYMGxShYXAoOr4rdreDyqGiaitNt\nxaFZcZCFmyyE2YT7yLX9V76H+wZ6qM7Runz/SJF/N/3fL1wjLdvP5GtSXQwinbz5WK+1q8NUsPJY\ncMg7kuKx1tZWjjvuuJiuO10wDHIXRGscg/tyI9FvTnTIWr5fsMJWJGMcg7FhY5gYHuBJt3na2OPY\nTWt+C/Wmej43fc56xTftJktk6Sq7fcVj/Sjs0kiH6if2K5sd+buHyhMH58rkGL1UMNKhsGDCQjYF\nIhuh+SItDocDyGe8zcbMXCvXf2FlRZsZc5avJ9Gr3+DMYENQogqKEBxog6Z2wU9LPTw82E12Amxe\nd0Za3zur37zlwSmccZUG4RNvj15K5OqJtHjM5XKRk5OTEiFrl8vFpEmT2LZtG1u2bGHcuHEJeV/D\nIHdBpMYxVOV0pPnKZOSQZc+11+uNaoxjOGSTzSDXYArcYzEfme1rx06tX8ikls9Mn7JOWet7vsgO\n9KS1CvJFPoij+Us4ukk7nU6cTmdYeeKucmWpaqS7qgw/7ILXd5n5WaWXp8a5jlwHuAQ4BHgF9DeB\n/DO4NXh0l5nf77RQ166ycooTNQlRV72RlrUVbrcbVVX90Rj9JCw9wd5ZMo10uoSsk+nNR1o8duWV\nV7Jr1y5KS0v55z//SUlJCRMmTGDIkCEJ/3v/8pe/ZNCgQXzyyScJfV/DIOsIDlmH04esaRqdnZ1+\ngxBJX26o949377NE5n3cbjdmszmuIiihwuM55DBCjGSEd6T/sXbaqVUP+ELeSi3bTNtYq6zxPV/k\nUOoto8xbRrmooEwrJ8uVhdPRcz9xOOvrjZE2m80xbw2RleGyRz1UZXhpluDvtSZ+1qRyWrGGokCW\nQkg1c7cGJxQITumn8Wa9iVV1JqaVx3fYelfIFIKMyHR17wIGLwRFRiTJMNLpFrJOpcNDd8Vj119/\nPR999BGrV6/mrbfeYuXKlQAUFRWxbds2KisrE7JG+f6vvvoqq1YFV2vEF0OpKwiXy+XXf/V4PF2G\nToIrp+Ughd58+Ht6z1igP0AA/rB6PL+0mqbR3NxMXl5eRPJ9QghaRIs/J12v1lFnqqVD6QAgx5vD\nQG8pFVRSofmMdB7xG/kXykjrvTiZH9P/RPp3lYWAMo8fSkFMsqNV4YbNVjYeVpk+1MvQHA2vAK9Q\njvwXOr2wq13lwyaVTq/CmDyN75Z7uW2Um8IkKCnKz59M6XRX5NjV6/WGWW7meroashEr0mlYg9Pp\nxOPxkJvb9Yz1VEIIwYQJE1i+fDmDBg1i8+bNbN26lV/96lcJOWzV19czceJE/va3v1FUVMTw4cNj\nGbI2lLqipStvVW6Ydrvdf7qPdFPpjnidvuUBorOz0+/JO53OlFDmCUbvDeVoOYxQRjJSGeUrOnN0\n0uxtpinryAQscz2b1U2sVT4EIE/Lo0zzhbvLjvzkEpvNKFxPWt8WEomRdrvd/sEFVqu1xwPeCQWC\nt89y8uDnZh770oJH0w12PDIbWRGQA/x8mIdrR3oYnZ+cc7WsU9BHkiIdaQldV3gHF/mFKhyLhZEO\nll9NdVLNQw6HlpYW+vfvT2VlJZWVlUybNi1h73311Vcze/ZsJkyYwNdff52w95UYBjkImcOSOS6J\nDO92dnbGLd8ajxxy8AFCX7AlowHxprsWq+C16jdWCJ0nLrGVUGGpQPEq4PXpQbcqrdSptf5Z0hss\nNTgUBwAFWoHfOPsMdRnZvZgvG3xtvTXSiqIECJfk5eWF/bkyKbB+u4nWPQoDsgV5VkGOBfIsvv/m\nWgT/Oazy3F4zZ+ZpjM5PfJhanwcP56ARKT0Z6eCQtyTenrRB5AghYi6d+atf/Yr777+/y39XFIUd\nO3bwj3/8g/b2du68807/WhKNEbIOItRMZK/X2+NEo1gQ66lI+tarUAeIcMYVxgIhBIcPHyY31zdf\nuKvnhNKdll5jpHligaBFafa1X6lHQ95OxReq76cV6rzoMsq0cmzYYnfRIa6vu3A34M9Hm83miMLd\nJ//JxrSRXn5/tjvkv3e4YOZqK6/vMvPQuS5uONUT8nmxJjgPHo+CwUjXE+xJw7HjKrsz0jKdZbPZ\nEjJ4prek6iCMrujo6KC8vByHw9HlXhEpTU1NNDU1dfuc4cOHc/nll/PGG28EPO71ejGbzfz4SErU\n3wAAIABJREFUxz9m6dKlvV2KMe0pUoJnIlssloANJR5KTxI5Fal///69eg95gJDrzsnJCdl6FWo6\nUrw4dOgQOTk52GyBRi9Y8UluhHL6j+zjjrYNK+C9EBxWDvsNdN0RI+1SfFXK/bX+fk9aGuqskCVS\nvUMWNdntPnlKWRQWbU76ytet/HuviQfOdVFVptHpVuj0QGOnwqcNKp80KGyqUznQrlJV5uX9nziP\n+R2xvr5w8+DJJlIjDT4jl04GWd6DdODAgQNUVVXR2tqa8IjFvn37aG1tDVjL1KlTefXVV5k0aRIV\nFRW9fQsjhxwpMncsi55kQYTVak1IL19v0Bdsqara47oTLUQSnAII7ieWz5ETsOQ1xGrjU1AoEkUU\neYs40TvWtw4Eh5Qmv4GuU2v50rILt+LzNou0ooBwd6lWhjVMRatQeL1ef3jabDZjs9l6nZN+5jsu\nZq62cv0/jj08DMgWjBuocfkJXs4c7OLMQfGfYCYPUlarlaysrJQOBYebkw7OTcuDU6qHu9Mthyx7\nkJOx5kGDBgX8f25uLkIIjjvuuFgY47AwDHIQnZ2dtLf7Jfn9/cSJQJ9rjeQDGVywFUnFd6LzJOHm\nieMdjZAoKBSLARR7B3CS92TAN0u6SWk64kkfoE6t4wvLTjyKBwQMEAMo1RWOlWqlWHqY6CTvkexT\n76qoKdqc9MKzTVxUamN/mxm3R8XhBKdTwelQGJatcduZHkxxtBnB1xfLg1SiCWWkpQKcx+Pxt7il\nS0463QxyKk16SvTfLj2/MXFEChRYrVZ/jjVRhFv8JJGhwXC1srt6v0Qgvd9Y5onjhYpKiSihxFvC\nyV5fu4MXL01KY4An/bllO17FiyIUBogSyrQyv5EeqJVixuwvBuzN9YVjpJ98N4v/72++li9VEfTL\nFvTLERTmCJatsbC7QeHJ6W5ibSOCr89msyUkmpQo9NcHBBwU4zFkIx7rTyfkpKdU+PwMHTr0mDqP\neGMY5CBkbihULineRGKQo9HKDvV+ibg++R6yqlsWLcnwrSyciGX7WKwx4Rs7OdBbyine8YDPSDco\nB48Y6DpqTT7FMU3RUIXKAG0AA1wlDFBKKM8qZ5BlMBY1NtGWYCN92RSF370huPt7Lm65oJNOl5ev\nG+CrRoU/fZDDsjU2bCYX9/53Z6/6pPVIdbpY5vlTCX3PdKjrCyfcnQpGOhWMW7j05VnIYBjkLpEf\n4kQpZ+nfszsjGVywFYlWdqj3i6dB1m9G+sEPesUrwC+ykE4bB/iMdJkop8xb7hvS4AYPHuqpZ5/2\nDbVqLQct9eywbUcoApMwUaKV6PLR5ZSIEkz0vvL4uIGCH5/uZcFfs1j8noW6lqObvEkVDCn2kmXx\nzYaOtk9aou8pluH3RKV1EkFwUVok19ebSVjSOMu/fywMdTp6yLFseUo3DIMchPwy6IuMEv3eod4z\n0oKtSIh14UeoPLGs8pR5RvBtWnLz0z8WrBmdLoZaCIHX5SXfmc/x4gTG2yZgFVY8bg8N6kF/Pnq/\naT9bzVv8RnqgVhrQgjVAlEQ1pnLBpS6mjPTyTZPK0AFuhhYLhg4QVPYXmP32Ia9XYiayFz9V0gux\nJh490+EO2ZApHT29MdLpJmICPoNseMgGIUkFgyyLZfQ5rFgJK8TjixpOnjh4o5OvkT8ej8dvoCHQ\nSMtCqFTbZLoaAgFgwUKFVkmFdlSL142berXen4/ea/qaTeaPQQGzMFOqlQa0YBWL4h6NtNsFg7IE\nefkahxsV1u9ReKtD4btneJlyUmDxUXc5aTlxKdhIy3tqMpnSpu0nXIKL0iIRZ4mGZBnpVCcVJj0l\nk8z5RsUI/UafaIMskV/E3hRshUO0Vd2hCNVPrKpqQBtMqDYfuQ4piKH/fcHGQRppvUHRe3DJMNJ6\n8YtIqostWBikDWKQdrTVwoWLOrXOb6T3mHbzsWWj7/nCQukRARPpTRcFzZK+9E4bW3fJjV7QPx9U\nFZ5caWblfU7Oqeo6/aL/m0qNZnkPZHWxxOv10tHRERPt7lRA7/UnsygtlJEObg/szkjr89F6pcF0\nuidtbW0MGTIk2ctIGoZB7oZkeMhSFMPpdPaqYCvc94Pe5Zni1U8cykgHh1n10p+hjHQ8PYdQ4he9\n3citWBmiDWGIdnRDcuDwDdU4Yqi/NO1io6XG93xhpVRX2f3jywez9XelzP2Rh5GDNPY3qPxnv8LL\nb5m57FdZbHjOwfCKyEeK6sO38vFYaHcnG/1hKlWLCrsq/ApnEpZE/luqXVsompubOfnkk5O9jKRh\nGORuSLRBlqFel8vV64KtSIjmGsPtJ46lxyH7P/WzVYPD3V0Z6UjlKLsjOM8YT/ELGzaGasMYqg3z\nP+ag02+ga9Vadpp2UmNZD9+Hu6fa2PtpBdu2V9JxuBKzo5xLzurH8Aoo7hfefQ6WvAwO33YVzejJ\nSMt7kOy6ANnKpO/bT1Ulsa4INe5TX+Etvwv6xyF1e6UlbW1tRlGXwVGCQ9aJqLKWG6DMEydiJCJE\nH8qKJk8cD/SbSrCRlqFuGXKVld298eD0bTCRDoGIJTayGaYNZ5g23P9YJ3Z/69XuE2tprtpCu/qB\n7/kimzKtjM26nHSBKAgId8OxXn+4hqq7lENXRjpZxXuZ3Kolw9Rut9tf/Cm9/kRMwooFRg7Z4Bik\nZ5yItiCn0+nPX2VnZyd0JGI0QiSh8sT6Ta6rPHGikJuKflZtb6qK5euToSIWCdnkMFw7jrZPRzCg\nVsHcoqA47bgHHODkc/dxOLuWT0zbWGdZC0COyPEP1SjTyhnoLsVkN6F5jy1Ki4ZwjHR3xXuxNtLB\nrVrprCTWFbIlUtac6Cvg02ESlhCxn/SUbmTWJzLGxMsgy1Os/ssjT7JutzthYfJwDXK4eeJU7UcN\nR+kqlJGWG7a8J4nw+nvD9p0Kp114dKqP1WpFiELGn3Q8f1vupCAf2mnze9J1ai1bTVtYa1kDWZCd\nnUO5Vk45FT7VMW85ecRuEliyjLQ+xZCJrVrBh42eIjeR6ndLEmGkDQ/Z4Bj0HnKsQ9Zyyo9U/8nL\nywvYoBK5UfRkkJORJ04UXRnprgwDHB0Mkao90sePEkwc72XjFhNnf8tL0yGF/+xR2LDZxKOLLMy7\nw00e+YzU8hnhHenLozo6aVfaac49TKO1kXpTLZvUj+lUfJOo8rS8oFnS5eSSG7M1x9NI61uZkpli\niCexOmykipHu6x6yMX4xBKFmIvd245VhXbk5pMJIRCG6nlPcVZ5YbgDp4DFGQ3B4Wl6f3pvWb0ip\nJmTy+S6FPy0zs+drlUEVGoMqBJXlgovO81J0ZMx2cIohuLpYIGhVWv3tV1K/26H4ahwKtIIgI11G\nNjlxva5QOemu7oPMmWaqvjYce9hI1KzpWMyU7gqPx0NxcTGHDx/OVC/ZmIccDcEzkQsLC6M++ekL\nthTFJ8PX3ebQ0dGBx+NJ2AcyeE5xcOGH/FKlUp44Hsg0QjhDIEJ5cPrvkawmTnaPdDDBoU05pzis\n1yJoUZp94W7dgA2n4iuW66cVBgzXKNPKsJHdw2/tHT0ZaQCLxZIy1d2xQu8Vp8Jhoyv97mDb0pN+\n96FDhxgxYgQOhyPj8vtHMOYhR4P8cPemTze4YMtms5GdnR1WxWqie5/1X6B0zRP3hp48xmBSuUfa\nboeaGoXmZmhuhtJS+M53RK8lLxUUCkV/Cr39Od57AuAz0oeVwwFe9FrLGlyKL7xcqPXXGWifkc7i\n2JnN0aK/D/oKccD/GU2V6u5YkKoh+FgN2ZCymZlS9R4NhkHuhmgMcnDBltVqJScnJ6KRiIk0yHDU\nmATniWMtfJFq6De43h42gnukITlG+t57VR55JHCTvuUWB7/8pT3mkQ0FhSJRRJG3iBO9YwGfkT6k\nNOm86Dq+tOzCrfiMYpFW7K/u9g3YKMOKtbu36RH9gSpUGiWZ1d2xIlXUxMIlmiEbn3zyCZBeymKx\nxghZh0Av2djS0hK2QIe+YMtsNvuH0EeCw+HAbrdTVFQU7fLDRghBS0sLQgi/p2Eymfy9u4kQvkgG\nweHpRG1wwUIm8jMmiYXK1WefwaRJgZ/V4cO9bNrkSFqrloZGk9Lk96Tr1Vrq1Xo8igcEFIsBAfno\ngVppWEY6OASfnZ0d9vctkpx0Mo20PkIla08y6bsoPejFixczf/58TjvtNFavXp1R16jDyCFHg9ws\nNU2jubmZvLy8gL7WUM/XF2z1pk81loVkXaEPTbvdbr9hCC7MMJvNWCyWuMtQJhK9tnYqCEOEar/q\nrZGur/fw9797KS/3MmyYyogRWdhsqeV1aGg0Kg0BnvRBtR6v4kURCgOOGGlpqEu0gVg4etCIRytT\nqhlpvVecir3vseCbb75h9uzZ1NbW8txzz1FdXZ1x16jDMMjRoC/U6aoKGY6eXvXKRr3dGGJRSNYV\n3eWJnU4nLpfLb4j1VdZwNMSqL1hKpy9O8BCISLypRBOJkTabzX7DECx5majK21jhxUuD0uAvGKtT\nazmoHkRTNFShcnPnrVg0S0KvsacCvngY6XTQ2O4tmqaxfPly7rrrLq6++mp++9vfkp0d3yLAFMAo\n6oqG4KKu4EKEaAu2InnvWOaRu+sn1hfCBIdu9SFW6UXL58rfkeqDBIKLfdIh/9aTkEmo8Yj62oP9\n+0385z+ClpYOTjvNxogRvcvRJgoTJspEGWXeMvBOAMCDb5Z0o9KI4lJod7QDJMxjDKeATz+JDHpn\npKVXDIm7xkRTX1/PnDlz2LFjB6+//jpnnnlmxl1jtBgGuQf0Y8xk7lFfQBLrE3qsDXJ3/cQOh6Pb\nPLG+RUGvFd2dwlWq5N6g+xnF6YbeSOvHI+pz4ZJzzqmnvf3o/2/dWsHw4VkpWazUE2bMDHSXUuDo\nR6enMyXuYzgFfJEaab1OeqZ6xUIIXn/9debOncull17K8uXLyc+PnRJcJmAY5BDovyjS8wgu2Coo\nKIhLyDNWBjlUP7HUnXY4HAGFZ5EcKHpSuOquilU/cSmehiE4dJuJusWhKsRlqmH+fC+3334IVYXC\nQoW2tk7a232HpkTfi96gj27IHv5UbbnrjZGWByvAfx9T9Z5Ey6FDh7jttttYu3YtL7zwAlOnTs24\na4wFRg45BHIjAPxVyHKeqNwU4vVhCreQrCvCyRNLUYh4fvGDQ92h8tGxbvkJ3sCl8EUmffHDrRD3\negUm09GUS3A+Ohk90pEQPOIyUxThgu+Fx+MJ+PdQdRrpfN1CCN58801uuukmzj33XP74xz/Sv3//\nZC8rWRg55GiRHogspsnJyUmIKH20HnK0eeJ4Eal4Rm/z0dJIZdoGric4utFdWFMaY0idHulwCPb8\nU0X8IlbIULU8IOvlWcO9F+lipFtbW/mf//kf3njjDZ566il+8IMfpMW6k4lhkEMghKC5udmfc5Vf\nmkSvIZLnRpsnTiTBhqGnfHRX1cR6UmVGcTzR99uGE7r1egX/+tdBOjq8XHTRQHJyjv2ah7oXwamH\nUIYhnlX26SZ+EQ2apmG32/1td/pi0N4cmFLJSAsh+OCDD7jhhhuYMGEC27Zto7S0NNnLSgsMgxwC\n2RZjsVj8HkmiiMRDDidPnMpGKppqYr3HJv9NtpxlWngaAj3/cPtt33mngR/+sAaA664byqOPjuvx\nfcIt4ItHlX1faPOJNB8ei6hGMoy03W5n/vz5rFixgscee4yrrroq4+5lPDEMchdkZ2cjhEiKlGVP\nX6Lu8sShCn3SyUh1VU2sz7kFz4yW033kASQTNoDgwrRIDlVnnz2AZcuqePvtBn760yFRr6GnA1NP\nUY2ejLS+ayGTD1U9SXuGSyobaSEEGzduZObMmQwbNowtW7YwePDgmL9PpmMUdXWBnPgkhT8SWYjQ\n3Nzs18DWEypPLL9cLpcLp9OZ0eG+YM/fYrEEGOuuNqJ0OpSkY2FasJGWKncSVVUDQt3yACWNVCq0\nMsUD/b1MpBhNpEV8vTXSTqeT++67j2eeeYZ7772XWbNmZdy9jBFGUVdvkZ6n9JYT+Z56QuWJFUUJ\nCGlm8sbW0xCIUDrRTqfT/+/pIGKSrpXF0bTCSaxWa8YeHmPhFUdDtPUBkRbxCSH49NNPmTlzJoWF\nhWzcuJERI0bE9doyHcMg94D8YCbLIKd7nrg3BLf4dJdDjUbEJJTnlgzDEI++6d27D/PJJw1ccsno\nGK0yMkJV2euLtvQdANJQp5KoTLToC/BUVU2JHviuvhu9MdIej4dHHnmERx55hP/93//llltuybj9\nJxkYBrkLguUzE5lHlgZZGmJ9nhjwD7KQxSHpFJINF72HEa3n310OVBaMdTeKT/5d49mrHa+pU6+8\nsoMFC9bQ1DQXmy25X3N9hMNkCtSfDlUfIO9HqhQqhYvX6/WPXY3VwIt4EY2RfuCBB9ixYwejR4/m\nzTffJCcnhzVr1jB27NhkXkpGYeSQu0C/YcvB2Yk46QohaG9vx+v1+tuU5OalzxOn+hc+WjRNCxAw\nSUTeLVR4Nd49ubE4cHSHEIK6ug7Ky/Ni9jujWYMMw0dy4Eg3IZNgrzhS9btURm+kFy9ezKuvvspn\nn31GW1sbABUVFVRVVfHQQw8xenRyojFphJFDjpZkeMjyg28ymfwbmVyDfP9gDyNTkAUwyShMi1TE\npDc9ucH58HiFNBVFSaox7o02czoJmcRjDGQqIT3pb775hr///e+0t7fzzjvvUFxczKZNm9i4cSMf\nf/wxeXnJ+6xlEoaH3AX6atHeSFmGgz483ZWwRzCpkv+MBekwBELvKejlQCU9FY0Fe4uZuHnDsVXi\nspUpHu/Tm/sRi/fvKgyfSWiaxrJly7j77ruZOXMm8+fP7wtjEuOF4SFHSyI85FD9xNIQyS+7Pk8M\nRz0Fj8cTMv8ZbKRTmXQaAhFN0Zj+Prjdbrxeb8YKX0BiK4ujLeKLhZHWHyAztcUQoLa2lptuuokv\nv/ySN954g9NPPz0jrzOVSM3dL4WIh0HuSXe6uzxxT6IZiZY7jIauvKhUWFskhNPuEyxiIvON6TBt\nKVxSpbK4t0ImXcmz6n+X3ivOxM4G8F3nypUrue2227jyyit55ZVXjJB0gjAMchjEUq2rq37iaMO2\n+vxnVlYWEJhvk2FvidyApEFIdKg7uNc22frasUbeD8B/OLJarZjN5gCD0F0lcTr9PVI9hxpOpX1X\nkQ39/ZAV1JksvAPQ2NjIrbfeyoYNG1ixYgXnn39+Rl5nqmIY5C7QfwgVRQmZx42EUHniUP3EsfAu\nehriINtLJHoPIV5eW18YAgHdS16GW6SUDiImvZH2TDbRCplI5bRUTav0BiEEq1atYs6cOUydOpWt\nW7dSWFiY7GX1OYyiri6QYVXwjRGTo+Ci+T2hdKchME+caInEcFt99EY62vfRTypKBynIaOit5GWo\n0GpXRUo9hVbjib53GsjY+wm+CIfsdDCZTAEpJvlYvA+yiaClpYU777yTt956i0WLFnHxxRen5XWk\nAUZRV7QEe8iRhqy7yxOHqz4VT8Jp9ZGGVK49EoMgq4ozfUYxxCYM31P+s7vJV4mqtNdHc1K1Gj4W\ndDd9KlQ+Ol3TD0II3nvvPWbPns2UKVPYtm0bJSUlyV5Wn8bwkLtBGqP29nY0TaOgoCCs18U6T5ws\nevLaulK10m/cZrMZm82WNuHMSAjuKU6GiInX6w1Ip+gL+GJlEBLVypQKSHlPCN/7TzchE4COjg7m\nzZvHX/7yFx5//HGuvPLKjDwspxiGh9wbpGccrofcVZ5YDiWPZZ44EUSaa5MGWRqIdK2e7ol4Sl72\nRLQiJtGmH9J14EWkxFLIJJQEpX7QibyHyagREEKwfv16Zs2axejRo9m6dSuVlZUJeW+DnjE85G6Q\nG5vdbsflcnVZ5BAqPC2/YH0hfyqNQKhpPulQoBQJ8Za8jAXBBkGGuyXh3JNg7z+T5CD1JConHkmN\nQLy+Jw6Hg9/97ncsWbKEBx54gGuuuSblPrsZjuEh94aePOTuDHEq5IkTgd5ASc9Cesk9CWakk8pY\nqvTahkO0ohnSa5PGGMjoFh+9Vxzvw1Vve6R7Y6SFEGzbto2ZM2f6JS+HDx8ek+syiC2puaOkGNIg\nS+MMmZMnjpZQHpQ+rxhpqDsV82wS/djAdD1chdOPG0r5TdM0f3FTulYRByO94s7OTr8SXjJy4oko\n5HO73Tz00EM88cQTzJ8/n1/84hcZGenIFAyD3A3B8pnQfZ64s7MzLWQge0O0+dNocp/JyrPp1xdt\nXjEdkAZBSnvKjV/eT2mM0+XgFA7BXrGM6KQK+r9xKDW+rg5O8qe5uZni4mJMJhM7duxg1qxZmM1m\n1q1bx/HHH5+syzIIEyOH3A3yhOpyuWhvb/dXWffFPDEcHXYRr/ypjDboFZSC82yJGKgR3Dstq6cz\n8Z6GkxMPp4o41eRZg8m0SvGuqu1/8IMf8NlnnzFy5Ei2b9/O97//fRYsWMCoUaNS8r70MXq8AYZB\n7gY5wMHtdtPe3u7fdGQfrjRQ6RzKDAd9X2ai2nskoWQO9W0+wcagtweEvlJVHJwTj+SehnNwSqVC\nvkQOvUgmQgj+3//7f6xYsYKvvvqKw4cPU1dXB0BRURHr1q0zZhYnlx4/dOkVb0owHR0deDwewCd7\nqGkaTqeTjo4O2tra/DmoTC18kZt2W1sbHo8Hm81GXl5eQkPx0gPLysoiJyeH/Px8CgoKyM3N9R+A\nXC4XdrudtrY2Wltb6ejowOl0BqiP9YRsTevo6EBRFPLy8lIunBkrPB4P7e3tOJ1OsrKyIr6nsmDM\narWSnZ1NXl4eBQUF/r+Z2Wz2H+I6OjpobW2lvb2dzs5OXC5XgIcdT+Tnt729HSEEubm5GXtPNU1j\nyZIlzJkzh/Hjx7Np0yZqa2upr69n1apV3HzzzQwdOjTh61q4cCHDhw8nOzubKVOmsGHDhm6f/+KL\nLzJ+/Hhyc3OpqKjgmmuu4dChQwlabfIxPORuOO644zCbzUycOJHq6mqGDx/O8uXLycnJ4b777vPn\njtMtfBcO6TQEQt/m091s3FADNXoreZlOBE8rivcM355ETOIpPdlXvGKA/fv384tf/IKvvvqK5557\njilTpqTEtb788stMnz6dZ555hkmTJvHII4/wl7/8hS+++IIBAwYc8/w1a9bw7W9/m8cee4xp06ax\nf/9+Zs2axZgxY1i5cmUSriDmGCHr3tDR0cHmzZt5//33+fOf/8znn39O//79Of300znuuOOYPHky\n1dXVlJWVHVMZKUm3Fp/goQHpKqYfqlo12BjI4R59oSJeHrCSPa0o1MEplqpWvQnFpxuapvHKK69w\nxx138JOf/IR7772X3NzcZC/Lz5QpU5g8eTKPPfYY4Ls3gwcPZs6cOfzyl7885vkPP/wwixYtYteu\nXf7HnnjiCR544AH27t2bsHXHEcMg95aGhgbGjx9PU1MTc+fOZcaMGXz66ad89NFHrF+/nk2bNtG/\nf38mTpzIpEmTqK6uZvz48Vit1pCeQfCmkyrFQn1hCITeGOgruiG2AzVSiXSoFO+uaCySfLTX6xuR\nmKqjIGPJwYMHueWWW9i6dSt/+tOfOPfcc1PqWt1uNzk5Obz66qtcfPHF/sdnzJhBS0sLr7322jGv\nWbt2Leeeey6vvfYa3/nOd6ivr+fyyy/nxBNP5Kmnnkrk8uOFIQzSW0pKSrj55pu57LLL/M30Y8aM\n4dJLL/W3AH3yySd89NFHfPTRRzz//PPs2bOHsWPHUl1dTXV1NZMmTWL48OEBG09X4/aSMclHtjFl\neiET+DZ/+beX3r/ek+7NQI1UIjgUn6xe23DoaVxoV4IZ+oOTy+Xye8XpNAoyUoQQvPHGG8yZM4fv\nfe97bNmyhX79+iV7WcfQ2NiI1+ultLQ04PHS0lJ27twZ8jWnn346f/7zn7niiiv8WvgXX3wxTzzx\nRCKWnBIYHnKMEUJw6NAh1q9f7/eiN2zYgKqqfgM9ceJEJk6cSF5e3jEbjyTW1cOhCJ5RHO+cYjIJ\nV/Iy2Bh4PJ6QeU99dCPVjHQm5k97SkEA/t7ddEgNRcPhw4f55S9/yXvvvcfTTz/Nd7/73ZS9xtra\nWiorK1m3bh2TJ0/2P37nnXfy/vvvs27dumNes337di644AJuu+02LrzwQmpra7n99tuprq7mT3/6\nUyKXHy+MkHUq4PV62blzJ+vXr/f/bN++nREjRgR40WPGjAEIaPOJh1BGX+qzDc4pylB8pL8jWJih\nq7xnMv+OfSl/KoTwC/HIeyAFeyTxmHyVDIQQvP3228yePZuzzjqLxx9/nOLi4mQvq1uiCVn/7Gc/\nw+Fw8Morr/gfW7NmDWeeeSa1tbXHeNtpiBGyTgVMJhMnnngiJ554IldffTVCCDo6Oti4cSPr1q3j\nX//6F/feey9tbW2ceuqpfgNdXV3NgAEDAgx0b2T0got7Mj3PFivJy3BUxvTTfJLRh6tPO2T6fdV3\nAAQXqMVz8lUyaG9v59e//jWvvfYaCxcu5LLLLkv5NYOvTbSqqoq3337bb5DlwWLOnDkhX2O32/3q\nZBK5pyWiTS4VMDzkFEEIwd69e1m3bh0fffQRNTU1bN68mbKyMr8XXV1dzbhx4zCbzREXjAUPgcjU\nGcVwbCFTIq41ktnRsQypBlfFZ3LaIZq2rVhMvkoGQgjWrl3LrFmzOOmkk3j66acpLy9P9rIi4pVX\nXmHGjBksWrTI3/a0cuVKPv/8c0pKSvjVr37FgQMHeP755wF4/vnnmTlzJo899hhTp07lwIEDzJ07\nF7PZzNq1a5N8NTHBCFmnKzL8uGXLFn+Yu6amhn379nHKKacEhLoHDRp0TN5TIsN0mqYFiJhkIqnW\nU9xdH25vW3wSNTYwVfB4PNjt9pi0bYUzCjEREq1d0dnZyYIFC3jhhRd4+OGHmT59etqG25988kke\neOAB6uvrGT9+PI8//jgTJ04E4Oqrr+brr7/mnXfe8T9/4cKFLFq0iD179lBYWMh5552lbFd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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#* Plot potential\n", + "from matplotlib import cm\n", + "from mpl_toolkits.mplot3d import Axes3D\n", + "\n", + "fig = plt.figure()\n", + "ax = fig.gca(projection = '3d')\n", + "Xp, Yp = np.meshgrid(x, y)\n", + "ax.contour(Xp,Yp,np.flipud(np.rot90(phi)),35)\n", + "ax.set_xlabel('x')\n", + "ax.set_ylabel('y')\n", + "ax.set_zlabel('Phi(x,y)')" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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GjeDt7Q1ZVsY4cXd3R/fu3aHTKQ/6HR0dMXjwYCQkKMMFp6en4/3330dBgfL8Oy0tDb6+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\nKrYM5eXluu1R3f52FV9WViZVSlW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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#* Plot electric field\n", + "plt.quiver(Xp,Yp,Ey,Ex) # Plot E field with vectors\n", + "plt.title('E field (Direction)'); \n", + "plt.xlabel('x')\n", + "plt.ylabel('y');\n", + "plt.axis('square'); \n", + "plt.axis([0., L, 0., L]);" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python [default]", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.12" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} diff --git a/Python/Ftdemo.ipynb b/Python/Ftdemo.ipynb new file mode 100644 index 0000000..48dc376 --- /dev/null +++ b/Python/Ftdemo.ipynb @@ -0,0 +1,147 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# ftdemo - Discrete Fourier transform demonstration program\n", + "\n", + "# Set up configuration options and special features\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "%matplotlib inline" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Initialize the sine wave time series to be transformed.\n", + "N = input('Enter the number of points: ')\n", + "freq = input('Enter frequency of the sine wave: ')\n", + "phase = input('Enter phase of the sine wave: ')\n", + "tau = 1. # Time increment\n", + "t = np.arange(N)*tau # t = [0, tau, 2*tau, ... ]\n", + "y = np.empty(N)\n", + "for i in range(N): # Sine wave time series\n", + " y[i] = np.sin(2*np.pi*t[i]*freq + phase) \n", + "f = np.arange(N)/(N*tau) # f = [0, 1/(N*tau), ... ] " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Compute the transform using desired method: direct summation\n", + "# or fast Fourier transform (FFT) algorithm.\n", + "yt = np.zeros(N,dtype=complex)\n", + "Method = input('Compute transform by: 1) Direct summation; 2) FFT :')\n", + "\n", + "import time\n", + "startTime = time.time()\n", + "if Method == 1 : # Direct summation\n", + " twoPiN = -2. * np.pi * (1j) /N\n", + " for k in range(N):\n", + " for j in range(N):\n", + " expTerm = np.exp( twoPiN*j*k )\n", + " yt[k] += y[j] * expTerm\n", + "else: # Fast Fourier transform\n", + " yt = np.fft.fft(y)\n", + "\n", + "stopTime = time.time()\n", + "\n", + "print 'Elapsed time = ', stopTime - startTime, ' seconds'" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Graph the time series and its transform.\n", + "plt.plot(t,y)\n", + "plt.title('Original time series')\n", + "plt.xlabel('Time')\n", + "plt.ylabel('Amplitude') " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "plt.plot(f,np.real(yt),'-',f,np.imag(yt),'--')\n", + "plt.legend(['Real','Imaginary '])\n", + "plt.title('Fourier transform')\n", + "plt.xlabel('Frequency')\n", + "plt.ylabel('Transform')" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Compute and graph the power spectrum of the time series\n", + "powspec = np.empty(N)\n", + "for i in range(N):\n", + " powspec[i] = abs(yt[i])**2\n", + "plt.semilogy(f,powspec,'-')\n", + "plt.title('Power spectrum (unnormalized)')\n", + "plt.xlabel('Frequency')\n", + "plt.ylabel('Power')" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python [default]", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.12" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} diff --git a/Python/Interp.ipynb b/Python/Interp.ipynb new file mode 100644 index 0000000..0a08b64 --- /dev/null +++ b/Python/Interp.ipynb @@ -0,0 +1,132 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# interp - Program to interpolate data using Lagrange \n", + "# polynomial to fit quadratic to three data points\n", + "\n", + "# Set up configuration options and special features\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "%matplotlib inline" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def intrpf(xi,x,y):\n", + " # Function to interpolate between data points\n", + " # using Lagrange polynomial (quadratic)\n", + " # Inputs\n", + " # x Vector of x coordinates of data points (3 values)\n", + " # y Vector of y coordinates of data points (3 values)\n", + " # xi The x value where interpolation is computed\n", + " # Output\n", + " # yi The interpolation polynomial evaluated at xi\n", + "\n", + " #* Calculate yi = p(xi) using Lagrange polynomial\n", + " yi = ( (xi-x[1])*(xi-x[2])/((x[0]-x[1])*(x[0]-x[2])) * y[0] \n", + " + (xi-x[0])*(xi-x[2])/((x[1]-x[0])*(x[1]-x[2])) * y[1] \n", + " + (xi-x[0])*(xi-x[1])/((x[2]-x[0])*(x[2]-x[1])) * y[2] )\n", + " return yi" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Initialize the data points to be fit by quadratic\n", + "x = np.empty(3)\n", + "y = np.empty(3)\n", + "print 'Enter data points as x,y pairs (e.g., [1, 2])'\n", + "for i in range(3):\n", + " temp = np.array(input('Enter data point: '))\n", + " x[i] = temp[0]\n", + " y[i] = temp[1]" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Establish the range of interpolation (from x_min to x_max)\n", + "xr = np.array(input('Enter range of x values as [x_min, x_max]: '))" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Find yi for the desired interpolation values xi using\n", + "# the function intrpf\n", + "nplot = 100 # Number of points for interpolation curve\n", + "xi = np.empty(nplot)\n", + "yi = np.empty(nplot)\n", + "for i in range(nplot) :\n", + " xi[i] = xr[0] + (xr[1]-xr[0])* i/float(nplot)\n", + " yi[i] = intrpf(xi[i], x, y) # Use intrpf function to interpolate" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Plot the curve given by (xi,yi) and mark original data points\n", + "plt.plot(x,y,'*',xi,yi,'-')\n", + "plt.xlabel('x')\n", + "plt.ylabel('y')\n", + "plt.title('Three point interpolation')\n", + "plt.legend(['Data points','Interpolation '])" + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "kernelspec": { + "display_name": "Python [default]", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.12" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} diff --git a/Python/Legndr.ipynb b/Python/Legndr.ipynb new file mode 100644 index 0000000..cff317d --- /dev/null +++ b/Python/Legndr.ipynb @@ -0,0 +1,109 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# test_legndr - Program to test the legndr function\n", + "\n", + "# Set up configuration options and special features\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "%matplotlib inline" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def legndr(n,x) :\n", + " # Legendre polynomials function\n", + " # Inputs \n", + " # n = Highest order polynomial returned\n", + " # x = Value at which polynomial is evaluated\n", + " # Output\n", + " # p = Vector containing P(x) for order 0,1,...,n\n", + "\n", + " #* Perform upward recursion\n", + " p = np.empty(n+1)\n", + " p[0] = 1. # P(x) for n=0\n", + " if n == 0 :\n", + " return p\n", + " p[1] = x # P(x) for n=1\n", + " if n == 1 :\n", + " return p\n", + " \n", + " # Use upward recursion to obtain other n's\n", + " for i in range(1,n) :\n", + " p[i+1] = ((2*i+1)*x*p[i] - i*p[i-1])/(i+1)\n", + "\n", + " return p" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Enter x: -3\n", + "For n=0; Computed = 1.0 Expected = 1\n", + "For n=1; Computed = -3.0 Expected = -3\n", + "For n=2; Computed = 13.0 Expected = 13.0\n", + "For n=3; Computed = -63.0 Expected = -63.0\n", + "For n=4; Computed = 321.0 Expected = 321.0\n", + "For n=5; Computed = -1683.0 Expected = -1683.0\n" + ] + } + ], + "source": [ + "x = input(\"Enter x: \")\n", + "n = 5\n", + "\n", + "p = np.empty(n)\n", + "p = legndr(n,x)\n", + "\n", + "print \"For n=0; Computed = \", p[0], \" Expected = 1\"\n", + "print \"For n=1; Computed = \", p[1], \" Expected = \", x\n", + "print \"For n=2; Computed = \", p[2], \" Expected = \", 0.5*(3*x*x-1)\n", + "print \"For n=3; Computed = \", p[3], \" Expected = \", 0.5*(5*x*x*x-3*x)\n", + "print \"For n=4; Computed = \", p[4], \" Expected = \", 0.125*(35*x*x*x*x-30*x*x+3)\n", + "print \"For n=5; Computed = \", p[5], \" Expected = \", 0.125*(63*x*x*x*x*x-70*x*x*x+15*x) " + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python [default]", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.12" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} diff --git a/Python/Lorenz.ipynb b/Python/Lorenz.ipynb new file mode 100644 index 0000000..e77c34a --- /dev/null +++ b/Python/Lorenz.ipynb @@ -0,0 +1,272 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# lorenz - Program to compute the trajectories of the Lorenz \n", + "# equations using the adaptive Runge-Kutta method.\n", + "\n", + "# Set up configuration options and special features\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "%matplotlib inline" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def rk4(x,t,tau,derivsRK,param):\n", + " # Runge-Kutta integrator (4th order)\n", + " # Input arguments -\n", + " # x = current value of dependent variable\n", + " # t = independent variable (usually time)\n", + " # tau = step size (usually timestep)\n", + " # derivsRK = right hand side of the ODE; derivsRK is the\n", + " # name of the function which returns dx/dt\n", + " # Calling format derivsRK (x,t,param).\n", + " # param = extra parameters passed to derivsRK\n", + " # Output arguments -\n", + " # xout = new value of x after a step of size tau\n", + " \n", + " half_tau = 0.5*tau\n", + " F1 = derivsRK(x,t,param) \n", + " t_half = t + half_tau\n", + " xtemp = x + half_tau*F1\n", + " F2 = derivsRK(xtemp,t_half,param) \n", + " xtemp = x + half_tau*F2\n", + " F3 = derivsRK(xtemp,t_half,param)\n", + " t_full = t + tau\n", + " xtemp = x + tau*F3\n", + " F4 = derivsRK(xtemp,t_full,param)\n", + " xout = x + tau/6.*(F1 + F4 + 2.*(F2+F3))\n", + " return xout" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def rka(x,t,tau,err,derivsRK,param):\n", + " # Adaptive Runge-Kutta routine\n", + " # Inputs\n", + " # x Current value of the dependent variable\n", + " # t Independent variable (usually time)\n", + " # tau Step size (usually time step)\n", + " # err Desired fractional local truncation error\n", + " # derivsRK Right hand side of the ODE; derivsRK is the\n", + " # name of the function which returns dx/dt\n", + " # Calling format derivsRK (x,t,param).\n", + " # param Extra parameters passed to derivsRK\n", + " # Outputs\n", + " # xSmall New value of the dependent variable\n", + " # t New value of the independent variable\n", + " # tau Suggested step size for next call to rka\n", + "\n", + " #* Set initial variables\n", + " tSave, xSave = t, x # Save initial values\n", + " safe1, safe2 = 0.9, 4.0 # Safety factors\n", + " eps = 1.e-15\n", + "\n", + " #* Loop over maximum number of attempts to satisfy error bound\n", + " xTemp = np.empty(len(x))\n", + " xSmall = np.empty(len(x)); xBig = np.empty(len(x))\n", + " maxTry = 100\n", + " for iTry in range(maxTry):\n", + "\n", + " #* Take the two small time steps\n", + " half_tau = 0.5 * tau\n", + " xTemp = rk4(xSave,tSave,half_tau,derivsRK,param)\n", + " t = tSave + half_tau\n", + " xSmall = rk4(xTemp,t,half_tau,derivsRK,param)\n", + " \n", + " #* Take the single big time step\n", + " t = tSave + tau\n", + " xBig = rk4(xSave,tSave,tau,derivsRK,param)\n", + " \n", + " #* Compute the estimated truncation error\n", + " scale = err * (abs(xSmall) + abs(xBig))/2.\n", + " xDiff = xSmall - xBig\n", + " errorRatio = np.max( np.absolute(xDiff) / (scale + eps) )\n", + " \n", + " #* Estimate new tau value (including safety factors)\n", + " tau_old = tau\n", + " tau = safe1*tau_old*errorRatio**(-0.20)\n", + " tau = max(tau, tau_old/safe2)\n", + " tau = min(tau, safe2*tau_old)\n", + " \n", + " #* If error is acceptable, return computed values\n", + " if errorRatio < 1 :\n", + " return np.array([xSmall, t, tau]) \n", + "\n", + " #* Issue error message if error bound never satisfied\n", + " print 'ERROR: Adaptive Runge-Kutta routine failed'\n", + " return np.array([xSmall, t, tau])" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def lorzrk(s,t,param):\n", + " # Returns right-hand side of Lorenz model ODEs\n", + " # Inputs\n", + " # s State vector [x y z]\n", + " # t Time (not used)\n", + " # param Parameters [r sigma b]\n", + " # Output\n", + " # deriv Derivatives [dx/dt dy/dt dz/dt]\n", + "\n", + " #* For clarity, unravel input vectors\n", + " x, y, z = s[0], s[1], s[2]\n", + " r = param[0]\n", + " sigma = param[1]\n", + " b = param[2]\n", + "\n", + " #* Return the derivatives [dx/dt dy/dt dz/dt]\n", + " deriv = np.empty(3)\n", + " deriv[0] = sigma*(y-x)\n", + " deriv[1] = r*x - y - x*z\n", + " deriv[2] = x*y - b*z\n", + " return deriv" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Set initial state x,y,z and parameters r,sigma,b\n", + "state = np.array(input('Enter the initial position [x, y, z]: '))\n", + "r = input('Enter the parameter r: ')\n", + "sigma = 10. # Parameter sigma\n", + "b = 8./3. # Parameter b\n", + "param = np.array([r, sigma, b]) # Vector of parameters passed to rka\n", + "tau = 1. # Initial guess for the timestep\n", + "err = 1.e-3 # Error tolerance" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Loop over the desired number of steps\n", + "time = 0.\n", + "nstep = input('Enter number of steps: ')\n", + "tplot = np.empty(nstep)\n", + "tauplot = np.empty(nstep)\n", + "xplot, yplot, zplot = np.empty(nstep), np.empty(nstep), np.empty(nstep)\n", + "for istep in range(nstep):\n", + "\n", + " #* Record values for plotting\n", + " x, y, z = state[0], state[1], state[2]\n", + " tplot[istep] = time\n", + " tauplot[istep] = tau \n", + " xplot[istep] = x \n", + " yplot[istep] = y \n", + " zplot[istep] = z \n", + " if istep % 50 < 1 :\n", + " print 'Finished ',istep, ' steps out of ',nstep\n", + "\n", + " #* Find new state using adaptive Runge-Kutta\n", + " [state, time, tau] = rka(state,time,tau,err,lorzrk,param);" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Print max and min time step returned by rka\n", + "print 'Adaptive time step: Max = ', np.max(tauplot[2:nstep]), \n", + "' Min = ', np.min(tauplot[2:nstep])\n", + "\n", + "#* Graph the time series x(t)\n", + "plt.plot(tplot,xplot,'-')\n", + "plt.xlabel('Time')\n", + "plt.ylabel('x(t)')\n", + "plt.title('Lorenz model time series')" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Graph the x,y,z phase space trajectory\n", + "# Mark the location of the three steady states\n", + "x_ss = np.empty(3); y_ss = np.empty(3); z_ss = np.empty(3)\n", + "x_ss[0] = 0\n", + "y_ss[0] = 0\n", + "z_ss[0] = 0\n", + "x_ss[1] = np.sqrt(b*(r-1))\n", + "y_ss[1] = x_ss[1]\n", + "z_ss[1] = r-1\n", + "x_ss[2] = -np.sqrt(b*(r-1))\n", + "y_ss[2] = x_ss[2]\n", + "z_ss[2] = r-1\n", + "\n", + "from mpl_toolkits.mplot3d import Axes3D\n", + "fig = plt.figure()\n", + "ax = fig.gca(projection='3d')\n", + "ax.plot(xplot,yplot,zplot,'-')\n", + "ax.plot(x_ss,y_ss,z_ss,'*')\n", + "ax.set_xlabel('x')\n", + "ax.set_ylabel('y')\n", + "ax.set_zlabel('z')\n", + "ax.set_title('Lorenz model phase space')" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python [default]", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.12" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} diff --git a/Python/Lsfdemo.ipynb b/Python/Lsfdemo.ipynb new file mode 100644 index 0000000..b4fdca2 --- /dev/null +++ b/Python/Lsfdemo.ipynb @@ -0,0 +1,215 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# lsfdemo - Program for demonstrating least squares fit routines\n", + "\n", + "# Set up configuration options and special features\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "%matplotlib inline" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def linreg(x,y,sigma):\n", + " # Function to perform linear regression (fit a line)\n", + " # Inputs\n", + " # x Independent variable\n", + " # y Dependent variable\n", + " # sigma Estimated error in y\n", + " # Outputs\n", + " # a_fit Fit parameters; a(1) is intercept, a(2) is slope\n", + " # sig_a Estimated error in the parameters a()\n", + " # yy Curve fit to the data\n", + " # chisqr Chi squared statistic\n", + "\n", + " #* Evaluate various sigma sums\n", + " s = 0; sx = 0; sy = 0; sxy = 0; sxx = 0\n", + " for i in range(len(x)):\n", + " sigmaTerm = sigma[i]**(-2)\n", + " s += sigmaTerm \n", + " sx += x[i] * sigmaTerm\n", + " sy += y[i] * sigmaTerm\n", + " sxy += x[i] * y[i] * sigmaTerm\n", + " sxx += x[i]**2 * sigmaTerm\n", + " denom = s*sxx - sx**2\n", + "\n", + " #* Compute intercept a_fit(1) and slope a_fit(2)\n", + " a_fit = np.empty(2)\n", + " a_fit[0] = (sxx*sy - sx*sxy)/denom\n", + " a_fit[1] = (s*sxy - sx*sy)/denom\n", + "\n", + " #* Compute error bars for intercept and slope\n", + " sig_a = np.empty(2)\n", + " sig_a[0] = np.sqrt(sxx/denom)\n", + " sig_a[1] = np.sqrt(s/denom)\n", + "\n", + " #* Evaluate curve fit at each data point and compute Chi^2\n", + " yy = np.empty(len(x))\n", + " chisqr = 0.\n", + " for i in range(len(x)):\n", + " yy[i] = a_fit[0]+a_fit[1]*x[i] # Curve fit to the data\n", + " chisqr += ((y[i]-yy[i])/sigma[i])**2 # Chi square\n", + " return [a_fit, sig_a, yy, chisqr]" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def pollsf(x, y, sigma, M):\n", + " # Function to fit a polynomial to data\n", + " # Inputs \n", + " # x Independent variable\n", + " # y Dependent variable\n", + " # sigma Estimate error in y\n", + " # M Number of parameters used to fit data\n", + " # Outputs\n", + " # a_fit Fit parameters; a(1) is intercept, a(2) is slope\n", + " # sig_a Estimated error in the parameters a()\n", + " # yy Curve fit to the data\n", + " # chisqr Chi squared statistic\n", + "\n", + " #* Form the vector b and design matrix A \n", + " N = len(x)\n", + " b = np.empty(N)\n", + " A = np.empty((N,M))\n", + " for i in range(N):\n", + " b[i] = y[i]/sigma[i]\n", + " for j in range(M):\n", + " A[i,j] = x[i]**j / sigma[i] \n", + "\n", + " #* Compute the correlation matrix C \n", + " C = np.linalg.inv( np.dot( np.transpose(A), A) )\n", + "\n", + " #* Compute the least squares polynomial coefficients a_fit\n", + " a_fit = np.dot(C, np.dot( np.transpose(A), np.transpose(b)) )\n", + "\n", + " #* Compute the estimated error bars for the coefficients\n", + " sig_a = np.empty(M)\n", + " for j in range(M):\n", + " sig_a[j] = np.sqrt(C[j,j])\n", + "\n", + " #* Evaluate curve fit at each data point and compute Chi^2\n", + " yy = np.zeros(N)\n", + " chisqr = 0.\n", + " for i in range(N):\n", + " for j in range(M):\n", + " yy[i] += a_fit[j]*x[i]**j # yy is the curve fit\n", + " chisqr += ((y[i]-yy[i]) / sigma[i])**2\n", + " \n", + " return [a_fit, sig_a, yy, chisqr]" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Initialize data to be fit. Data is quadratic plus random number.\n", + "print 'Curve fit data is created using the quadratic'\n", + "print ' y(x) = c(0) + c(1)*x + c(2)*x**2'\n", + "c = np.array(input('Enter the coefficients as [c(0) c(1) c(2)]: '))\n", + "N = 50; # Number of data points\n", + "x = np.arange(1,N+1) # x = [1, 2, ..., N]\n", + "y = np.empty(N)\n", + "sigma = np.empty(N)\n", + "np.random.seed(0) # Initialize random number generator\n", + "alpha = input('Enter estimated error bar: ')\n", + "for i in range(N):\n", + " r = alpha * np.random.normal() # Gaussian distributed random vector\n", + " y[i] = c[0] + c[1]*x[i] + c[2]*x[i]**2 + r\n", + " sigma[i] = alpha # Constant error bar" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Fit the data to a straight line or a more general polynomial\n", + "M = input('Enter number of fit parameters (=2 for line): ')\n", + "if M == 2 : \n", + " #* Linear regression (Straight line) fit\n", + " [a_fit, sig_a, yy, chisqr] = linreg(x,y,sigma)\n", + "else: \n", + " #* Polynomial fit\n", + " [a_fit, sig_a, yy, chisqr] = pollsf(x,y,sigma,M)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Print out the fit parameters, including their error bars.\n", + "print 'Fit parameters:'\n", + "for i in range(M):\n", + " print ' a[', i, '] = ', a_fit[i], ' +/- ', sig_a[i]\n", + "\n", + "#* Graph the data, with error bars, and fitting function.\n", + "plt.errorbar(x,y,sigma,None,'o') # Graph data with error bars\n", + "plt.plot(x,yy,'-') # Plot the fit on same graph as data\n", + "plt.xlabel('x_i') \n", + "plt.ylabel('y_i and Y(x)') \n", + "plt.title([r\"\\chi^2 = \",chisqr,' N-M = ',N-M])" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python [default]", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.12" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} diff --git a/Python/Neutrn.ipynb b/Python/Neutrn.ipynb new file mode 100644 index 0000000..32480f0 --- /dev/null +++ b/Python/Neutrn.ipynb @@ -0,0 +1,154 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# neutrn - Program to solve the neutron diffusion equation \n", + "# using the Forward Time Centered Space (FTCS) scheme.\n", + "\n", + "# Set up configuration options and special features\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "%matplotlib inline" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Initialize parameters (time step, grid points, etc.).\n", + "tau = input('Enter time step: ')\n", + "N = input('Enter the number of grid points: ')\n", + "L = input('Enter system length: ')\n", + "# The system extends from x=-L/2 to x=L/2\n", + "h = L/float(N-1) # Grid size\n", + "D = 1. # Diffusion coefficient\n", + "C = 1. # Generation rate\n", + "coeff = D*tau/h**2\n", + "coeff2 = C*tau \n", + "if coeff < 0.5 :\n", + " print 'Solution is expected to be stable'\n", + "else:\n", + " print 'WARNING: Solution is expected to be unstable'" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Set initial and boundary conditions.\n", + "nn = np.zeros(N) # Initialize density to zero at all points\n", + "nn_new = np.zeros(N) # Initialize temporary array used by FTCS\n", + "nn[int(N/2.)] = 1/h # Initial cond. is delta function in center\n", + "## The boundary conditions are nn[0] = nn[N-1] = 0\n", + "\n", + "#* Set up loop and plot variables.\n", + "xplot = np.arange(N)*h - L/2. # Record the x scale for plots\n", + "iplot = 0 # Counter used to count plots\n", + "nstep = input('Enter number of time steps: ')\n", + "nplots = 50 # Number of snapshots (plots) to take\n", + "plot_step = nstep/nplots # Number of time steps between plots" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Loop over the desired number of time steps.\n", + "nnplot = np.empty((N,nplots))\n", + "tplot = np.empty(nplots)\n", + "nAve = np.empty(nplots)\n", + "for istep in range(nstep): ## MAIN LOOP ##\n", + "\n", + " #* Compute the new density using FTCS scheme.\n", + " nn[1:(N-1)] = ( nn[1:(N-1)] + \n", + " coeff*( nn[2:N] + nn[0:(N-2)] - 2*nn[1:(N-1)] ) +\n", + " coeff2*nn[1:(N-1)] )\n", + " \n", + " #* Periodically record the density for plotting.\n", + " if (istep+1) % plot_step < 1: # Every plot_step steps\n", + " nnplot[:,iplot] = np.copy(nn) # record nn[i] for plotting\n", + " tplot[iplot] = istep*tau # Record time for plots\n", + " nAve[iplot] = np.mean(nn) # Record average density \n", + " iplot += 1 \n", + " print 'Finished ', istep, ' of ', nstep, ' steps'" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Plot density versus x and t as a 3D-surface plot\n", + "from matplotlib import cm\n", + "from mpl_toolkits.mplot3d import Axes3D\n", + "\n", + "fig = plt.figure()\n", + "ax = fig.gca(projection = '3d')\n", + "Tp, Xp = np.meshgrid(tplot, xplot)\n", + "ax.plot_surface(Tp, Xp, nnplot, rstride=2, cstride=2, cmap=cm.gray)\n", + "ax.set_xlabel('Time')\n", + "ax.set_ylabel('x')\n", + "ax.set_zlabel('n(x,t)');\n", + "ax.set_title('Neutron diffusion');" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Plot average neutron density versus time\n", + "plt.plot(tplot,nAve,'*')\n", + "plt.xlabel('Time')\n", + "plt.ylabel('Average density')\n", + "plt.title(['L = ', L ,' (L_c = pi)'])" + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "kernelspec": { + "display_name": "Python [default]", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.12" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} diff --git a/Python/Newtn.ipynb b/Python/Newtn.ipynb new file mode 100644 index 0000000..302113b --- /dev/null +++ b/Python/Newtn.ipynb @@ -0,0 +1,141 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# newtn - Program to solve a system of nonlinear equations \n", + "# using Newton's method. Equations defined by function fnewt.\n", + "\n", + "# Set up configuration options and special features\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "%matplotlib inline" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def fnewt(x,a):\n", + " # Function used by the N-variable Newton's method\n", + " # Inputs\n", + " # x State vector [x y z]\n", + " # a Parameters [r sigma b]\n", + " # Outputs\n", + " # f Lorenz model r.h.s. [dx/dt dy/dt dz/dt]\n", + " # D Jacobian matrix, D(i,j) = df(j)/dx(i)\n", + "\n", + " # Evaluate f(i)\n", + " f = np.empty(3)\n", + " f[0] = a[1] * (x[1]-x[0])\n", + " f[1] = a[0]*x[0] -x[1] -x[0]*x[2]\n", + " f[2] = x[0]*x[1] -a[2]*x[2]\n", + "\n", + " # Evaluate D(i,j)\n", + " D = np.empty((3,3))\n", + " D[0,0] = -a[1] # df(0)/dx(0)\n", + " D[0,1] = a[0]-x[2] # df(1)/dx(0)\n", + " D[0,2] = x[1] # df(2)/dx(0)\n", + " D[1,0] = a[1] # df(0)/dx(1)\n", + " D[1,1] = -1 # df(1)/dx(1)\n", + " D[1,2] = x[0] # df(2)/dx(1)\n", + " D[2,0] = 0 # df(0)/dx(2)\n", + " D[2,1] = -x[0] # df(1)/dx(2)\n", + " D[2,2] = -a[2] # df(2)/dx(2)\n", + "\n", + " return [f, D]" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Set initial guess and parameters\n", + "x0 = np.array(input('Enter the initial guess (row vector): '))\n", + "x = np.copy(x0) # Copy initial guess\n", + "a = np.array(input('Enter the parameter a: '))" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Loop over desired number of steps \n", + "nStep = 10 # Number of iterations before stopping\n", + "xp = np.empty((len(x), nStep))\n", + "xp[:,0] = np.copy(x[:]) # Record initial guess for plotting\n", + "for iStep in range(nStep):\n", + "\n", + " #* Evaluate function f and its Jacobian matrix D\n", + " [f, D] = fnewt(x,a) # fnewt returns value of f and D\n", + " #* Find dx by Gaussian elimination; transpose D for column vectors\n", + " dx = np.linalg.solve( np.transpose(D), f) \n", + " #* Update the estimate for the root \n", + " x = x - dx # Newton iteration for new x\n", + " xp[:,iStep] = np.copy(x[:]) # Save current estimate for plotting" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Print the final estimate for the root\n", + "print 'After', nStep, ' iterations the root is'\n", + "print x\n", + "\n", + "# %* Plot the iterations from initial guess to final estimate\n", + "from mpl_toolkits.mplot3d import Axes3D\n", + "fig = plt.figure()\n", + "ax = fig.gca(projection='3d')\n", + "ax.plot(xp[0,:],xp[1,:],xp[2,:],'o-')\n", + "ax.plot([x[0]],[x[1]],[x[2]],'*')\n", + "ax.set_xlabel('x')\n", + "ax.set_ylabel('y')\n", + "ax.set_zlabel('z')\n", + "ax.set_title('Steady state of the Lorenz model')" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python [default]", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.12" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} diff --git a/Python/Orbit.ipynb b/Python/Orbit.ipynb new file mode 100644 index 0000000..85d812c --- /dev/null +++ b/Python/Orbit.ipynb @@ -0,0 +1,324 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# orbit - Program to compute the orbit of a comet.\n", + "\n", + "# Set up configuration options and special features\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "%matplotlib inline" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def gravrk(s,t,GM):\n", + " # Returns right-hand side of Kepler ODE; used by Runge-Kutta routines\n", + " # Inputs\n", + " # s State vector [r(1) r(2) v(1) v(2)]\n", + " # t Time (not used)\n", + " # GM Parameter G*M (gravitational const. * solar mass)\n", + " # Output\n", + " # deriv Derivatives [dr(1)/dt dr(2)/dt dv(1)/dt dv(2)/dt]\n", + "\n", + " #* Compute acceleration\n", + " r = np.array([s[0], s[1]]) # Unravel the vector s into position and velocity\n", + " v = np.array([s[2], s[3]])\n", + " accel = -GM*r/np.linalg.norm(r)**3 # Gravitational acceleration\n", + "\n", + " #* Return derivatives [dr(1)/dt dr(2)/dt dv(1)/dt dv(2)/dt]\n", + " deriv = np.array([v[0], v[1], accel[0], accel[1]])\n", + " return deriv" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def rk4(x,t,tau,derivsRK,param):\n", + " # Runge-Kutta integrator (4th order)\n", + " # Input arguments -\n", + " # x = current value of dependent variable\n", + " # t = independent variable (usually time)\n", + " # tau = step size (usually timestep)\n", + " # derivsRK = right hand side of the ODE; derivsRK is the\n", + " # name of the function which returns dx/dt\n", + " # Calling format derivsRK (x,t,param).\n", + " # param = extra parameters passed to derivsRK\n", + " # Output arguments -\n", + " # xout = new value of x after a step of size tau\n", + " \n", + " half_tau = 0.5*tau\n", + " F1 = derivsRK(x,t,param) \n", + " t_half = t + half_tau\n", + " xtemp = x + half_tau*F1\n", + " F2 = derivsRK(xtemp,t_half,param) \n", + " xtemp = x + half_tau*F2\n", + " F3 = derivsRK(xtemp,t_half,param)\n", + " t_full = t + tau\n", + " xtemp = x + tau*F3\n", + " F4 = derivsRK(xtemp,t_full,param)\n", + " xout = x + tau/6.*(F1 + F4 + 2.*(F2+F3))\n", + " return xout" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def rka(x,t,tau,err,derivsRK,param):\n", + " # Adaptive Runge-Kutta routine\n", + " # Inputs\n", + " # x Current value of the dependent variable\n", + " # t Independent variable (usually time)\n", + " # tau Step size (usually time step)\n", + " # err Desired fractional local truncation error\n", + " # derivsRK Right hand side of the ODE; derivsRK is the\n", + " # name of the function which returns dx/dt\n", + " # Calling format derivsRK (x,t,param).\n", + " # param Extra parameters passed to derivsRK\n", + " # Outputs\n", + " # xSmall New value of the dependent variable\n", + " # t New value of the independent variable\n", + " # tau Suggested step size for next call to rka\n", + "\n", + " #* Set initial variables\n", + " tSave, xSave = t, x # Save initial values\n", + " safe1, safe2 = 0.9, 4.0 # Safety factors\n", + " eps = 1.e-15\n", + "\n", + " #* Loop over maximum number of attempts to satisfy error bound\n", + " xTemp = np.empty(len(x))\n", + " xSmall = np.empty(len(x)); xBig = np.empty(len(x))\n", + " maxTry = 100\n", + " for iTry in range(maxTry):\n", + "\n", + " #* Take the two small time steps\n", + " half_tau = 0.5 * tau\n", + " xTemp = rk4(xSave,tSave,half_tau,derivsRK,param)\n", + " t = tSave + half_tau\n", + " xSmall = rk4(xTemp,t,half_tau,derivsRK,param)\n", + " \n", + " #* Take the single big time step\n", + " t = tSave + tau\n", + " xBig = rk4(xSave,tSave,tau,derivsRK,param)\n", + " \n", + " #* Compute the estimated truncation error\n", + " scale = err * (abs(xSmall) + abs(xBig))/2.\n", + " xDiff = xSmall - xBig\n", + " errorRatio = np.max( np.absolute(xDiff) / (scale + eps) )\n", + " \n", + " #* Estimate new tau value (including safety factors)\n", + " tau_old = tau\n", + " tau = safe1*tau_old*errorRatio**(-0.20)\n", + " tau = max(tau, tau_old/safe2)\n", + " tau = min(tau, safe2*tau_old)\n", + " \n", + " #* If error is acceptable, return computed values\n", + " if errorRatio < 1 :\n", + " return np.array([xSmall, t, tau]) \n", + "\n", + " #* Issue error message if error bound never satisfied\n", + " print 'ERROR: Adaptive Runge-Kutta routine failed'\n", + " return np.array([xSmall, t, tau])" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Enter initial radial distance (AU): 1\n", + "Enter initial tangential velocity (AU/yr): 1.57\n" + ] + } + ], + "source": [ + "#* Set initial position and velocity of the comet.\n", + "r0 = input('Enter initial radial distance (AU): ') \n", + "v0 = input('Enter initial tangential velocity (AU/yr): ')\n", + "r = np.array([r0, 0])\n", + "v = np.array([0, v0])\n", + "state = np.array([ r[0], r[1], v[0], v[1] ]) # Used by R-K routines\n", + "\n", + "#* Set physical parameters (mass, G*M)\n", + "GM = 4 * np.pi**2 # Grav. const. * Mass of Sun (au^3/yr^2)\n", + "mass = 1.0 # Mass of comet \n", + "adaptErr = 1.0e-3 # Error parameter used by adaptive Runge-Kutta\n", + "time = 0.0" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Enter number of steps: 40\n", + "Enter time step (yr): .1\n", + "Choose a numerical method: 1) Euler; 2) Euler-Cromer; 3) Runge-Kutta; 4) Adaptive R-K4\n" + ] + } + ], + "source": [ + "#* Loop over desired number of steps using specified\n", + "# numerical method.\n", + "nStep = input('Enter number of steps: ')\n", + "tau = input('Enter time step (yr): ')\n", + "NumericalMethod = input(\n", + " 'Choose a numerical method: 1) Euler; 2) Euler-Cromer; 3) Runge-Kutta; 4) Adaptive R-K')\n", + "rplot = np.empty(nStep) \n", + "thplot = np.empty(nStep)\n", + "tplot = np.empty(nStep)\n", + "kinetic = np.empty(nStep)\n", + "potential = np.empty(nStep)\n", + "\n", + "for iStep in range(nStep): \n", + "\n", + " #* Record position and energy for plotting.\n", + " rplot[iStep] = np.linalg.norm(r) # Record position for polar plot\n", + " thplot[iStep] = np.arctan2(r[1],r[0])\n", + " tplot[iStep] = time\n", + " kinetic[iStep] = .5*mass*np.linalg.norm(v)**2 # Record energies\n", + " potential[iStep] = - GM*mass/np.linalg.norm(r)\n", + " \n", + " #* Calculate new position and velocity using desired method.\n", + " if NumericalMethod == 1 :\n", + " accel = -GM*r/np.linalg.norm(r)**3 \n", + " r = r + tau*v # Euler step\n", + " v = v + tau*accel \n", + " time = time + tau \n", + " elif NumericalMethod == 2 :\n", + " accel = -GM*r/np.linalg.norm(r)**3 \n", + " v = v + tau*accel \n", + " r = r + tau*v # Euler-Cromer step\n", + " time = time + tau \n", + " elif NumericalMethod == 3 :\n", + " state = rk4(state,time,tau,gravrk,GM)\n", + " r = [state[0], state[1]] # 4th order Runge-Kutta\n", + " v = [state[2], state[3]]\n", + " time = time + tau \n", + " else : \n", + " [state, time, tau] = rka(state,time,tau,adaptErr,gravrk,GM);\n", + " r = [state[0], state[1]] # Adaptive Runge-Kutta\n", + " v = [state[2], state[3]]" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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Dd+3aRa1atbJbvYcOHULNmjVRpkwZu9UpkTiD6OhoBAQEoHz58natd/fu3WjS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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#* Graph the trajectory of the comet.\n", + "ax = plt.subplot(111, projection='polar') # Use polar plot for graphing orbit\n", + "ax.plot(thplot,rplot,'+') \n", + "ax.set_title('Distance (AU)') \n", + "ax.grid(True)" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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3zi3117kGeNXM/uic+yWyTykSP3btgk8+gb59IS0t2tFIvFq3fR3r8tYFLW+Z2JJ+7ftV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\nEhceHPFgtEMQEQlJXVp8kqnc0lOmLd4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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#* Graph the energy of the comet versus time.\n", + "totalE = kinetic + potential # Total energy\n", + "plt.plot(tplot,kinetic,'-.',tplot,potential,'--',tplot,totalE,'-')\n", + "plt.legend(['Kinetic','Potential','Total']);\n", + "plt.xlabel('Time (yr)')\n", + "plt.ylabel('Energy (M AU^2/yr^2)')" + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "kernelspec": { + "display_name": "Python [default]", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.12" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} diff --git a/Python/Orthog.ipynb b/Python/Orthog.ipynb new file mode 100644 index 0000000..0476b1c --- /dev/null +++ b/Python/Orthog.ipynb @@ -0,0 +1,84 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# orthog - Program to test if a pair of vectors \n", + "# is orthogonal. Assumes vectors are in 3D space\n", + "\n", + "# Set up configuration options and special features\n", + "import numpy as np" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Initialize the vectors a and b\n", + "a = np.array(input('Enter the first vector: '))\n", + "b = np.array(input('Enter the second vector: '))" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Evaluate the dot product as sum over products of elements\n", + "a_dot_b = 0\n", + "for i in range(3):\n", + " a_dot_b += a[i] * b[i]" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Print dot product and state whether vectors are orthogonal\n", + "if a_dot_b == 0:\n", + " print 'Vectors are orthogonal'\n", + "else:\n", + " print 'Vectors are NOT orthogonal'\n", + " print 'Dot product = ' , a_dot_b" + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "kernelspec": { + "display_name": "Python [default]", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.12" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} diff --git a/Python/Pendul.ipynb b/Python/Pendul.ipynb new file mode 100644 index 0000000..cb041b6 --- /dev/null +++ b/Python/Pendul.ipynb @@ -0,0 +1,134 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# pendul - Program to compute the motion of a simple pendulum\n", + "# using the Euler or Verlet method\n", + "\n", + "# Set up configuration options and special features\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "%matplotlib inline" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Select the numerical method to use: Euler or Verlet\n", + "NumericalMethod = input('Choose a numerical method (1: Euler; 2: Verlet): ')\n", + "\n", + "#* Set initial position and velocity of pendulum\n", + "theta0 = input('Enter initial angle (in degrees): ')\n", + "theta = theta0 * np.pi /180 # Convert angle to radians\n", + "omega = 0.0 # Set the initial velocity\n", + "\n", + "#* Set the physical constants and other variables\n", + "g_over_L = 1.0 # The constant g/L\n", + "time = 0.0 # Initial time\n", + "irev = 0 # Used to count number of reversals\n", + "tau = input('Enter time step: ')\n", + "\n", + "#* Take one backward step to start Verlet\n", + "accel = -g_over_L * np.sin(theta) # Gravitational acceleration\n", + "theta_old = theta - omega*tau + 0.5*accel*tau**2 " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Loop over desired number of steps with given time step\n", + "# and numerical method\n", + "nstep = input('Enter number of time steps: ')\n", + "t_plot = np.empty(nstep)\n", + "th_plot = np.empty(nstep)\n", + "period = np.empty(nstep)\n", + "for istep in range(nstep): \n", + "\n", + " #* Record angle and time for plotting\n", + " t_plot[istep] = time \n", + " th_plot[istep] = theta*180/np.pi # Convert angle to degrees\n", + " time = time + tau\n", + " \n", + " #* Compute new position and velocity using \n", + " # Euler or Verlet method\n", + " accel = -g_over_L * np.sin(theta) # Gravitational acceleration\n", + " if NumericalMethod == 1 :\n", + " theta_old = theta # Save previous angle\n", + " theta = theta + tau*omega # Euler method\n", + " omega = omega + tau*accel \n", + " else: \n", + " theta_new = 2*theta - theta_old + tau**2*accel\n", + " theta_old = theta # Verlet method\n", + " theta = theta_new \n", + " \n", + " #* Test if the pendulum has passed through theta = 0;\n", + " # if yes, use time to estimate period\n", + " if theta*theta_old < 0 : # Test position for sign change\n", + " print 'Turning point at time t = ',time\n", + " if irev == 0 : # If this is the first change,\n", + " time_old = time # just record the time\n", + " else:\n", + " period[irev-1] = 2*(time - time_old)\n", + " time_old = time\n", + " irev = irev + 1 # Increment the number of reversals" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# Estimate period of oscillation, including error bar\n", + "nPeriod = irev-1 # Number of times the period was measured\n", + "AvePeriod = np.mean(period[0:(nPeriod-1)])\n", + "ErrorBar = np.std(period[0:(nPeriod-1)])/np.sqrt(nPeriod)\n", + "print 'Average period = ', AvePeriod, ' +/- ', ErrorBar\n", + "\n", + "# Graph the oscillations as theta versus time\n", + "plt.plot(t_plot,th_plot,'+')\n", + "plt.xlabel('Time')\n", + "plt.ylabel(r'$\\theta$ (degrees)')" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python [default]", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.12" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} diff --git a/Python/Relax.ipynb b/Python/Relax.ipynb new file mode 100644 index 0000000..63e03c4 --- /dev/null +++ b/Python/Relax.ipynb @@ -0,0 +1,280 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# relax - Program to solve the Laplace equation using \n", + "# Jacobi, Gauss-Seidel and SOR methods on a square grid\n", + "\n", + "# Set up configuration options and special features\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "%matplotlib inline" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Choose numerical method, 1) Jacobi; 2) Gauss-Seidel; 3) SOR1\n", + "Enter number of grid points on a side: 50\n" + ] + } + ], + "source": [ + "#* Initialize parameters (system size, grid spacing, etc.)\n", + "method = input('Choose numerical method, 1) Jacobi; 2) Gauss-Seidel; 3) SOR')\n", + "N = input('Enter number of grid points on a side: ')\n", + "L = 1. # System size (length)\n", + "h = L/(N-1) # Grid spacing\n", + "x = np.arange(N)*h # x coordinate\n", + "y = np.arange(N)*h # y coordinate\n", + "\n", + "#* Select over-relaxation factor (SOR only)\n", + "if method == 3 :\n", + " omegaOpt = 2./(1.+np.sin(np.pi/N)) # Theoretical optimum\n", + " print 'Theoretical optimum omega = ', omegaOpt\n", + " omega = input('Enter desired omega: ')" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Potential at y=L equals 1.0\n", + "Potential is zero on all other boundaries\n" + ] + } + ], + "source": [ + "#* Set initial guess as first term in separation of variables soln.\n", + "phi0 = 1. # Potential at y=L\n", + "phi = np.empty((N,N))\n", + "for i in range(N) :\n", + " for j in range(N) :\n", + " phi[i,j] = phi0 * 4/(np.pi*np.sinh(np.pi)\n", + " ) * np.sin(np.pi*x[i]/L)*np.sinh(np.pi*y[j]/L)\n", + "\n", + "#* Set boundary conditions\n", + "phi[0,:] = 0.\n", + "phi[-1,:] = 0.\n", + "phi[:,0] = 0.\n", + "phi[:,-1] = phi0*np.ones(N) \n", + "print 'Potential at y=L equals ', phi0\n", + "print 'Potential is zero on all other boundaries'" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Desired fractional change = 0.0001\n", + "After 1 iterations, fractional change = 0.00319908232239\n", + "After 11 iterations, fractional change = 0.00101431842757\n", + "After 21 iterations, fractional change = 0.000676675910769\n", + "After 31 iterations, fractional change = 0.000518352216807\n", + "After 41 iterations, fractional change = 0.000421260894724\n", + "After 51 iterations, fractional change = 0.000354282266423\n", + "After 61 iterations, fractional change = 0.000304339085997\n", + "After 71 iterations, fractional change = 0.000265130738214\n", + "After 81 iterations, fractional change = 0.00023333363901\n", + "After 91 iterations, fractional change = 0.000206935591989\n", + "After 101 iterations, fractional change = 0.000184631365955\n", + "After 111 iterations, fractional change = 0.000165528254489\n", + "After 121 iterations, fractional change = 0.000148989702437\n", + "After 131 iterations, fractional change = 0.000134587783661\n", + "After 141 iterations, fractional change = 0.000121938312056\n", + "After 151 iterations, fractional change = 0.000110750286041\n", + "After 161 iterations, fractional change = 0.000100786804246\n", + "Desired accuracy achieved after 162 iterations\n", + "Breaking out of main loop\n" + ] + } + ], + "source": [ + "#* Loop until desired fractional change per iteration is obtained\n", + "#flops(0); # Reset the flops counter to zero;\n", + "newphi = np.copy(phi) # Copy of the solution (used only by Jacobi)\n", + "iterMax = N**2 # Set max to avoid excessively long runs\n", + "change = np.empty(iterMax)\n", + "changeDesired = 1.e-4 # Stop when the change is given fraction\n", + "print 'Desired fractional change = ', changeDesired\n", + "for iter in range(iterMax) :\n", + " changeSum = 0\n", + " \n", + " if method == 1 : ## Jacobi method ##\n", + " for i in range(1,N-1) : # Loop over interior points only\n", + " for j in range(1,N-1) : \n", + " newphi[i,j] = .25*( phi[i+1,j] + phi[i-1,j] + \n", + " phi[i,j-1] + phi[i,j+1] )\n", + " changeSum += abs( 1 - phi[i,j]/newphi[i,j] )\n", + " phi = np.copy(newphi) \n", + "\n", + " elif method == 2 : ## G-S method ##\n", + " for i in range(1,N-1) : # Loop over interior points only\n", + " for j in range(1,N-1) : \n", + " temp = .25*( phi[i+1,j] + phi[i-1,j] + \n", + " phi[i,j-1] + phi[i,j+1] )\n", + " changeSum += abs( 1 - phi[i,j]/temp )\n", + " phi[i,j] = temp\n", + "\n", + " else : ## SOR method ## \n", + " for i in range(1,N-1) : # Loop over interior points only\n", + " for j in range(1,N-1) : \n", + " temp = .25*omega*( phi[i+1,j] + phi[i-1,j] + \n", + " phi[i,j-1] + phi[i,j+1] ) + (1-omega)*phi[i,j]\n", + " \n", + " changeSum += abs( 1 - phi[i,j]/temp )\n", + " phi[i,j] = temp\n", + "\n", + " #* Check if fractional change is small enough to halt the iteration\n", + " change[iter] = changeSum/(N-2)**2\n", + " if iter % 10 < 1 :\n", + " print 'After ', iter+1, ' iterations, fractional change = ', change[iter]\n", + "\n", + " if change[iter] < changeDesired : \n", + " print 'Desired accuracy achieved after ', iter+1, ' iterations' \n", + " print 'Breaking out of main loop'\n", + " break" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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+otjbGcIkNLaFrvaJhwoMbLa1xUOVeDEEiS4sAM/nokJ0QY15+mFDwBTKvmVl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\nziyxIZeseA2AYsU0qlaVrrQnn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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#* Plot final estimate of potential as a contour plot\n", + "from matplotlib import cm\n", + "from mpl_toolkits.mplot3d import Axes3D\n", + "\n", + "levels = np.linspace(0., 1., num=11) \n", + "ct = plt.contour(x, y, np.flipud(np.rot90(phi)), levels) \n", + "plt.clabel(ct, fmt='%1.2f') \n", + "plt.xlabel('x')\n", + "plt.ylabel('y')\n", + "plt.title('Potential after %g iterations' % iter)\n" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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VahU55H+IP8oh/9O8iKgdHByeErXcC/8sUcsf82VELSJqAQghC14BsojT09NJSkpS+oXl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\nYMyYMZg8eTI2btyIvXv34m9/+xs6dOiAESNGNIDENwa6d++OixcvonXr1g7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F9yEjI4N2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\nRK5CYII=\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#* Plot final estimate of potential as contour and surface plots\n", + "\n", + "fig = plt.figure()\n", + "ax = fig.gca(projection = '3d')\n", + "Xp, Yp = np.meshgrid(x, y)\n", + "ax.plot_surface(Xp, Yp, np.flipud(np.rot90(phi)), rstride=1, cstride=1, cmap=cm.gray)\n", + "ax.view_init(elev=30., azim=210.)\n", + "ax.set_xlabel('x')\n", + "ax.set_ylabel('y')\n", + "ax.set_zlabel('Phi(x,y)')" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python [default]", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.12" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} diff --git a/Python/Rk4.ipynb b/Python/Rk4.ipynb new file mode 100644 index 0000000..79397fa --- /dev/null +++ b/Python/Rk4.ipynb @@ -0,0 +1,60 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def rk4(x,t,tau,derivsRK,param):\n", + " # Runge-Kutta integrator (4th order)\n", + " # Input arguments -\n", + " # x = current value of dependent variable\n", + " # t = independent variable (usually time)\n", + " # tau = step size (usually timestep)\n", + " # derivsRK = right hand side of the ODE; derivsRK is the\n", + " # name of the function which returns dx/dt\n", + " # Calling format derivsRK (x,t,param).\n", + " # param = extra parameters passed to derivsRK\n", + " # Output arguments -\n", + " # xout = new value of x after a step of size tau\n", + " \n", + " half_tau = 0.5*tau\n", + " F1 = derivsRK(x,t,param) \n", + " t_half = t + half_tau\n", + " xtemp = x + half_tau*F1\n", + " F2 = derivsRK(xtemp,t_half,param) \n", + " xtemp = x + half_tau*F2\n", + " F3 = derivsRK(xtemp,t_half,param)\n", + " t_full = t + tau\n", + " xtemp = x + tau*F3\n", + " F4 = derivsRK(xtemp,t_full,param)\n", + " xout = x + tau/6.*(F1 + F4 + 2.*(F2+F3))\n", + " return xout" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python [default]", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.12" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} diff --git a/Python/Rombf.ipynb b/Python/Rombf.ipynb new file mode 100644 index 0000000..2412310 --- /dev/null +++ b/Python/Rombf.ipynb @@ -0,0 +1,155 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# Program to test the bess function\n", + "\n", + "# Set up configuration options and special features\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "%matplotlib inline" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def rombf(a,b,N,func,param) :\n", + " # Function to compute integrals by Romberg algorithm\n", + " # R = rombf(a,b,N,func,param)\n", + " # Inputs\n", + " # a,b Lower and upper bound of the integral\n", + " # N Romberg table is N by N\n", + " # func Name of integrand function in a string such as\n", + " # func='errintg'. The calling sequence is func(x,param)\n", + " # param Set of parameters to be passed to function\n", + " # Output \n", + " # R Romberg table; Entry R(N,N) is best estimate of\n", + " # the value of the integral\n", + "\n", + " #* Compute the first term R(1,1)\n", + " h = b - a # This is the coarsest panel size\n", + " npanels = 1 # Current number of panels\n", + " R = np.zeros((N+1,N+1))\n", + " R[1,1] = h/2. * (func(a,param) + func(b,param))\n", + "\n", + " #* Loop over the desired number of rows, i = 2,...,N\n", + " for i in range(2,N+1) :\n", + "\n", + " #* Compute the summation in the recursive trapezoidal rule\n", + " h = h/2. # Use panels half the previous size\n", + " npanels *= 2 # Use twice as many panels\n", + " sumT = 0.\n", + " # This for loop goes k=1,3,5,...,npanels-1\n", + " for k in range(1,npanels,2) : \n", + " sumT += func(a + k*h, param)\n", + " \n", + " #* Compute Romberg table entries R(i,1), R(i,2), ..., R(i,i)\n", + " R[i,1] = 0.5 * R[i-1,1] + h * sumT \n", + " m = 1\n", + " for j in range(2,i+1) :\n", + " m *= 4\n", + " R[i,j] = R[i,j-1] + ( R[i,j-1] - R[i-1,j-1] )/(m-1)\n", + "\n", + " return R" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def errintg(x,param) :\n", + " # Error function integrand\n", + " # Inputs\n", + " # x Value where integrand is evaluated\n", + " # param Parameter list (not used)\n", + " # Output\n", + " # f Integrand of the error function\n", + " \n", + " f = np.exp(-x**2)\n", + " return f" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Error function estimate from rombf routine:\n", + "0.771743332258\n", + "0.825262955597 0.843102830043\n", + "0.838367777441 0.842736051389 0.842711599479\n", + "Expected value = 0.842701\n" + ] + } + ], + "source": [ + "N = 3\n", + "a = 0\n", + "b = 1\n", + "R = np.empty((N+1,N+1))\n", + "param = None\n", + "\n", + "R = rombf(a,b,N,errintg,param)\n", + "\n", + "print \"Error function estimate from rombf routine:\" \n", + "for i in range(1,N+1) :\n", + " for j in range(1,i+1) :\n", + " print 2./np.sqrt(np.pi) * R[i,j],\n", + " print\n", + "print \"Expected value = 0.842701\"\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python [default]", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.12" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} diff --git a/Python/Schro.ipynb b/Python/Schro.ipynb new file mode 100644 index 0000000..d2e4c1b --- /dev/null +++ b/Python/Schro.ipynb @@ -0,0 +1,441 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# schro - Program to solve the Schrodinger equation \n", + "# for a free particle using the Crank-Nicolson scheme\n", + "\n", + "# Set up configuration options and special features\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "%matplotlib inline" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Enter number of grid points: 500\n", + "Enter time step: 1.\n" + ] + } + ], + "source": [ + "#* Initialize parameters (grid spacing, time step, etc.)\n", + "i_imag = 1j # Imaginary i\n", + "N = input('Enter number of grid points: ');\n", + "L = 100. # System extends from -L/2 to L/2\n", + "h = L/(N-1) # Grid size\n", + "x = np.arange(N)*h - L/2. # Coordinates of grid points\n", + "h_bar = 1. # Natural units\n", + "mass = 1. # Natural units\n", + "tau = input('Enter time step: ')" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Set up the Hamiltonian operator matrix\n", + "ham = np.zeros((N,N)) # Set all elements to zero\n", + "coeff = -h_bar**2/(2*mass*h**2)\n", + "for i in range(1,N-1) :\n", + " ham[i,i-1] = coeff\n", + " ham[i,i] = -2*coeff # Set interior rows\n", + " ham[i,i+1] = coeff\n", + "\n", + "# First and last rows for periodic boundary conditions\n", + "ham[0,-1] = coeff; ham[0,0] = -2*coeff; ham[0,1] = coeff\n", + "ham[-1,-2] = coeff; ham[-1,-1] = -2*coeff; ham[-1,0] = coeff\n", + "\n", + "#* Compute the Crank-Nicolson matrix\n", + "dCN = np.dot( np.linalg.inv(np.identity(N) + .5*i_imag*tau/h_bar*ham), \n", + " (np.identity(N) - .5*i_imag*tau/h_bar*ham) )" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Initialize the wavefunction \n", + "x0 = 0. # Location of the center of the wavepacket\n", + "velocity = 0.5 # Average velocity of the packet\n", + "k0 = mass*velocity/h_bar; # Average wavenumber\n", + "sigma0 = L/10. # Standard deviation of the wavefunction\n", + "Norm_psi = 1/(np.sqrt(sigma0*np.sqrt(np.pi))) # Normalization\n", + "psi = np.empty(N,dtype=complex)\n", + "for i in range(N) :\n", + " psi[i] = Norm_psi * np.exp(i_imag*k0*x[i]) * np.exp(-(x[i]-x0)**2/(2*sigma0**2))" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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2VpQTQjQ6yagIIdz6fu/3DGo3yO2xU1qfwop9KwJ2b2egYjWjUn6snN/1+h09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\n4qX1L9G2r+3A/eta1rGmeQ0LqxVURHJJmxKKSMYmT4aCAvj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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#* Plot the initial wavefunction\n", + "plt.plot(x,np.real(psi),'-',x,np.imag(psi),'--')\n", + "plt.xlabel('x'); plt.ylabel('psi(x)')\n", + "plt.legend(('Real ','Imag '))\n", + "plt.title('Initial wave function')" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Initialize loop and plot variables \n", + "max_iter = int(L/(velocity*tau)+.5) # Particle should circle system\n", + "plot_iter = max_iter/20 # Produce 20 curves\n", + "p_plot = np.empty((N,max_iter+1)) # Note that P(x,t) is real\n", + "p_plot[:,0] = np.absolute(psi[:])**2 # Record initial condition\n", + "iplot = 0\n", + "axisV = [-L/2., L/2., 0., max(p_plot[:,0])] # Fix axis min and max" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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WKSdKPEQkduU2Y2mmqiqYOTOszCtS6pR4iEjsynVES0pVFaxaBW+8EXckIm1P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\nStyRiDRPiYeIbJbJk2H33UN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lThQ8RKRk1dTAfvtBu3ahKwmrosIvoqal0yUOFDxEpGSV+8DShIoKWL0aFi8O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\nrxz70kuhK5FSoOAhIrH00kt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meUjrKHiIiGRh+XJ4553KDh4dO8K++yp4SOsoeIiIZCExvFDJwQPC61fwkNZQ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\nU6ZoIbFKoeAhIhVn6lTYdVf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t2zbuSOLVq1f4qeGW4qLEQ0QkYVTfEbRuDV27KvEoNko8REQSZMOGsHBWqdd3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\nxCNpDjkEysth5cq4IxFQ4iE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mhabEQ0SkQsyYoWaWTFqptvCUeIiIVIBFi2DePNhvv9iRFJchQ8JicUuWxI6k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\nOc7jybbzgX+6+1XJ458licn3gXPzcxo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1KfEQEZFmqamB1q2hT5+4Iyks7dvDrrsq8UilxENERJqlpgZ23z0kH7KuRD8P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\namYpLkOHwnvvwdtvxx1J8yj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h6d0bvvkGXn457kjqp2ASDzM738xmm9lyM5tiZnvVUb6nmVWb2bdmNt3MBqbc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\nwUsvhf4dUnwOOADatg3JYy4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UXgDg7h49Rrc0h3WN7k82pprymNl+UawvZRKXiIiULg2jrVm+htXWpsZjF2Av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\nUQeNGkF5OTz2GCxbFnc0IiL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IbHIm8TCzs8zsUzNbaGYTzKx7LeX3NrNKM1tkZtPM7IS0+08ws+Vmtiz6u9zMFjTtsxAR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\n3F6+PHyITpoUOqm+9x48/nhoe66y2mr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C6t+/P02bNl1lX0lJCSW1XKe12WZh5rmHH4bjj6/VhxIRkTw1dixMn55sM0tp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\nKfz008ptzpzwd/Zs+P778H5O/Z0+Pdy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WW7DffvDii3DYYZXfb8KECZSUlACUuPuETOWq2qulkZk1BgxYP3pcujQBjgTm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\ne8LDD8O33yYdjYhIfhowALb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uhLk4KsTdJ0S1JYMJTSbTgePdfXFUpAWwfUr5eWZ2EnAb0I8wlPc8d08d6dIQ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\nkk3/OX9+WIa8Tp2SyxR3ojUreavqMff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d+JJw/vnQrFnDW8W1XTs444yQePTqBRtumHREIiKSS9VqajGzPxNqO54HjgB+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\nyp6vyTZzJtxzT+Xlli8PP5PqbIsXh+S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TpjCzDkBpaWlpbW/YIyIiEquysjKKiooAity9LFM51XiIiIhIbJR4iIiISGyUeIiIiEhs\nlHiIiIhIbJR4iIiISGyUeIiIiEhslHiIiIhIbJR4iIiISGyUeIiIiEhslHiIiIhIbJR4iIiISGyU\neIiIiEhslHiIiIhIbJR4iIiISGyUeIiIiEhslHiIiIhIbJR4iIiISGyUeIiIiEhslHiIiIhIbJR4\niIiISGyUeIiIiEhs8ibxMLMeZjbdzJaY2SQz22MN5TuZWamZLTWzz8zstLTnTzOzFWa2PPq5wsx+\nqtmjEBERkcrkReJhZicANwEDgN2AD4BxZtY8Q/nWwFjgRaAdcAtwt5l1Tiu6AGiZsrSqgfBFRESk\nivIi8QB6A3e6+wPuPhk4F/gJODND+fOAae7e192nuPsI4PFoP6nc3ee4+3fRMqfGjkBERETWKPHE\nw8waAEWE2gsgZAvABKBjhs32jp5PNa6C8o3NbIaZzTSzp81s5xyFLSIiIllIPPEAmgP1gNlp62cT\nbo9UpGWG8k3NrGH0eAqhxuSPwMmEY33DzDbPRdAiIiJSffWTDqCmuPskYFL5YzN7E/gU6EZoSyIi\nIiIxy4fEYy6wHGiRtr4FMCvDNrMylF/o7ssq2sDdfzWz94Bt1xRQ7969adas2SrriouLKS4uXtOm\nIiIiBa+kpISSkpJV1i1YsKBK21poTpEsM5sEvOXuvaLHBswEbnX3oRWUHwx0dfd2KeseBjZ098My\nvMY6wCfAc+5+cYYyHYDS0tJSOnTosLaHJSIiUmeUlZVRVFQEUOTuZZnK5UMbD4BhwDlmdqqZ7QiM\nBBoBowHM7Hozuz+l/EhgazMbYmY7mFl34LhoP0Tb9DezzmbWxsx2A8YAWwF3x3NIIiIiki4fbrXg\n7o9FY3YMItwyeR/oktL9tSWwZUr5GWZ2ODAc6Al8BZzl7qk9XTYC7oq2nQ+UAh2j7roiIiKSgLxI\nPADc/Xbg9gzPnVHBuomEbriZ9tcH6JOzAEVERGSt5cutFhEREakDlHiIiIhIbJR4iIiISGyUeIiI\niEhslHiIiIhIbJR4iIiISGyUeIiIiEhslHiIiIhIbJR4iIiISGyUeIiIiEhslHiIiIhIbJR4iIiI\nSGyUeIiIiEhslHiIiIhIbJR4iIiISGyUeIiIiEhslHiIiIhIbJR4iIiISGyUeIiIiEhslHiIiIhI\nbJR4iIiISGyUeIiIiEhslHiIiIhIbJR4iIiISGyUeIiIiEhslHiIiIhIbJR4iIiISGyUeIiIiEhs\nlHiIiIhIbJR4iIiISGyUeIiIiEhslHiIiIhIbJR4iIiISGyUeIiIiEhslHiIiIhIbJR4iIiISGyU\neIiIiEhslHiIiIhIbJR4iIiISGyUeIiIiEhslHiIiIhIbJR4iIiISGyUeIiIiEhslHiIiIhIbPIm\n8TCzHmY23cyWmNkkM9tjDeU7mVmpmS01s8/M7LRKyp5oZivM7MncRy4iIiJVlReJh5mdANwEDAB2\nAz4AxplZ8wzlWwNjgReBdsAtwN1m1jlD2aHAxNxHLiIiItWRF4kH0Bu4090fcPfJwLnAT8CZGcqf\nB0xz977uPsXdRwCPR/v5HzNbB3gI+BswvcaiFxERkSpJPPEwswZAEaH2AgB3d2AC0DHDZntHz6ca\nV0H5AcBsd78vN9GKiIjI2qifdABAc6AeMDtt/WxghwzbtMxQvqmZNXT3ZWa2L3AG4VaMiIiI5IHE\nazxqgpk1Bh4AznH3+UnHIyIiIkE+1HjMBZYDLdLWtwBmZdhmVobyC6Pajh2BVsCzZmbR8+sAmNnP\nwA7unrHNR+/evWnWrNkq64qLiykuLq7C4YiIiBS2kpISSkpKVlm3YMGCKm1roTlFssxsEvCWu/eK\nHhswE7jV3YdWUH4w0NXd26WsexjY0N0PM7OGwDZpm10LNAZ6AlPd/dcK9tsBKC0tLaVDhw45OjoR\nEZHCV1ZWRlFREUCRu5dlKpcPNR4Aw4DRZlYKvE3ondIIGA1gZtcDm7t7+VgdI4EeZjYEuBc4CDgO\nOAzA3ZcB/0l9ATP7ITzln9b40YiIiEiF8iLxcPfHojE7BhFumbwPdHH3OVGRlsCWKeVnmNnhwHBC\nDcZXwFnunt7TRURERPJIXiQeAO5+O3B7hufOqGDdREI33Kruf7V9iIiISLwKsleLiIiI5CclHiIi\nIhIbJR4iIiISGyUeIiIiEhslHiIiIhIbJR4iIiISGyUeIiIiEhslHiIiIhIbJR4iIiISGyUeIiIi\nEhslHiIiIhIbJR4iIiISGyUeIiIiEhslHiIiIhIbJR4iIiISGyUeIiIiEhslHiIiIhIbJR4iIiIS\nGyUeIiIiEhslHiIiIhIbJR4iIiISGyUeIiIiEhslHiIiIhIbJR4iIiISGyUeIiIiEhslHiIiIhIb\nJR4iIiISGyUeIiIiEhslHiIiIhIbJR4iIiISm/pJByCF75df4JNP4OOP4auvYOFCWGcdaNoUWrWC\nnXcOS716SUcqIiI1TYmH1IilS+Hpp+GRR+Cll2DRorB+442hWTNYsQIWLIAffli5vnNnOPlk6NoV\n6uudKSJSkHSrRXJq/nwYOBA23xyKi+G77+DSS+H110OSMW8eTJsGM2aEsvPmwSuvwPnnw5Qp8Mc/\nwlZbwbBhsHhxwgcjIiI5p8RDcuLXX+Hmm6F1a7jhBjj11JBIvPEGXHEF/P73oaYj3cYbwx/+AFdd\nBe+9F5auXUOyss028MADoXZEREQKgxIPWWsffABFRdCnT7hVMn16SEK23776+2rfHu65B6ZOhU6d\n4LTT4IADQg2JiIjUfko8JGvuIcHYc8/w+zvvwO23Q4sWa7/v1q1D+5AJE+C//4W2bcNjERGp3ZR4\nSFaWLoXTT4fevaFHj5B0FBXl/nUOOijUqBx5ZGgz0q+fbr2IiNRm6jsg1TZ7Nhx9NJSVwZgxcNJJ\nNft6zZrBQw/BbrtB376ha+5DD0GTJjX7uiIiknuq8ZBqmTkzNBSdPh0mTqz5pKOcGVx8MTz7LLz8\nMnTpErrjiohI7aLEQ6ps+vTQA2X5cnjzzdC2I26HHx7GBZk8GQ4+GL7/Pv4YREQke0o8pEq++AL2\n3z8M7DVxYmj8mZTddw/Jx4wZoQ2Ikg8RkdpDiYes0ezZcMgh0KgRvPoqbLll0hGFbrcvvxyGYD/y\nSFiyJOmIRESkKpR4SKUWLYLDDgsX9vHjw4ik+eJ3v4PnnoP334cTTwyDmImISH5T4iEZ/fwzHHMM\nfP45/PvfYUK3fLPnnvD44yEB6dEjjCciIiL5K28SDzPrYWbTzWyJmU0ysz3WUL6TmZWa2VIz+8zM\nTkt7/mgze8fM5pvZj2b2npmdUrNHUVguvDDcWnnmmTCAV77q2hVGjYK77oLbbks6GhERqUzWiYeZ\nNTCzLc1sBzPbeG2CMLMTgJuAAcBuwAfAODNrnqF8a2As8CLQDrgFuNvMOqcUmwdcA+wN7ArcB9yX\nVkYyGDUK7rgjjETaqVPS0azZGWeEIdv79AmTzomISH6qVuJhZk3M7DwzexVYCMwAPgXmmNl/zWzU\nmmoqMugN3OnuD7j7ZOBc4CfgzAzlzwOmuXtfd5/i7iOAx6P9AODuE939mej56e5+K/AhsG8W8dUp\nb7wRblucdx6cfXbS0VTdkCEhSfrzn8Mw6yIikn+qnHiYWR9ConEGMAH4E9Ae2B7oCFxFGAl1vJn9\n28y2q+J+GwBFhNoLANzdo9fomGGzvaPnU42rpDxmdlAU66tViauumj0bjj0W9t47zMNSm9SvD48+\nCo0bh7Ypy5YlHZGIiKSrzpDpewD7u/snGZ5/G7jXzM4DTgf2A6ZWYb/NgXrA7LT1s4EdMmzTMkP5\npmbW0N2XAZhZU+BroCHwK9Dd3V+qQkx10ooVYTp7d3jsMVh33aQjqr5NNoEnngiJ02WXwfDhSUck\nIiKpqpx4uHtxFcstBUZmHVFuLSK0AWkMHAQMN7Np7j4x2bDy0403hi6z48dDy5ZJR5O9Dh3ghhvC\nBHYHHxxGOxURkfyQ1SRxZnYv0MvdF6Wt3wC4zd0ztc2oyFxgOZA+mXoLYFaGbWZlKL+wvLYD/nfL\nZlr08EMz2xm4HKg08ejduzfNmjVbZV1xcTHFxVXKvWqlSZPgiitCLUHnAmh+26sXvPhimEH3gw/y\na/wREZHarqSkhJKSklXWLajiBFrmWQx8YGbLgc3c/bu09c2BWe5erYTGzCYBb7l7r+ixATOBW919\naAXlBwNd3b1dyrqHgQ3d/bBKXuceoI27H5jh+Q5AaWlpKR06dKjOIdRqP/4Yusu2aBGGQ2/QIOmI\ncmPuXGjXDnbZBcaNCxPNiYhIzSgrK6OoqAigyN3LMpWrbq+WpmbWDDCgSfS4fNkIOAz4rvK9VGgY\ncI6ZnWpmOxJu1TQCRkeve72Z3Z9SfiSwtZkNibrzdgeOi/ZTHutlZnawmbUxsx3N7CLgFODBLOIr\naJdeGhqVPvRQ4SQdAM2bw733wgsvhDE+REQkedW91fID4NHyWQXPO2Esjmpx98ei2pJBhFsm7wNd\n3H1OVKQlsGVK+RlmdjgwHOgJfAWc5e6pPV02AEYAWwBLgMnAye7+eHXjK2QvvhjG6rjtNthmm6Sj\nyb0uXeCvf4WLLgrzzbRpk3REIiJ1W7VutZjZHwi1HS8BxwKp84L+DPzX3b/JaYQxqmu3WhYtgl13\nDRfjF1+EdfJmHNvcKj/O1q3DrLaFepwiIkmq6q2WatV4uPurAGbWBpjp2TQQkbxxySWhHcTLLxf2\nxbhJE7jvPjjwQBg5Erp3TzoiEZG6K6vLjbv/N1PSYWZbmVm9tQtLatqECXDnnTB0aN24/XDAAdCt\nG1x+OXxTa+vkRERqv5r4njsD+I+ZHVMD+5YcWLIkXITLL8Z1xfXXw3rrhcnvREQkGTWReBwADAZO\nqIF9Sw5cdx189VWYBK6Qb7Gk22ijMAz8P/4Bzz2XdDQiInVTzi877v6qu9/n7ko88tDkyWEytcsu\ngx0yDUhfwE48MfRu6dEDFi9OOhoRkbonq8QjGmsj03Ndsg9HapJ7mHF2q61CW4e6yCx0H549G666\nKuloRETqnmxrPMrMrEfqCjNraGZ/B55Z+7CkJowZA6+8Ei68662XdDTJ2WYb+NvfYNgw+PjjpKMR\nEalbsk08TgcGmdm/zKyFmbUH3gMOJsxKK3lm/nzo02flrYa67qKLQgLSq1eoCRIRkXhk2532McKs\nrw2AT4A3gVeBDu7+Tu7Ck1wZOBCWLg3f8gXWXReGDw8Dij31VNLRiIjUHWvbuHRdoF60fAssXeuI\nJOf+8x8YMQL694fNNks6mvxx2GFhueiikJSJiEjNy7Zx6YnAR8ACYHvgcOCvwGtmtnXuwpO15R7G\nrWjdGnr2TDqa/DNsWOhafNNNSUciIlI3ZFvjcQ/Qz93/6O5z3P0FYFfga8IEb5Inxo4Ns7MOGwYN\nGyYdTf7ZYYfQzqN8bBMREalZ2SYeHdz9jtQV7j7f3Y8HemTYRmK2bFloUNq5Mxx5ZNLR5K/+/aFx\nY7j00qQjEREpfNk2Lp1SyXMPZh+O5NJtt8H06aERpVnS0eSvZs3g2mvh4Yfh3XeTjkZEpLBVOfEw\ns8vMbP0qlt3LzA7PPixZW3PmwKBBYcCwXXZJOpr8d/rp4Txdcom614qI1KTq1HjsDMw0s9vNrKuZ\n/ab8CTOrb2Ztzay7mb0BPAosynWwUnVXXx3mYRk4MOlIaof69cNQ8q+8As8/n3Q0IiKFq8qJh7uf\nShggrAHwMDDLzH42s0XAMsIAYmcCDwA7uvvEGohXquDzz8MEcJdfDptsknQ0tcdhh0GnTtC3Lyxf\nnnQ0IiKFqX51Crv7B8A5ZtYNaAu0AtYH5gLvu/vc3Ico1dWvH7Rsqe6z1WUGN9wAe+4J998PZ56Z\ndEQiIoWnWo1LzWwdM+sLvAaMAjoCz7j7BCUd+eGtt8K071dfDetXqUWOpNpjjzCsfP/+8NNPSUcj\nIlJ4qtur5QrgOkL7ja+BXsCIXAcl2XEPtwl23RX+8peko6m9rr02NM69+eakIxERKTzVTTxOBbq7\n+6Hu/ifgSOBkM1vbodclB8aOhYkTQyPJevWSjqb22npr6NEDBg8OCYiIiOROdROGrYD/tfl39wmA\nA5vnMiiLk5+OAAAgAElEQVSpvl9/hcsugwMOgEMPTTqa2u/KK0OvoGuuSToSEZHCUt3Eoz6rTwT3\nC6GniyRo9OgwGdwNN2iwsFzYZBO4+GIYORJmzkw6GhGRwlGtXi2AAaPNbFnKuvWAkWa2uHyFux+T\ni+CkapYuhauughNOgN13TzqawtGrF9xyS2ioO2pU0tGIiBSG6tZ43A98R5iVtnx5CPgmbZ3E6O67\n4ZtvQvIhudOkSRgL5b77YOrUpKMRESkM1R3H44yaCkSys2RJmFn1lFPCTKuSW+edBzfdFEaAHTMm\n6WhERGo/9Uap5UaOhO++C+NOSO6tv344tyUl8PHHSUcjIlL7KfGoxRYvDl0+Tz8dtt026WgK15ln\nQuvWSu5ERHJBiUctNmIEzJ8fun5KzVl33XCr5emn4Z13ko5GRKR2U+JRSy1aFLrOnnVW+DYuNevk\nk2GnnZTkiYisLSUetdStt4bko1+/pCOpG+rVg0GDYPz4MDqsiIhkR4lHLfTDD3DjjdCtG2y5ZdLR\n1B3HHAPt24daD/ekoxERqZ2UeNRCN98cBg27/PKkI6lbyodQf+01mDAh6WhERGonJR61zPffw/Dh\n0L07bLZZ0tHUPYcdBnvuGRqbqtZDRKT6lHjUMjfdFCaEu/TSpCOpm8xC0vHGG6r1EBHJhhKPWmTO\nnDB3yAUXwKabJh1N3XXooar1EBHJlhKPWmTo0PCN++KLk46kblOth4hI9pR41BKzZsHf/w4XXgjN\nmycdjRx6KOy1l2o9RESqS4lHLTFkSBhBs0+fpCMRWLXW44UXko5GRKT2UOJRC3z9NdxxR0g6Ntoo\n6WikXJcuqvUQEakuJR61wPXXQ6NG0KtX0pFIqvJajzffVK2HiEhVKfHIczNnwqhRcMkl0KxZ0tFI\nOtV6iIhUjxKPPHfttdC0aehCK/lHtR4iItWjxCOPTZsG994bBgtr3DjpaCSTLl1g771V6yEiUhV5\nk3iYWQ8zm25mS8xskpntsYbyncys1MyWmtlnZnZa2vNnm9lEM/s+Wl5Y0z7zzTXXwCabhOHRJX+p\n1kNEpOryIvEwsxOAm4ABwG7AB8A4M6twxAozaw2MBV4E2gG3AHebWeeUYn8AHgY6AXsDXwLjzaxW\nzHAydSo88ECYCK5Ro6SjkTU55JBQ6zFggGo9REQqkxeJB9AbuNPdH3D3ycC5wE/AmRnKnwdMc/e+\n7j7F3UcAj0f7AcDd/+LuI939Q3f/DDibcLwH1eiR5MigQdCiBXTrlnQkUhXltR6TJsH48UlHIyKS\nvxJPPMysAVBEqL0AwN0dmAB0zLDZ3tHzqcZVUh5gA6AB8H3Wwcbk009hzBi44gpYb72ko5GqKq/1\nUFsPEZHMEk88gOZAPWB22vrZQMsM27TMUL6pmTXMsM0Q4GtWT1jyzlVXwZZbwllnJR2JVIdZ+NtN\nmgTjxiUdjYhIfsqHxKPGmdllwPHAn9z956TjqcxHH8Gjj8KVV0LDTCmU5K3OnaFjR9V6iIhkUj/p\nAIC5wHKgRdr6FsCsDNvMylB+obsvS11pZhcDfYGD3P2TqgTUu3dvmqWN1lVcXExxcXFVNl8rAwdC\nmzZw+uk1/lJSA8rbenTpAv/+N3TtmnREIiK5V1JSQklJySrrFixYUKVtzfPga5mZTQLecvde0WMD\nZgK3uvvQCsoPBrq6e7uUdQ8DG7r7YSnr+gKXA4e4+ztViKMDUFpaWkqHDh3W9rCq7b33oEMHuO8+\nJR61mTvsuy/8+mu47WKWdEQiIjWvrKyMoqIigCJ3L8tULl9utQwDzjGzU81sR2Ak0AgYDWBm15vZ\n/SnlRwJbm9kQM9vBzLoDx0X7IdrmUmAQoWfMTDNrES0bxHNI1TdgAGy3HZxyStKRyNoob+vx9tvw\n/PNJRyMikl/yIvFw98eAiwmJwntAW6CLu8+JirQEtkwpPwM4HDgYeJ/QjfYsd09tOHouoRfL48A3\nKctFNXks2XrnHXj22ZB81M+HG2CyVg46KNR6aFwPEZFV5c0lzt1vB27P8NwZFaybSOiGm2l/bXIX\nXc37299gp53gxBOTjkRyobytx8EHw3PPwRFHJB2RiEh+yIsaj7rujTdCQ8SBA6FevaSjkVw58EDY\nbz/1cBERSaXEIw/87W+w665w3HFJRyK5VN7Wo7QUxo5NOhoRkfygxCNhr74KL74YLlDr6K9RcDp1\ngv33V62HiEg5XeoS5B5qO3bbDf70p6SjkZpQXutRVgb//GfS0YiIJE+JR4JefBEmTgwTwmmsh8LV\nqVNYVOshIqLEIzHuYVj0vfaCww9POhqpaQMHwvvvwzPPJB2JiEiylHgk5Lnn4K234JprVNtRF/zh\nD3DAASEBWbEi6WhERJKjxCMBK1ZA//7hYnTQQUlHI3G56ir44AN4+umkIxERSY4SjwQ8+WSodr/6\natV21CX77RcSTdV6iEhdpsQjZsuXh54sXbqEC5HULQMHwkcfwVNPJR2JiEgylHjE7OGH4dNPQ22H\n1D377huGUVeth4jUVUo8YvTLL+GCc9RRsMceSUcjSbnqKvj4Y3jiiaQjERGJnxKPGI0eDdOnh3E7\npO7aZx845JCQgKjWQ0TqGiUeMVm6NCQcJ5wAbdsmHY0kbeBA+OQTePzxpCMREYmXEo+YjBoF33wT\nLjgiHTuGBsYDBoQGxyIidYUSjxgsXgzXXgunngo77JB0NJIvrrkGJk+Ghx5KOhIRkfgo8YjBiBEw\nb17oRitSbvfd4ZhjQq3HsmVJRyMiEg8lHjXshx9gyBA4+2xo0ybpaCTfXH01fPlluBUnIlIXKPGo\nYTfcEBqWqrZDKrLzzvCXv4TbLosXJx2NiEjNU+JRg77+Gm6+GXr3hs02SzoayVcDBsD338OttyYd\niYhIzVPiUYOuugoaNYJLLkk6EslnbdrAX/8aasfmz086GhGRmqXEo4ZMngz33ANXXgnNmiUdjeS7\nK68MDUxvvDHpSEREapYSjxrSrx9suSWcd17SkUht0LIl9OoVbs3NmpV0NCIiNUeJRw14880w++g1\n10DDhklHI7VF377QoAFcd13SkYiI1BwlHjnmDpdeCu3awUknJR2N1CYbbRSSj5EjYcaMpKMREakZ\nSjxy7Lnn4LXXYPBgWEdnV6qpZ0/YeGPo3z/pSEREaoYujTm0fDlcdhkccECYh0Okuho3Dr2hHnoI\nysqSjkZEJPeUeOTQAw+EGUcHDwazpKOR2uqss2DHHUM3bPekoxERyS0lHjny44+hJ8sJJ8CeeyYd\njdRm9euHYfZfegmefz7paEREckuJR44MGRIGfxoyJOlIpBAceSTsv39obLp8edLRiIjkjhKPHJg5\nMwz81KcPtGqVdDRSCMzCe+qTT2D06KSjERHJHSUeOXD55WF00ssvTzoSKSR77AEnnhh6uGgCOREp\nFEo81tKkSfDww3DttdCkSdLRSKG57jqYOxeGDUs6EhGR3FDisRbcw8yz7dvD6acnHY0UojZt4Pzz\nwwRy336bdDQiImtPicdaeOSRUOMxbBjUq5d0NFKo+vcPQ+/rVp6IFAIlHln66acwWNhRR4UBw0Rq\nykYbhXl/7r8f3n476WhERNaOEo8sDR4cZhEdOjTpSKQuOOecMP9Pz56wYkXS0YiIZE+JRxY+/zyM\n19G3L2y3XdLRSF1Qrx7ccgu89RaMGZN0NCIi2VPiUU3u4VvnZpvpnrvE6w9/gD//Ocx+vGhR0tGI\niGRHiUc1/fOfYRjrm2+GRo2SjkbqmqFDwwi5112XdCQiItlR4lENP/0EvXpB166hUalI3Fq1CjUe\nw4bBF18kHY2ISPUp8aiG668PYynceqtmn5Xk9O0LLVrAhRdq9loRqX2UeFTR1KlhEKdLL4Vtt006\nGqnLGjUKt/rGjoWnn046GhGR6lHiUQXuYfTIzTYLY3eIJO3oo+GII+CCC9TQVERql7xJPMysh5lN\nN7MlZjbJzPZYQ/lOZlZqZkvN7DMzOy3t+Z3N7PFonyvMrGe2sY0ZA+PHw9//rgalkh/Mwvtx/nwY\nMCDpaEREqi4vEg8zOwG4CRgA7AZ8AIwzs+YZyrcGxgIvAu2AW4C7zaxzSrFGwBfApUDWs1zMnRvm\nYznhhPANUyRftGoFAweG8T3eey/paEREqiYvEg+gN3Cnuz/g7pOBc4GfgDMzlD8PmObufd19iruP\nAB6P9gOAu7/r7pe6+2PAz9kG1qcPLF8ePtxF8s2FF8Iuu0C3buF9KiKS7xJPPMysAVBEqL0AwN0d\nmAB0zLDZ3tHzqcZVUj4r48bBgw/CTTeFXgQi+aZBAxg5Et55J/wUEcl3iSceQHOgHjA7bf1soGWG\nbVpmKN/UzBrmIqjFi+Hcc+HAAzXlveS3ffaBv/4V+vWDb75JOhoRkcrlQ+KRl664IkwCd+edGrND\n8t/118P668N552lsDxHJb/WTDgCYCywH0m9mtABmZdhmVobyC9192doGdMYZvfnww2bsskto4wFQ\nXFxMcXHx2u5apEZsvDHccQcccwyUlMBJJyUdkYgUspKSEkpKSlZZt2DBgipta54HX4/MbBLwlrv3\nih4bMBO41d1Xm3jezAYDXd29Xcq6h4EN3f2wCspPB4a7+61riKMDULrZZqVst10HXn4Z1lGdkNQi\nxcWh6/cnn0DLTDcqRURqQFlZGUVFRQBF7l6WqVy+XFaHAeeY2almtiMwktAddjSAmV1vZvenlB8J\nbG1mQ8xsBzPrDhwX7YdomwZm1s7M2gPrAr+NHm+zpmDmz4f77lPSIbXPbbdBvXrQvbtuuYhIfsqL\nS2vU5fViYBDwHtAW6OLuc6IiLYEtU8rPAA4HDgbeJ3SjPcvdU3u6bB7tqzTa/mKgDBi1pnh694at\nt167YxJJQvPm4ZbLU0/BY48lHY2IyOry4lZLvii/1fLuu6UUFXVIOhyRrB1/PLz0Enz8sW65iEg8\natutlryiXixS240YEcb4OP10WLEi6WhEpNCtWBHGvqoKJR4iBeg3vwntlMaNC3O6iIjUpJtvDmMJ\nVYUSD5ECdeih0LMn9O0bbrmIiNSE0tIwc/vJJ1etvBIPkQI2ZAhst10Y12Pp0qSjEZFCs2gRnHgi\ntG0LF1xQtW2UeIgUsPXWgzFjYMqU8I1ERCRX3EPX/Vmz4JFHQruyqlDiIVLg2raFoUPDDMtPPZV0\nNCJSKO66Cx56KEwtsu22Vd9OiYdIHXDBBXDssaGXyxdfJB2NiNR2b78d2pB17179KRqUeIjUAWZw\nzz2w6aZw3HGwZEnSEYlIbTVnTvgc6dABhg+v/vZKPETqiGbN4PHHYfJk6NUr6WhEpDZavnxlY/V/\n/APWXbf6+1DiIVKHtGsXBhcbNQpGj046GhGpba68MoyK/MgjsMUW2e2jfm5DEpF8d+aZ8Oab0K0b\n7LADdOyYdEQiUhs8+CAMHhwaqx94YPb7UY2HSB00YgTstRf86U8wc2bS0YhIvnv9dTj77PDF5aKL\n1m5fSjxE6qB114UnnoD114ejjoLFi5OOSETy1bRpcPTRoXb0jjvWfj4zJR4iddRvfgP//CdMnQqn\nnabJ5ERkdQsWwBFHwIYbhi8r2TQmTafEQ6QOa9s2jGz65JMa2VREVrV0aagR/fZbGDsWNtkkN/tV\n4iFSxx11VJhZcujQ7Prki0jh+fVXKC4OA4WNHRsaoueKerWICD17wjffQJ8+0LJl+MARkbrJHc49\nF559Fp55Bn7/+9zuX4mHiABw/fWhSvW006B5c+jcOemIRCQJl18eRjp+8EE4/PDc71+3WkQECC3V\n774bDjootGD/v/9LOiIRidvAgTBkCAwbBqecUjOvocRDRP6nQYMwrPruu0PXrjBpUtIRiUhcBg6E\nq66C666D3r1r7nWUeIjIKjbYIDQma98eunQJjctEpHC5w4ABIem4/vpwq6UmKfEQkdU0bgzPPQe/\n+x0ccgi8+27SEYlITXCH/v1h0KAwHHoc3eqVeIhIhZo0geefh512CvMyvPJK0hGJSC4tXw7du8O1\n18INN8Cll8bzuko8RCSjpk1h/Pgwr8uhh8LTTycdkYjkwtKlcPzxcNddoVH5JZfE99pKPESkUk2a\nhDYfRx4Jxx4L992XdEQisjZ++CF8kfjXv+Cpp+Css+J9fSUeIrJGDRvCI4/AOeeE2SmvvjrcGxaR\n2uWLL8KAYB9+CBMmwB//GH8MGkBMRKqkXr0wM+Vvfwt/+xv85z9w771hhlsRyX8TJoTbK7/5Dbzx\nBuy4YzJxqMZDRKrMLLSA/8c/wlDK++8fhloXkfzlDrfcEm6v7LknvPVWckkHKPEQkSwcd1wY2XTW\nLNhjD3jttaQjEpGKLFwIJ58MF14YlueeC1PcJ0mJh4hkZbfd4J13YNtt4YADwmiHK1YkHZWIlHv3\nXejQITQOLymBG28Mt0yTpsRDRLLWsiW8+GIY6fDKK0NV7uzZSUclUretWBHmWtlnH9hoI3jvPTjx\nxKSjWkmJh4islfr1Qy+X8eNDS/m2beHJJ5OOSqRumjoVOnWCiy6CCy4It0S32SbpqFalxENEcuLg\ng+H996FjxzDex4knwty5SUclUjcsXw433RQS/6+/hpdfDo/XXTfpyFanxENEcqZlyzAg0cMPwwsv\nwM47h3vLGvNDpOa89VZI+C+5BM49N9Q8duqUdFSZKfEQkZwyg+LiMM7H/vvDSSeFD8EPP0w6MpHC\nMmsWnH467L03/PwzvP46DB8eZpjOZ0o8RKRGtGgBjz8e2n58913oBXP++br9IrK2fvwx9CLbfvvQ\nY2XkSCgtDY1JawMlHiJSozp3DrUdQ4fCAw9AmzZh5NMFC5KOTKR2WbIk1GhsvTUMHAhnnAGffQbd\nuuVHN9mqUuIhIjWuQQPo0wemTYPzzgtJSJs2MHiwEhCRNVm4MHSP3W670I7jqKNC75VbboGNN046\nuupT4iEisWneHG64IUxUVVwcaj623DJ8mH71VdLRieSXb76BSy+FrbYKPw86CD79FEaNglatko4u\ne0o8RCR2m28OI0bAjBnQvXv4IG3TBk45JQy/rl4wUletWAHjxoUu6a1ahYkZzzkHpk+H++8PtR61\nnRIPEUnM5puH2y1ffglDhoRugfvvH7rhDhumUVCl7pgyBQYNCoN9HXpoaLtx003hf2PoUNhii6Qj\nzB0lHiKSuCZNQhuQKVPgpZegfXu47LKQmBx0ENx1l3rDSOGZNi0k3u3bh9lib7wxdD1/883QILtn\nT2jWLOkoc0+Jh4jkjXXWCRPOlZTAt9+GboJmoUFqy5ZwyCFw663h26Bux0ht8/PPYUTRvn1h111D\n7cagQbDDDmGagdmz4b77wrgcZklHW3PM9d/7P2bWASgtLS2lQ4cOSYcjIpHvvoMnngjLa6+FD/A2\nbaBLl9Bd9/e/D+OGiOSTn38OE7S9/jpMnBhq8378MbxXDz0UDjssLI0bJx1pbpSVlVFUVARQ5O5l\nmcrlTY2HmfUws+lmtsTMJpnZHmso38nMSs1sqZl9ZmanVVDmz2b2abTPD8ysa80dQbJKSkqSDqHO\n0TmPz6abhlqPs84qYd48ePZZOPzwMCz7sceG2pBtt4XTTgu3ZcrKYOnSpKMuDHqfV82KFaEm7rHH\nwmzNBxwAG24Yai/69w9dYi+/PAz09c03MHo0HH98xUlHoZ/zvEg8zOwE4CZgALAb8AEwzsyaZyjf\nGhgLvAi0A24B7jazzill9gEeBkYB7YFngKfNbOcaO5AEFfobNR/pnMevpKSExo3hiCPgttvg889D\n47tHHgnfHD/+OPSSKSoKH+i77BKGbB88GP71rzD2wS+/JH0UtYve56tavjy0zfj3v8N7sEePUOPW\ntGm4ZXLCCfDQQ6FtxtVXw6RJYayal1+Gfv2gQ4dwS7EyhX7O6ycdQKQ3cKe7PwBgZucChwNnAjdU\nUP48YJq7940eTzGzfaP9vBCt6wk87+7Dosd/ixKT84HuNXMYIhK3LbYIH/YnnBAeL14MH30UGud9\n8EFYxo6FRYvC8/XqhW6K224bllat4Le/Dcvmm4ef+T7XhdScJUvC7K5ffhmWr75a+fsXX4Sk4+ef\nQ9mGDcN7qH17OPro8LNdO/jNb5I9hnyXeOJhZg2AIuC68nXu7mY2AeiYYbO9gQlp68YBw1MedyTU\noqSXOWqtAhaRvLbBBqF6e++9V65zDxeOzz9fdZk4MaxPHz21WbOQhDRvDptssnJJfbzhhqE3TurS\nqFFhNwqsLdzhp5/C7Y2FC8PfN/X3efNgzpzQU2rOnFWXhQtX3dcmm4TkdostQuPm7bcPY2lsv30Y\n/K42DVWeLxJPPIDmQD0gvcf+bGCHDNu0zFC+qZk1dPdllZRpuXbhikhtYxZGf9xqKzjwwNWf//HH\ncN/9669X/TlvXrg4ffhh+H3evMqHeF9nnXCLpzwRadwY1luv4mX99Vd93LAh1K8fLmRV/VmRTP0F\nKutH4B7aKLiv+vuKFeE8PPpo5ufT163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Hr14xhLbc7b479O0L/frBe+9lHY2ISHFraOJxIHCemT1pZu3NbEPgHWBrYlVa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\n8MgjWUcjIuVKiUeRuOkmePN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d6i88kcV98gnsu2/Mg3HXXdCsIQaFF4GyMnjkkUhAzjor62hEROpHXd+y7wDO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\nJitWxZB4FAUzWxrYAGDcuHEZR1N7M2b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ceOWVaDfRkvXvD08/HW0/+vWDb7/NOiIRaY0a27j0w1q23dX4cESKw6efxoyw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\naaV45LXiisU1yGUxJB5Fwcw6AesCjBk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EVkf3PH265+nTPU9fqd9zrU6bw8zKgIqKioqW3rFHREQkVZWVlfTq1Qugl7tXFiqnGg8R\nERFJjRIPERERSY0SDxEREUmNEg8RERFJjRIPERERSY0SDxEREUmNEg8RERFJjRIPERERSY0SDxER\nEUmNEg8RERFJjRIPERERSY0SDxEREUmNEg8RERFJjRIPERERSY0SDxEREUmNEg8RERFJjRIPERER\nSY0SDxEREUmNEg8RERFJjRIPERERSY0SDxEREUlN0SQeZtbfzD41szlm9pKZbVlH+T5mVmFmP5jZ\nODM7Mu/4kWa20MwWJP8uNLPZzfsqREREpDZFkXiY2cHA1cCFwObAm8BIM+taoHwP4DHgP0BP4Frg\nFjPbPa/odKB7zrZmM4QvIiIi9VQUiQcwALjR3e9y9w+AfsBs4JgC5U8Cxrv7QHf/0N2vB+5PrpPL\n3f1rd/8q2b5utlcgIiIidco88TCz9kAvovYCiGwBGAX0LnDaNsnxXCNrKN/ZzCaY2UQze8jMNmyi\nsEVERKQRMk88gK5AW2BK3v4pRPNITboXKL+cmXVMHn9I1Jj8CjiMeK0vmtkqTRG0iIiINFy7rANo\nLu7+EvBS9WMzGwu8D5xI9CURERGRlBVD4jEVWAB0y9vfDZhc4JzJBcrPcPeqmk5w9/lm9jrws7oC\nGjBgAF26dFlkX3l5OeXl5XWdKiIiUvKGDx/O8OHDF9k3ffr0ep1r0Z0iW2b2EvCyu5+ePDZgIjDE\n3a+qofzlwF7u3jNn373A8u6+d4HnaAO8Czzu7mcVKFMGVFRUVFBWVrakL0tERKTVqKyspFevXgC9\n3L2yULli6OMBMBg43syOMLP1gWFAJ+AOADO7zMzuzCk/DFjbzK4ws/XM7GTgwOQ6JOdcYGa7m9la\nZrY5cA+wBnBLOi9JRERE8hVDUwvuPiKZs+NiosnkDWDPnOGv3YHVc8pPMLN9gGuA04BJwLHunjvS\nZQXgpuTc74AKoHcyXFdEREQyUBSJB4C7DwWGFjh2dA37xhDDcAtd73fA75osQBEREVlixdLUIiIi\nIq2AEg8RERFJjRIPERERSY0SDxEREUmNEg8RERFJjRIPERERSY0SDxEREUmNEg8RERFJjRIPERER\nSY0SDxEREUmNEg8RERFJjRIPERERSY0SDxEREUmNEg8RERFJjRIPERERSY0SDxEREUmNEg8RERFJ\njRIPERERSY0SDxEREUmNEg8RERFJjRIPERERSY0SDxEREUmNEg8RERFJjRIPERERSY0SDxEREUmN\nEg8RERFJjRIPERERSY0SDxEREUmNEg8RERFJjRIPERERSY0SDxEREUmNEg8RERFJjRIPERERSY0S\nDxEREUmNEg8RERFJjRIPERERSY0SDxEREUmNEg8RERFJjRIPERERSY0SDxEREUmNEg8RERFJjRIP\nERERSY0SDxEREUmNEg8RERFJTdEkHmbW38w+NbM5ZvaSmW1ZR/k+ZlZhZj+Y2TgzO7KWsoeY2UIz\ne7DpIxcREZH6KorEw8wOBq4GLgQ2B94ERppZ1wLlewCPAf8BegLXAreY2e4Fyl4FjGn6yEVERKQh\niiLxAAYAN7r7Xe7+AdAPmA0cU6D8ScB4dx/o7h+6+/XA/cl1/sfM2gB3A78HPm226EVERKReMk88\nzKw90IuovQDA3R0YBfQucNo2yfFcI2sofyEwxd1vb5poRUREZEm0yzoAoCvQFpiSt38KsF6Bc7oX\nKL+cmXV09yoz2x44mmiKERERkSKQeY1HczCzzsBdwPHu/l3W8YiIiEgohhqPqcACoFve/m7A5ALn\nTC5QfkZS27E+sCbwqJlZcrwNgJnNBdZz94J9PgYMGECXLl0W2VdeXk55eXk9Xo6IiEhpGz58OMOH\nD19k3/Tp0+t1rkV3imyZ2UvAy+5+evLYgInAEHe/qobylwN7uXvPnH33Asu7+95m1hFYJ++0S4HO\nwGnAR+4+v4brlgEVFRUVlJWVNdGrExERKX2VlZX06tULoJe7VxYqVww1HgCDgTvMrAJ4hRid0gm4\nA8DMLgNWcffquTqGAf3N7ArgNmBX4EBgbwB3rwLey30CM5sWh/z9Zn81IiIiUqOiSDzcfUQyZ8fF\nRJPJG8Ce7v51UqQ7sHpO+Qlmtg9wDVGDMQk41t3zR7qIiIhIESmKxAPA3YcCQwscO7qGfWOIYbj1\nvf5i1xAREZF0leSoFhERESlOSjxEREQkNUo8REREJDVKPERERCQ1SjxEREQkNUo8REREJDVKPERE\nRCQ1SjxEREQkNUo8REREJDVKPERERCQ1SjxEREQkNUo8REREJDVKPERERCQ1SjxEREQkNUo8RERE\nJDVKPERERCQ1SjxEREQkNUo8REREJDVKPERERCQ1SjxEREQkNUo8REREJDVKPERERCQ1SjxEREQk\nNUo8REREJDVKPERERCQ1SjxEREQkNUo8REREJDVKPERERCQ1SjxEREQkNUo8REREJDVKPERERCQ1\nSjxEREQkNUo8REREJDVKPERERCQ1SjxEREQkNUo8REREJDVKPERERCQ1SjxEREQkNUo8REREJDVK\nPERERCQ1SjxEREQkNUo8REREJDVKPERERCQ1SjxEREQkNUWTeJhZfzP71MzmmNlLZrZlHeX7mFmF\nmf1gZuPM7Mi84782s1fN7Dszm2lmr5tZ3+Z9FSIiIlKbRiceZtbezFY3s/XMbMUlCcLMDgauBi4E\nNgfeBEaaWdcC5XsAjwH/AXoC1wK3mNnuOcW+AS4BtgE2AW4Hbs8rIyIiIilqUOJhZsua2Ulm9iww\nA5gAvA98bWafmdnNddVUFDAAuNHd73L3D4B+wGzgmALlTwLGu/tAd//Q3a8H7k+uA4C7j3H3h5Pj\nn7r7EOAtYPtGxCciIiJNoN6Jh5n9jkg0jgZGAfsDmwHrAr2Bi4B2wJNm9m8z+3k9r9se6EXUXgDg\n7p48R+8Cp22THM81spbymNmuSazP1icuERERaXrtGlB2S2BHd3+3wPFXgNvM7CTgKGAH4KN6XLcr\n0BaYkrd/CrBegXO6Fyi/nJl1dPcqADNbDvgC6AjMB05299H1iElERESaQb0TD3cvr2e5H4BhjY6o\naX1P9AHpDOwKXGNm4919TLZhiYiItE4NqfH4HzO7DTjd3b/P278M8Fd3L9Q3oyZTgQVAt7z93YDJ\nBc6ZXKD8jOraDvhfk8345OFbZrYhcB5Qa+IxYMAAunTpssi+8vJyysvrlXuJiIiUtOHDhzN8+PBF\n9k2fPr1e51p8NjeMmS0AfuruX+Xt7wpMdvcGJTRm9hLwsrufnjw2YCIwxN2vqqH85cBe7t4zZ9+9\nwPLuvnctz3MrsJa771LgeBlQUVFRQVlZWUNegoiISKtWWVlJr169AHq5e2Whcg1NEJYDLNmWNbMf\ncg63BfYGvqrp3DoMBu4wswqir8gAoBNwR/K8lwGruHv1XB3DgP5mdgVwG9GMcmDy/NWxngu8BnxC\n9PHYB+hLjJgRERGRDDS0qWUa4Mk2robjTszF0SDuPiKpLbmYaDJ5A9jT3b9OinQHVs8pP8HM9gGu\nAU4DJgHHunvuSJdlgOuB1YA5wAfAYe5+f0PjExERkabR0MRjZ6K2YzTwG+DbnGNzgc/c/b+NCcTd\nhwJDCxw7uoZ9Y4hhuIWudwFwQWNiERERkebRoMTD3Z8FMLO1gInemA4iIiIi0mo1asp0d/+sUNJh\nZmuYWdslC0tERERKUXMsEjcBeM/MDmiGa4uIiEgL1qh5POqwM7A2cDDwYDNcX0RERFqoJk88kn4g\nzxKrwYqIiIj8T6OaWsxs/VqO7dn4cERERKSUNbaPR6WZ9c/dYWYdzew64OElD0tERERKUWMTj6OA\ni83sCTPrZmabAa8DuxGr0oqIiIgsprHDaUcQq762B94FxhL9Osrc/dWmC09ERERKyZIOp+1ArNHS\nFvgS+KH24iIiItKaNbZz6SHA28B0YF1iAbYTgOfMbO2mC09ERERKSWOH094KnOXuNySPnzKzTYAb\niQXelmuK4ESkuHz7Lbz/Pnz5JXz1VTxeuBDMoH17WHnl2NZcE9ZbDzp0yDpiESk2jU08ytz9w9wd\n7v4dcJCZHb7kYYlI1hYsgMpKeOaZ2CorYfLkH4+3awcrrghtknrTqir47rtFj6+7Lmy9NeyyC+y8\nM6y6apqvQESKUaMSj/ykI+/Y3xofjohkaeFCeO45GDECHngApkyBTp1g++3h+ONho41ggw1g9dVh\n+eWjpiPX3LkwdSqMHw/vvANvvQUvvAC3J9MJbrEFHHwwHHQQrLFG+q9PRLJX78TDzM4FrnX3OfUo\nuzXQ1d0fX5LgRCQd334bycENN8Ann0Ri0bcv7L8/bLVV/ZtMOnSAVVaJbfvtf9z/9dcwahTcfz/8\n3//BwIGw995wyimwxx4/1pqISOlryJ/7hsBEMxtqZnuZ2UrVB8ysnZltamYnm9mLwD+A75s6WBFp\nWl9+CQMGwGqrwaBBsM02UePx2Wfw5z9H8tAU/TRWWgnKy6MW5auv4Oab4YsvYK+9YMMN4W9/i6Yd\nESl99U483P0IYoKw9sC9wGQzm2tm3wNVxARixwB3Aeu7+5hmiFdEmsA338AZZ8Daa0dNx8CB8Pnn\ncPfdkWzkN6E0peWWg2OPjT4jzz8fnVCPOCISkH/8A9yb77lFJHsNquB09zfd/XjgJ0Av4LfA8cCe\nQDd338Ldh7m75vMQKULz5sGQIfDzn8Ntt8F550Xtxh/+EKNR0mQG220HDz8Mr70WMR1yCOywQyQl\nIlKaGpR4mFkbMxsIPAfcDPQGHnb3Ue4+tTkCFJGm8eqrUFYWNR2//S18/DH8/vfQpUvWkUGvXvDY\nY9EPZNq06ITavz98rwZbkZLT0C5d5wN/IvpvfAGcDlzf1EGJSNOZMwfOOSf6b3ToABUVcOON6ddw\n1Meuu8Ibb8A118Cdd8LGG8OTT2YdlYg0pYYmHkcAJ7v7L9x9f+CXwGFmpj7pIkXolVdg883hL3+B\nSy6Bl1+Ox8WsXTs4/XR4++1oftlzTzj1VPhBDbgiJaGhCcMawL+qH7j7KMCBVZoyKBFZMu6RbGy/\nfXTmfOON6M/RrrFTBmZgrbXgqafg+utjFEzv3jBuXNZRiciSamji0Y7FF4KbR4x0EZEi8N13cMAB\nMUz21FNj5MgGG2QdVeOYwcknR03N7NnRF+See7KOSkSWREO//xhwh5lV5exbChhmZrOqd7j7AU0R\nnIg0zJtvwq9/HcnHQw/BfvtlHVHT6Nkz+qb07x8Tm1VUwJVXtqwaHBEJDf2zvbOGfXc3RSAismQe\neQQOPTTWRxk9Gnr0yDqiptW5c3Q43Wqr6APy/vvw978Xx6gcEam/BiUe7n50cwUiIo3jHrOMnnNO\n1HbcdRcss0zWUTWf/v0juTrooBip8+ij8LOfZR2ViNSXRqOItGDz5sXibQMHRufR++4r7aSj2u67\nR7+PhQsj+XjllawjEpH6UuIh0kLNmROdSO+8M7ZLL21di62tuy6MHRv/7rJLjIARkeLXit6mRErH\ntGmxquvo0dHUcMQRWUeUjRVXjIRjxx1hn31irRcRKW5KPERamMmTYaed4N13Y4rxX/wi64iytcwy\nsd7LwQfHCrjDhmUdkYjURoPRRFqQL76AnXeGWbNi+fqNNso6ouLQvn00N624Ipx0EixYEJ1QRaT4\nKPEQaSEmTYqko6oKxoyBddbJOqLi0qZNzNbati2cckp0PD311KyjEpF8SjxEWoDPP4+kY/58ePbZ\nmE5cFmcGV18dSchpp0XycfrpWUclIrmUeIgUuc8/hz59ovngmWdKb2KwpmYGV10VyccZZ0QzzMkn\nZx2ViFRT4iFSxKZMgd12i6Tj2WdhzTWzjqhlMIMrroh5Tvr3j9lNDzss66hEBJR4iBStadNiSfgZ\nM2KhNyUdDVPd7DJ9Ohx5ZKzS+8tfZh2ViGg4rUgRmjUr5qWYODHmqVBH0sZp0wZuugn23x9++1t4\n+umsIxIRJR4iRaaqKtZceest+Pe/YeONs46oZWvXDu65J+Y++dWvNL26SNaUeIgUkQULYoXZMWNi\ntdmttso6otLQsSM8+CD07Al77QXjxmUdkUjrpcRDpEi4x7wTDz8ci73tvHPWEZWWZZaJ6eW7d4/k\n46uvso6x4l/LAAAfuklEQVRIpHVS4iFSJK68Em64ITZ1gmweK6wATzwBs2fDvvtGXxoRSZcSD5Ei\ncM89cO65cMEFscy9NJ8114THH4f33otmrQULso5IpHVR4iGSsdGj4eijY8jnRRdlHU3rUFYWzVmP\nPx4znLpnHZFI66HEQyRD77wTI1j69IGbb465JyQde+0VzVpDh8LgwVlHI9J6FE3iYWb9zexTM5tj\nZi+Z2ZZ1lO9jZhVm9oOZjTOzI/OOH2dmY8zs22R7qq5riqRp8mTYe+9Yd+X++2Nqb0nX8cfDeefB\n2WfDY49lHY1I61AUiYeZHQxcDVwIbA68CYw0s64FyvcAHgP+A/QErgVuMbPdc4rtBNwL9AG2AT4H\nnjSznzbLixBpgB9+iJqOefPiA2+55bKOqPW65JKY36O8PGqgRKR5FUXiAQwAbnT3u9z9A6AfMBs4\npkD5k4Dx7j7Q3T909+uB+5PrAODuh7v7MHd/y93HAccRr3fXZn0lInVwh+OOgzfeiKGzq62WdUSt\nW5s2cPfdsPbakYBMnZp1RCKlLfPEw8zaA72I2gsA3N2BUUDvAqdtkxzPNbKW8gDLAO2BbxsdrEgT\nuPzyGMVyxx2aIKxYdO4cE7bNnAm/+Q3MnZt1RCKlK/PEA+gKtAWm5O2fAnQvcE73AuWXM7OOBc65\nAviCxRMWkdQ8+CAMGgS//z0cfHDW0UiuNdeEf/4Txo6NFW010kWkeRRD4tHszOxc4CBgf3fXdxnJ\nxOuvw+GHx2JlF16YdTRSk+22i0XlbrkFhgzJOhqR0tQu6wCAqcACoFve/m7A5ALnTC5Qfoa7V+Xu\nNLOzgIHAru7+bn0CGjBgAF26dFlkX3l5OeXl5fU5XWQxkydH/4ENNogmljatIuVvmY46KjqZ/u53\nsOGGsPvudZ4i0uoMHz6c4cOHL7Jv+vTp9TrXvAjqE83sJeBldz89eWzARGCIu19VQ/nLgb3cvWfO\nvnuB5d1975x9A4HzgD3c/dV6xFEGVFRUVFBWVrakL0sEiBEsffrA55/Hyqirrpp1RFKXBQtiqPNr\nr0FFBfTokXVEIsWvsrKSXr16AfRy98pC5Yrle9dg4HgzO8LM1geGAZ2AOwDM7DIzuzOn/DBgbTO7\nwszWM7OTgQOT65Cccw5wMTEyZqKZdUu2ZdJ5SSLRT6BfP3jzzRjBoqSjZWjbFu69N4Y5H3AAzJmT\ndUQipaMoEg93HwGcRSQKrwObAnu6+9dJke7A6jnlJwD7ALsBbxDDaI9199yOo/2IUSz3A//N2c5s\nztcikmvoULjzzpiVdIstso5GGuInP4nOph98ACeeqM6mIk2lGPp4AODuQ4GhBY4dXcO+McQw3ELX\nW6vpohNpuOeegzPOgNNPh759s45GGmOzzSJp7Ns3hj6fckrWEYm0fEWTeIiUkkmT4MADY5TEVYv1\nUpKW5LDD4NVXYcAA6NkTdtgh64hEWraiaGoRKSVVVTEJVYcOMGKE1mApBVddBdtuG0Ohv/gi62hE\nWjYlHiJNyD0mn3rzzZgsbOWVs45ImkL79pFEtmsXNVlVVXWfIyI1U+Ih0oRuugluvRWGDYMttRZy\nSenWDR54ACoro++OiDSOEg+RJjJ2LJx6atR4HHVU1tFIc9h6a7juukgsb7st62hEWiZ1LhVpAl9+\nGf06tt4aBg+uu7y0XMcfH51NTz45Opv2Kji2TkRqohoPkSU0d260+5vBffdFp1IpbUOGwCabRLL5\nzTdZRyPSsijxEFlCZ5wRU2s/8AB0L7SespSUpZaKn/fMmXDooTHFuojUjxIPkSVw221www1w/fWw\nzTZZRyNpWmMN+PvfYdQo+MMfso5GpOVQ4iHSSK+9Fu38xx8Pxx2XdTSShd12g0suie3RR7OORqRl\nUOIh0ghTp0b7fs+e8Ne/Zh2NZOmcc2C//eDww+Hjj7OORqT4KfEQaaAFC6C8PFYsvf9+6Ngx64gk\nS23axEKAK60UK9nOmpV1RCLFTYmHSANdcAGMHh3t+6uvXnd5KX1dusRKtp98AiecoJVsRWqjxEOk\nAR56CC67DC6/HHbZJetopJhsvDHccgvce290NhaRmmkCMZF6+vBDOOKI6Ntx1llZRyPFqLwcXn45\nVrItK4uF5URkUarxEKmHmTOj/X7VVeH222OyMJGaXHVVzGD729/C5MlZRyNSfJR4iNTBHY45BiZO\njHb8ZZfNOiIpZu3bxwy2CxfCwQfDvHlZRyRSXJR4iNRh8OD4ILnjDlh//ayjkZbgpz+FESPgxRfh\n3HOzjkakuCjxEKnFM8/EPA0DB0bfDpH62mEH+POfI3EdMSLraESKhxIPkQImTYKDDoKddoJLL806\nGmmJTjsNDjkkmureey/raESKgxIPkRpUVcWKs0stFfN1tNP4L2kEM7j5ZujRIzonz5iRdUQi2VPi\nIVKDM86A11+PFUhXWinraKQl69wZHnwQ/vtfOPpoTS4mosRDJM8dd8CwYXDddbDllllHI6Vg3XVj\nWvUHH4zhtiKtmRIPkRyVldCvHxx7bKw6K9JUfv3rGOFy3nkx5b5Ia6XEQyTxzTfRDr/JJlHbIdLU\nLrkkpto/5BD4/POsoxHJhhIPEWD+/JjueubMWHF2qaWyjkhKUdu2sZbLUkvFzKZVVVlHJJI+JR4i\nRBX46NHwj3/AmmtmHY2UspVWiuT29ddjTReR1kaJh7R699wDV18dkz3tumvW0UhrsNVW8Ne/wg03\nRKdTkdZEiYe0ahUVcNxxcOSRcPrpWUcjrcnxx8fw2n79ovZDpLVQ4iGt1ldfxUiDTTaJ4bNacVbS\nZAbXXw8bbhjT8X/7bdYRiaRDiYe0SvPmRee+uXNjbgV1JpUsLL10TFI3fTr07Rsr2oqUOiUe0iqd\ncQaMHRtv+qutlnU00pr16BH9jP79b/jjH7OORqT5KfGQVueWW2Do0Ojct912WUcjAr/4BVx0UWxP\nPJF1NCLNS4mHtCpjx8LJJ8OJJ8YmUizOPx/23hsOOwzGj886GpHmo8RDWo1Jk2Jm0q22giFDso5G\nZFFt2sDf/gYrrhi/p7NnZx2RSPNQ4iGtwqxZ8KtfQfv2MXlThw5ZRySyuBVWiM7O48bBSSdpJVsp\nTUo8pOQtXBgjBsaNg8ceg+7ds45IpLCePeHmm+Guu2JiO5FS0y7rAESa2/nnw8MPx7bppllHI1K3\nww6Dd96BgQNh/fVh332zjkik6ajGQ0ranXfC5ZfDlVfCL3+ZdTQi9XfppdE8WF4eSYhIqVDiISXr\n+edjWupjjoEzz8w6GpGGadMG7r4b1lknkuavv846IpGmocRDStL48TEd+rbbxkJcmg5dWqLOneGR\nR2KEywEHQFVV1hGJLDklHlJypk+Pb4jLLx8zk2oEi7Rka6wBDz0Er7yikS5SGpR4SEmZNw8OOgi+\n+AIefRR+8pOsIxJZcr17x4y7t98OgwdnHY3IktGoFikZ7jEb6dNPx7oX66+fdUQiTefww+G99+Ds\ns2HdddVZWlquoqnxMLP+Zvapmc0xs5fMbMs6yvcxswoz+8HMxpnZkXnHNzSz+5NrLjSz05r3FUjW\nLroovhHedhvsskvW0Yg0vUs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rNU08DBhmZg+Xb0BLYGjePhFpRCZPht69oXv3+LC//354/3045pjoJJqVNm2g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\nMAC42d3vcvcPgb7AL8BRBcr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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#* Loop over desired number of steps (wave circles system once)\n", + "for iter in range(max_iter) :\n", + "\n", + " #* Compute new wave function using the Crank-Nicolson scheme\n", + " psi = np.dot(dCN,psi) \n", + " \n", + " #* Periodically record values for plotting\n", + " if (iter+1) % plot_iter < 1 : \n", + " iplot += 1\n", + " p_plot[:,iplot] = np.absolute(psi[:])**2 \n", + " plt.plot(x,p_plot[:,iplot]); # Display snap-shot of P(x)\n", + " plt.xlabel('x'); plt.ylabel('P(x,t)')\n", + " plt.title('Finished %d of %d iterations' % (iter,max_iter))\n", + " plt.axis(axisV)\n", + " plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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kXET2iMjtLttvFxG7iFRbP+0iUnp2j8JgMHjD8eNw8KDOrg0GSw8vZXCbwUSF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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#* Plot probability versus position at various times\n", + "pFinal = np.empty(N)\n", + "pFinal = np.absolute(psi[:])**2\n", + "for i in range(iplot+1) :\n", + " plt.plot(x,p_plot[:,i])\n", + "plt.xlabel('x'); plt.ylabel('P(x,t)')\n", + "plt.title('Probability density at various times')" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + } + ], + "metadata": { + "anaconda-cloud": {}, + "kernelspec": { + "display_name": "Python [default]", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.12" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} diff --git a/Python/Schro_T.ipynb b/Python/Schro_T.ipynb new file mode 100644 index 0000000..ac33b06 --- /dev/null +++ b/Python/Schro_T.ipynb @@ -0,0 +1,299 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Populating the interactive namespace from numpy and matplotlib\n" + ] + } + ], + "source": [ + "# schro_T - Program to solve the Schrodinger equation \n", + "# for a free particle using the Crank-Nicolson scheme\n", + "# Tridiagonal matrix version\n", + "\n", + "# Set up configuration options and special features\n", + "%pylab inline \n", + "\n", + "############## NOT WORKING ######################" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def tri_ge(a,b) :\n", + " # Function to solve b = a*x by Gaussian elimination where\n", + " # the matrix a is a packed tridiagonal matrix\n", + " # Inputs\n", + " # a Packed tridiagonal matrix, N by N unpacked\n", + " # b Column vector of length N\n", + " # Output \n", + " # x Solution of b = a*x; Column vector of length N\n", + "\n", + " #* Check that dimensions of a and b are compatible\n", + " N_a = shape(a)\n", + " N = len(b)\n", + " if N_a[0] != N or N_a[1] != 3 :\n", + " print 'Problem in tri_GE, inputs are incompatible'\n", + " return None\n", + "\n", + " #* Unpack diagonals of triangular matrix into vectors\n", + " alpha = empty(N-1,dtype=complex)\n", + " beta = empty(N,dtype=complex)\n", + " gamma = empty(N-1,dtype=complex)\n", + " alpha = a[1:N,0]\n", + " beta = a[:,1]\n", + " gamma = a[0:(N-1),2]\n", + "\n", + " #* Perform forward elimination\n", + " for i in range(1,N) :\n", + " coeff = alpha[i-1]/beta[i-1]\n", + " beta[i] = beta[i] - coeff*gamma[i-1]\n", + " b[i] = b[i] - coeff*b[i-1]\n", + "\n", + " #* Perform back substitution\n", + " x = empty(N,dtype=complex)\n", + " x[-1] = b[-1]/beta[-1]\n", + " for i in reversed(range(N-1)) :\n", + " x[i] = (b[i] - gamma[i] * x[i+1])/beta[i]\n", + "\n", + " return x" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Enter number of grid points: 100\n", + "Enter time step: 1\n" + ] + } + ], + "source": [ + "#* Initialize parameters (grid spacing, time step, etc.)\n", + "i_imag = 1j # Imaginary i\n", + "N = input('Enter number of grid points: ');\n", + "L = 100. # System extends from -L/2 to L/2\n", + "h = L/(N-1) # Grid size\n", + "x = arange(N)*h - L/2. # Coordinates of grid points\n", + "h_bar = 1. # Natural units\n", + "mass = 1. # Natural units\n", + "tau = input('Enter time step: ')" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Set up the Hamiltonian operator matrix\n", + "ham = zeros((N,3)) # Set all elements to zero\n", + "coeff = -h_bar**2/(2*mass*h**2)\n", + "for i in range(1,N-1) :\n", + " ham[i,0] = coeff\n", + " ham[i,1] = -2*coeff # Set interior rows\n", + " ham[i,2] = coeff\n", + "\n", + "# First and last rows for periodic boundary conditions\n", + "ham[0,0] = 0.; ham[0,1] = 0.; ham[0,2] = 0.\n", + "ham[-1,0] = 0.; ham[-1,1] = 0.; ham[-1,2] = 0.\n", + "\n", + "#* Compute the Q matrix\n", + "tri_eye = zeros((N,3))\n", + "tri_eye[:,1] = 1.\n", + "Q = 0.5 * (tri_eye + 0.5*i_imag*tau/h_bar*ham) " + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Initialize the wavefunction \n", + "x0 = 0. # Location of the center of the wavepacket\n", + "velocity = 0.5 # Average velocity of the packet\n", + "k0 = mass*velocity/h_bar; # Average wavenumber\n", + "sigma0 = L/10. # Standard deviation of the wavefunction\n", + "Norm_psi = 1/(sqrt(sigma0*sqrt(pi))) # Normalization\n", + "psi = empty(N,dtype=complex)\n", + "for i in range(N) :\n", + " psi[i] = Norm_psi * exp(i_imag*k0*x[i]) * exp(-(x[i]-x0)**2/(2*sigma0**2))" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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pFuu79ajYnaNywVsXMO3baQG0UghRHyRQEULY1rtFbwDW5a4LyfVdS5OVsli/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\npjFllgE/BfpjHxyfA4rCrntUHrGgMpIYVNRu49ro/bE2SnycAUbUZin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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#* Plot the initial wavefunction\n", + "plot(x,real(psi),'-',x,imag(psi),'--')\n", + "xlabel('x'); ylabel('psi(x)')\n", + "legend(('Real ','Imag '))\n", + "title('Initial wave function')" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Initialize loop and plot variables \n", + "max_iter = int(L/(velocity*tau)+.5) # Particle should circle system\n", + "plot_iter = max_iter/20 # Produce 20 curves\n", + "p_plot = empty((N,max_iter+1)) # Note that P(x,t) is real\n", + "p_plot[:,0] = absolute(psi[:])**2 # Record initial condition\n", + "iplot = 0\n", + "axisV = [-L/2., L/2., 0., max(p_plot[:,0])] # Fix axis min and max" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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hRWQssFct9UYSxhv1aOzrzPK8tU2n7U5IEBZHj6VPU29PWNNiZvSa5kW/2xcDFRnX6cIs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\nk45CpHjorUakjC1bFrpaNL6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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#* Loop over desired number of steps (wave circles system once)\n", + "for iter in range(max_iter) :\n", + "\n", + " #* Use Gaussian Elimination for the Crank-Nicolson scheme\n", + " chi = tri_ge(Q,psi)\n", + " psi = chi - psi \n", + " \n", + " #* Periodically record values for plotting\n", + " if iter % plot_iter < 1 : \n", + " iplot += 1\n", + " p_plot[:,iplot] = absolute(psi[:])**2 \n", + " plot(x,p_plot[:,iplot]); # Display snap-shot of P(x)\n", + " xlabel('x'); ylabel('P(x,t)')\n", + " title(('Finished ', iter, ' of ', max_iter, ' iterations'))\n", + " axis(axisV)" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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24Llsb5a2XQy8pek+mmNbW1M8x/pZjxxEnUr+IriNPNhujxleYy/yjIwbqvWPB7bqWHdP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\n0f46CvjuLOv03W+LKRMxBmw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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#* Plot probability versus position at various times\n", + "pFinal = empty(N)\n", + "pFinal = absolute(psi[:])**2\n", + "#plot(x,p_plot(:,1:3:iplot),x,pFinal)\n", + "plot(x,pFinal)\n", + "xlabel('x'); ylabel('P(x,t)')\n", + "title('Probability density at various times')" + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "kernelspec": { + "display_name": "Python [default]", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.12" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} diff --git a/Python/Sprfft.ipynb b/Python/Sprfft.ipynb new file mode 100644 index 0000000..287131e --- /dev/null +++ b/Python/Sprfft.ipynb @@ -0,0 +1,222 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# sprfft - Program to compute the power spectrum of a \n", + "# coupled mass-spring system.\n", + "\n", + "# Set up configuration options and special features\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "%matplotlib inline" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def rk4(x,t,tau,derivsRK,param):\n", + " # Runge-Kutta integrator (4th order)\n", + " # Input arguments -\n", + " # x = current value of dependent variable\n", + " # t = independent variable (usually time)\n", + " # tau = step size (usually timestep)\n", + " # derivsRK = right hand side of the ODE; derivsRK is the\n", + " # name of the function which returns dx/dt\n", + " # Calling format derivsRK (x,t,param).\n", + " # param = extra parameters passed to derivsRK\n", + " # Output arguments -\n", + " # xout = new value of x after a step of size tau\n", + " \n", + " half_tau = 0.5*tau\n", + " F1 = derivsRK(x,t,param) \n", + " t_half = t + half_tau\n", + " xtemp = x + half_tau*F1\n", + " F2 = derivsRK(xtemp,t_half,param) \n", + " xtemp = x + half_tau*F2\n", + " F3 = derivsRK(xtemp,t_half,param)\n", + " t_full = t + tau\n", + " xtemp = x + tau*F3\n", + " F4 = derivsRK(xtemp,t_full,param)\n", + " xout = x + tau/6.*(F1 + F4 + 2.*(F2+F3))\n", + " return xout" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def sprrk(s,t,param):\n", + " # Returns right-hand side of 3 mass-spring system\n", + " # equations of motion\n", + " # Inputs\n", + " # s State vector [x(1) x(2) ... v(3)]\n", + " # t Time (not used)\n", + " # param (Spring constant)/(Block mass)\n", + " # Output\n", + " # deriv [dx(1)/dt dx(2)/dt ... dv(3)/dt]\n", + " deriv = np.empty(6)\n", + " deriv[0] = s[3]\n", + " deriv[1] = s[4]\n", + " deriv[2] = s[5]\n", + " param2 = -2.*param\n", + " deriv[3] = param2*s[0] + param*s[1]\n", + " deriv[4] = param2*s[1] + param*(s[0]+s[2])\n", + " deriv[5] = param2*s[2] + param*s[1]\n", + " return deriv" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Set parameters for the system (initial positions, etc.).\n", + "x = np.array(input('Enter initial displacement [x0, x1, x2]: ')) \n", + "v = np.array([0, 0, 0]) # Masses are initially at rest\n", + "# Positions and velocities; used by rk4\n", + "state = np.array([x[0], x[1], x[2], v[0], v[1], v[2]]) \n", + "tau = input('Enter timestep: ') \n", + "k_over_m = 1 # Ratio of spring const. over mass" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Loop over the desired number of time steps.\n", + "time = 0. # Set initial time\n", + "nstep = 256 # Number of steps in the main loop\n", + "nprint = nstep/8 # Number of steps between printing progress\n", + "tplot = np.empty(nstep)\n", + "xplot = np.empty((nstep,3))\n", + "for istep in range(nstep): ### MAIN LOOP ###\n", + "\n", + " #* Use Runge-Kutta to find new displacements of the masses.\n", + " state = rk4(state,time,tau,sprrk,k_over_m) \n", + " time = time + tau\n", + " \n", + " #* Record the positions for graphing and to compute spectra.\n", + " xplot[istep,:] = np.copy(state[0:3]) # Record positions\n", + " tplot[istep] = time\n", + " if istep % nprint < 1 :\n", + " print 'Finished ', istep, ' out of ', nstep, ' steps'" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Graph the displacements of the three masses.\n", + "plt.plot(tplot,xplot[:,0],'-',tplot,xplot[:,1],'-.',tplot,xplot[:,2],'--')\n", + "plt.legend(['Mass #1 ','Mass #2 ','Mass #3 '])\n", + "plt.title('Displacement of masses (relative to rest positions)')\n", + "plt.xlabel('Time') \n", + "plt.ylabel('Displacement')" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Calculate the power spectrum of the time series for mass #1\n", + "f = np.arange(nstep)/(tau*nstep) # Frequency\n", + "x1 = xplot[:,0] # Displacement of mass 1\n", + "\n", + "x1fft = np.fft.fft(x1) # Fourier transform of displacement\n", + "\n", + "spect = np.empty(len(x1fft)) # Power spectrum of displacement\n", + "for i in range(len(x1fft)):\n", + " spect[i] = abs(x1fft[i])**2" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Apply the Hanning window to the time series and calculate\n", + "# the resulting power spectrum\n", + "x1w = np.empty(len(x1))\n", + "for i in range(len(x1)):\n", + " window = 0.5 * (1. - np.cos(2*np.pi*float(i)/nstep)) # Hanning window\n", + " x1w[i] = x1[i] * window # Windowed time series\n", + " \n", + "x1wfft = np.fft.fft(x1w) # Fourier transf. (windowed data)\n", + "\n", + "spectw = np.empty(len(x1wfft)) # Power spectrum (windowed data)\n", + "for i in range(len(x1wfft)):\n", + " spectw[i] = abs(x1wfft[i])**2" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Graph the power spectra for original and windowed data\n", + "plt.semilogy(f[0:(nstep/2)],spect[0:(nstep/2)],'-', f[0:(nstep/2)],spectw[0:(nstep/2)],'--');\n", + "plt.title('Power spectrum (dashed is windowed data)')\n", + "plt.xlabel('Frequency')\n", + "plt.ylabel('Power')" + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "kernelspec": { + "display_name": "Python [default]", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.12" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} diff --git a/Python/Test_bess.ipynb b/Python/Test_bess.ipynb new file mode 100644 index 0000000..c12bada --- /dev/null +++ b/Python/Test_bess.ipynb @@ -0,0 +1,133 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Populating the interactive namespace from numpy and matplotlib\n" + ] + } + ], + "source": [ + "# test_bess - Program to test the bess function\n", + "\n", + "# Set up configuration options and special features\n", + "%pylab inline " + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def bess(m_max,x) :\n", + " # Bessel function\n", + " # Inputs\n", + " # m_max = Largest desired order\n", + " # x = Value at which Bessel function J(x) is evaluated\n", + " # Output\n", + " # jj = Vector of J(x) for all orders <= m_max\n", + "\n", + " #* Perform downward recursion from initial guess\n", + " eps = 1.0e-15\n", + " m_top = max(m_max,x)+15 # Top value of m for recursion\n", + " m_top = int(2*ceil( m_top/2 )) # Round up to an even number\n", + " j = empty(m_top+1)\n", + " j[m_top] = 0.\n", + " j[m_top-1] = 1.\n", + " for m in reversed(range(m_top-1)) : # Downward recursion\n", + " j[m] = 2.*(m+1)/(x+eps)*j[m+1] - j[m+2]\n", + "\n", + " #* Normalize using identity and return requested values\n", + " norm = j[0] \n", + " for m in range(2,m_top,2) :\n", + " norm = norm + 2*j[m]\n", + " \n", + " jj = empty(m_max+1) # Send back only the values for\n", + " for m in range(m_max+1) : # m=0,...,m_max and discard values\n", + " jj[m] = j[m]/norm # for m=m_max+1,...,m_top\n", + " \n", + " return jj" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Enter m: 3\n" + ] + }, + { + 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uxhh7whgcqEiS5CRJUg9Jkl7Iy0/596ZGB8uafZf2oXWN1mhRvYW6DcXGAsuX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\nWRKoCCGEEKLM+n90pWvsCpY37gAAAABJRU5ErkJggg==\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "nplot = 200\n", + "m = input(\"Enter m: \")\n", + "x = linspace(0.,20.,nplot)\n", + "\n", + "jj = empty((nplot,m+1))\n", + "for i in range(nplot) :\n", + " jj[i,:] = bess(m,x[i])\n", + "\n", + "for mi in range(m+1) :\n", + " plot(x,jj[:,mi],'-')\n", + " xlabel('x'); ylabel('J_m(x)')" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python [default]", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.12" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} diff --git a/Python/Test_legndr.ipynb b/Python/Test_legndr.ipynb new file mode 100644 index 0000000..67e5b75 --- /dev/null +++ b/Python/Test_legndr.ipynb @@ -0,0 +1,115 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Populating the interactive namespace from numpy and matplotlib\n" + ] + } + ], + "source": [ + "# test_legndr - Program to test the legndr function\n", + "\n", + "# Set up configuration options and special features\n", + "%pylab inline " + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def legndr(n,x) :\n", + " # Legendre polynomials function\n", + " # Inputs \n", + " # n = Highest order polynomial returned\n", + " # x = Value at which polynomial is evaluated\n", + " # Output\n", + " # p = Vector containing P(x) for order 0,1,...,n\n", + "\n", + " #* Perform upward recursion\n", + " p = empty(n+1)\n", + " p[0] = 1. # P(x) for n=0\n", + " if n == 0 :\n", + " return p\n", + " p[1] = x # P(x) for n=1\n", + " if n == 1 :\n", + " return p\n", + " \n", + " # Use upward recursion to obtain other n's\n", + " for i in range(1,n) :\n", + " p[i+1] = ((2*i+1)*x*p[i] - i*p[i-1])/(i+1)\n", + "\n", + " return p" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Enter x: 3.\n", + "For n=0; Computed = 1.0 Expected = 1\n", + "For n=1; Computed = 3.0 Expected = 3.0\n", + "For n=2; Computed = 13.0 Expected = 13.0\n", + "For n=3; Computed = 63.0 Expected = 63.0\n", + "For n=4; Computed = 321.0 Expected = 321.0\n", + "For n=5; Computed = 1683.0 Expected = 1683.0\n" + ] + } + ], + "source": [ + "x = input(\"Enter x: \")\n", + "n = 5\n", + "\n", + "p = empty(n)\n", + "p = legndr(n,x)\n", + "\n", + "print \"For n=0; Computed = \", p[0], \" Expected = 1\"\n", + "print \"For n=1; Computed = \", p[1], \" Expected = \", x\n", + "print \"For n=2; Computed = \", p[2], \" Expected = \", 0.5*(3*x*x-1)\n", + "print \"For n=3; Computed = \", p[3], \" Expected = \", 0.5*(5*x*x*x-3*x)\n", + "print \"For n=4; Computed = \", p[4], \" Expected = \", 0.125*(35*x*x*x*x-30*x*x+3)\n", + "print \"For n=5; Computed = \", p[5], \" Expected = \", 0.125*(63*x*x*x*x*x-70*x*x*x+15*x) " + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python [default]", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.12" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} diff --git a/Python/Traffic.ipynb b/Python/Traffic.ipynb new file mode 100644 index 0000000..bc17eea --- /dev/null +++ b/Python/Traffic.ipynb @@ -0,0 +1,228 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# traffic - Program to solve the generalized Burger \n", + "# equation for the traffic at a stop light problem\n", + "\n", + "# Set up configuration options and special features\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "%matplotlib inline" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Choose a numerical method, 1) FTCS; 2) Lax; 3) Lax-Wendroff :3\n", + "Enter the number of grid points: 80\n", + "Suggested timestep is 0.2\n", + "Enter time step (tau): .2\n", + "Last car starts moving after 20.0 steps\n", + "Enter number of steps: 100\n" + ] + } + ], + "source": [ + "#* Select numerical parameters (time step, grid spacing, etc.).\n", + "method = input('Choose a numerical method, 1) FTCS; 2) Lax; 3) Lax-Wendroff :')\n", + "N = input('Enter the number of grid points: ')\n", + "L = 400 # System size (meters)\n", + "h = L/N # Grid spacing for periodic boundary conditions\n", + "v_max = 25. # Maximum car speed (m/s)\n", + "print 'Suggested timestep is ', h/v_max\n", + "tau = input('Enter time step (tau): ')\n", + "print 'Last car starts moving after ', (L/4)/(v_max*tau), 'steps'\n", + "nstep = input('Enter number of steps: ')\n", + "coeff = tau/(2*h) # Coefficient used by all schemes\n", + "coefflw = tau**2/(2*h**2) # Coefficient used by Lax-Wendroff" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Set initial and boundary conditions\n", + "rho_max = 1.0 # Maximum density\n", + "Flow_max = 0.25*rho_max*v_max # Maximum Flow\n", + "Flow = np.empty(N)\n", + "cp = np.empty(N); cm = np.empty(N)\n", + "# Initial condition is a square pulse from x = -L/4 to x = 0\n", + "rho = np.zeros(N)\n", + "for i in range(int(N/4),int(N/2)) :\n", + " rho[i] = rho_max # Max density in the square pulse\n", + "\n", + "rho[int(N/2)] = rho_max/2 # Try running without this line\n", + "\n", + "# Use periodic boundary conditions\n", + "ip = np.arange(N) + 1 \n", + "ip[N-1] = 0 # ip = i+1 with periodic b.c.\n", + "im = np.arange(N) - 1 \n", + "im[0] = N-1 # im = i-1 with periodic b.c.\n", + "\n", + "#* Initialize plotting variables.\n", + "iplot = 1\n", + "xplot = (np.arange(N)-1/2.)*h - L/2. # Record x scale for plot\n", + "rplot = np.empty((N,nstep+1))\n", + "tplot = np.empty(nstep+1)\n", + "rplot[:,0] = np.copy(rho) # Record the initial state\n", + "tplot[0] = 0 # Record the initial time (t=0)" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#* Loop over desired number of steps.\n", + "for istep in range(nstep) :\n", + "\n", + " #* Compute the flow = (Density)*(Velocity)\n", + " Flow[:] = rho[:] * (v_max*(1 - rho[:]/rho_max))\n", + " \n", + " #* Compute new values of density using \n", + " # FTCS, Lax or Lax-Wendroff method.\n", + " if method == 1 : ### FTCS method ###\n", + " rho[:] = rho[:] - coeff*( Flow[ip] - Flow[im] )\n", + " elif method == 2 : ### Lax method ###\n", + " rho[:] = .5*( rho[ip] + rho[im] ) - coeff*( Flow[ip] - Flow[im] )\n", + " else : ### Lax-Wendroff method ###\n", + " cp[:] = v_max*(1 - (rho[ip]+rho[:])/rho_max);\n", + " cm[:] = v_max*(1 - (rho[:]+rho[im])/rho_max);\n", + " rho[:] = rho[:] - coeff*( Flow[ip] - Flow[im] ) + coefflw*(\n", + " cp[:]*(Flow[ip]-Flow[:]) - cm[:]*(Flow[:]-Flow[im]) )\n", + "\n", + " #* Record density for plotting.\n", + " rplot[:,iplot] = np.copy(rho)\n", + " tplot[iplot] = tau*istep\n", + " iplot += 1" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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Y7XZlBTscDuLi4nA6nTidTux2e5O3b1IbU5BNgMDSmNJCDje4QTDt+eHXHJx5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TPmz5+PdevWqXKOREl0kJVbUCYYDCIcDsPlcsWIiFYV4gg1NTVs4KSaFeK40A7mIml73KhxbqlM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\ngLeJSEGNb71hAF7kOG5e546OwWB0Vf4/Cksgz/uG9+oAAAAASUVORK5CYII=\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# %* Graph density versus position and time as wire-mesh plot\n", + "\n", + "from matplotlib import cm\n", + "from mpl_toolkits.mplot3d import Axes3D\n", + "\n", + "fig = plt.figure()\n", + "ax = fig.gca(projection = '3d')\n", + "Tp, Xp = np.meshgrid(tplot[0:iplot], xplot)\n", + "ax.plot_surface(Tp, Xp, rplot[:,0:iplot], rstride=1, cstride=1, cmap=cm.gray)\n", + "ax.view_init(elev=30., azim=10.)\n", + "ax.set_xlabel('t')\n", + "ax.set_ylabel('x')\n", + "ax.set_zlabel('rho')\n", + "ax.set_title('Density versus position and time')" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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IASOXwa6T2n56vbbOwMVQ7X6bmrBnkkogXG3jRhuff25h5EivTJVAHDkSSrt2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4wj0x3HRAqgTh0lQ4eqef99HRcuPKkyeHkJeHgI3L5tBqBbNzVLlmisPkRLFEV27bpO7do/0LPn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\nqb+AMsCv6GM/CpH+N/ZCwJ7737u76jzZx3YeCFJK5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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# %* Graph contours of density versus position and time.\n", + "\n", + "levels = np.linspace(0., 1., num=11) \n", + "ct = plt.contour(xplot, tplot, np.flipud(np.rot90(rplot)), levels) \n", + "plt.clabel(ct, fmt='%1.2f') \n", + "plt.xlabel('x')\n", + "plt.ylabel('time')\n", + "plt.title('Density contours')" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python [default]", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.12" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} diff --git a/Python/Untitled.ipynb b/Python/Untitled.ipynb new file mode 100644 index 0000000..a68b8c1 --- /dev/null +++ b/Python/Untitled.ipynb @@ -0,0 +1,141 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "x = input('Enter x: ')" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "math.pi" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Using matplotlib backend: Qt5Agg\n", + "Populating the interactive namespace from numpy and matplotlib\n" + ] + } + ], + "source": [ + "%pylab" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "math.pi" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[1, 3, 1, 3]\n" + ] + } + ], + "source": [ + "r = [1, 3]\n", + "a = 2*r\n", + "print(a)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "norm(r)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "r / norm(r)**3" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "x" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python [default]", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.12" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +}