From 8449c6ec97cec869e8b0645bdcb252699324e47b Mon Sep 17 00:00:00 2001 From: Homer Reid Date: Fri, 8 Feb 2019 14:31:29 -0500 Subject: [PATCH 01/16] add --without-scheme option to configure to bypass building the scheme interface --- Makefile.am | 2 + configure.ac | 321 ++++++++++++++++++++++++++------------------------- 2 files changed, 168 insertions(+), 155 deletions(-) diff --git a/Makefile.am b/Makefile.am index 3b0c93ab0..e3d96f690 100644 --- a/Makefile.am +++ b/Makefile.am @@ -3,8 +3,10 @@ ACLOCAL_AMFLAGS=-I m4 SUBDIRS = src tests if WITH_LIBCTL +if WITH_SCHEME SUBDIRS += scheme endif +endif if WITH_MPB if WITH_LIBCTLGEOM SUBDIRS += libpympb diff --git a/configure.ac b/configure.ac index ca5532052..8831230c9 100644 --- a/configure.ac +++ b/configure.ac @@ -242,175 +242,187 @@ fi AM_CONDITIONAL(WITH_LIBCTL, test "x$with_libctl" != xno) ############################################################################## -# Check for Guile library and its behavior (for libctl front end): - -if test "x$with_libctl" != xno; then - -save_LIBS=$LIBS -save_CPPFLAGS=$CPPFLAGS - -AC_CHECK_PROG(GUILE_CONFIG, guile-config, guile-config, unknown) -if test "x$GUILE_CONFIG" = "xunknown"; then - AC_CHECK_LIB(readline, readline) - AC_CHECK_LIB(dl, dlopen) - AC_CHECK_LIB(guile-ltdl, scm_lt_dlinit, [], [AC_CHECK_LIB(ltdl, dlopen)]) - AC_CHECK_LIB(guile, gh_eval_str, [], - [AC_CHECK_LIB(guile, scm_eval_string, [], - [AC_MSG_ERROR([linking to guile failed])])]) - GUILE_LIBS="-lguile -lguile-ltdl -lreadline" - GUILE_CPPFLAGS="" -else - GUILE_LIBS=`$GUILE_CONFIG link` - GUILE_CPPFLAGS=`$GUILE_CONFIG compile` - CPPFLAGS="$CPPFLAGS $GUILE_CPPFLAGS" - LIBS="$GUILE_LIBS $LIBS" - AC_MSG_CHECKING([if linking to guile works]) - AC_TRY_LINK_FUNC(gh_enter, AC_MSG_RESULT(yes), - [AC_TRY_LINK_FUNC(scm_boot_guile, AC_MSG_RESULT(yes), - [AC_MSG_RESULT(no) - AC_MSG_ERROR([guile-config is broken])])]) -fi -AC_CHECK_HEADERS([libguile.h guile/gh.h]) - -# Check how smob types work in this Guile version: +# the scheme interface is built by default, but this may be changed by +# configuring --without-scheme +############################################################################## +AM_CONDITIONAL(WITH_SCHEME, test "x$with_scheme" != xno) +AC_ARG_WITH(scheme, + [AC_HELP_STRING([--without-scheme], [compile without scheme interface])], + with_scheme=$withval,with_scheme=yes) -AC_CHECK_FUNCS(scm_make_smob_type) -AC_MSG_CHECKING([for SCM_SMOB_PREDICATE]) -AC_TRY_LINK([#include -#include ], - [int x; SCM_SMOB_PREDICATE(1,x);], - ok=yes, ok=no) -AC_MSG_RESULT($ok) -if test $ok = yes; then - AC_DEFINE(HAVE_SCM_SMOB_PREDICATE, 1, [define if we have SCM_SMOB_PREDICATE]) -fi -AC_MSG_CHECKING([for SCM_SMOB_DATA]) -AC_TRY_LINK([#include +############################################################################## +# Check for Guile library and its behavior (not needed if building +# --without-scheme). Note that scheme-related checks occupy the next +# 167 lines. +############################################################################## +if test "x$with_scheme" != xno -a "x$with_libctl" != xno; then + + save_LIBS=$LIBS + save_CPPFLAGS=$CPPFLAGS + + AC_CHECK_PROG(GUILE_CONFIG, guile-config, guile-config, unknown) + if test "x$GUILE_CONFIG" = "xunknown"; then + AC_CHECK_LIB(readline, readline) + AC_CHECK_LIB(dl, dlopen) + AC_CHECK_LIB(guile-ltdl, scm_lt_dlinit, [], [AC_CHECK_LIB(ltdl, dlopen)]) + AC_CHECK_LIB(guile, gh_eval_str, [], + [AC_CHECK_LIB(guile, scm_eval_string, [], + [AC_MSG_ERROR([linking to guile failed])])]) + GUILE_LIBS="-lguile -lguile-ltdl -lreadline" + GUILE_CPPFLAGS="" + else + GUILE_LIBS=`$GUILE_CONFIG link` + GUILE_CPPFLAGS=`$GUILE_CONFIG compile` + CPPFLAGS="$CPPFLAGS $GUILE_CPPFLAGS" + LIBS="$GUILE_LIBS $LIBS" + AC_MSG_CHECKING([if linking to guile works]) + AC_TRY_LINK_FUNC(gh_enter, AC_MSG_RESULT(yes), + [AC_TRY_LINK_FUNC(scm_boot_guile, AC_MSG_RESULT(yes), + [AC_MSG_RESULT(no) + AC_MSG_ERROR([guile-config is broken])])]) + fi + AC_CHECK_HEADERS([libguile.h guile/gh.h]) + + # Check how smob types work in this Guile version: + + AC_CHECK_FUNCS(scm_make_smob_type) + AC_MSG_CHECKING([for SCM_SMOB_PREDICATE]) + AC_TRY_LINK([#include + #include ], + [int x; SCM_SMOB_PREDICATE(1,x);], + ok=yes, ok=no) + AC_MSG_RESULT($ok) + if test $ok = yes; then + AC_DEFINE(HAVE_SCM_SMOB_PREDICATE, 1, [define if we have SCM_SMOB_PREDICATE]) + fi + AC_MSG_CHECKING([for SCM_SMOB_DATA]) + AC_TRY_LINK([#include #include ], [int x; SCM_SMOB_DATA(x);], ok=yes, ok=no) -AC_MSG_RESULT($ok) -if test $ok = yes; then - AC_DEFINE(HAVE_SCM_SMOB_DATA, 1, [define if we have SCM_SMOB_DATA]) -fi -AC_MSG_CHECKING([for SCM_NEWSMOB]) -AC_TRY_LINK([#include + AC_MSG_RESULT($ok) + if test $ok = yes; then + AC_DEFINE(HAVE_SCM_SMOB_DATA, 1, [define if we have SCM_SMOB_DATA]) + fi + + AC_MSG_CHECKING([for SCM_NEWSMOB]) + AC_TRY_LINK([#include #include ], [int x; SCM_NEWSMOB(x,1,0);], ok=yes, ok=no) -AC_MSG_RESULT($ok) -if test $ok = yes; then - AC_DEFINE(HAVE_SCM_NEWSMOB, 1, [define if we have SCM_NEWSMOB]) -fi + AC_MSG_RESULT($ok) + if test $ok = yes; then + AC_DEFINE(HAVE_SCM_NEWSMOB, 1, [define if we have SCM_NEWSMOB]) + fi -# Check how to activate Guile readline support: + # Check how to activate Guile readline support: + ACTIVATE_READLINE="" + if test "x$cross_compiling" = xno; then + AC_MSG_CHECKING(how to activate readline in Guile) + ractivate="(use-modules (readline-activator)) (activate-readline)" + if guile -c "$ractivate" > /dev/null 2>&1; then + AC_MSG_RESULT(readline-activator) + ACTIVATE_READLINE="$ractivate" + else + ractivate="(use-modules (ice-9 readline)) (activate-readline)" + if guile -c "$ractivate" >& /dev/null; then + AC_MSG_RESULT(ice-9 readline) + ACTIVATE_READLINE="$ractivate" + else + AC_MSG_RESULT(cannot) + ACTIVATE_READLINE="" + fi + fi + fi -ACTIVATE_READLINE="" -if test "x$cross_compiling" = xno; then -AC_MSG_CHECKING(how to activate readline in Guile) -ractivate="(use-modules (readline-activator)) (activate-readline)" -if guile -c "$ractivate" > /dev/null 2>&1; then - AC_MSG_RESULT(readline-activator) - ACTIVATE_READLINE="$ractivate" -else - ractivate="(use-modules (ice-9 readline)) (activate-readline)" - if guile -c "$ractivate" >& /dev/null; then - AC_MSG_RESULT(ice-9 readline) - ACTIVATE_READLINE="$ractivate" - else - AC_MSG_RESULT(cannot) - ACTIVATE_READLINE="" - fi -fi -fi -AC_SUBST(ACTIVATE_READLINE) + AC_SUBST(ACTIVATE_READLINE) -AC_SUBST(GUILE_LIBS) -AC_SUBST(GUILE_CPPFLAGS) -LIBS=$save_LIBS -CPPFLAGS=$save_CPPFLAGS + AC_SUBST(GUILE_LIBS) + AC_SUBST(GUILE_CPPFLAGS) + LIBS=$save_LIBS + CPPFLAGS=$save_CPPFLAGS -fi # if with_libctl +fi # if with_scheme -a with_libctl ############################################################################## # Check for libctl library and files -if test "x$with_libctl" != xno; then +if test "x$with_scheme" != xno -a "x$with_libctl" != xno; then -save_LIBS=$LIBS -save_CPPFLAGS=$CPPFLAGS -LIBS="$GUILE_LIBS $LIBS" -CPPFLAGS="$CPPFLAGS $GUILE_CPPFLAGS" - -AC_MSG_CHECKING([for libctl dir]) -if test x != x"$LIBCTL_DIR" -a ! -r "$LIBCTL_DIR/base/ctl.scm"; then - LIBCTL_DIR="" -fi -if test x = x"$LIBCTL_DIR" -a -r /usr/local/share/libctl/base/ctl.scm; then - LIBCTL_DIR="/usr/local/share/libctl" -fi -if test x = x"$LIBCTL_DIR" -a -r /usr/share/libctl3/base/ctl.scm; then - LIBCTL_DIR="/usr/share/libctl3" -fi -if test x = x"$LIBCTL_DIR" -a -r /usr/share/libctl/base/ctl.scm; then - LIBCTL_DIR="/usr/share/libctl" -fi -if test x = x"$LIBCTL_DIR"; then - AC_MSG_ERROR([could not find libctl files; use --with-libctl=]) -fi -AC_MSG_RESULT($LIBCTL_DIR) -AC_SUBST(LIBCTL_DIR) + save_LIBS=$LIBS + save_CPPFLAGS=$CPPFLAGS + LIBS="$GUILE_LIBS $LIBS" + CPPFLAGS="$CPPFLAGS $GUILE_CPPFLAGS" -AC_CHECK_PROGS(GEN_CTL_IO, gen-ctl-io, echo) -if test x"$GEN_CTL_IO" = xecho; then - AC_MSG_ERROR([could not find gen-ctl-io program; check your PATH]) -fi + AC_MSG_CHECKING([for libctl dir]) + if test x != x"$LIBCTL_DIR" -a ! -r "$LIBCTL_DIR/base/ctl.scm"; then + LIBCTL_DIR="" + fi + if test x = x"$LIBCTL_DIR" -a -r /usr/local/share/libctl/base/ctl.scm; then + LIBCTL_DIR="/usr/local/share/libctl" + fi + if test x = x"$LIBCTL_DIR" -a -r /usr/share/libctl3/base/ctl.scm; then + LIBCTL_DIR="/usr/share/libctl3" + fi + if test x = x"$LIBCTL_DIR" -a -r /usr/share/libctl/base/ctl.scm; then + LIBCTL_DIR="/usr/share/libctl" + fi + if test x = x"$LIBCTL_DIR"; then + AC_MSG_ERROR([could not find libctl files; use --with-libctl=]) + fi + AC_MSG_RESULT($LIBCTL_DIR) + AC_SUBST(LIBCTL_DIR) -# check for -lctl: -AC_CHECK_LIB(ctl, ctl_get_vector3, [], [AC_MSG_ERROR([Couldn't find the required libctl library.])]) + AC_CHECK_PROGS(GEN_CTL_IO, gen-ctl-io, echo) + if test x"$GEN_CTL_IO" = xecho; then + AC_MSG_ERROR([could not find gen-ctl-io program; check your PATH]) + fi -# check for ctl.h (Fedora puts it in /usr/include/ctl, grrr) -CTL_H_CPPFLAG="" -AC_CHECK_HEADER(ctl.h, [CTL_H_CPPFLAG=" "], [ + # check for -lctl: + AC_CHECK_LIB(ctl, ctl_get_vector3, [], [AC_MSG_ERROR([Couldn't find the required libctl library.])]) + + # check for ctl.h (Fedora puts it in /usr/include/ctl, grrr) + CTL_H_CPPFLAG="" + AC_CHECK_HEADER(ctl.h, [CTL_H_CPPFLAG=" "], [ + save_CPPFLAGS=$CPPFLAGS + AC_MSG_CHECKING([for alternate ctl.h location]) + for ctl_h_path in /usr/include/ctl /usr/local/include/ctl; do + CPPFLAGS="$save_CPPFLAGS -I$ctl_h_path" + AC_COMPILE_IFELSE([AC_LANG_PROGRAM([[#include ]],[])], [CTL_H_CPPFLAG=-I$ctl_h_path; break]) + done + AC_MSG_RESULT([$CTL_H_CPPFLAG]) + CPPFLAGS=$save_CPPFLAGS]) + if test "x$CTL_H_CPPFLAG" = "x"; then + AC_MSG_ERROR([Couldn't find the ctl.h header file for libctl.]) + fi + AC_SUBST(CTL_H_CPPFLAG) + save_CPPFLAGS=$CPPFLAGS - AC_MSG_CHECKING([for alternate ctl.h location]) - for ctl_h_path in /usr/include/ctl /usr/local/include/ctl; do - CPPFLAGS="$save_CPPFLAGS -I$ctl_h_path" - AC_COMPILE_IFELSE([AC_LANG_PROGRAM([[#include ]],[])], [CTL_H_CPPFLAG=-I$ctl_h_path; break]) - done - AC_MSG_RESULT([$CTL_H_CPPFLAG]) - CPPFLAGS=$save_CPPFLAGS]) -if test "x$CTL_H_CPPFLAG" = "x"; then - AC_MSG_ERROR([Couldn't find the ctl.h header file for libctl.]) -fi -AC_SUBST(CTL_H_CPPFLAG) - -save_CPPFLAGS=$CPPFLAGS -CPPFLAGS="$CPPFLAGS $CTL_H_CPPFLAG" -# Check libctl version >= LIBCTL_MAJOR.LIBCTL_MINOR.LIBCTL_BUGFIX -LIBCTL_MAJOR=4; LIBCTL_MINOR=2; LIBCTL_BUGFIX=0 -AC_MSG_CHECKING([whether libctl version is at least ${LIBCTL_MAJOR}.${LIBCTL_MINOR}.${LIBCTL_BUGFIX}]) -AC_EGREP_CPP(yes, [[ -#include -#if LIBCTL_MAJOR_VERSION > $LIBCTL_MAJOR || (LIBCTL_MAJOR_VERSION == $LIBCTL_MAJOR && (LIBCTL_MINOR_VERSION > $LIBCTL_MINOR || (LIBCTL_MINOR_VERSION == $LIBCTL_MINOR && LIBCTL_BUGFIX_VERSION >= $LIBCTL_BUGFIX))) - yes -#endif -]], [AC_MSG_RESULT(ok)], [AC_MSG_ERROR([libctl version ${LIBCTL_MAJOR}.${LIBCTL_MINOR}.${LIBCTL_BUGFIX} or later is required])]) -CPPFLAGS=$save_CPPFLAGS - -# Check for libctl_quiet feature (in libctl 3.1.1 or later): -AC_MSG_CHECKING([for libctl_quiet feature]) -if grep libctl_quiet "$LIBCTL_DIR/base/main.c" 2>&1 > /dev/null; then - AC_MSG_RESULT(yes) - AC_DEFINE([HAVE_LIBCTL_QUIET], [1], [If we have the libctl_quiet variable]) -else + CPPFLAGS="$CPPFLAGS $CTL_H_CPPFLAG" + # Check libctl version >= LIBCTL_MAJOR.LIBCTL_MINOR.LIBCTL_BUGFIX + LIBCTL_MAJOR=4; LIBCTL_MINOR=2; LIBCTL_BUGFIX=0 + AC_MSG_CHECKING([whether libctl version is at least ${LIBCTL_MAJOR}.${LIBCTL_MINOR}.${LIBCTL_BUGFIX}]) + AC_EGREP_CPP(yes, [[ + #include + #if LIBCTL_MAJOR_VERSION > $LIBCTL_MAJOR || (LIBCTL_MAJOR_VERSION == $LIBCTL_MAJOR && (LIBCTL_MINOR_VERSION > $LIBCTL_MINOR || (LIBCTL_MINOR_VERSION == $LIBCTL_MINOR && LIBCTL_BUGFIX_VERSION >= $LIBCTL_BUGFIX))) + yes + #endif + ]], [AC_MSG_RESULT(ok)], [AC_MSG_ERROR([libctl version ${LIBCTL_MAJOR}.${LIBCTL_MINOR}.${LIBCTL_BUGFIX} or later is required])]) + CPPFLAGS=$save_CPPFLAGS + + # Check for libctl_quiet feature (in libctl 3.1.1 or later): + AC_MSG_CHECKING([for libctl_quiet feature]) + if grep libctl_quiet "$LIBCTL_DIR/base/main.c" 2>&1 > /dev/null; then + AC_MSG_RESULT(yes) + AC_DEFINE([HAVE_LIBCTL_QUIET], [1], [If we have the libctl_quiet variable]) + else AC_MSG_RESULT(no) -fi + fi -LIBS=$save_LIBS -CPPFLAGS=$save_CPPFLAGS + LIBS=$save_LIBS + CPPFLAGS=$save_CPPFLAGS -fi # if with_libctl +fi # if with_scheme && with_libctl ############################################################################## @@ -420,7 +432,6 @@ AC_SUBST(LIBCTL_LIBS) AC_SUBST(LIBCTL_CPPFLAGS) ############################################################################## - # check for -lctlgeom: AC_CHECK_LIB(ctlgeom, vector3_dot, [have_libctlgeom=yes], [have_libctlgeom=no]) AM_CONDITIONAL(WITH_LIBCTLGEOM, test x"$have_libctlgeom" = "xyes") @@ -483,7 +494,6 @@ AC_C_RESTRICT AC_TRY_COMPILE([], [_Pragma("ivdep")], [], [AC_DEFINE([_Pragma],[],[define to nothing if C99 _Pragma is not supported])]) ############################################################################## - # checks for python ############################################################################## AC_ARG_WITH(python, @@ -545,21 +555,22 @@ AC_SUBST(PYTHON_INCLUDES) AM_CONDITIONAL(WITH_PYTHON, test x"$have_python" = "xyes") AM_CONDITIONAL(WITH_COVERAGE, test x"$have_coverage" = "xyes") -# Copy/symlink casimir.scm and materials.scm to builddir for out-of-tree builds -AC_CONFIG_LINKS(scheme/casimir.scm:scheme/casimir.scm) -AC_CONFIG_LINKS(scheme/materials.scm:scheme/materials.scm) - ############################################################################## - AC_CONFIG_FILES([ Makefile meep-pkgconfig src/Makefile tests/Makefile - scheme/Makefile - scheme/meep.scm libpympb/Makefile python/Makefile ]) +if test "x$with_scheme" != xno; then + # Copy/symlink casimir.scm and materials.scm to builddir for out-of-tree builds + AC_CONFIG_LINKS(scheme/casimir.scm:scheme/casimir.scm) + AC_CONFIG_LINKS(scheme/materials.scm:scheme/materials.scm) + + AC_CONFIG_FILES([scheme/Makefile scheme/meep.scm]) +fi + AC_OUTPUT From c925b01feb6779de0d17b8c0a031084ec5c826f6 Mon Sep 17 00:00:00 2001 From: Homer Reid Date: Sat, 9 Feb 2019 02:33:03 -0500 Subject: [PATCH 02/16] revised normalization of eigenmode sources to yield unit power flux (in the CW case); added discussion to FAQ section of documentation --- doc/docs/FAQ.md | 50 ++++++++++++++++++++++++++++++++++++++++++++++++ python/source.py | 2 ++ src/meep.hpp | 1 + src/mpb.cpp | 13 +++++++++---- src/sources.cpp | 9 +++++++++ 5 files changed, 71 insertions(+), 4 deletions(-) diff --git a/doc/docs/FAQ.md b/doc/docs/FAQ.md index e6d804013..05f30894a 100644 --- a/doc/docs/FAQ.md +++ b/doc/docs/FAQ.md @@ -241,6 +241,56 @@ Meep can run in parallel on a shared-memory machine using MPI. However, it doesn The field from a point source is singular — it blows up as you approach the source. At any finite resolution, this singularity is truncated to a finite value by the discretization but the peak field at the source location increases as you increase the resolution. +### What normalization convention does meep use for the fields of eigenmode sources? + +An [eigenmode source](Python_User_Interface.md#eigenmodesource) +is a localized distribution of electric and magnetic currents +$\mathbf{J}(\mathbf{x}), \mathbf{M}(\mathbf{x})$, +confined to a cross-sectional line (2D) or plane (3D) through a +waveguide or similar geometry, with the property that the +spatial distribution of the +electric and magnetic fields radiated by the sources +exactly reproduces the spatial distribution of +one specific (quasi-)normal mode of the +geometry (and is thus orthogonal to all other modes). +This condition leaves unspecified an overall scale +factor---if a field distribution +$\{\mathbf{E}(\mathbf x), \mathbf{H}(\mathbf x)\}$ +satisfies the single-mode condition, +then so does the scaled distribution +$\{\lambda \mathbf{E}(\mathbf x), \lambda \mathbf{H}(\mathbf x)\}$ +for any arbitrary $\lambda.$ To pin down this +ambiguity, MEEP chooses the overall amplitude of eigenmode +sources to ensure that the total power flux +carried by the fields they produce---the integral +of the normal Poynting vector over the cross-sectional +line or plane---evaluates numerically to 1. + +More specifically, +in a time-harmonic problem in which all sources and fields +have time dependence $e^{-i\omega_m t}$ (where $\omega$ + +In practice, this has the following ramifications for MEEP +calculations using eigenmode sources: + ++ For [frequency-domain calculations](Python_User_Interface.md#frequency-domain-solver) + involving an eigenmode source with a `ContinuousSrc` time envelope---corresponding + to monochromatic fields and sources that oscillate forever at the eigenfrequency + of the mode---the total flux + ++ On the other hand, for the typical case of *time-domain* calculations, + in which the spatial current distributions + $\mathbf{J}(\mathbf{x}), \mathbf{M}(\mathbf x)}$ of the eigenmode source + are paired with a temporal envelope function $W(t)$---in practice + either a + [gaussian](Python_User_Interface.md#gaussiansource) or a + [user-specified custom envelope](Python_User_Interface.md#customsource)---the + values reported by MEEP for all frequency-domain field amplitudes at + frequency $\omega$ will include factors of $\widetwiddle{W}(\omega)$ + (the Fourier transform of the temporal envelope), while + while field-bilinear quantities like Poynting vectors and power fluxes + will include factors of $|\widetwiddle{W}(\omega)|^2.$ + ### How does Meep deal with numerical dispersion? Numerical dispersion can be analyzed and quantified analytically for a homogeneous medium. For details, see e.g., Chapter 4 ("Numerical Dispersion and Stability") of [Computational Electrodynamics: The Finite Difference Time-Domain Method (3rd edition)](https://www.amazon.com/Computational-Electrodynamics-Finite-Difference-Time-Domain-Method/dp/1580538320). However, in practice numerical dispersion is rarely the dominant source of error in FDTD calculations which almost always involve material inhomogeneities that give rise to much larger errors. Similar to other errors associated with the finite grid resolution, numerical dispersion decreases with resolution, so you can deal with it by increasing the resolution until convergence is obtained to the desired accuracy. In particular, the errors from numerical dispersion vary *quadratically* with resolution (in the ordinary center-difference FDTD scheme). On the other hand, the errors introduced by discretization of material interfaces go *linearly* with the resolution, so they are almost always dominant. Meep can partially correct for these errors using [subpixel averaging](Introduction.md#the-illusion-of-continuity). diff --git a/python/source.py b/python/source.py index 9f0bceb6f..838091a9f 100644 --- a/python/source.py +++ b/python/source.py @@ -66,6 +66,8 @@ def __init__(self, frequency=None, width=0, fwidth=float('inf'), start_time=0, c self.start_time + 2 * self.width * self.cutoff) self.swigobj.is_integrated = self.is_integrated + def fourier_transform(self, omega): + return self.swigobj.fourier_transform(omega) class CustomSource(SourceTime): diff --git a/src/meep.hpp b/src/meep.hpp index fd3d0d8ba..20ffa549d 100644 --- a/src/meep.hpp +++ b/src/meep.hpp @@ -834,6 +834,7 @@ class gaussian_src_time : public src_time { virtual bool is_equal(const src_time &t) const; virtual std::complex frequency() const { return freq; } virtual void set_frequency(std::complex f) { freq = real(f); } + std::complex fourier_transform(const double omega); private: double freq, width, peak_time, cutoff; diff --git a/src/mpb.cpp b/src/mpb.cpp index b054b4424..85f839a15 100644 --- a/src/mpb.cpp +++ b/src/mpb.cpp @@ -543,11 +543,16 @@ void *fields::get_eigenmode(double omega_src, direction d, const volume where, c scalar_complex *fft_data_E = (scalar_complex *)malloc(NFFT * sizeof(scalar_complex)); maxwell_compute_d_from_H(mdata, H, fft_data_E, band_num - 1, 1); - // d_from_H actually computes -omega*D (see mpb/src/maxwell/maxwell_op.c) - double scale = -1.0 / omega_src; - cdouble *efield = (cdouble *)fft_data_E; + + // d_from_H actually computes -omega*D (see mpb/src/maxwell/maxwell_op.c), + // so we need to divide the E-field amplitudes by -omega; we also take this + // opportunity to rescale the overall E and H amplitudes to yield unit power flux. + double scale = -1.0/omega_src, factor=2.0/sqrt(vgrp); + cdouble *efield = (cdouble *)fft_data_E, *hfield = (cdouble *)(mdata->fft_data); for (int n = 0; n < NFFT; ++n) - efield[n] *= scale; + { efield[n] *= factor * scale; + hfield[n] *= factor; + } maxwell_compute_e_from_d(mdata, fft_data_E, 1); diff --git a/src/sources.cpp b/src/sources.cpp index a8302d40d..538ec7882 100644 --- a/src/sources.cpp +++ b/src/sources.cpp @@ -92,6 +92,15 @@ complex gaussian_src_time::dipole(double time) const { return exp(-tt * tt / (2 * width * width)) * polar(1.0, -2 * pi * freq * tt) * amp; } +// (1/\sqrt{2*pi}) \int e^{i\omega t} G(t) dt +// where G(t) is the *current* envelope, i.e. the time derivative +// of the dipole envelope +std::complex gaussian_src_time::fourier_transform(const double omega) +{ double omega0=2.0*pi*freq; + double delta=(omega-omega0)*width; + return width * polar(1.0,omega0*peak_time) * exp(-0.5*delta*delta); +} + bool gaussian_src_time::is_equal(const src_time &t) const { const gaussian_src_time *tp = dynamic_cast(&t); if (tp) From 57339828262a351a7d5024045177eff2a359c1b3 Mon Sep 17 00:00:00 2001 From: Homer Reid Date: Sat, 9 Feb 2019 05:03:25 -0500 Subject: [PATCH 03/16] updates --- doc/docs/FAQ.md | 30 +++++++++++++++++++----------- 1 file changed, 19 insertions(+), 11 deletions(-) diff --git a/doc/docs/FAQ.md b/doc/docs/FAQ.md index 05f30894a..42b5079ae 100644 --- a/doc/docs/FAQ.md +++ b/doc/docs/FAQ.md @@ -241,7 +241,7 @@ Meep can run in parallel on a shared-memory machine using MPI. However, it doesn The field from a point source is singular — it blows up as you approach the source. At any finite resolution, this singularity is truncated to a finite value by the discretization but the peak field at the source location increases as you increase the resolution. -### What normalization convention does meep use for the fields of eigenmode sources? +### What normalization convention does MEEP use for the fields of eigenmode sources? An [eigenmode source](Python_User_Interface.md#eigenmodesource) is a localized distribution of electric and magnetic currents @@ -253,22 +253,30 @@ electric and magnetic fields radiated by the sources exactly reproduces the spatial distribution of one specific (quasi-)normal mode of the geometry (and is thus orthogonal to all other modes). -This condition leaves unspecified an overall scale -factor---if a field distribution +This condition determines the fields only up to +an arbitrary overall scale factor---if a field distribution $\{\mathbf{E}(\mathbf x), \mathbf{H}(\mathbf x)\}$ satisfies the single-mode condition, -then so does the scaled distribution +then so does the scaled field distribution $\{\lambda \mathbf{E}(\mathbf x), \lambda \mathbf{H}(\mathbf x)\}$ -for any arbitrary $\lambda.$ To pin down this -ambiguity, MEEP chooses the overall amplitude of eigenmode -sources to ensure that the total power flux -carried by the fields they produce---the integral +for any arbitrary $\lambda$---whereupon by linearity +the spatial current distributions $\mathbf{J,M}(\mathbf x)$ + +To pin down this +ambiguity, MEEP chooses the overall amplitude of +eigenmode +sources to ensure that, for the specific case of a time-harmonic +problem with all sources and fields x +time dependence $e^{-i\omega_m t}$ (where $\omega_m$ +is the eigenfrequency of the mode) + the total power flux +carried by the fields they produce (the integral of the normal Poynting vector over the cross-sectional -line or plane---evaluates numerically to 1. +line or plane) evaluates numerically to 1 in a +time-harmonic More specifically, -in a time-harmonic problem in which all sources and fields -have time dependence $e^{-i\omega_m t}$ (where $\omega$ +in a time-harmonic problem In practice, this has the following ramifications for MEEP calculations using eigenmode sources: From 4a6403006375ce9d89613bf202b53c804bf8bd4e Mon Sep 17 00:00:00 2001 From: Homer Reid Date: Sat, 9 Feb 2019 08:45:03 -0500 Subject: [PATCH 04/16] update FAQ entry regarding normalization of eigenmode sources --- doc/docs/FAQ.md | 92 ++++++++++++++++++++++++++++++------------------- 1 file changed, 57 insertions(+), 35 deletions(-) diff --git a/doc/docs/FAQ.md b/doc/docs/FAQ.md index 42b5079ae..1b9c8456f 100644 --- a/doc/docs/FAQ.md +++ b/doc/docs/FAQ.md @@ -244,14 +244,13 @@ The field from a point source is singular — it blows up as you approach th ### What normalization convention does MEEP use for the fields of eigenmode sources? An [eigenmode source](Python_User_Interface.md#eigenmodesource) -is a localized distribution of electric and magnetic currents -$\mathbf{J}(\mathbf{x}), \mathbf{M}(\mathbf{x})$, +is a localized distribution of electric and magnetic currents +$\{\mathbf{J}(\mathbf{x}), \mathbf{M}(\mathbf{x})\}$, confined to a cross-sectional line (2D) or plane (3D) through a waveguide or similar geometry, with the property that the -spatial distribution of the -electric and magnetic fields radiated by the sources -exactly reproduces the spatial distribution of -one specific (quasi-)normal mode of the +spatial distribution of the electric and magnetic fields +radiated by the sources exactly reproduces the spatial distribution +of one specific (quasi-)normal mode of the geometry (and is thus orthogonal to all other modes). This condition determines the fields only up to an arbitrary overall scale factor---if a field distribution @@ -260,44 +259,67 @@ satisfies the single-mode condition, then so does the scaled field distribution $\{\lambda \mathbf{E}(\mathbf x), \lambda \mathbf{H}(\mathbf x)\}$ for any arbitrary $\lambda$---whereupon by linearity -the spatial current distributions $\mathbf{J,M}(\mathbf x)$ - -To pin down this -ambiguity, MEEP chooses the overall amplitude of -eigenmode -sources to ensure that, for the specific case of a time-harmonic -problem with all sources and fields x -time dependence $e^{-i\omega_m t}$ (where $\omega_m$ -is the eigenfrequency of the mode) - the total power flux -carried by the fields they produce (the integral -of the normal Poynting vector over the cross-sectional -line or plane) evaluates numerically to 1 in a -time-harmonic - -More specifically, -in a time-harmonic problem - -In practice, this has the following ramifications for MEEP -calculations using eigenmode sources: +the source-amplitude functions $\mathbf{J,M}$ also +contain an arbitrary undetermined overall scale factor. + +To pin down this ambiguity, MEEP chooses the overall scale +of the $\mathbf{J}(\mathbf{x}), \mathbf{M}(\mathbf{x})$ +source distributions to ensure that, in the specific case +of a time-harmonic problem with all sources and fields +having monochromatic time dependence $e^{-i\omega_m t}$ +(with $\omega_m$ the eigenfrequency of the mode), the +total time-average power carried by the fields radiated +by the sources---that is, the integral of the normal Poynting +vector over the full cross-sectional line or plane---comes +out equal to 1.0 power units +(where [the choice of power units is up to you](Introduction.md#units-in-meep)). +This convention has the following practical ramifications for MEEP +calculations using eigenmode sources. + For [frequency-domain calculations](Python_User_Interface.md#frequency-domain-solver) involving an eigenmode source with a `ContinuousSrc` time envelope---corresponding - to monochromatic fields and sources that oscillate forever at the eigenfrequency - of the mode---the total flux + to monochromatic sources that oscillate forever at frequency $\omega_m$, producing + monochromatic fields that oscillate forever at the same frequency---the + total time-average power carried by those fields takes the numerical + value 1. + + **Note:** Due to discretization effects, the normalization of eigenmode + sources to yield unit power transmission is only *approximate;* + at any finite resolution, the power carried by the fields of + eigenmode sources as computed by MEEP will not take the precise + numerical value 1, but will rather include discretization errors + that shrink with resolution. + On the other hand, for the typical case of *time-domain* calculations, in which the spatial current distributions - $\mathbf{J}(\mathbf{x}), \mathbf{M}(\mathbf x)}$ of the eigenmode source - are paired with a temporal envelope function $W(t)$---in practice - either a - [gaussian](Python_User_Interface.md#gaussiansource) or a + $\mathbf{J}(\mathbf{x}), \mathbf{M}(\mathbf{x})$ of the eigenmode source + are paired with a temporal envelope function $W(t)$---which, in practice, + is either a [Gaussian](Python_User_Interface.md#gaussiansource) or a [user-specified custom envelope](Python_User_Interface.md#customsource)---the values reported by MEEP for all frequency-domain field amplitudes at - frequency $\omega$ will include factors of $\widetwiddle{W}(\omega)$ - (the Fourier transform of the temporal envelope), while + frequency $\omega$ will include factors of $\widetilde W(\omega)$ + (the Fourier transform of the temporal envelope), while field-bilinear quantities like Poynting vectors and power fluxes - will include factors of $|\widetwiddle{W}(\omega)|^2.$ + will include factors of $|\widetilde W(\omega)|^2$. + + In particular, + + +In a MEEP time-stepping run excited by an eigenmode source + with Gaussian temporal envelope $G(t;\omega_0, \Delta \omega)$ + centered at angular frequency $\omega_0$ and frequency width + $\Delta \omega$, + + +the time-harmonic power carried by the frequency-domain fields + at angular frequency $\omega$ is numerically equal to + $|\widetilde{G}(\omega; \omega_0, \Delta\omega)|^2$, + where values of $\widetilde{G}$, the Fourier transform + of the temporal profile, are computed by + by the `fourier_transform` method of the + [`GaussianSource`](Python_User_Interface.md#GaussianSource) + class in the python `meep` module. + + [Here's](index.html) an example showing how the unit-power normalization + of eigenmode sources may be put to convenient use in MEEP calculations. ### How does Meep deal with numerical dispersion? From 6fccac0d4405b3e197e8d5a5e4be9f66bb9127db Mon Sep 17 00:00:00 2001 From: Homer Reid Date: Sat, 9 Feb 2019 09:46:06 -0500 Subject: [PATCH 05/16] updates --- .../AdjointImplementationNotes.md | 423 ++++++++++++++++++ doc/docs/Python_Tutorials/AdjointSolver.md | 334 ++++++++++++++ doc/docs/meep_documentation.css | 5 + mkdocs.yml | 5 + 4 files changed, 767 insertions(+) create mode 100644 doc/docs/Python_Tutorials/AdjointImplementationNotes.md create mode 100644 doc/docs/Python_Tutorials/AdjointSolver.md create mode 100644 doc/docs/meep_documentation.css diff --git a/doc/docs/Python_Tutorials/AdjointImplementationNotes.md b/doc/docs/Python_Tutorials/AdjointImplementationNotes.md new file mode 100644 index 000000000..f103d735e --- /dev/null +++ b/doc/docs/Python_Tutorials/AdjointImplementationNotes.md @@ -0,0 +1,423 @@ + + + +$$ + \newcommand{\vb}{\mathbf} + \newcommand{\wt}{\widetilde} + \newcommand{\mc}{\mathcal} + \newcommand{\bmc}[1]{\boldsymbol{\mathcal{#1}}} + \newcommand{\sup}[1]{^{\text{#1}}} + \newcommand{\pard}[2]{\frac{\partial #1}{\partial #2}} + \newcommand{\VMV}[3]{ \Big\langle #1 \Big| #2 \Big| #3 \Big\rangle} +$$ + +# Adjoint-based optimization in meep: Implementation Notes + +These notes are intended as something of a companion to the +[user's manual and tutorial documentation for adjoint-based +optimization in meep](Python_Tutorials/Adjoint_Based_Optimization.md); +whereas the goal of those pages is to document the user interface +and explain how to *use* the solver for practical problems, +our focus here will be what's going on beneath the hood---how +the solver actually *works.* + +Actually, as will be clear to anyone who has ever reviewed the +fundamentals of +[adjoint sensitivity analysis](https://en.wikipedia.org/wiki/Adjoint_state_method), +the theoretical basis of the method and the derivation of its key +formulas are almost trivially straightforward, with the only +potential source of difficulty being how to massage the mechanics +of the procedure into a meep-friendly form. + +## Toy problem + +Ultimately we will want to use adjoint methods to differentiate +complex objective functions---involving quantities such as +Poynting fluxes and mode-expansion coefficients---with respect +to various different types of parameters describing material geometries. +However, before tackling the problem in that full generality, +it's useful to build up to it by starting with a simple toy problem +and adding complications one at a time. Thus we consider a +simple waveguide geometry, excited by a point source at +$\vb{x}\sup{src}$, and define our objective function to be +simply the frequency-domain electric-field amplitude at +a point $\vb{x}\sup{obj}$; we will compute the derivative +of this objective function with respect to the permittivity +$\epsilon\sup{des}$ +in a small "design region" $\mc{V}\sup{des}$ +centered at a third point $\vb{x}\sup{des}$. + +![AdjointToyGeometry1](/images/AdjointToyGeometry1.png) + +### Permittivity derivative by finite-differencing + +An obvious brute-force way to get at this is simply +to do two meep calculations, with $\epsilon\sup{des}$ +augmented by a small finite amount $\Delta\epsilon$ on the +second run, then compute the difference between the frequency-domain +electric fields at $\vb{x}\sup{obj}$ and divide +by $\Delta\epsilon$ to estimate the derivative. +Here are plots of the unperturbed field and the field perturbation +(difference between perturbed and unperturbed field): + ++ $\wt{E_{z0}}(\omega_0, \vb{x})$ (unperturbed): + +![Unperturbed field](/images/AdjointToyEz0.png) + ++ $\Delta {\wt E_z}(\omega_0, \vb{x})$ (perturbed-unperturbed): +![Perturbation field](/images/AdjointToydEz_FD.png) + +(Here and below we use the tilde sign ($\sim$) to indicate frequency-domain +fields and sources.) + +### Permittivity derivative from effective sources + +One way to think about the effect of a localized permittivity +bump goes like this: Increasing the permittivity in some localized +region of a material body corresponds to increasing the +polarizability in that region---that is, the ease with which +positive and negative charges in the material, ordinarily bound +so tightly together that they neutralize each other as sources, +can be induced by applied electric fields to separate ("polarize"), +whereupon they cease to cancel each other and act as effective +sources contributing to electromagnetic fields. +Of course, if there were no electric field in the material, +then we could increase its polarizability as much as we pleased +without producing any sources---zero times a bigger +coefficient being still zero---but here there *is* a nonzero +electric field throughout our geometry, due to the point source +in the unperturbed problem, which means that the effect of bumping the +permittivity of the design region may be approximated by +adding new *sources* in that region, with strength +proportional to $\Delta\epsilon$ and to the unperturbed electric field. +More specifically, in a frequency-domain problem involving time-harmonic +fields and sources with angular frequency $\omega$ (time dependence +$\propto e^{-i\omega t}$), the following perturbations are +equivalent: +$$ +\begin{array}{ccc} + \left(\begin{array}{c} + \text{a permittivity shift of } \Delta\epsilon \\ + \text{over a small region } \mc{V} \text{ in which} \\ + \text{the electric field is } \wt{\vb{E}} + \end{array}\right) + &\Longleftrightarrow & + \left(\begin{array}{c} + \text{a localized electric current } \\ + \text{flowing in }\mc{V} \text{ with amplitude } \\ + \Delta\wt{\vb J}=-i\omega\Delta\epsilon \wt{\vb{E}} + \end{array}\right) +\end{array} +$$ + +![AdjointToyGeometry1](/images/AdjointToyGeometry2.png) + +Superposing this effective source with the original point source +at $\vb{x}\sup{src}$ yields a source configuration that, +acting on the *unperturbed* geometry, produces the same fields +as the point source alone acting on the *perturbed* geometry. + +Alternatively, by exploiting the linearity of Maxwell's equations +(and assuming we have linear media!) we could just as easily +remove the original point source and compute the fields of +$\wt{\Delta \vb{J}}$ *alone*, which, upon dividing through by +$\Delta\epsilon$, give just the derivatives of field components +with respect to $\epsilon$. In other words, +$$ \pard{ \wt{\vb E} (\vb x\sup{obj}) }{\epsilon\sup{des}} + \equiv + \left(\begin{array}{cc} + \text{electric field at }\vb{x}\sup{obj} \text{ due to }\\ + \text{current at }\vb{x}\sup{des}\text{ with amplitude}\\ + \wt{\Delta \vb J}=-i\omega\wt{\vb{E}}(\vb{x}\sup{obj}) + \end{array}\right) + \tag{1a} +$$ +Analogous reasoning yields a prescription for magnetic-field derivatives: +$$ \pard{\wt{\vb{H}}(\vb x\sup{obj})}{\epsilon\sup{des}} + \equiv + \left( + \begin{array}{cc} + \text{magnetic field at }\vb{x}\sup{obj} \text{ due to }\\ + \text{current at }\vb{x}\sup{des}\text{ with amplitude}\\ + \wt{\Delta \vb J}=-i\omega\wt{\vb{E}}(\vb{x}\sup{obj}) + \end{array} + \right) + \tag{1b} +$$ + +### Digression: Configuring time-domain sources for desired frequency-domain fields in meep + +In frequency-domain electromagnetism we usually consider +a time-harmonic source distribution of the form +$$ + \vb{J}\sup{monochromatic}(t,\vb{x})\equiv + \wt{\vb{J}}(\vb x)e^{-i\omega t} +$$ +and we ask for the time-harmonic electric field distribution +radiated by this distribution: +$$ + \vb{E}\sup{monochromatic}(t,\vb{x})\equiv + \wt{\vb{E}}(\vb x)e^{-i\omega t} +$$ +where $\sim$ indicates frequency-domain amplitudes. +A typical frequency-domain solver might input +$\wt{\vb J}(\vb x)$ and output +$\wt{\vb E}(\vb x)$: +$$ \wt{\vb J}(\vb x) + \quad \Longrightarrow \quad + \begin{array}{|c|}\hline\\ + \text{ frequency-domain solver }\\ + \\\hline\end{array} + \quad \Longrightarrow \quad + \wt{\vb E}(\vb x) +$$ + +On the other hand, when using meep to compute +the fields produced by a given spatial source distribution, +we typically construct a time-domain source of the form +$$\vb{J}\sup{meep}(t,\vb{x})=G(t)\wt{\vb{J}}(\vb x)$$ +where $G(t)$ is a Gaussian temporal envelope. +More specifically, for meep's `GaussianSrc` with +center frequency $\omega_0=2\pi f_0$, +frequency width $\Delta \omega =2\pi \Delta f$, and +peak time $t_0$, we have +$$ G(t) = e^{-i\omega_0(t-t_0) - \frac{1}{2}[\Delta f(t-t_0)]^2}.$$ +The Fourier transform of this is +$$ + \wt G(\omega) \equiv \frac{1}{\sqrt{2\pi}} + \int e^{i\omega t}G(t)\,dt = + \frac{1}{\Delta f} + e^{i\omega t_0 -\frac{(\omega-\omega_0)^2}{2\Delta f^2}}. +$$ +The meep version of the above +input/output diagram looks like +$$ G(t)\wt{\vb J}(\vb x) + \quad \Longrightarrow \quad + \begin{array}{|c|}\hline\\ + \text{ MEEP }\\ + \text{ (timestepping + DFT) } \\ + \\\hline\end{array} + \quad \Longrightarrow \quad + \wt{G}(\omega)\wt{\vb E}(\vb x) +$$ + +The upshot is that the frequency-domain fields obtained from a +meep run with a Gaussian source +come out multiplied by a factor of $\wt{G}(\omega)$ that should +be divided out to yield the desired frequency-domain quantities. + +## Invoking reciprocity + +It is convenient to describe the process described above +in the language of frequency-domain Green's functions, which +express the fields radiated by monochromatic source distributions +as spatial convolutions: +$$ \wt{E_i}(\omega, \vb{x}\sup{dest}) = + \int + \mc{G}\sup{EE}_{ij}(\omega, \vb{x}\sup{dest}, \vb{x}\sup{src}) + \wt{J_j}(\omega, \vb{x}\sup{src}) + \,d\vb{x}\sup{src} +$$ +with $\bmc{G}\sup{EE}$ the +electric-electric dyadic Green's function of the material geometry +(giving the electric field produced by a unit-strength electric +current). +In this language, the effective-source representation +of the permittivity derivative reads +$$ \pard{\wt{E}_i(\vb{x}\sup{obj})}{\epsilon\sup{des}} + = + \int \mc{G}\sup{EE}_{ij}(\vb{x}\sup{obj}, \vb{x}\sup{des}) + \left[-i\omega \wt{E}_j(\vb{x}\sup{des})\right] + \,d\vb{x}\sup{des} +$$ +It is convenient to think of the RHS here as a double convolution +of two vector-valued functions with the $\bmc{G}\sup{EE}$ kernel: +$$ \pard{\wt{E}_i(\vb{x}\sup{obj})}{\epsilon\sup{des}} + = + \left[ \vphantom{\wt{\vb E}\sup{des}} + \,\, \boldsymbol{\delta}_i\sup{obj}\,\, + \right] + \star \bmc{G}\sup{EE} \star + \left[-i\omega \wt{\vb E}\sup{des}\right] +$$ +or +$$ \pard{\wt E_i(\vb{x}\sup{obj})}{\epsilon\sup{des}} + =-i\omega\VMV{ \boldsymbol{\delta}_i\sup{obj} } + { \bmc G\sup{EE} } + { \wt{\vb E}\sup{des} } +$$ +where $\star$ denotes convolution, +$\boldsymbol{\delta}_i\sup{obj}$ is short for +$\delta_{ij} \delta(\vb{x}-\vb{x}\sup{obj}),$ +and the bra-ket notation describes a machine that inputs two +vector-valued functions $\vb{f},\vb{g}$ and a kernel $\mc{K}$ +and outputs a scalar quantity: +$$ \VMV{\vb f}{\bmc K}{\vb g} + \equiv \sum_{ij} \iint f_i(\vb{x}) + \mc{K}_{ij}(\vb{x},\vb{x}^\prime) + g_j(\vb{x}^\prime) + \,d\vb{x} \,d\vb{x}^\prime +$$ +(Note that this is not a Hermitian inner product, i.e. the first +factor is not conjugated.) + +For the magnetic-field derivative we have similarly +$$ \pard{\wt{H}_i(\vb{x}\sup{obj})}{\epsilon\sup{des}} + =-i\omega\VMV{ \boldsymbol{\delta}_i\sup{obj} } + { \boldsymbol{\mc G}\sup{ME} } + { \wt{\vb E}\sup{des} } +$$ +where $\bmc{G}\sup{ME}$ is the magnetic-electric +Green's function, giving the magnetic field produced +by an electric current. + +Computationally, inner products like +$\VMV{\vb f}{\bmc G\sup{EE}}{\vb g}$ +for arbitrary functions $\vb{f}(\vb x), \vb{g}(\vb x)$ +may be evaluated in meep +as follows: + +1. Create an electric current source with + spatially-varying amplitude $\vb{g}(\vb x)$ + and Gaussian temporal envelope $G(t)$. + +2. Timestep and DFT to compute the frequency-domain electric field + $\wt{\vb E}(\omega; \vb{x})$ produced by this source. + +3. Compute the inner product + $[\wt{G}(\omega)]^{-1} + \int \vb{f}\cdot \wt{\vb E}\,dV.$ + (The normalization prefactor was discussed above.) + +The virtue of writing things this way is that it allows the physical +property of reciprocity to be expressed as the mathematical property +that the aforementioned inner-product machine is insensitive to the +order of its arguments, i.e. we can flip the $\vb f$ and $\vb g$ +inputs and still get the same scalar output: +$$ \VMV{\vb f}{\bmc K}{\vb g} = \VMV{\vb g}{\bmc K}{\vb f} + \quad\text{ for }\quad \bmc K= \bmc{G}\sup{EE}, \bmc{G}\sup{ME}. +$$ + +Applying reciprocity to the above expressions for field derivatives yields +\begin{align*} +\pard{\wt E_i(\vb{x}\sup{obj})}{\epsilon\sup{des}} + &=-i\omega\VMV{ \wt{\vb E }\sup{des} } + { \bmc{G}\sup{EE} } + { \boldsymbol{\delta}_i\sup{obj} } + \tag{2} +\\[5pt] +\pard{\wt H_i(\vb{x}\sup{obj})}{\epsilon\sup{des}} + &=-i\omega\VMV{ \wt{\vb E }\sup{des} } + { \bmc{G}\sup{ME} } + { \boldsymbol{\delta}_i\sup{obj} } + \tag{3a} +\\ + \hphantom{\pard{\wt H_i(\vb{x}\sup{obj})}{\epsilon\sup{des}}} + &=+i\omega\VMV{ \wt{\vb E}\sup{des} } + { \bmc{G}\sup{EM} } + { \boldsymbol{\delta}_i\sup{obj} } + \tag{3b} +\end{align*} +where in going to the last line we invoked the identity +$\bmc{G}\sup{EM}=-\bmc{G}\sup{ME}.$ + +Note that equations (3a) and (3b), notwithstanding their nearly +identical appearance, describe two rather different +meep calculations: In the former case +we place an electric source at $\vb x\sup{obj}$ and timestep to +compute the resulting magnetic field, while in the latter +case we place a magnetic source and timestep +to compute the resulting electric field. (In both cases, +upon computing the field in question we proceed to compute its +overlap with the unperturbed $\vb E$ field in the design region.) + +## Differentiating more complicated functions of field components + +Thus far we have only considered derivatives of individual +field components, and then only at a single point $\vb{x}\sup{obj}$; +more generally, we will want to differentiate functions of +multiple field components over a subregion of the grid, +which we will call the *objective region* $\mc{V}\sup{obj}$. + +### **E**-field energy in region + +As one example, the electric field energy in the objective +region is defined by an integral over that region, which meep +approximate by a weighted sum over grid points: +$$ \mc{E}= + \frac{1}{2}\int_{\mc{V}\sup{obj}} \epsilon |\wt{\vb E}|^2 \,d\mc{V} + \approx + \frac{1}{2}\sum_{i,\vb{n}\in\mc{V}\sup{obj}} w_{\vb{n}} + \epsilon_\vb {n} \wt E_{i\vb n}^* \wt E_{i\vb n} +$$ +Here the sum is over all field components $i=\{x,y,z\}$ and +all grid points $\vb{n}$ lying in $\mc{V}\sup{obj}$, +and $w_{\vb{n}}$ is a cubature weight associated with point $\vb{n}$ +(as returned by [`get_dft_array_metadata`](/Python_User_Interface#metadata)). +Differentiating, we have +\begin{align*} + \pard{\mc E}{\epsilon\sup{des}} + &=\text{Re }\sum_{i\vb{n}\in\mc V\sup{obj}} w_{\vb n}\epsilon_{\vb n} + \wt{E}^*_{i\vb n} \pard{\wt{E}_{i\vb n}} {\epsilon\sup{des}} +\\ +&\hspace{-1.5in}\text{Insert equation (1a):} +\\ + &=\text{Re }\left\{ -i\omega \VMV{\epsilon \wt{\vb E}\sup{obj*}} + {{\bmc G}\sup{EE}} + {\wt{\vb E}\sup{des}} + \right\} +\\ +&\hspace{-1.5in}\text{Invoke reciprocity:} +\\ + &=\text{Re }\left\{ -i\omega \VMV{\wt{\vb E}\sup{des}} + {{\bmc G}\sup{EE}} + {\epsilon \wt{\vb E}\sup{obj*}} + \right\} +\end{align*} + +### Poynting flux + +A case that arises frequently is that in which the objective region +is a cross-sectional surface $\mc S\sup{obj}$ cutting normally through a +waveguide or similar structure and the objective function is the +normal Poynting flux through $\mc S$. +For example, the $x$-directed Poynting flux is given by +$$ + S_x += +\frac{1}{2}\text{Re }\left\{ \int_{\mc S\sup{obj}} \Big(E^*_y H_z + \cdots\Big) \, d\mathbf{x} \right\} +\approx \frac{1}{2}\text{Re }\sum_{\vb n\in \mc S\sup{obj}} w_{\vb n} + \Big(E^*_{y\vb n} H_{z\vb n} + \cdots\Big) +$$ +where $\cdots$ refers to three other terms of the form $\pm E^*_i H_j$. +Differentiating and rearranging slightly, we have +\begin{align*} + \pard{S_x}{\epsilon\sup{des}} + &=\text{Re }\sum_{\vb n\in \mc S\sup{obj}} w + \left\{ \wt{E}^*_{y} \pard{\wt{H}_z}{\epsilon\sup{des}} + +\wt{H}^*_{z} \pard{\wt{E}_y}{\epsilon\sup{des}} + +\cdots + \right\} +\\[5pt] +&\hspace{-0.5in}\text{Use (1a) and (1b):} +\\[5pt] + &=\text{Re }\left\{ -i\omega \VMV{\wt{\vb E}_{y}\sup{obj*}} + {\bmc G\sup{ME}} + {\wt{\vb E}\sup{des}} + -i\omega \VMV{\wt{\vb H}_z\sup{obj*}} + {\bmc G\sup{EE}} + {\wt{\vb E}\sup{des}} + +\cdots + \right\} +\\[5pt] +&\hspace{-0.5in}\text{Use reciprocity:} +\\[5pt] +&=\text{Re }\left\{ -i\omega \VMV{\wt{\vb E}\sup{des}} + {\bmc G\sup{ME}} + {\wt{\vb E}_y\sup{obj*}} + -i\omega \VMV{\wt{\vb E}\sup{des}} + {\bmc G\sup{EE}} + {\wt{\vb H}_z\sup{obj*}} + +\cdots + \right\} +\end{align*} diff --git a/doc/docs/Python_Tutorials/AdjointSolver.md b/doc/docs/Python_Tutorials/AdjointSolver.md new file mode 100644 index 000000000..c2132cea3 --- /dev/null +++ b/doc/docs/Python_Tutorials/AdjointSolver.md @@ -0,0 +1,334 @@ +--- +# Automated design optimization via adjoint sensitivity analysis +--- + +This tutorial demonstrates the use of meep's support for +[*adjoint sensitivity analysis*](https://en.wikipedia.org/wiki/Adjoint_state_method) +to facilitate automated design optimization via derivative-based +numerical optimization. + +## Overview and Invitation +-------------------------------- + +Before jumping into technical details, let's start by +recalling the bird's-eye view of + +### Photonic design optimization: Common problem structure and simple examples + +The problems we'll consider all have the following common +general structure: We are given an early-stage draft of a +photonic device design in which some features are fixed +and immutable, but + +---which, for our purposes, amounts +to a description of the spatially-varying scalar permittivity +function $\epsilon(\mathbf{x})$ throught + + +we excite it + +and compute + +where a ``device design'' amounts + +kklsp$k +We excite + +### Specifying objective regions and defining objective functions + +### + + +### Examples + +in which +some regions are fixed and immutable + +---for example, the +input and output waveguide sections in the taper problem +below---but + +We excite this geometry using a given fixed source of incident +radiation and +which will typically be a function + +### + +The metric for ``improvement' + +We have a + +In a nutshell, +Suppose + +### + +The rest of this page + +you +communicating to + ++ Set up your + ++ Invoke +`get_objective_and_gradient` +1. + +## User's manual: +-------------------------------- + +## Setting up your +-------------------------------- + +Setting up meep geometry for automated design +optimization +is + ++ Your simulation + ++ When instantiating the material configuration of your geometry, +you will + +### Objective regions and design regions +-------------------------------- + +The methods we'll illustrate are applicable to a broad class of +optimization problems in which we seek to optimize Poynting fluxes +and/or mode-expansion coefficients in one or more regions of a +geometry by tuning the structure---that is, the spatial +permittivity distribution $\epsilon(\mathbf x)$---of some portion +of the geometry. + +More specifically, we'll consider problems with the following characteristics: + ++ The objective function is of the form + $$F\Big( \big\{S_n\big\}, \big\{|\alpha_{nm}|^2\big\}\Big)$$ + where + + + $\{S_n\}=\{S_1, \cdots, S_N\}$ are the Poynting fluxes + at some user-specified set of $N$ + [flux regions](https://meep.readthedocs.io/en/latest/Python_User_Interface/#fluxregion) + $\{\mathcal{V}^o_1, \cdots, \mathcal{V}^o_N\}$, which we call the *objective regions* for + the optimization problem + + + $\alpha_{nm}$ is the + [eigenmode-expansion coefficient](https://meep.readthedocs.io/en/latest/Mode_Decomposition) + for the $m$th eigenmode in the $n$th objective region + + + $F$ is an arbitrary user-specified function of its inputs + ++ The quantity to be optimized is the permittivity distribution $\epsilon(\mathbf x)$ + within some user-specified [volume](https://meep.readthedocs.io/en/latest/Python_User_Interface/#volume) + $\mathcal{V}^d$, which we call the *design region*. + ++ The permittivity in the design region is expressed as an expansion + in some (arbitrary, user-specified) set of basis functions: + + $$ \epsilon(\mathbf x) \equiv \sum_{p=1}^P a_p \psi_p(\mathbf x), + \qquad \mathbf x\in \mathcal{V}^d$$ + + Here $\{\psi_p(\mathbf x)\}, p=1,\cdots,P$ is a set of $P$ scalar-valued basis functions, + defined for $\mathbf x \in \mathcal{V}^d$ the objective region, and the expansion coefficients $\{a_p\}$ + are the variable parameters in our optimization. + +Thus, problems for adjoint-based solvers in meep, you will specify + ++ a list of objective regions $\{\mathcal{V}^o_n\}$ + ++ a design region $\mathcal{V}^d$ + ++ a basis set $\{b_d(\mathbf{x})\}$ + ++ an objective function $F$ + +### Sample geometries + ++ Warmup: circular defect in waveguide + +A simple warmup problem is a uniform waveguide with a +circular inclusion, in which we want to optimize the +permittivity distribution in the circle to maximize +power flux through the waveguide: + +![](images/AdjointExample1.png) + +In this case we have only a single objective region, +and the objective function is simply + +$$ F\Big\(\mathcal{V}^o_1\Big)=S_1.$$ + ++ Bidirectional coupler + +## Basis functions and parameterized geometries + +### Specifying basis sets + +The basis of expansion functions for the permittivity in the design region +is described by a single routine that inputs the normalized coordinates of a point +$\mathbf{x}$ in the design region and returns a vector of length $P$ +containing $[\psi_1(\mathbf{x}), \cdots, \psi_P(\mathbf{x})]$. +Here "normalized coordinates" refers to a shifted and scaled coordinate system +in which the design region is centered at the origin and has length 1 in +all directions; so that the normalized coordinates $\overline{\mathbf{x}}$ +for points in the design region satisfy $-0.5<\overline{x}_i<0.5$ for all $i$. +then every component of $\overline{\mathbf{x}}$ lies in the range $[-0.5,0.5]$ + +Here are some examples of basis sets for 2D design regions: + ++ A simple polynomial basis set with 4 functions $\{1,x,y,xy\}$: + +```python + def basis(pbar): + x=pbar[0] + y=pbar[1] + return [1,x,y,x*y] +``` + ++ A basis set for the circular-hole example above + that contains a single function that vanishes + outside a circle of (normalized) radius 0.25 + and is 1 inside that circle: + +```python + def basis(pbar): + x=pbar[0] + y=pbar[1] + return [1.0] if (x*x+y*y)<=0.25*0.25 else [0.0] +``` + + (Note that normalized radius 0.5 would correspond to the + maximal inscribed circle in the design region.) + +The file `adjoint.py` defines some convenient predefined basis sets: + ++ `fourier_basis(kxMax, kyMax)` + + 2D Fourier basis. `kxMax, kyMax` are integers specifying the + maximum spatial frequency in each direction as a multiple of the + base frequency. The size of the basis is `(2*kxMax+1)*(2*kyMax+1).` + (The return values of e.g. `fourier_basis(4,3)` is a function + that may be passed as the `basis` parameter to functions like + `custom_dielectric` below.) + ++ `annular_basis(NR=2, kMax=2, rho_max=0.5, rho_min=0.0)` + + A basis for a disc or annular region, consisting of a + sinusoids in the angular direction paired with Legendre polynomials + in the radial direction. + +### Parameterized geometries + +Having defined a set of basis functions, a design region +with parametrized permittivity described by a basis-set function `basis` +and a vector of basis-coefficients `coeffs` +may be added to a meep geometry by including the following block among its objects: + +```python + mp.Block(center=design_center, size=design_size, + material=custom_dielectric(design_center, design_size, basis, coeffs) + ) +``` + +Here `design_center, design_size` are the center and size of the design region +and `custom_dielectric` is a function defined in `adjoint.py` that defines +a meep material function given by the weighted basis set. + +## Computing objective functions and gradients + +Having defined an optimization problem, we compute the value of the +objective function, and its gradient with respect to the expansion coefficients, +by calling + +``` + f,gradf = get_objective_and_gradient(sim, forward_sources, + objective_regions, design_region, basis, + objective) +``` + +where the inputs are + ++ `sim`: `simulation` containing your geometry (but no sources, DFT regions, etc.) ++ `forward_sources`: sources for the fields considered by your objective function. ++ `objective_regions`: List of DFT regions on which arguments to your objective function are defined. ++ `design_region`: Design region of your problem ++ `basis`: Function describing basis set, as defined above ++ `objective`: Function describing objective function, as defined above + +## Defining basis sets + +### Predefined basis sets + +**Nomenclature for sinusoids** + +In what follows it will be convenient to introduce some +shorthand notation for sinusoids. +For $n=0,1,2,\cdots$ we define +$$ s_n(\theta)\equiv + \begin{cases} + cos \nu\theta , \qquad &n=2\nu \text{even} \\ + sin \nu\theta , \qquad &n=2\nu-1 \text{odd} + \end{cases} +$$ +In general we will specify the size of a Fourier basis +by stating its nonnegative-integer-valued maximum frequency +$\nu\sup{max}\ge 0$, in which case the set contains +$(2\nu\sup{max}+1)$ basis functions +$\{s_0, \cdots, s_{2\nu\sup{max}}\}. +(The $n$ index ranges from 0 to $2\nu\sup{max}$ inclusive.) +The first few sinusoids are +$$ s_0(\theta)=1, + \qquad + s_1(\theta)=\sin \theta, + \qquad + s_2(\theta)=\cos \theta, + \qquad + s_3(\theta)=\sin 2\theta, + \qquad + s_4(\theta)=\cos 2\theta, \cdots +$$ + +#### Rectangular design regions: Plane-wave basis + +#### Disc-shaped or annular design regions: + Legendre-Fourier basis + +``` + disc_basis(ell_max=2, nu_max=2, rhobar_max=0.5, rhobar_min=0.0) +``` + +Returns a basis suitable for a disc-shaped or annular region defined by +$$ \overline{\rho}\sup{min}\le \overline{\rho} \overline{\rho}\sup{max}, + \qquad 0\le \theta < 2\pi +$$ +Here $\overline{\rho}$ is a normalized radial coordinate running from 0 +(at the center of the design region) to 1 (on the inscribed circle +of the design region). + +The basis functions are products of Legendre polynomials in +$\overline{\rho$} with sinusoids in $\theta$: +$$ b_{\ell n}(\overline{\rho},\theta)\equiv P_\ell(u)s_n(\theta), + \qquad + 0\le \ell \le \ell\sup{max}, \qquad + 0\le n \le 2\nu\sup{max} +$$ +where $u\equiv 2\overline{\rho}-1$ runs over the usual range +$[-1,1]$ of the Legendre polynomials as $\overline{\rho}$ +runs from 0 to 1.$ The total number of basis functions +is $(\ell\sup{max}+1)(2\nu\sup{max}+1)$, and the index +of $b_{\ell n}$ within the full basis set is +$ (2\nu\sup{max}+1)\ell + n.$ For example, with $\nu\sup{max}=2$ the +first few functions are +$$ \begin{array}{cccccccccc} + b_0(\overline{\rho},\theta})&=&1, + b_1(\overline{\rho},\theta})&=&\sin \theta, + b_2(\overline{\rho},\theta})&=&\cos \theta, + b_3(\overline{\rho},\theta})&=&\sin 2\theta, + b_4(\overline{\rho},\theta})&=&\cos 2\theta, +\\ + b_5(\overline{\rho},\theta})&=&u, + b_6(\overline{\rho},\theta})&=&u\sin \theta, + b_7(\overline{\rho},\theta})&=&u\cos \theta, + b_8(\overline{\rho},\theta})&=&u\sin 2\theta, + b_9(\overline{\rho},\theta})&=&u\cos 2\theta. + \end{array} +$$ diff --git a/doc/docs/meep_documentation.css b/doc/docs/meep_documentation.css new file mode 100644 index 000000000..96b611dac --- /dev/null +++ b/doc/docs/meep_documentation.css @@ -0,0 +1,5 @@ +.SC{ + font-variant: small-caps; + font-size: 110%; + font-variant-numeric: oldstyle-nums; +} diff --git a/mkdocs.yml b/mkdocs.yml index 146591b00..f4ecb9062 100644 --- a/mkdocs.yml +++ b/mkdocs.yml @@ -22,6 +22,9 @@ markdown_extensions: extra_javascript: - 'https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS_HTML' +extra_css: + - 'meep_documentation.css' + pages: - 'Manual': 'index.md' - 'Introduction': 'Introduction.md' @@ -59,6 +62,8 @@ pages: - 'Tutorial/Eigenmode Source': 'Python_Tutorials/Eigenmode_Source.md' - 'Tutorial/Mode Decomposition': 'Python_Tutorials/Mode_Decomposition.md' - 'Tutorial/GDSII Import': 'Python_Tutorials/GDSII_Import.md' + - 'Tutorial/Adjoint-based Optimization': 'Python_Tutorials/AdjointSolver.md' + - 'Tutorial/Adjoint implementation notes': 'Python_Tutorials/AdjointImplementationNotes.md' - 'Scheme Interface': - 'User Interface': 'Scheme_User_Interface.md' - 'Tutorial/Basics': 'Scheme_Tutorials/Basics.md' From dd9c36cb48b4e41f0d7f210fd6cbb524e23f4da0 Mon Sep 17 00:00:00 2001 From: Homer Reid Date: Sat, 16 Mar 2019 01:01:04 -0400 Subject: [PATCH 06/16] purged extraneous adjoint-related content from master; also, renamed 'omega->freq' in python/source.py/fourier_transform --- .../AdjointImplementationNotes.md | 423 ------------------ doc/docs/Python_Tutorials/AdjointSolver.md | 334 -------------- doc/docs/meep_documentation.css | 5 - mkdocs.yml | 5 - python/source.py | 4 +- 5 files changed, 2 insertions(+), 769 deletions(-) delete mode 100644 doc/docs/Python_Tutorials/AdjointImplementationNotes.md delete mode 100644 doc/docs/Python_Tutorials/AdjointSolver.md delete mode 100644 doc/docs/meep_documentation.css diff --git a/doc/docs/Python_Tutorials/AdjointImplementationNotes.md b/doc/docs/Python_Tutorials/AdjointImplementationNotes.md deleted file mode 100644 index f103d735e..000000000 --- a/doc/docs/Python_Tutorials/AdjointImplementationNotes.md +++ /dev/null @@ -1,423 +0,0 @@ - - - -$$ - \newcommand{\vb}{\mathbf} - \newcommand{\wt}{\widetilde} - \newcommand{\mc}{\mathcal} - \newcommand{\bmc}[1]{\boldsymbol{\mathcal{#1}}} - \newcommand{\sup}[1]{^{\text{#1}}} - \newcommand{\pard}[2]{\frac{\partial #1}{\partial #2}} - \newcommand{\VMV}[3]{ \Big\langle #1 \Big| #2 \Big| #3 \Big\rangle} -$$ - -# Adjoint-based optimization in meep: Implementation Notes - -These notes are intended as something of a companion to the -[user's manual and tutorial documentation for adjoint-based -optimization in meep](Python_Tutorials/Adjoint_Based_Optimization.md); -whereas the goal of those pages is to document the user interface -and explain how to *use* the solver for practical problems, -our focus here will be what's going on beneath the hood---how -the solver actually *works.* - -Actually, as will be clear to anyone who has ever reviewed the -fundamentals of -[adjoint sensitivity analysis](https://en.wikipedia.org/wiki/Adjoint_state_method), -the theoretical basis of the method and the derivation of its key -formulas are almost trivially straightforward, with the only -potential source of difficulty being how to massage the mechanics -of the procedure into a meep-friendly form. - -## Toy problem - -Ultimately we will want to use adjoint methods to differentiate -complex objective functions---involving quantities such as -Poynting fluxes and mode-expansion coefficients---with respect -to various different types of parameters describing material geometries. -However, before tackling the problem in that full generality, -it's useful to build up to it by starting with a simple toy problem -and adding complications one at a time. Thus we consider a -simple waveguide geometry, excited by a point source at -$\vb{x}\sup{src}$, and define our objective function to be -simply the frequency-domain electric-field amplitude at -a point $\vb{x}\sup{obj}$; we will compute the derivative -of this objective function with respect to the permittivity -$\epsilon\sup{des}$ -in a small "design region" $\mc{V}\sup{des}$ -centered at a third point $\vb{x}\sup{des}$. - -![AdjointToyGeometry1](/images/AdjointToyGeometry1.png) - -### Permittivity derivative by finite-differencing - -An obvious brute-force way to get at this is simply -to do two meep calculations, with $\epsilon\sup{des}$ -augmented by a small finite amount $\Delta\epsilon$ on the -second run, then compute the difference between the frequency-domain -electric fields at $\vb{x}\sup{obj}$ and divide -by $\Delta\epsilon$ to estimate the derivative. -Here are plots of the unperturbed field and the field perturbation -(difference between perturbed and unperturbed field): - -+ $\wt{E_{z0}}(\omega_0, \vb{x})$ (unperturbed): - -![Unperturbed field](/images/AdjointToyEz0.png) - -+ $\Delta {\wt E_z}(\omega_0, \vb{x})$ (perturbed-unperturbed): -![Perturbation field](/images/AdjointToydEz_FD.png) - -(Here and below we use the tilde sign ($\sim$) to indicate frequency-domain -fields and sources.) - -### Permittivity derivative from effective sources - -One way to think about the effect of a localized permittivity -bump goes like this: Increasing the permittivity in some localized -region of a material body corresponds to increasing the -polarizability in that region---that is, the ease with which -positive and negative charges in the material, ordinarily bound -so tightly together that they neutralize each other as sources, -can be induced by applied electric fields to separate ("polarize"), -whereupon they cease to cancel each other and act as effective -sources contributing to electromagnetic fields. -Of course, if there were no electric field in the material, -then we could increase its polarizability as much as we pleased -without producing any sources---zero times a bigger -coefficient being still zero---but here there *is* a nonzero -electric field throughout our geometry, due to the point source -in the unperturbed problem, which means that the effect of bumping the -permittivity of the design region may be approximated by -adding new *sources* in that region, with strength -proportional to $\Delta\epsilon$ and to the unperturbed electric field. -More specifically, in a frequency-domain problem involving time-harmonic -fields and sources with angular frequency $\omega$ (time dependence -$\propto e^{-i\omega t}$), the following perturbations are -equivalent: -$$ -\begin{array}{ccc} - \left(\begin{array}{c} - \text{a permittivity shift of } \Delta\epsilon \\ - \text{over a small region } \mc{V} \text{ in which} \\ - \text{the electric field is } \wt{\vb{E}} - \end{array}\right) - &\Longleftrightarrow & - \left(\begin{array}{c} - \text{a localized electric current } \\ - \text{flowing in }\mc{V} \text{ with amplitude } \\ - \Delta\wt{\vb J}=-i\omega\Delta\epsilon \wt{\vb{E}} - \end{array}\right) -\end{array} -$$ - -![AdjointToyGeometry1](/images/AdjointToyGeometry2.png) - -Superposing this effective source with the original point source -at $\vb{x}\sup{src}$ yields a source configuration that, -acting on the *unperturbed* geometry, produces the same fields -as the point source alone acting on the *perturbed* geometry. - -Alternatively, by exploiting the linearity of Maxwell's equations -(and assuming we have linear media!) we could just as easily -remove the original point source and compute the fields of -$\wt{\Delta \vb{J}}$ *alone*, which, upon dividing through by -$\Delta\epsilon$, give just the derivatives of field components -with respect to $\epsilon$. In other words, -$$ \pard{ \wt{\vb E} (\vb x\sup{obj}) }{\epsilon\sup{des}} - \equiv - \left(\begin{array}{cc} - \text{electric field at }\vb{x}\sup{obj} \text{ due to }\\ - \text{current at }\vb{x}\sup{des}\text{ with amplitude}\\ - \wt{\Delta \vb J}=-i\omega\wt{\vb{E}}(\vb{x}\sup{obj}) - \end{array}\right) - \tag{1a} -$$ -Analogous reasoning yields a prescription for magnetic-field derivatives: -$$ \pard{\wt{\vb{H}}(\vb x\sup{obj})}{\epsilon\sup{des}} - \equiv - \left( - \begin{array}{cc} - \text{magnetic field at }\vb{x}\sup{obj} \text{ due to }\\ - \text{current at }\vb{x}\sup{des}\text{ with amplitude}\\ - \wt{\Delta \vb J}=-i\omega\wt{\vb{E}}(\vb{x}\sup{obj}) - \end{array} - \right) - \tag{1b} -$$ - -### Digression: Configuring time-domain sources for desired frequency-domain fields in meep - -In frequency-domain electromagnetism we usually consider -a time-harmonic source distribution of the form -$$ - \vb{J}\sup{monochromatic}(t,\vb{x})\equiv - \wt{\vb{J}}(\vb x)e^{-i\omega t} -$$ -and we ask for the time-harmonic electric field distribution -radiated by this distribution: -$$ - \vb{E}\sup{monochromatic}(t,\vb{x})\equiv - \wt{\vb{E}}(\vb x)e^{-i\omega t} -$$ -where $\sim$ indicates frequency-domain amplitudes. -A typical frequency-domain solver might input -$\wt{\vb J}(\vb x)$ and output -$\wt{\vb E}(\vb x)$: -$$ \wt{\vb J}(\vb x) - \quad \Longrightarrow \quad - \begin{array}{|c|}\hline\\ - \text{ frequency-domain solver }\\ - \\\hline\end{array} - \quad \Longrightarrow \quad - \wt{\vb E}(\vb x) -$$ - -On the other hand, when using meep to compute -the fields produced by a given spatial source distribution, -we typically construct a time-domain source of the form -$$\vb{J}\sup{meep}(t,\vb{x})=G(t)\wt{\vb{J}}(\vb x)$$ -where $G(t)$ is a Gaussian temporal envelope. -More specifically, for meep's `GaussianSrc` with -center frequency $\omega_0=2\pi f_0$, -frequency width $\Delta \omega =2\pi \Delta f$, and -peak time $t_0$, we have -$$ G(t) = e^{-i\omega_0(t-t_0) - \frac{1}{2}[\Delta f(t-t_0)]^2}.$$ -The Fourier transform of this is -$$ - \wt G(\omega) \equiv \frac{1}{\sqrt{2\pi}} - \int e^{i\omega t}G(t)\,dt = - \frac{1}{\Delta f} - e^{i\omega t_0 -\frac{(\omega-\omega_0)^2}{2\Delta f^2}}. -$$ -The meep version of the above -input/output diagram looks like -$$ G(t)\wt{\vb J}(\vb x) - \quad \Longrightarrow \quad - \begin{array}{|c|}\hline\\ - \text{ MEEP }\\ - \text{ (timestepping + DFT) } \\ - \\\hline\end{array} - \quad \Longrightarrow \quad - \wt{G}(\omega)\wt{\vb E}(\vb x) -$$ - -The upshot is that the frequency-domain fields obtained from a -meep run with a Gaussian source -come out multiplied by a factor of $\wt{G}(\omega)$ that should -be divided out to yield the desired frequency-domain quantities. - -## Invoking reciprocity - -It is convenient to describe the process described above -in the language of frequency-domain Green's functions, which -express the fields radiated by monochromatic source distributions -as spatial convolutions: -$$ \wt{E_i}(\omega, \vb{x}\sup{dest}) = - \int - \mc{G}\sup{EE}_{ij}(\omega, \vb{x}\sup{dest}, \vb{x}\sup{src}) - \wt{J_j}(\omega, \vb{x}\sup{src}) - \,d\vb{x}\sup{src} -$$ -with $\bmc{G}\sup{EE}$ the -electric-electric dyadic Green's function of the material geometry -(giving the electric field produced by a unit-strength electric -current). -In this language, the effective-source representation -of the permittivity derivative reads -$$ \pard{\wt{E}_i(\vb{x}\sup{obj})}{\epsilon\sup{des}} - = - \int \mc{G}\sup{EE}_{ij}(\vb{x}\sup{obj}, \vb{x}\sup{des}) - \left[-i\omega \wt{E}_j(\vb{x}\sup{des})\right] - \,d\vb{x}\sup{des} -$$ -It is convenient to think of the RHS here as a double convolution -of two vector-valued functions with the $\bmc{G}\sup{EE}$ kernel: -$$ \pard{\wt{E}_i(\vb{x}\sup{obj})}{\epsilon\sup{des}} - = - \left[ \vphantom{\wt{\vb E}\sup{des}} - \,\, \boldsymbol{\delta}_i\sup{obj}\,\, - \right] - \star \bmc{G}\sup{EE} \star - \left[-i\omega \wt{\vb E}\sup{des}\right] -$$ -or -$$ \pard{\wt E_i(\vb{x}\sup{obj})}{\epsilon\sup{des}} - =-i\omega\VMV{ \boldsymbol{\delta}_i\sup{obj} } - { \bmc G\sup{EE} } - { \wt{\vb E}\sup{des} } -$$ -where $\star$ denotes convolution, -$\boldsymbol{\delta}_i\sup{obj}$ is short for -$\delta_{ij} \delta(\vb{x}-\vb{x}\sup{obj}),$ -and the bra-ket notation describes a machine that inputs two -vector-valued functions $\vb{f},\vb{g}$ and a kernel $\mc{K}$ -and outputs a scalar quantity: -$$ \VMV{\vb f}{\bmc K}{\vb g} - \equiv \sum_{ij} \iint f_i(\vb{x}) - \mc{K}_{ij}(\vb{x},\vb{x}^\prime) - g_j(\vb{x}^\prime) - \,d\vb{x} \,d\vb{x}^\prime -$$ -(Note that this is not a Hermitian inner product, i.e. the first -factor is not conjugated.) - -For the magnetic-field derivative we have similarly -$$ \pard{\wt{H}_i(\vb{x}\sup{obj})}{\epsilon\sup{des}} - =-i\omega\VMV{ \boldsymbol{\delta}_i\sup{obj} } - { \boldsymbol{\mc G}\sup{ME} } - { \wt{\vb E}\sup{des} } -$$ -where $\bmc{G}\sup{ME}$ is the magnetic-electric -Green's function, giving the magnetic field produced -by an electric current. - -Computationally, inner products like -$\VMV{\vb f}{\bmc G\sup{EE}}{\vb g}$ -for arbitrary functions $\vb{f}(\vb x), \vb{g}(\vb x)$ -may be evaluated in meep -as follows: - -1. Create an electric current source with - spatially-varying amplitude $\vb{g}(\vb x)$ - and Gaussian temporal envelope $G(t)$. - -2. Timestep and DFT to compute the frequency-domain electric field - $\wt{\vb E}(\omega; \vb{x})$ produced by this source. - -3. Compute the inner product - $[\wt{G}(\omega)]^{-1} - \int \vb{f}\cdot \wt{\vb E}\,dV.$ - (The normalization prefactor was discussed above.) - -The virtue of writing things this way is that it allows the physical -property of reciprocity to be expressed as the mathematical property -that the aforementioned inner-product machine is insensitive to the -order of its arguments, i.e. we can flip the $\vb f$ and $\vb g$ -inputs and still get the same scalar output: -$$ \VMV{\vb f}{\bmc K}{\vb g} = \VMV{\vb g}{\bmc K}{\vb f} - \quad\text{ for }\quad \bmc K= \bmc{G}\sup{EE}, \bmc{G}\sup{ME}. -$$ - -Applying reciprocity to the above expressions for field derivatives yields -\begin{align*} -\pard{\wt E_i(\vb{x}\sup{obj})}{\epsilon\sup{des}} - &=-i\omega\VMV{ \wt{\vb E }\sup{des} } - { \bmc{G}\sup{EE} } - { \boldsymbol{\delta}_i\sup{obj} } - \tag{2} -\\[5pt] -\pard{\wt H_i(\vb{x}\sup{obj})}{\epsilon\sup{des}} - &=-i\omega\VMV{ \wt{\vb E }\sup{des} } - { \bmc{G}\sup{ME} } - { \boldsymbol{\delta}_i\sup{obj} } - \tag{3a} -\\ - \hphantom{\pard{\wt H_i(\vb{x}\sup{obj})}{\epsilon\sup{des}}} - &=+i\omega\VMV{ \wt{\vb E}\sup{des} } - { \bmc{G}\sup{EM} } - { \boldsymbol{\delta}_i\sup{obj} } - \tag{3b} -\end{align*} -where in going to the last line we invoked the identity -$\bmc{G}\sup{EM}=-\bmc{G}\sup{ME}.$ - -Note that equations (3a) and (3b), notwithstanding their nearly -identical appearance, describe two rather different -meep calculations: In the former case -we place an electric source at $\vb x\sup{obj}$ and timestep to -compute the resulting magnetic field, while in the latter -case we place a magnetic source and timestep -to compute the resulting electric field. (In both cases, -upon computing the field in question we proceed to compute its -overlap with the unperturbed $\vb E$ field in the design region.) - -## Differentiating more complicated functions of field components - -Thus far we have only considered derivatives of individual -field components, and then only at a single point $\vb{x}\sup{obj}$; -more generally, we will want to differentiate functions of -multiple field components over a subregion of the grid, -which we will call the *objective region* $\mc{V}\sup{obj}$. - -### **E**-field energy in region - -As one example, the electric field energy in the objective -region is defined by an integral over that region, which meep -approximate by a weighted sum over grid points: -$$ \mc{E}= - \frac{1}{2}\int_{\mc{V}\sup{obj}} \epsilon |\wt{\vb E}|^2 \,d\mc{V} - \approx - \frac{1}{2}\sum_{i,\vb{n}\in\mc{V}\sup{obj}} w_{\vb{n}} - \epsilon_\vb {n} \wt E_{i\vb n}^* \wt E_{i\vb n} -$$ -Here the sum is over all field components $i=\{x,y,z\}$ and -all grid points $\vb{n}$ lying in $\mc{V}\sup{obj}$, -and $w_{\vb{n}}$ is a cubature weight associated with point $\vb{n}$ -(as returned by [`get_dft_array_metadata`](/Python_User_Interface#metadata)). -Differentiating, we have -\begin{align*} - \pard{\mc E}{\epsilon\sup{des}} - &=\text{Re }\sum_{i\vb{n}\in\mc V\sup{obj}} w_{\vb n}\epsilon_{\vb n} - \wt{E}^*_{i\vb n} \pard{\wt{E}_{i\vb n}} {\epsilon\sup{des}} -\\ -&\hspace{-1.5in}\text{Insert equation (1a):} -\\ - &=\text{Re }\left\{ -i\omega \VMV{\epsilon \wt{\vb E}\sup{obj*}} - {{\bmc G}\sup{EE}} - {\wt{\vb E}\sup{des}} - \right\} -\\ -&\hspace{-1.5in}\text{Invoke reciprocity:} -\\ - &=\text{Re }\left\{ -i\omega \VMV{\wt{\vb E}\sup{des}} - {{\bmc G}\sup{EE}} - {\epsilon \wt{\vb E}\sup{obj*}} - \right\} -\end{align*} - -### Poynting flux - -A case that arises frequently is that in which the objective region -is a cross-sectional surface $\mc S\sup{obj}$ cutting normally through a -waveguide or similar structure and the objective function is the -normal Poynting flux through $\mc S$. -For example, the $x$-directed Poynting flux is given by -$$ - S_x -= -\frac{1}{2}\text{Re }\left\{ \int_{\mc S\sup{obj}} \Big(E^*_y H_z + \cdots\Big) \, d\mathbf{x} \right\} -\approx \frac{1}{2}\text{Re }\sum_{\vb n\in \mc S\sup{obj}} w_{\vb n} - \Big(E^*_{y\vb n} H_{z\vb n} + \cdots\Big) -$$ -where $\cdots$ refers to three other terms of the form $\pm E^*_i H_j$. -Differentiating and rearranging slightly, we have -\begin{align*} - \pard{S_x}{\epsilon\sup{des}} - &=\text{Re }\sum_{\vb n\in \mc S\sup{obj}} w - \left\{ \wt{E}^*_{y} \pard{\wt{H}_z}{\epsilon\sup{des}} - +\wt{H}^*_{z} \pard{\wt{E}_y}{\epsilon\sup{des}} - +\cdots - \right\} -\\[5pt] -&\hspace{-0.5in}\text{Use (1a) and (1b):} -\\[5pt] - &=\text{Re }\left\{ -i\omega \VMV{\wt{\vb E}_{y}\sup{obj*}} - {\bmc G\sup{ME}} - {\wt{\vb E}\sup{des}} - -i\omega \VMV{\wt{\vb H}_z\sup{obj*}} - {\bmc G\sup{EE}} - {\wt{\vb E}\sup{des}} - +\cdots - \right\} -\\[5pt] -&\hspace{-0.5in}\text{Use reciprocity:} -\\[5pt] -&=\text{Re }\left\{ -i\omega \VMV{\wt{\vb E}\sup{des}} - {\bmc G\sup{ME}} - {\wt{\vb E}_y\sup{obj*}} - -i\omega \VMV{\wt{\vb E}\sup{des}} - {\bmc G\sup{EE}} - {\wt{\vb H}_z\sup{obj*}} - +\cdots - \right\} -\end{align*} diff --git a/doc/docs/Python_Tutorials/AdjointSolver.md b/doc/docs/Python_Tutorials/AdjointSolver.md deleted file mode 100644 index c2132cea3..000000000 --- a/doc/docs/Python_Tutorials/AdjointSolver.md +++ /dev/null @@ -1,334 +0,0 @@ ---- -# Automated design optimization via adjoint sensitivity analysis ---- - -This tutorial demonstrates the use of meep's support for -[*adjoint sensitivity analysis*](https://en.wikipedia.org/wiki/Adjoint_state_method) -to facilitate automated design optimization via derivative-based -numerical optimization. - -## Overview and Invitation --------------------------------- - -Before jumping into technical details, let's start by -recalling the bird's-eye view of - -### Photonic design optimization: Common problem structure and simple examples - -The problems we'll consider all have the following common -general structure: We are given an early-stage draft of a -photonic device design in which some features are fixed -and immutable, but - ----which, for our purposes, amounts -to a description of the spatially-varying scalar permittivity -function $\epsilon(\mathbf{x})$ throught - - -we excite it - -and compute - -where a ``device design'' amounts - -kklsp$k -We excite - -### Specifying objective regions and defining objective functions - -### - - -### Examples - -in which -some regions are fixed and immutable - ----for example, the -input and output waveguide sections in the taper problem -below---but - -We excite this geometry using a given fixed source of incident -radiation and -which will typically be a function - -### - -The metric for ``improvement' - -We have a - -In a nutshell, -Suppose - -### - -The rest of this page - -you -communicating to - -+ Set up your - -+ Invoke -`get_objective_and_gradient` -1. - -## User's manual: --------------------------------- - -## Setting up your --------------------------------- - -Setting up meep geometry for automated design -optimization -is - -+ Your simulation - -+ When instantiating the material configuration of your geometry, -you will - -### Objective regions and design regions --------------------------------- - -The methods we'll illustrate are applicable to a broad class of -optimization problems in which we seek to optimize Poynting fluxes -and/or mode-expansion coefficients in one or more regions of a -geometry by tuning the structure---that is, the spatial -permittivity distribution $\epsilon(\mathbf x)$---of some portion -of the geometry. - -More specifically, we'll consider problems with the following characteristics: - -+ The objective function is of the form - $$F\Big( \big\{S_n\big\}, \big\{|\alpha_{nm}|^2\big\}\Big)$$ - where - - + $\{S_n\}=\{S_1, \cdots, S_N\}$ are the Poynting fluxes - at some user-specified set of $N$ - [flux regions](https://meep.readthedocs.io/en/latest/Python_User_Interface/#fluxregion) - $\{\mathcal{V}^o_1, \cdots, \mathcal{V}^o_N\}$, which we call the *objective regions* for - the optimization problem - - + $\alpha_{nm}$ is the - [eigenmode-expansion coefficient](https://meep.readthedocs.io/en/latest/Mode_Decomposition) - for the $m$th eigenmode in the $n$th objective region - - + $F$ is an arbitrary user-specified function of its inputs - -+ The quantity to be optimized is the permittivity distribution $\epsilon(\mathbf x)$ - within some user-specified [volume](https://meep.readthedocs.io/en/latest/Python_User_Interface/#volume) - $\mathcal{V}^d$, which we call the *design region*. - -+ The permittivity in the design region is expressed as an expansion - in some (arbitrary, user-specified) set of basis functions: - - $$ \epsilon(\mathbf x) \equiv \sum_{p=1}^P a_p \psi_p(\mathbf x), - \qquad \mathbf x\in \mathcal{V}^d$$ - - Here $\{\psi_p(\mathbf x)\}, p=1,\cdots,P$ is a set of $P$ scalar-valued basis functions, - defined for $\mathbf x \in \mathcal{V}^d$ the objective region, and the expansion coefficients $\{a_p\}$ - are the variable parameters in our optimization. - -Thus, problems for adjoint-based solvers in meep, you will specify - -+ a list of objective regions $\{\mathcal{V}^o_n\}$ - -+ a design region $\mathcal{V}^d$ - -+ a basis set $\{b_d(\mathbf{x})\}$ - -+ an objective function $F$ - -### Sample geometries - -+ Warmup: circular defect in waveguide - -A simple warmup problem is a uniform waveguide with a -circular inclusion, in which we want to optimize the -permittivity distribution in the circle to maximize -power flux through the waveguide: - -![](images/AdjointExample1.png) - -In this case we have only a single objective region, -and the objective function is simply - -$$ F\Big\(\mathcal{V}^o_1\Big)=S_1.$$ - -+ Bidirectional coupler - -## Basis functions and parameterized geometries - -### Specifying basis sets - -The basis of expansion functions for the permittivity in the design region -is described by a single routine that inputs the normalized coordinates of a point -$\mathbf{x}$ in the design region and returns a vector of length $P$ -containing $[\psi_1(\mathbf{x}), \cdots, \psi_P(\mathbf{x})]$. -Here "normalized coordinates" refers to a shifted and scaled coordinate system -in which the design region is centered at the origin and has length 1 in -all directions; so that the normalized coordinates $\overline{\mathbf{x}}$ -for points in the design region satisfy $-0.5<\overline{x}_i<0.5$ for all $i$. -then every component of $\overline{\mathbf{x}}$ lies in the range $[-0.5,0.5]$ - -Here are some examples of basis sets for 2D design regions: - -+ A simple polynomial basis set with 4 functions $\{1,x,y,xy\}$: - -```python - def basis(pbar): - x=pbar[0] - y=pbar[1] - return [1,x,y,x*y] -``` - -+ A basis set for the circular-hole example above - that contains a single function that vanishes - outside a circle of (normalized) radius 0.25 - and is 1 inside that circle: - -```python - def basis(pbar): - x=pbar[0] - y=pbar[1] - return [1.0] if (x*x+y*y)<=0.25*0.25 else [0.0] -``` - - (Note that normalized radius 0.5 would correspond to the - maximal inscribed circle in the design region.) - -The file `adjoint.py` defines some convenient predefined basis sets: - -+ `fourier_basis(kxMax, kyMax)` - - 2D Fourier basis. `kxMax, kyMax` are integers specifying the - maximum spatial frequency in each direction as a multiple of the - base frequency. The size of the basis is `(2*kxMax+1)*(2*kyMax+1).` - (The return values of e.g. `fourier_basis(4,3)` is a function - that may be passed as the `basis` parameter to functions like - `custom_dielectric` below.) - -+ `annular_basis(NR=2, kMax=2, rho_max=0.5, rho_min=0.0)` - - A basis for a disc or annular region, consisting of a - sinusoids in the angular direction paired with Legendre polynomials - in the radial direction. - -### Parameterized geometries - -Having defined a set of basis functions, a design region -with parametrized permittivity described by a basis-set function `basis` -and a vector of basis-coefficients `coeffs` -may be added to a meep geometry by including the following block among its objects: - -```python - mp.Block(center=design_center, size=design_size, - material=custom_dielectric(design_center, design_size, basis, coeffs) - ) -``` - -Here `design_center, design_size` are the center and size of the design region -and `custom_dielectric` is a function defined in `adjoint.py` that defines -a meep material function given by the weighted basis set. - -## Computing objective functions and gradients - -Having defined an optimization problem, we compute the value of the -objective function, and its gradient with respect to the expansion coefficients, -by calling - -``` - f,gradf = get_objective_and_gradient(sim, forward_sources, - objective_regions, design_region, basis, - objective) -``` - -where the inputs are - -+ `sim`: `simulation` containing your geometry (but no sources, DFT regions, etc.) -+ `forward_sources`: sources for the fields considered by your objective function. -+ `objective_regions`: List of DFT regions on which arguments to your objective function are defined. -+ `design_region`: Design region of your problem -+ `basis`: Function describing basis set, as defined above -+ `objective`: Function describing objective function, as defined above - -## Defining basis sets - -### Predefined basis sets - -**Nomenclature for sinusoids** - -In what follows it will be convenient to introduce some -shorthand notation for sinusoids. -For $n=0,1,2,\cdots$ we define -$$ s_n(\theta)\equiv - \begin{cases} - cos \nu\theta , \qquad &n=2\nu \text{even} \\ - sin \nu\theta , \qquad &n=2\nu-1 \text{odd} - \end{cases} -$$ -In general we will specify the size of a Fourier basis -by stating its nonnegative-integer-valued maximum frequency -$\nu\sup{max}\ge 0$, in which case the set contains -$(2\nu\sup{max}+1)$ basis functions -$\{s_0, \cdots, s_{2\nu\sup{max}}\}. -(The $n$ index ranges from 0 to $2\nu\sup{max}$ inclusive.) -The first few sinusoids are -$$ s_0(\theta)=1, - \qquad - s_1(\theta)=\sin \theta, - \qquad - s_2(\theta)=\cos \theta, - \qquad - s_3(\theta)=\sin 2\theta, - \qquad - s_4(\theta)=\cos 2\theta, \cdots -$$ - -#### Rectangular design regions: Plane-wave basis - -#### Disc-shaped or annular design regions: - Legendre-Fourier basis - -``` - disc_basis(ell_max=2, nu_max=2, rhobar_max=0.5, rhobar_min=0.0) -``` - -Returns a basis suitable for a disc-shaped or annular region defined by -$$ \overline{\rho}\sup{min}\le \overline{\rho} \overline{\rho}\sup{max}, - \qquad 0\le \theta < 2\pi -$$ -Here $\overline{\rho}$ is a normalized radial coordinate running from 0 -(at the center of the design region) to 1 (on the inscribed circle -of the design region). - -The basis functions are products of Legendre polynomials in -$\overline{\rho$} with sinusoids in $\theta$: -$$ b_{\ell n}(\overline{\rho},\theta)\equiv P_\ell(u)s_n(\theta), - \qquad - 0\le \ell \le \ell\sup{max}, \qquad - 0\le n \le 2\nu\sup{max} -$$ -where $u\equiv 2\overline{\rho}-1$ runs over the usual range -$[-1,1]$ of the Legendre polynomials as $\overline{\rho}$ -runs from 0 to 1.$ The total number of basis functions -is $(\ell\sup{max}+1)(2\nu\sup{max}+1)$, and the index -of $b_{\ell n}$ within the full basis set is -$ (2\nu\sup{max}+1)\ell + n.$ For example, with $\nu\sup{max}=2$ the -first few functions are -$$ \begin{array}{cccccccccc} - b_0(\overline{\rho},\theta})&=&1, - b_1(\overline{\rho},\theta})&=&\sin \theta, - b_2(\overline{\rho},\theta})&=&\cos \theta, - b_3(\overline{\rho},\theta})&=&\sin 2\theta, - b_4(\overline{\rho},\theta})&=&\cos 2\theta, -\\ - b_5(\overline{\rho},\theta})&=&u, - b_6(\overline{\rho},\theta})&=&u\sin \theta, - b_7(\overline{\rho},\theta})&=&u\cos \theta, - b_8(\overline{\rho},\theta})&=&u\sin 2\theta, - b_9(\overline{\rho},\theta})&=&u\cos 2\theta. - \end{array} -$$ diff --git a/doc/docs/meep_documentation.css b/doc/docs/meep_documentation.css deleted file mode 100644 index 96b611dac..000000000 --- a/doc/docs/meep_documentation.css +++ /dev/null @@ -1,5 +0,0 @@ -.SC{ - font-variant: small-caps; - font-size: 110%; - font-variant-numeric: oldstyle-nums; -} diff --git a/mkdocs.yml b/mkdocs.yml index 335213946..4c2a1a6db 100644 --- a/mkdocs.yml +++ b/mkdocs.yml @@ -23,9 +23,6 @@ markdown_extensions: extra_javascript: - 'https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS_HTML' -extra_css: - - 'meep_documentation.css' - pages: - 'Manual': 'index.md' - 'Introduction': 'Introduction.md' @@ -63,8 +60,6 @@ pages: - 'Tutorial/Eigenmode Source': 'Python_Tutorials/Eigenmode_Source.md' - 'Tutorial/Mode Decomposition': 'Python_Tutorials/Mode_Decomposition.md' - 'Tutorial/GDSII Import': 'Python_Tutorials/GDSII_Import.md' - - 'Tutorial/Adjoint-based Optimization': 'Python_Tutorials/AdjointSolver.md' - - 'Tutorial/Adjoint implementation notes': 'Python_Tutorials/AdjointImplementationNotes.md' - 'Scheme Interface': - 'User Interface': 'Scheme_User_Interface.md' - 'Tutorial/Basics': 'Scheme_Tutorials/Basics.md' diff --git a/python/source.py b/python/source.py index 98188f8f6..1243af427 100644 --- a/python/source.py +++ b/python/source.py @@ -66,8 +66,8 @@ def __init__(self, frequency=None, width=0, fwidth=float('inf'), start_time=0, c self.start_time + 2 * self.width * self.cutoff) self.swigobj.is_integrated = self.is_integrated - def fourier_transform(self, omega): - return self.swigobj.fourier_transform(omega) + def fourier_transform(self, freq): + return self.swigobj.fourier_transform(freq) class CustomSource(SourceTime): From 1a131a1a9c778291a4979e89778b81a4dc851f53 Mon Sep 17 00:00:00 2001 From: Homer Reid Date: Sat, 16 Mar 2019 01:02:38 -0400 Subject: [PATCH 07/16] purged extraneous adjoint-related content from master; 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/* Copyright (C) 2005-2019 Massachusetts Institute of Technology
%
% This program is free software; you can redistribute it and/or modify
% it under the terms of the GNU General Public License as published by
% the Free Software Foundation; either version 2, or (at your option)
% any later version.
%
% This program is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
% GNU General Public License for more details.
%
% You should have received a copy of the GNU General Public License
% along with this program; if not, write to the Free Software Foundation,
% Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
*/
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#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <complex>
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#include "meep.hpp"
#include "meep_internals.hpp"
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using namespace std;
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namespace meep {
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/*********************************************************************/
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// this function is necessary to make equality commutative ... ugh
bool src_times_equal(const src_time &t1, const src_time &t2) {
return t1.is_equal(t2) && t2.is_equal(t1);
}
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src_time *src_time::add_to(src_time *others, src_time **added) const {
if (others) {
if (src_times_equal(*this, *others))
*added = others;
else
others->next = add_to(others->next, added);
return others;
} else {
src_time *t = clone();
t->next = others;
*added = t;
return t;
}
}
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double src_time::last_time_max(double after) {
after = max(last_time(), after);
if (next)
return next->last_time_max(after);
else
return after;
}
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gaussian_src_time::gaussian_src_time(double f, double fwidth, double s) {
freq = f;
width = 1.0 / fwidth;
peak_time = width * s;
cutoff = width * s;
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// this is to make last_source_time as small as possible
while (exp(-cutoff * cutoff / (2 * width * width)) < 1e-100)
cutoff *= 0.9;
cutoff = float(cutoff); // don't make cutoff sensitive to roundoff error
}
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gaussian_src_time::gaussian_src_time(double f, double w, double st, double et) {
freq = f;
width = w;
peak_time = 0.5 * (st + et);
cutoff = (et - st) * 0.5;
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// this is to make last_source_time as small as possible
while (exp(-cutoff * cutoff / (2 * width * width)) < 1e-100)
cutoff *= 0.9;
cutoff = float(cutoff); // don't make cutoff sensitive to roundoff error
}
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complex<double> gaussian_src_time::dipole(double time) const {
double tt = time - peak_time;
if (float(fabs(tt)) > cutoff) return 0.0;
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// correction factor so that current amplitude (= d(dipole)/dt) is
// ~ 1 near the peak of the Gaussian.
complex<double> amp = 1.0 / complex<double>(0, -2 * pi * freq);
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return exp(-tt * tt / (2 * width * width)) * polar(1.0, -2 * pi * freq * tt) * amp;
}
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// (1/\sqrt{2*pi}) \int e^{i\omega t} G(t) dt
// where G(t) is the *current* envelope, i.e. the time derivative
// of the dipole envelope
std::complex<double> gaussian_src_time::fourier_transform(const double f) {
double omega = 2.0 * pi * f;
double omega0 = 2.0 * pi * freq;
double delta = (omega - omega0) * width;
return width * polar(1.0, omega * peak_time) * exp(-0.5 * delta * delta);
}
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bool gaussian_src_time::is_equal(const src_time &t) const {
const gaussian_src_time *tp = dynamic_cast<const gaussian_src_time *>(&t);
if (tp)
return (tp->freq == freq && tp->width == width && tp->peak_time == peak_time &&
tp->cutoff == cutoff);
else
return 0;
}
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complex<double> continuous_src_time::dipole(double time) const {
float rtime = float(time);
if (rtime < start_time || rtime > end_time) return 0.0;
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// correction factor so that current amplitude (= d(dipole)/dt) is 1.
complex<double> amp = 1.0 / (complex<double>(0, -1.0) * (2 * pi) * freq);
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if (width == 0.0)
return exp(complex<double>(0, -1.0) * (2 * pi) * freq * time) * amp;
else {
double ts = (time - start_time) / width - slowness;
double te = (end_time - time) / width - slowness;
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return exp(complex<double>(0, -1.0) * (2 * pi) * freq * time) * amp *
(1.0 + tanh(ts)) // goes from 0 to 2
* (1.0 + tanh(te)) // goes from 2 to 0
* 0.25;
}
}
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bool continuous_src_time::is_equal(const src_time &t) const {
const continuous_src_time *tp = dynamic_cast<const continuous_src_time *>(&t);
if (tp)
return (tp->freq == freq && tp->width == width && tp->start_time == start_time &&
tp->end_time == end_time && tp->slowness == slowness);
else
return 0;
}
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bool custom_src_time::is_equal(const src_time &t) const {
const custom_src_time *tp = dynamic_cast<const custom_src_time *>(&t);
if (tp)
return (tp->start_time == start_time && tp->end_time == end_time && tp->func == func &&
tp->data == data);
else
return 0;
}
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/*********************************************************************/
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src_vol::src_vol(component cc, src_time *st, size_t n, ptrdiff_t *ind, complex<double> *amps) {
c = cc;
if (is_D(c)) c = direction_component(Ex, component_direction(c));
if (is_B(c)) c = direction_component(Hx, component_direction(c));
t = st;
next = NULL;
npts = n;
index = ind;
A = amps;
}
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src_vol::src_vol(const src_vol &sv) {
c = sv.c;
t = sv.t;
npts = sv.npts;
index = new ptrdiff_t[npts];
A = new complex<double>[npts];
for (size_t j = 0; j < npts; j++) {
index[j] = sv.index[j];
A[j] = sv.A[j];
}
if (sv.next)
next = new src_vol(*sv.next);
else
next = NULL;
}
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src_vol *src_vol::add_to(src_vol *others) {
if (others) {
if (*this == *others) {
if (npts != others->npts)
abort("Cannot add grid_volume sources with different number of points\n");
/* Compare all of the indices...if this ever becomes too slow,
we can just compare the first and last indices. */
for (size_t j = 0; j < npts; j++) {
if (others->index[j] != index[j]) abort("Different indices\n");
others->A[j] += A[j];
}
} else
others->next = add_to(others->next);
return others;
} else {
next = others;
return this;
}
}
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/*********************************************************************/
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// THIS VARIANT IS FOR BACKWARDS COMPATIBILITY, and is DEPRECATED:
void fields::add_point_source(component c, double freq, double width, double peaktime,
double cutoff, const vec &p, complex<double> amp, int is_c) {
width /= freq;
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if (is_c) { // TODO: don't ignore peaktime?
continuous_src_time src(freq, width, time(), infinity, cutoff);
if (is_magnetic(c)) src.is_integrated = false;
add_point_source(c, src, p, amp);
} else {
cutoff = gv.inva + cutoff * width;
if (peaktime <= 0.0) peaktime = time() + cutoff;
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// backward compatibility (slight phase shift in old Meep version)
peaktime += is_magnetic(c) ? -dt * 0.5 : dt;
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gaussian_src_time src(freq, width, peaktime - cutoff, peaktime + cutoff);
if (is_magnetic(c)) src.is_integrated = false;
add_point_source(c, src, p, amp);
}
}
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void fields::add_point_source(component c, const src_time &src, const vec &p, complex<double> amp) {
add_volume_source(c, src, volume(p, p), amp);
}
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static complex<double> one(const vec &pt) {
(void)pt;
return 1.0;
}
void fields::add_volume_source(component c, const src_time &src, const volume &where,
complex<double> amp) {
add_volume_source(c, src, where, one, amp);
}
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struct src_vol_chunkloop_data {
complex<double> (*A)(const vec &);
complex<double> amp;
src_time *src;
vec center;
};
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/* Adding source volumes can be treated as a kind of "integration"
problem, since we need to loop over all the chunks that intersect
the source grid_volume, with appropriate interpolation weights at the
boundaries so that the integral of the current is fixed regardless
of resolution. Unlike most uses of fields::loop_in_chunks, however, we
set use_symmetry=false: we only find the intersection of the grid_volume
with the untransformed chunks (since the transformed versions are
implicit). */
static void src_vol_chunkloop(fields_chunk *fc, int ichunk, component c, ivec is, ivec ie, vec s0,
vec s1, vec e0, vec e1, double dV0, double dV1, ivec shift,
complex<double> shift_phase, const symmetry &S, int sn, void *data_) {
src_vol_chunkloop_data *data = (src_vol_chunkloop_data *)data_;
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(void)S;
(void)sn; // these should be the identity
(void)dV0;
(void)dV1; // grid_volume weighting is included in data->amp
(void)ichunk;
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size_t npts = 1;
LOOP_OVER_DIRECTIONS(is.dim, d) { npts *= (ie.in_direction(d) - is.in_direction(d)) / 2 + 1; }
ptrdiff_t *index_array = new ptrdiff_t[npts];
complex<double> *amps_array = new complex<double>[npts];
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complex<double> amp = data->amp * conj(shift_phase);
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direction cd = component_direction(c);
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double inva = fc->gv.inva;
size_t idx_vol = 0;
LOOP_OVER_IVECS(fc->gv, is, ie, idx) {
IVEC_LOOP_ILOC(fc->gv, iloc);
if (!fc->gv.owns(iloc)) continue;
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IVEC_LOOP_LOC(fc->gv, loc);
loc += shift * (0.5 * inva);
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vec rel_loc = loc - data->center;
amps_array[idx_vol] = IVEC_LOOP_WEIGHT(s0, s1, e0, e1, 1) * amp * data->A(rel_loc);
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/* for "D" sources, multiply by epsilon. FIXME: this is not quite
right because it doesn't handle non-diagonal chi1inv!
similarly, for "B" sources, multiply by mu. */
if (is_D(c) && fc->s->chi1inv[c - Dx + Ex][cd])
amps_array[idx_vol] /= fc->s->chi1inv[c - Dx + Ex][cd][idx];
if (is_B(c) && fc->s->chi1inv[c - Bx + Hx][cd])
amps_array[idx_vol] /= fc->s->chi1inv[c - Bx + Hx][cd][idx];
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index_array[idx_vol++] = idx;
}
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if (idx_vol > npts) abort("add_volume_source: computed wrong npts (%zd vs. %zd)", npts, idx_vol);
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src_vol *tmp = new src_vol(c, data->src, idx_vol, index_array, amps_array);
field_type ft = is_magnetic(c) ? B_stuff : D_stuff;
fc->sources[ft] = tmp->add_to(fc->sources[ft]);
}
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static realnum *amp_func_data_re = NULL;
static realnum *amp_func_data_im = NULL;
static const volume *amp_func_vol = NULL;
static size_t amp_file_dims[3];
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complex<double> amp_file_func(const vec &p) {
double x_size = 0, y_size = 0, z_size = 0;
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switch (amp_func_vol->dim) {
case D1: z_size = amp_func_vol->in_direction(Z); break;
case D2:
x_size = amp_func_vol->in_direction(X);
y_size = amp_func_vol->in_direction(Y);
break;
case D3:
x_size = amp_func_vol->in_direction(X);
y_size = amp_func_vol->in_direction(Y);
z_size = amp_func_vol->in_direction(Z);
break;
case Dcyl:
x_size = amp_func_vol->in_direction(X);
z_size = amp_func_vol->in_direction(Z);
break;
}
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double rx = x_size == 0 ? 0 : 0.5 + p.x() / x_size;
double ry = y_size == 0 ? 0 : 0.5 + p.y() / y_size;
double rz = z_size == 0 ? 0 : 0.5 + p.z() / z_size;
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complex<double> res;
res.real(linear_interpolate(rx, ry, rz, amp_func_data_re, amp_file_dims[0], amp_file_dims[1],
amp_file_dims[2], 1));
res.imag(linear_interpolate(rx, ry, rz, amp_func_data_im, amp_file_dims[0], amp_file_dims[1],
amp_file_dims[2], 1));
return res;
}
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void fields::add_volume_source(component c, const src_time &src, const volume &where_,
complex<double> *arr, size_t dim1, size_t dim2, size_t dim3,
complex<double> amp) {
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amp_func_vol = &where_;
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amp_file_dims[0] = dim1;
amp_file_dims[1] = dim2;
amp_file_dims[2] = dim3;
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size_t total_size = dim1 * dim2 * dim3;
amp_func_data_re = new double[total_size];
amp_func_data_im = new double[total_size];
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for (size_t i = 0; i < total_size; ++i) {
amp_func_data_re[i] = real(arr[i]);
amp_func_data_im[i] = imag(arr[i]);
}
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add_volume_source(c, src, where_, amp_file_func, amp);
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delete[] amp_func_data_re;
delete[] amp_func_data_im;
}
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// Reads amplitude function data from h5file 'filename.' Assumes real and imaginary components
// of 'dataset' exist with '.re' and '.im' extensions.
void fields::add_volume_source(component c, const src_time &src, const volume &where_,
const char *filename, const char *dataset, complex<double> amp) {
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meep::h5file eps_file(filename, meep::h5file::READONLY, false);
int rank;
std::string dataset_re = std::string(dataset) + ".re";
std::string dataset_im = std::string(dataset) + ".im";
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size_t re_dims[] = {1, 1, 1};
double *real_data = eps_file.read(dataset_re.c_str(), &rank, re_dims, 3);
master_printf("read in %zdx%zdx%zd amplitude function file \"%s:%s\"\n", re_dims[0], re_dims[1],
re_dims[2], filename, dataset_re.c_str());
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size_t im_dims[] = {1, 1, 1};
double *imag_data = eps_file.read(dataset_im.c_str(), &rank, im_dims, 3);
master_printf("read in %zdx%zdx%zd amplitude function file \"%s:%s\"\n", im_dims[0], im_dims[1],
im_dims[2], filename, dataset_im.c_str());
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for (int i = 0; i < 3; ++i) {
if (re_dims[i] != im_dims[i]) {
abort("Imaginary and real datasets have different dimensions");
}
}
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size_t total_size = re_dims[0] * re_dims[1] * re_dims[2];
complex<double> *amp_data = new complex<double>[total_size];
for (size_t i = 0; i < total_size; ++i) {
amp_data[i] = complex<double>(real_data[i], imag_data[i]);
}
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add_volume_source(c, src, where_, amp_data, re_dims[0], re_dims[1], re_dims[2], amp);
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delete[] real_data;
delete[] imag_data;
delete[] amp_data;
}
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void fields::add_volume_source(component c, const src_time &src, const volume &where_,
complex<double> A(const vec &), complex<double> amp) {
volume where(where_); // make a copy to adjust size if necessary
if (gv.dim != where.dim)
abort("incorrect source grid_volume dimensionality in add_volume_source");
LOOP_OVER_DIRECTIONS(gv.dim, d) {
double w = user_volume.boundary_location(High, d) - user_volume.boundary_location(Low, d);
if (where.in_direction(d) > w + gv.inva)
abort("Source width > cell width in %s direction!\n", direction_name(d));
else if (where.in_direction(d) > w) { // difference is less than 1 pixel
double dw = where.in_direction(d) - w;
where.set_direction_min(d, where.in_direction_min(d) - dw * 0.5);
where.set_direction_max(d, where.in_direction_min(d) + w);
}
}
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src_vol_chunkloop_data data;
data.A = A ? A : one;
data.amp = amp;
LOOP_OVER_DIRECTIONS(gv.dim, d) {
if (where.in_direction(d) == 0.0 && !nosize_direction(d)) // delta-fun
data.amp *= gv.a; // correct units for J delta-function amplitude
}
sources = src.add_to(sources, &data.src);
data.center = (where.get_min_corner() + where.get_max_corner()) * 0.5;
loop_in_chunks(src_vol_chunkloop, (void *)&data, where, c, false);
require_component(c);
}
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} // namespace meep
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- - - - +/* Copyright (C) 2005-2019 Massachusetts Institute of Technology +% +% This program is free software; you can redistribute it and/or modify +% it under the terms of the GNU General Public License as published by +% the Free Software Foundation; either version 2, or (at your option) +% any later version. +% +% This program is distributed in the hope that it will be useful, +% but WITHOUT ANY WARRANTY; without even the implied warranty of +% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +% GNU General Public License for more details. +% +% You should have received a copy of the GNU General Public License +% along with this program; if not, write to the Free Software Foundation, +% Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. +*/ + +#include +#include +#include +#include + +#include "meep.hpp" +#include "meep_internals.hpp" + +using namespace std; + +namespace meep { + +/*********************************************************************/ + +// this function is necessary to make equality commutative ... ugh +bool src_times_equal(const src_time &t1, const src_time &t2) { + return t1.is_equal(t2) && t2.is_equal(t1); +} + +src_time *src_time::add_to(src_time *others, src_time **added) const { + if (others) { + if (src_times_equal(*this, *others)) + *added = others; + else + others->next = add_to(others->next, added); + return others; + } else { + src_time *t = clone(); + t->next = others; + *added = t; + return t; + } +} + +double src_time::last_time_max(double after) { + after = max(last_time(), after); + if (next) + return next->last_time_max(after); + else + return after; +} + +gaussian_src_time::gaussian_src_time(double f, double fwidth, double s) { + freq = f; + width = 1.0 / fwidth; + peak_time = width * s; + cutoff = width * s; + + // this is to make last_source_time as small as possible + while (exp(-cutoff * cutoff / (2 * width * width)) < 1e-100) + cutoff *= 0.9; + cutoff = float(cutoff); // don't make cutoff sensitive to roundoff error +} + +gaussian_src_time::gaussian_src_time(double f, double w, double st, double et) { + freq = f; + width = w; + peak_time = 0.5 * (st + et); + cutoff = (et - st) * 0.5; + + // this is to make last_source_time as small as possible + while (exp(-cutoff * cutoff / (2 * width * width)) < 1e-100) + cutoff *= 0.9; + cutoff = float(cutoff); // don't make cutoff sensitive to roundoff error +} + +complex gaussian_src_time::dipole(double time) const { + double tt = time - peak_time; + if (float(fabs(tt)) > cutoff) return 0.0; + + // correction factor so that current amplitude (= d(dipole)/dt) is + // ~ 1 near the peak of the Gaussian. + complex amp = 1.0 / complex(0, -2 * pi * freq); + + return exp(-tt * tt / (2 * width * width)) * polar(1.0, -2 * pi * freq * tt) * amp; +} + +// (1/\sqrt{2*pi}) \int e^{i\omega t} G(t) dt +// where G(t) is the *current* envelope, i.e. the time derivative +// of the dipole envelope +std::complex gaussian_src_time::fourier_transform(const double f) { + double omega = 2.0 * pi * f; + double omega0 = 2.0 * pi * freq; + double delta = (omega - omega0) * width; + return width * polar(1.0, omega * peak_time) * exp(-0.5 * delta * delta); +} + +bool gaussian_src_time::is_equal(const src_time &t) const { + const gaussian_src_time *tp = dynamic_cast(&t); + if (tp) + return (tp->freq == freq && tp->width == width && tp->peak_time == peak_time && + tp->cutoff == cutoff); + else + return 0; +} + +complex continuous_src_time::dipole(double time) const { + float rtime = float(time); + if (rtime < start_time || rtime > end_time) return 0.0; + + // correction factor so that current amplitude (= d(dipole)/dt) is 1. + complex amp = 1.0 / (complex(0, -1.0) * (2 * pi) * freq); + + if (width == 0.0) + return exp(complex(0, -1.0) * (2 * pi) * freq * time) * amp; + else { + double ts = (time - start_time) / width - slowness; + double te = (end_time - time) / width - slowness; + + return exp(complex(0, -1.0) * (2 * pi) * freq * time) * amp * + (1.0 + tanh(ts)) // goes from 0 to 2 + * (1.0 + tanh(te)) // goes from 2 to 0 + * 0.25; + } +} + +bool continuous_src_time::is_equal(const src_time &t) const { + const continuous_src_time *tp = dynamic_cast(&t); + if (tp) + return (tp->freq == freq && tp->width == width && tp->start_time == start_time && + tp->end_time == end_time && tp->slowness == slowness); + else + return 0; +} + +bool custom_src_time::is_equal(const src_time &t) const { + const custom_src_time *tp = dynamic_cast(&t); + if (tp) + return (tp->start_time == start_time && tp->end_time == end_time && tp->func == func && + tp->data == data); + else + return 0; +} + +/*********************************************************************/ + +src_vol::src_vol(component cc, src_time *st, size_t n, ptrdiff_t *ind, complex *amps) { + c = cc; + if (is_D(c)) c = direction_component(Ex, component_direction(c)); + if (is_B(c)) c = direction_component(Hx, component_direction(c)); + t = st; + next = NULL; + npts = n; + index = ind; + A = amps; +} + +src_vol::src_vol(const src_vol &sv) { + c = sv.c; + t = sv.t; + npts = sv.npts; + index = new ptrdiff_t[npts]; + A = new complex[npts]; + for (size_t j = 0; j < npts; j++) { + index[j] = sv.index[j]; + A[j] = sv.A[j]; + } + if (sv.next) + next = new src_vol(*sv.next); + else + next = NULL; +} + +src_vol *src_vol::add_to(src_vol *others) { + if (others) { + if (*this == *others) { + if (npts != others->npts) + abort("Cannot add grid_volume sources with different number of points\n"); + /* Compare all of the indices...if this ever becomes too slow, + we can just compare the first and last indices. */ + for (size_t j = 0; j < npts; j++) { + if (others->index[j] != index[j]) abort("Different indices\n"); + others->A[j] += A[j]; + } + } else + others->next = add_to(others->next); + return others; + } else { + next = others; + return this; + } +} + +/*********************************************************************/ + +// THIS VARIANT IS FOR BACKWARDS COMPATIBILITY, and is DEPRECATED: +void fields::add_point_source(component c, double freq, double width, double peaktime, + double cutoff, const vec &p, complex amp, int is_c) { + width /= freq; + + if (is_c) { // TODO: don't ignore peaktime? + continuous_src_time src(freq, width, time(), infinity, cutoff); + if (is_magnetic(c)) src.is_integrated = false; + add_point_source(c, src, p, amp); + } else { + cutoff = gv.inva + cutoff * width; + if (peaktime <= 0.0) peaktime = time() + cutoff; + + // backward compatibility (slight phase shift in old Meep version) + peaktime += is_magnetic(c) ? -dt * 0.5 : dt; + + gaussian_src_time src(freq, width, peaktime - cutoff, peaktime + cutoff); + if (is_magnetic(c)) src.is_integrated = false; + add_point_source(c, src, p, amp); + } +} + +void fields::add_point_source(component c, const src_time &src, const vec &p, complex amp) { + add_volume_source(c, src, volume(p, p), amp); +} + +static complex one(const vec &pt) { + (void)pt; + return 1.0; +} +void fields::add_volume_source(component c, const src_time &src, const volume &where, + complex amp) { + add_volume_source(c, src, where, one, amp); +} + +struct src_vol_chunkloop_data { + complex (*A)(const vec &); + complex amp; + src_time *src; + vec center; +}; + +/* Adding source volumes can be treated as a kind of "integration" + problem, since we need to loop over all the chunks that intersect + the source grid_volume, with appropriate interpolation weights at the + boundaries so that the integral of the current is fixed regardless + of resolution. Unlike most uses of fields::loop_in_chunks, however, we + set use_symmetry=false: we only find the intersection of the grid_volume + with the untransformed chunks (since the transformed versions are + implicit). */ +static void src_vol_chunkloop(fields_chunk *fc, int ichunk, component c, ivec is, ivec ie, vec s0, + vec s1, vec e0, vec e1, double dV0, double dV1, ivec shift, + complex shift_phase, const symmetry &S, int sn, void *data_) { + src_vol_chunkloop_data *data = (src_vol_chunkloop_data *)data_; + + (void)S; + (void)sn; // these should be the identity + (void)dV0; + (void)dV1; // grid_volume weighting is included in data->amp + (void)ichunk; + + size_t npts = 1; + LOOP_OVER_DIRECTIONS(is.dim, d) { npts *= (ie.in_direction(d) - is.in_direction(d)) / 2 + 1; } + ptrdiff_t *index_array = new ptrdiff_t[npts]; + complex *amps_array = new complex[npts]; + + complex amp = data->amp * conj(shift_phase); + + direction cd = component_direction(c); + + double inva = fc->gv.inva; + size_t idx_vol = 0; + LOOP_OVER_IVECS(fc->gv, is, ie, idx) { + IVEC_LOOP_ILOC(fc->gv, iloc); + if (!fc->gv.owns(iloc)) continue; + + IVEC_LOOP_LOC(fc->gv, loc); + loc += shift * (0.5 * inva); + + vec rel_loc = loc - data->center; + amps_array[idx_vol] = IVEC_LOOP_WEIGHT(s0, s1, e0, e1, 1) * amp * data->A(rel_loc); + + /* for "D" sources, multiply by epsilon. FIXME: this is not quite + right because it doesn't handle non-diagonal chi1inv! + similarly, for "B" sources, multiply by mu. */ + if (is_D(c) && fc->s->chi1inv[c - Dx + Ex][cd]) + amps_array[idx_vol] /= fc->s->chi1inv[c - Dx + Ex][cd][idx]; + if (is_B(c) && fc->s->chi1inv[c - Bx + Hx][cd]) + amps_array[idx_vol] /= fc->s->chi1inv[c - Bx + Hx][cd][idx]; + + index_array[idx_vol++] = idx; + } + + if (idx_vol > npts) abort("add_volume_source: computed wrong npts (%zd vs. %zd)", npts, idx_vol); + + src_vol *tmp = new src_vol(c, data->src, idx_vol, index_array, amps_array); + field_type ft = is_magnetic(c) ? B_stuff : D_stuff; + fc->sources[ft] = tmp->add_to(fc->sources[ft]); +} + +static realnum *amp_func_data_re = NULL; +static realnum *amp_func_data_im = NULL; +static const volume *amp_func_vol = NULL; +static size_t amp_file_dims[3]; + +complex amp_file_func(const vec &p) { + double x_size = 0, y_size = 0, z_size = 0; + + switch (amp_func_vol->dim) { + case D1: z_size = amp_func_vol->in_direction(Z); break; + case D2: + x_size = amp_func_vol->in_direction(X); + y_size = amp_func_vol->in_direction(Y); + break; + case D3: + x_size = amp_func_vol->in_direction(X); + y_size = amp_func_vol->in_direction(Y); + z_size = amp_func_vol->in_direction(Z); + break; + case Dcyl: + x_size = amp_func_vol->in_direction(X); + z_size = amp_func_vol->in_direction(Z); + break; + } + + double rx = x_size == 0 ? 0 : 0.5 + p.x() / x_size; + double ry = y_size == 0 ? 0 : 0.5 + p.y() / y_size; + double rz = z_size == 0 ? 0 : 0.5 + p.z() / z_size; + + complex res; + res.real(linear_interpolate(rx, ry, rz, amp_func_data_re, amp_file_dims[0], amp_file_dims[1], + amp_file_dims[2], 1)); + res.imag(linear_interpolate(rx, ry, rz, amp_func_data_im, amp_file_dims[0], amp_file_dims[1], + amp_file_dims[2], 1)); + return res; +} + +void fields::add_volume_source(component c, const src_time &src, const volume &where_, + complex *arr, size_t dim1, size_t dim2, size_t dim3, + complex amp) { + + amp_func_vol = &where_; + + amp_file_dims[0] = dim1; + amp_file_dims[1] = dim2; + amp_file_dims[2] = dim3; + + size_t total_size = dim1 * dim2 * dim3; + amp_func_data_re = new double[total_size]; + amp_func_data_im = new double[total_size]; + + for (size_t i = 0; i < total_size; ++i) { + amp_func_data_re[i] = real(arr[i]); + amp_func_data_im[i] = imag(arr[i]); + } + + add_volume_source(c, src, where_, amp_file_func, amp); + + delete[] amp_func_data_re; + delete[] amp_func_data_im; +} + +// Reads amplitude function data from h5file 'filename.' Assumes real and imaginary components +// of 'dataset' exist with '.re' and '.im' extensions. +void fields::add_volume_source(component c, const src_time &src, const volume &where_, + const char *filename, const char *dataset, complex amp) { + + meep::h5file eps_file(filename, meep::h5file::READONLY, false); + int rank; + std::string dataset_re = std::string(dataset) + ".re"; + std::string dataset_im = std::string(dataset) + ".im"; + + size_t re_dims[] = {1, 1, 1}; + double *real_data = eps_file.read(dataset_re.c_str(), &rank, re_dims, 3); + master_printf("read in %zdx%zdx%zd amplitude function file \"%s:%s\"\n", re_dims[0], re_dims[1], + re_dims[2], filename, dataset_re.c_str()); + + size_t im_dims[] = {1, 1, 1}; + double *imag_data = eps_file.read(dataset_im.c_str(), &rank, im_dims, 3); + master_printf("read in %zdx%zdx%zd amplitude function file \"%s:%s\"\n", im_dims[0], im_dims[1], + im_dims[2], filename, dataset_im.c_str()); + + for (int i = 0; i < 3; ++i) { + if (re_dims[i] != im_dims[i]) { + abort("Imaginary and real datasets have different dimensions"); + } + } + + size_t total_size = re_dims[0] * re_dims[1] * re_dims[2]; + complex *amp_data = new complex[total_size]; + for (size_t i = 0; i < total_size; ++i) { + amp_data[i] = complex(real_data[i], imag_data[i]); + } + + add_volume_source(c, src, where_, amp_data, re_dims[0], re_dims[1], re_dims[2], amp); + + delete[] real_data; + delete[] imag_data; + delete[] amp_data; +} + +void fields::add_volume_source(component c, const src_time &src, const volume &where_, + complex A(const vec &), complex amp) { + volume where(where_); // make a copy to adjust size if necessary + if (gv.dim != where.dim) + abort("incorrect source grid_volume dimensionality in add_volume_source"); + LOOP_OVER_DIRECTIONS(gv.dim, d) { + double w = user_volume.boundary_location(High, d) - user_volume.boundary_location(Low, d); + if (where.in_direction(d) > w + gv.inva) + abort("Source width > cell width in %s direction!\n", direction_name(d)); + else if (where.in_direction(d) > w) { // difference is less than 1 pixel + double dw = where.in_direction(d) - w; + where.set_direction_min(d, where.in_direction_min(d) - dw * 0.5); + where.set_direction_max(d, where.in_direction_min(d) + w); + } + } + + src_vol_chunkloop_data data; + data.A = A ? A : one; + data.amp = amp; + LOOP_OVER_DIRECTIONS(gv.dim, d) { + if (where.in_direction(d) == 0.0 && !nosize_direction(d)) // delta-fun + data.amp *= gv.a; // correct units for J delta-function amplitude + } + sources = src.add_to(sources, &data.src); + data.center = (where.get_min_corner() + where.get_max_corner()) * 0.5; + loop_in_chunks(src_vol_chunkloop, (void *)&data, where, c, false); + require_component(c); +} + +} // namespace meep From da1246e0482afee3e6fc79382d056fed5db85d3c Mon Sep 17 00:00:00 2001 From: Homer Reid Date: Sat, 16 Mar 2019 15:45:08 -0400 Subject: [PATCH 08/16] added meep.adjoint python module for adjoint solver; added python/examples/adjoint_optimization with two examples so far; rearranged python/Makefile.am to accommodate adjoint module; update python/Makefile.am to byte-compile mpb python source files that were previously not getting byte-compiled (intentionally?) --- Makefile.am | 3 +- configure.ac | 6 +- python/Makefile.am | 129 ++- python/adjoint/Basis.py | 123 +++ python/adjoint/ObjectiveFunction.py | 655 ++++++++++++ python/adjoint/OptimizationProblem.py | 351 +++++++ python/adjoint/Visualization.py | 962 ++++++++++++++++++ python/adjoint/__init__.py | 91 ++ .../adjoint_optimization/HoleCloak.py | 161 +++ .../adjoint_optimization/HoleyWaveguide.py | 156 +++ 10 files changed, 2582 insertions(+), 55 deletions(-) create mode 100644 python/adjoint/Basis.py create mode 100644 python/adjoint/ObjectiveFunction.py create mode 100644 python/adjoint/OptimizationProblem.py create mode 100644 python/adjoint/Visualization.py create mode 100644 python/adjoint/__init__.py create mode 100644 python/examples/adjoint_optimization/HoleCloak.py create mode 100644 python/examples/adjoint_optimization/HoleyWaveguide.py diff --git a/Makefile.am b/Makefile.am index e3d96f690..ce4b0e022 100644 --- a/Makefile.am +++ b/Makefile.am @@ -7,12 +7,13 @@ if WITH_SCHEME SUBDIRS += scheme endif endif + +if WITH_PYTHON if WITH_MPB if WITH_LIBCTLGEOM SUBDIRS += libpympb endif endif -if WITH_PYTHON SUBDIRS += python endif diff --git a/configure.ac b/configure.ac index 0876964b6..900ab2c80 100644 --- a/configure.ac +++ b/configure.ac @@ -550,15 +550,15 @@ if test "x$with_scheme" = xyes; then AC_CONFIG_FILES([scheme/Makefile scheme/meep.scm]) fi -############################################################################## +if test "x$with_python" = xyes; then + AC_CONFIG_FILES([libpympb/Makefile python/Makefile]) +fi AC_CONFIG_FILES([ Makefile meep-pkgconfig src/Makefile tests/Makefile - libpympb/Makefile - python/Makefile ]) AC_OUTPUT diff --git a/python/Makefile.am b/python/Makefile.am index 2e6ab16b6..98c58a4a9 100644 --- a/python/Makefile.am +++ b/python/Makefile.am @@ -1,43 +1,6 @@ -HPPFILES= \ - $(top_srcdir)/src/meep.hpp \ - $(top_srcdir)/src/meep_internals.hpp \ - $(top_srcdir)/src/bicgstab.hpp \ - $(top_srcdir)/src/meep/vec.hpp \ - $(top_srcdir)/src/meep/mympi.hpp \ - $(top_srcdir)/src/meepgeom.hpp \ - $(top_srcdir)/src/material_data.hpp - -BUILT_SOURCES = meep-python.cxx __init__.py -EXTRA_DIST = $(BUILT_SOURCES) typemap_utils.cpp materials.py examples tests - -CLEANFILES = $(BUILT_SOURCES) meep.py .coverage - -if WITH_MPB - PYMPBINCLUDE=-I$(top_srcdir)/libpympb - LIBPYMPB=$(top_builddir)/libpympb/libpympb.la - BUILT_SOURCES += mpb-python.cxx mpb.py - EXTRA_DIST += solver.py mpb_data.py -endif - -LIBMEEP = $(top_builddir)/src/libmeep.la - -AM_CPPFLAGS = -I$(top_srcdir)/src \ - $(PYMPBINCLUDE) \ - -I$(top_builddir) # for config.h - -_meep_la_SOURCES = meep-python.cxx -_meep_la_LIBADD = $(LIBMEEP) $(PYTHON_LIBS) -_meep_la_LDFLAGS = -module -version-info @SHARED_VERSION_INFO@ -_meep_la_CPPFLAGS = $(PYTHON_INCLUDES) $(AM_CPPFLAGS) - -if WITH_MPB -_mpb_la_SOURCES = mpb-python.cxx -_mpb_la_LIBADD = $(PYTHON_LIBS) $(LIBPYMPB) -_mpb_la_LDFLAGS = -module -version-info @SHARED_VERSION_INFO@ -_mpb_la_CPPFLAGS = $(PYTHON_INCLUDES) $(AM_CPPFLAGS) -MPB_LA = _mpb.la -endif # WITH_MPB - +################################################## +# description of unit tests +################################################## TEST_DIR = tests # material_dispersion.py test must be excluded from test suite for MPI build @@ -112,30 +75,70 @@ endif TEST_EXTENSIONS = .py TESTS_ENVIRONMENT = export PYTHONPATH=$(abs_top_builddir)/python:$$PYTHONPATH; -if WITH_PYTHON - pkgpython_PYTHON = geom.py __init__.py source.py simulation.py materials.py - pkgpyexec_LTLIBRARIES = _meep.la +###################################################################### +# instructions for building the _meep binary library that implements +# the low-level interface between python codes and the libmeep C++ library +###################################################################### +BUILT_SOURCES = meep-python.cxx __init__.py +EXTRA_DIST = $(BUILT_SOURCES) typemap_utils.cpp materials.py examples tests +CLEANFILES = $(BUILT_SOURCES) meep.py .coverage + +AM_CPPFLAGS = -I$(top_srcdir)/src \ + -I$(top_srcdir)/libpympb \ + -I$(top_builddir) # for config.h + +LIBMEEP = $(top_builddir)/src/libmeep.la + +_meep_la_SOURCES = meep-python.cxx +_meep_la_LIBADD = $(LIBMEEP) $(PYTHON_LIBS) +_meep_la_LDFLAGS = -module -version-info @SHARED_VERSION_INFO@ +_meep_la_CPPFLAGS = $(PYTHON_INCLUDES) $(AM_CPPFLAGS) + +pkgpyexec_LTLIBRARIES = _meep.la + +###################################################################### +# instructions for building the _mpb binary library that implements +# the low-level interface between python codes and the libmpb C++ library +###################################################################### if WITH_MPB + BUILT_SOURCES += mpb-python.cxx mpb.py + EXTRA_DIST += solver.py mpb_data.py + MPB_LA = _mpb.la pympbdir = $(pkgpythondir)/mpb pympb_DATA = mpb.py solver.py mpb_data.py pympb_LTLIBRARIES = _mpb.la -endif # WITH_MPB -endif # WITH_PYTHON + _mpb_la_SOURCES = mpb-python.cxx + _mpb_la_LIBADD = $(PYTHON_LIBS) $(top_builddir)/libpympb/libpympb.la + _mpb_la_LDFLAGS = -module -version-info @SHARED_VERSION_INFO@ + _mpb_la_CPPFLAGS = $(PYTHON_INCLUDES) $(AM_CPPFLAGS) -if WITH_MPB install-data-hook: mv $(DESTDIR)$(pkgpythondir)/mpb/mpb.py $(DESTDIR)$(pkgpythondir)/mpb/__init__.py uninstall-hook: rm -f $(DESTDIR)$(pkgpythondir)/mpb/__init__.py + endif +################################################## +# instructions for running SWIG to generate the +# source files for the previous step +################################################## if MAINTAINER_MODE SWIG ?= swig SWIG_VERSION = $(shell $(SWIG) -version | grep Version | awk '{print $$3}') MEEP_SWIG_SRC = meep.i numpy.i vec.i +HPPFILES= \ + $(top_srcdir)/src/meep.hpp \ + $(top_srcdir)/src/meep_internals.hpp \ + $(top_srcdir)/src/bicgstab.hpp \ + $(top_srcdir)/src/meep/vec.hpp \ + $(top_srcdir)/src/meep/mympi.hpp \ + $(top_srcdir)/src/meepgeom.hpp \ + $(top_srcdir)/src/material_data.hpp + meep-python.cxx: $(MEEP_SWIG_SRC) $(HPPFILES) $(SWIG) -Wextra $(AM_CPPFLAGS) -outdir $(builddir) -c++ -python -o $@ $(srcdir)/meep.i @@ -166,23 +169,47 @@ endif INIT_PY = __init__.py MPB_PY_PATH = $(builddir)/mpb.py -else + +else # not maintainer mode INIT_PY = $(srcdir)/__init__.py MPB_PY_PATH = $(srcdir)/mpb.py endif # MAINTAINER_MODE +###################################################################### +# specification of python source files to be byte-compiled at installation +# time. Note that files in `pkgpython_PYTHON` are both byte-compiled and +# installed in the 'meep' subdirectory of the python site-packages +# installation. The `nodist` version does the byte-compiling but omits the +# installation, so we can install the files to a custom destination. +# note: previously the pympb source files were excluded from this; was +# that intentional? +###################################################################### HL_IFACE = \ $(srcdir)/geom.py \ $(srcdir)/simulation.py \ $(srcdir)/source.py \ $(srcdir)/materials.py -PY_PKG_FILES = \ - $(INIT_PY) \ - $(HL_IFACE) \ - .libs/_meep.so +pkgpython_PYTHON = __init__.py $(HL_IFACE) + +adjointdir = $(pkgpythondir)/adjoint +adjoint_DATA = $(srcdir)/adjoint/__init__.py \ + $(srcdir)/adjoint/Basis.py \ + $(srcdir)/adjoint/ObjectiveFunction.py \ + $(srcdir)/adjoint/OptimizationProblem.py \ + $(srcdir)/adjoint/Visualization.py + +nodist_python_PYTHON = $(adjoint_DATA) $(pympb_DATA) + +###################################################################### +# finally, specification of what gets installed in the meep python +# module directory of the python site-packages installation +# Q: Why is this not redundant since e.g. the HL_IFACE files should +# already be installed by virtue of being in pkgpython_PYTHON +###################################################################### +PY_PKG_FILES = $(INIT_PY) $(HL_IFACE) .libs/_meep.so meep: _meep.la $(MPB_LA) __init__.py $(HL_IFACE) mkdir -p meep diff --git a/python/adjoint/Basis.py b/python/adjoint/Basis.py new file mode 100644 index 000000000..9579a4cf1 --- /dev/null +++ b/python/adjoint/Basis.py @@ -0,0 +1,123 @@ +###################################################################### +# Basis.py -- general support for spatially-varying permittivity +# functions described by expansions in user-defined sets +# of basis functions, plus predefined implementations of +# some simple basis sets for common cases +###################################################################### +import numpy as np +import meep as mp + +################################################# +################################################# +################################################## +def parameterized_dielectric(center, basis, beta): + def _eps_func(p): + return np.dot(beta,basis( (p-center).__array__())) + return _eps_func + + +################################################## +# Fourier basis for a periodic function of one variable +# u (-0.5 < u < 0.5). +# For a given max frequency kmax, there are 2*kmax+1 basis functions, +# [1, sin(2*pi*u), cos(2*pi*u), sin(4*pi*u), ..., cos(2*kmax*pi*u)] +################################################## +def sinusoid(k,u): + arg = 2.0*np.pi*np.floor((k+1)/2)*u + return np.sin(arg) if (k%2) else np.cos(arg) + +def sinusoid_names(arg,kmax): + sinusoid_names=['1'] + for nu in range(1,kmax+1): + sinusoid_names.append('sin({}{})'.format('' if nu==1 else str(nu),arg)) + sinusoid_names.append('cos({}{})'.format('' if nu==1 else str(nu),arg)) + return sinusoid_names + + +################################################## +# Plane-wave basis for a rectangular region. +# +# f_{nx,ny} = S_{nx}(x/lx) * S_{ny}(y/ly) +# +# S_{0}(u) = 1 +# S_{2k-1}(u) = sin(2*pi*k*u) +# S_{2k} (u) = cos(2*pi*k*u) +# +# The size of the basis is (2*kx_max+1)*(2*ky_max+1) +################################################## +def plane_wave_basis(lx, ly, kx_max=0, ky_max=0): + + def _get_bf_vector(p=[0.0,0.0]): + b=np.zeros( (2*kx_max+1)*(2*ky_max+1) ) + for kx in range(0,2*kx_max+1): + for ky in range(0,2*ky_max+1): + b[ kx*(2*ky_max+1) + ky ] = sinusoid(kx,p[0]/lx)*sinusoid(ky,p[1]/ly) + return b + + return _get_bf_vector + + +################################################## +# basis of expansion functions f{m,n}(rho,phi) for +# a disc or annulus. +# +# f(rho,phi) = (legendre polynomial in rho) * (sinusoid in phi) +# +# f_{nr, 0} = L_{nr}(u) +# f_{nr, 2*k-1} = L_{nr}(u) * sin(k*phi) +# f_{nr, 2*k} = L_{nr}(u) * cos(k*phi) +# +# for nr=[0,...,nr_max], k=[0,1,...,kphi_max] +# +# Here u is a rescaled version of rho that runs over [-1:1] +# as rho runs over [inner_radius:outer_radius]. +# +# The size of the basis is (nr_max+1)*(2*kphiMax+1) +################################################## +def fourier_legendre_basis(radius=None, outer_radius=None, inner_radius=0.0, + nr_max=0, kphi_max=0): + + num_radial=nr_max+1 + num_angular=(2*kphi_max+1) + outer_radius=radius if outer_radius is None else outer_radius + + def _get_bf_vector(p=[0.0,0.0]): + b=np.zeros( num_radial*num_angular ) + r=np.sqrt(p[0]*p[0] + p[1]*p[1]) + if router_radius: + b[0]=1.0; + return b + u = -1.0 + 2.0*(r-inner_radius)/(outer_radius-inner_radius) + phi=np.arctan2(p[1],p[0]) + (Lm1, L)=(0.0,1.0) + for nr in range(0,num_radial): + for nphi in range(0,num_angular): + b[ nr*num_angular + nphi ] = L*sinusoid(nphi,phi/(2.0*np.pi)) + (Lm2,Lm1)=(Lm1,L) + L = ( (2*nr+1)*u*Lm1 - nr*Lm2 )/(nr+1) # Legendre recursion + return b + + return _get_bf_vector + +def fl_basis_names(nr_max, kphi_max): + snames=sinusoid_names('phi',kphi_max) + flb_names=snames[:] + for nr in range(1,nr_max+1): + flb_names += ['L{}(r)'.format(nr) + ('' if s=='1' else s) for s in snames] + return flb_names + +######################################################### +# utility routine to project an arbitrary function f(x) +# onto a basis set {b_n(x)}, i.e. computes the N-vector +# of overlap integrals +######################################################### +def project_basis(basis,xyzw,f): + projection=1.0j*np.zeros(len(basis())) + (x,y,z,w)=xyzw[0],xyzw[1],xyzw[2],xyzw[3] + xyz=[mp.Vector3(xx,yy,zz) for xx in x for yy in y for zz in z] + it=np.nditer(w,flags=['f_index','multi_index']) + while not it.finished: + n, nn = it.index, it.multi_index + projection+=w[nn]*basis(xyz[n])*f[nn] + it.iternext() + return projection diff --git a/python/adjoint/ObjectiveFunction.py b/python/adjoint/ObjectiveFunction.py new file mode 100644 index 000000000..41e6fc7a7 --- /dev/null +++ b/python/adjoint/ObjectiveFunction.py @@ -0,0 +1,655 @@ +############################################### +# ObjectiveFunction.py --- routines for evaluating +# objective quantities and objective functions for +# adjoint-based optimization in meep +##################################################### +import datetime +from collections import namedtuple +import numpy as np +import sympy + +import meep as mp + +from .Basis import project_basis + +###################################################################### +# various global options affecting the adjoint solver, user-tweakable +# via command-line arguments or set_adjoint_option() +###################################################################### +adjoint_options={ + 'dft_reltol': 1.0e-6, + 'dft_timeout': 10.0, + 'dft_interval': 0.25, + 'verbosity': 'default', + 'visualize': False, + 'logfile': None, + 'plot_pause': 0.01, + 'animate_components': None, + 'animate_interval': 1.0 +} + +################################################## +# some convenient constants and typedefs +################################################## +xHat=mp.Vector3(1.0,0.0,0.0) +yHat=mp.Vector3(0.0,1.0,0.0) +zHat=mp.Vector3(0.0,0.0,1.0) +origin=mp.Vector3() + +EHTransverse=[ [mp.Ey, mp.Ez, mp.Hy, mp.Hz], + [mp.Ez, mp.Ex, mp.Hz, mp.Hx], + [mp.Ex, mp.Ey, mp.Hx, mp.Hy] ] +Exyz=[mp.Ex, mp.Ey, mp.Ez] +Hxyz=[mp.Hx, mp.Hy, mp.Hz] +EHxyz=Exyz+Hxyz + +# GridInfo stores the extents and resolution of the full Yee grid in a MEEP +# simulation; this is the minimal information needed to compute array metadata. +GridInfo = namedtuple('GridInfo', ['size', 'res']) + +################################################## +# miscellaneous utilities +################################################## +#CU=1.0+0.0j # complex unity, to force numbers to be treated as complex + + +def abs2(z): + return np.real(np.conj(z)*z) + + +def unit_vector(n,N): + return np.array([1.0 if i==n else 0.0 for i in range(N)]) + + +# error relative to magnitude, returns value in range [0,2] +def rel_diff(a,b): + return ( 2.0 if np.isinf(a) or np.isinf(b) \ + else 0.0 if a==0.0 and b==0.0 \ + else abs(a-b)/max(abs(a),abs(b)) \ + ) + + +def log(msg): + if not mp.am_master() or adjoint_options['logfile'] is None: + return + dt=datetime.datetime.now().strftime("%T ") + with open(adjoint_options['logfile'],'a') as f: + f.write("{} {}\n".format(dt,msg)) + +##################################################################### +# A FluxLine is essentially a 2D mp.FluxRegion with a convenient constructor +# prototype and a user-specified label to facilitate identification. +###################################################################### +FluxLineT=namedtuple('FluxLine','center size direction weight name') + + +def FluxLine(x0,y0,length,dir,name=None): + return FluxLineT( center=mp.Vector3(x0,y0), + size=length*(xHat if dir is mp.Y else yHat), + direction=dir, weight=1.0, name=name) + +###################################################################### +# DFTCell is an improved data structure for working with frequency-domain +# field components in MEEP calculations. It consolidates and replaces the +# zoo of 8 quasi-redundant DFT-related data structures in core meep (namely: +# DftFlux, DftFields, DftNear2Far, DftForce, DftLdos, DftObj, FluxRegion, +# FieldsRegion) and has a different relationship to individual MEEP +# simulations described by instances of mp.simulation(). +# +# In a nutshell, the core constituents of a DFT cell are the three metadata +# fields that define the set of frequency-domain field amplitudes tabulated +# by the cell: a grid subvolume (including the associated 'xyzw' metadata), +# a set of field components, and a set of frequencies. These fields are passed +# to the DFTCell constructor and do not change over the lifetime of the DFTCell, +# which will generally encompass the lifetimes of several mp.simulation() +# instances. +# +# On the other hand, the frequency-domain field-amplitude data arrays produced by +# DFT calculations are considered less intrinsic: the DFT cell may have *no* such +# data (as when a calculation is first initiated), or may have multiple sets of +# data arrays resulting from multiple different timestepping runs. These multiple +# data sets may correspond, for example, to timestepping runs excited by different +# sources (such as the forward and adjoint sources in an adjoint-based value-and-gradient +# calculation) and/or to runs in the full and 'vacuum' versions of a geometry, +# where the latter is the 'bare' version of a geometry (with scatterers and obstacles +# removed) that one runs to tabulate incident-field profiles. +# +# Although not strictly related to DFT calculations, dft_cells describing flux-monitor +# regions also know how to compute and cache arrays of eigenmode field amplitudes. +# +# We use the following semantic conventions for choosing names for entities in the +# hierarchy of +# +# -- At the most granular level, we have 1D, 2D, or 3D arrays (slices) +# of frequency-domain amplitudes for a single field component at a +# single frequency in a single calculation. For our purposes these +# only ever arise as loop variables, which we typically call 'F' for field. +# +# -- We often have occasion to refer to the full set of such slices +# for all field components stored in the DFTCell, again at a single +# frequency in a single simulation. Since this set typically includes +# data for both E and H field components, we call it simply EH. +# Thus, in general, EH[2] = data array for field component #2, +# at a single frequency in a single simulation. +# +# -- EHData refers to a collection (one-dimensional list) of EH arrays, one +# for each component in the cell. Thus e.g. EHData[2] = array slice of +# amplitudes for field component components[2], all at a single frequency. +# +# -- EHCatalog refers to a collection (one-dimensional list) of EHData +# entities, one for each frequency in the DFTCell---that is, a 2D matrix, +# with rows corresponding to frequencies and columns corresponding to +# components of EH arrays. Thus e.g. EHCatalog[3][2] = array slice of +# amplitudes for component components[2] at frequency #3. +# +# -- Arrays of eigenmode field amplitudes are named similarly with the +# substitution "EH" -> "eh" +# +# Note: for now, all arrays are stored in memory. For large calculations with +# many DFT frequencies this may become impractical. TODO: disk caching. +###################################################################### +global_dft_cell_names=[] +class DFTCell(object): + +# Why does this not work?! I would have thought DFTCell.DFTCellNames would +# be globally accessible like a static member of a C++ class, and in fact it +# **is** accessible from most code, but seems to go out of scope when we're +# in the body of a method of some other class. +# DFTCellNames=[] +# @classmethod +# def get_index(cls, region_name): +# cell_name = region_name + '_flux' +# if cell_name in cls.DFTCellNames: +# return cls.DFTCellNames.index(cell_name) +# raise ValueError("reference to nonexistent DFT cell {}",region_name) + @classmethod + def get_index(cls, region_name): + cell_name = region_name + '_flux' + if cell_name in global_dft_cell_names: + return global_dft_cell_names.index(cell_name) + raise ValueError("reference to nonexistent DFT cell {}",region_name) + + + ###################################################################### + ###################################################################### + ###################################################################### + def __init__(self, grid_info=None, region=None, center=origin, size=None, + components=None, fcen=None, df=0, nfreq=1, name=None): + + if region is not None: + self.center, self.size, self.region = region.center, region.size, region + elif size is not None: + self.center, self.size, self.region = center, size, mp.Volume(center=center, size=size) + else: + self.center, self.size, self.region = origin, grid_info.size, mp.Volume(center=center, size=size) + + self.nHat = region.direction if hasattr(region,'direction') else None + self.celltype = 'flux' if self.nHat is not None else 'fields' # TODO extend to other cases + self.components = components if components is not None \ + else EHTransverse[self.nHat] if self.celltype is 'flux' \ + else EHxyz + self.fcen = fcen + self.df = df if nfreq>1 else 0.0 + self.nfreq = nfreq + self.freqs = [fcen] if nfreq==1 else np.linspace(fcen-0.5*df, fcen+0.5*df, nfreq) + + self.sim = None # mp.simulation for current simulation + self.dft_obj = None # meep DFT object for current simulation + + self.EH_cache = {} # cache of frequency-domain field data computed in previous simulations + self.eigencache = {} # cache of eigenmode field data to avoid redundant recalculationsq + + self.name = name + if self.name is None: + if hasattr(self.region,'name'): + self.name = '{}_{}'.format(self.region.name, self.celltype) + elif grid_info and self.size==grid_info.size: + self.name = 'fullgrid_{}'.format(self.celltype) + else: + self.name = '{}_{}'.format(self.celltype, len(global_dft_cell_names)) +# self.name = '{}_{}'.format(self.celltype, len(self.DFTCellNames)) +# self.DFTCellNames.append(self.name) + global_dft_cell_names.append(self.name) + + # FIXME At present the 'xyzw' metadata cannot be computed until a mp.simulation / meep::fields + # object has been created, but in fact the metadata only depend on the GridInfo + # (resolution and extents of the computational lattice) and are independent + # of the specific material geometry and source configuration of any particular + # 'fields' instance or simulation. In keeping with the spirit of 'DFTCell' it should + # be possible to compute the metadata once and for all right here before any mp.simulation() + # or meep::fields is created, but that will require some code refactoring. For the time being + # we punt on this until later, after a fields object has been created. + self.xyzw = self.slice_dims = None + + ###################################################################### + # 'register' the cell with a MEEP timestepping simulation to request + # computation of frequency-domain fields + ###################################################################### + def register(self, sim): + self.sim = sim + self.dft_obj = sim.add_flux(self.fcen,self.df,self.nfreq,self.region) if self.celltype=='flux' \ + else sim.add_dft_fields(self.components, self.freqs[0], self.freqs[-1], self.nfreq, where=self.region) + + # take the opportunity to fill in the metadata if not done yet; #FIXME to be removed as discussed above + if self.xyzw is None: + self.xyzw = sim.get_dft_array_metadata(center=self.center, size=self.size) + self.slice_dims = np.shape(self.xyzw[3]) + + + ###################################################################### + # Compute an array of frequency-domain field amplitudes, i.e. a + # frequency-domain array slice, for a single field component at a + # single frequency in the current simulation. This is like + # mp.get_dft_array(), but 'zero-padded:' when the low-level DFT object + # does not have data for the requested component (perhaps because it vanishes + # identically by symmetry), this routine returns an array of the expected + # dimensions with all zero entries, instead of a rank-0 array that prints + # out as a single preposterously large or small floating-point number, + # which is the not-very-user-friendly behavior of mp.get_dft_array(). + ###################################################################### + def get_EH_slice(self, c, nf=0): + EH = self.sim.get_dft_array(self.dft_obj, c, nf) + return EH if np.ndim(EH)>0 else 0.0j*np.zeros(self.slice_dims) + + ###################################################################### + # Return a 1D array (list) of arrays of frequency-domain field amplitudes, + # one for each component in this DFTCell, at a single frequency in a + # single MEEP simulation. The simulation in question may be the present, + # ongoing simulation (if label==None), in which case the array slices are + # read directly from the currently active meep DFT object; or it may be a + # previous simulation (identified by label) for which DFTCell::save_fields + # was called at the end of timestepping. + ###################################################################### + def get_EH_slices(self, nf=0, label=None): + if label is None: + return [ self.get_EH_slice(c, nf=nf) for c in self.components ] + elif label in self.EH_cache: + return self.EH_cache[label][nf] + raise ValueError("DFTCell {} has no saved data for label '{}'".format(self.name, label)) + + ###################################################################### + # substract incident from total fields to yield scattered fields + ###################################################################### + def subtract_incident_fields(self, EHT, nf=0): + EHI = self.get_EH_slices(nf=nf, label='incident') + for nc, c in enumerate(self.components): + EHT[nc] -= EHI[nc] + + #################################################################### + # This routine tells the DFTCell to create and save an archive of + # the frequency-domain array slices for the present simulation---i.e. + # to copy the frequency-domain field data out of the sim.dft_obj + # structure and into an appropriate data buffer in the DFTCell, + # before the sim.dft_obj data vanish when sim is deleted and replaced + # by a new simulation. This routine should be called after timestepping + # is complete. The given label is used to identify the stored data + # for purposes of future retrieval. + ###################################################################### + def save_fields(self, label): + if label in self.EH_cache: + raise ValueError("DFTCell {}: data for label {} has already been saved in cache".format(self.name,label)) + self.EH_cache[label] = [self.get_EH_slices(nf=nf) for nf in range(len(self.freqs))] + + ###################################################################### + # Return a 1D array (list) of arrays of field amplitudes for all + # tangential E,H components at a single frequency---just like + # get_EH_slices()---except that the sliced E and H fields are the + # fields of eigenmode #mode. + ###################################################################### + def get_eigenfield_slices(self, mode, nf=0): + + # look for data in cache + tag='M{}.F{}'.format(mode,nf) + log('DFTCell {}: Getting eigenfields for tag {}...'.format(self.name,tag)) + if self.eigencache and tag in self.eigencache: + log("...found in cache") + return self.eigencache[tag] + + # data not in cache; compute eigenmode and populate slice arrays + freq=self.freqs[nf] + dir=self.nHat + vol=mp.Volume(self.region.center,self.region.size) + k_initial=mp.Vector3() + eigenmode=self.sim.get_eigenmode(freq, dir, vol, mode, k_initial) + + def get_eigenslice(eigenmode, xyzw, c): + slice=[eigenmode.amplitude(mp.Vector3(x,y,z), c) \ + for x in xyzw[0] for y in xyzw[1] for z in xyzw[2] + ] + return np.reshape(slice,self.slice_dims) + + eh_slices=[get_eigenslice(eigenmode,self.xyzw,c) for c in self.components] + + # store in cache before returning + if self.eigencache is not None: + log("Adding eigenfields for tag {}".format(tag)) + self.eigencache[tag]=eh_slices + + return eh_slices + + ################################################## + # compute an objective quantity, i.e. an eigenmode + # coefficient or a scattered or total power. + ################################################## + def eval_quantity(self, qcode, mode, nf=0): + + w = self.xyzw[3] + EH = self.get_EH_slices(nf) + if qcode.islower(): + self.subtract_incident_fields(EH,nf) + + if qcode in 'sS': + return 0.25*np.real(np.sum(w*( np.conj(EH[0])*EH[3] - np.conj(EH[1])*EH[2]) )) + elif qcode in 'PM': + eh = self.get_eigenfield_slices(mode, nf) # EHList of eigenmode fields + eH = np.sum( w*(np.conj(eh[0])*EH[3] - np.conj(eh[1])*EH[2]) ) + hE = np.sum( w*(np.conj(eh[3])*EH[0] - np.conj(eh[2])*EH[1]) ) + sign=1.0 if qcode=='P' else -1.0 + return (eH + sign*hE)/8.0 + else: # TODO: support other types of objectives quantities? + ValueError('DFTCell {}: unsupported quantity type {}'.format(self.name,qcode)) + +######################################################### +# a 'qrule' is a specification for how to evaluate an +# objective quantity: which DFT cell, which physical +# quantity (power flux, eigenmode coefficient, etc, +# encoded in 'code') and (if necessary) which eigenmode. +# qrules are constructed from the string names of +# objective variables like 'P2_3' or 'M1_north' or 's_0'. +######################################################### +qrule = namedtuple('qrule', 'code mode ncell') + +def qname_to_qrule(qname): + + pieces=qname.split('_') + codemode, cellstr = pieces[0], '_'.join(pieces[1:]) + ncell=int(cellstr) if cellstr.isdigit() else DFTCell.get_index(cellstr) + if codemode.upper()=='S': + return qrule(codemode, 0, ncell) + elif codemode[0] in 'PM': + if codemode[1:].isdigit() and int(codemode[1:])>0: + return qrule(codemode[0], int(codemode[1:]) , ncell) + raise ValueError("Objective quantity {}: invalid mode index {}".format(qname,codemode[1:])) + raise ValueError("Objective quantity {}: unknown quantity code {}".format(qname,codemode[0])) + +######################################################### +# ObjectiveFunction is a simple class for evaluating +# a scalar function f of multiple inputs {q_i}, where +# the q_i are complex-valued in general and f may be +# real- or complex-valued. The fstr input to the class +# constructor is an string expression for the function. +# Class instances store the following data: +# -- fexpr: sympy expression constructed from fstr +# -- qsyms: array of sympy symbols identified by sympy +# as the objective quantities, i.e. the inputs +# on which f depends +# -- qnames: stringified names of the qsyms +# -- qrules: array of 'qrule' structures encoding how +# the objective quantities are to be computed +# from MEEP data (specifically, from frequency- +# domain field data stored in DFTCells) +# -- qvals: numpy array storing most recent updates of +# objective-quantity values +# -- riqsyms, riqvals: the same data content as +# qsyms and qvalues, but with each complex-valued +# 'q' quantity split up into real-valued 'r' and 'i' +# components. We do this to facilitate symbolic +# differentiation of non-analytic functions +# of the objective quantities such as |q_i|^2. +######################################################### +class ObjectiveFunction(object): + + ###################################################################### + # try to create a sympy expression from the given string and determine + # names for all input variables (objective quantities) needed to + # evaluate it + ###################################################################### + def __init__(self, fstr='S_0'): + + # try to parse the function string to yield a sympy expression + try: + fexpr = sympy.sympify(fstr) + except: + raise ValueError("failed to parse function {}".format(fstr)) + + # qnames = names of all objective quantities (i.e. all symbols + # qnames = names of all objective quantities (i.e. all symbols + # identified by sympy as quantities on which fexpr depends) + fprime = sympy.sympify(fstr.replace('0.0','1.0')) + self.qsyms = sorted(fprime.free_symbols, key=str) + self.qnames = [str(s) for s in self.qsyms] + + # qrules = 'qrules' for all objective quantities, where a 'qrule' + # is metadata defining how a quantity is computed + self.qrules = [qname_to_qrule(qn) for qn in self.qnames] + + # qvals = cached values of objective quantities + self.qvals = 0.0j*np.zeros(len(self.qnames)) + + # for each (generally complex-valued) objective quantity, + # we now introduce two real-valued symbols for the real and + # imaginary parts, stored in riqsymbols. q2ri is a dict of + # sympy substitutions q -> qr + I*qi that we use below to + # recast fexpr as a function of the ri quantities. riqvals + # is a dict of numerical values of the ri quantities used + # later to evaluate f and its partial derivatives. + self.riqsymbols, self.riqvals, q2ri = [], {}, {} + for nq,(qn,qs) in enumerate(zip(self.qnames,self.qsyms)): + rqn, iqn = 'r'+qn, 'i'+qn + rqs, iqs = sympy.symbols( [rqn, iqn], real=True) + q2ri[qs] = rqs + iqs*sympy.I + self.riqvals[rqn]=self.riqvals[iqn]=0.0 + self.riqsymbols += [rqs, iqs] + + self.fexpr = fexpr.subs(q2ri) + + # expressions for partial derivatives, dfexpr[q] = \partial f / \partial q_n + self.dfexpr=[] + for nq in range(len(self.qnames)): + df_drqn = sympy.diff(self.fexpr,self.riqsymbols[2*nq+0]) + df_diqn = sympy.diff(self.fexpr,self.riqsymbols[2*nq+1]) + self.dfexpr.append( df_drqn - sympy.I*df_diqn ) + + + ###################################################################### + ###################################################################### + ###################################################################### + def get_fq(self, DFTCells, nf=0): + + # fetch updated values for all objective quantities + for nq, qr in enumerate(self.qrules): + self.qvals[nq] = DFTCells[qr.ncell].eval_quantity(qr.code,qr.mode,nf) + self.riqvals[self.riqsymbols[2*nq+0]]=np.real(self.qvals[nq]) + self.riqvals[self.riqsymbols[2*nq+1]]=np.imag(self.qvals[nq]) + + # plug in objective-quantity values to get value of objective function + fval=self.fexpr.evalf(subs=self.riqvals) + fval=complex(fval) if fval.is_complex else float(fval) + + return np.array( [fval] + list(self.qvals) ) + + # compute values of all partial derivatives \partial f / \partial q + def get_partials(self): + return np.array( [ df.evalf(subs=self.riqvals) for df in self.dfexpr ] ) + +######################################################### +# end of ObjectiveFunction class definition +######################################################### + +######################################################### +######################################################### +######################################################### +class AdjointSolver(object): + + ######################################################### + ######################################################### + ######################################################### + def __init__(self, obj_func, dft_cells, basis, sim, vis=None): + + self.obj_func = obj_func + self.dft_cells = dft_cells + self.basis = basis + self.sim = sim + self.vis = vis + + # prefetch names of outputs computed by forward and + # adjoint solves, for use in writing log files + self.fqnames = ['f'] + obj_func.qnames + self.bnames = ['b'+str(n) for n in range(len(self.basis()))] + + ######################################################### + ######################################################### + ######################################################### + def eval_fq(self, nf=0): + return self.obj_func.get_fq(self.dft_cells,nf=nf) + + def eval_gradf(self, nf=0): + gradient=0.0j*np.zeros(len(self.basis())) + cell=self.dft_cells[-1] # design cell + EH_forward=cell.get_EH_slices(nf,label='forward') + EH_adjoint=cell.get_EH_slices(nf) # no label->current simulation + f=np.sum( [EH_forward[nc]*EH_adjoint[nc] + for nc,c in enumerate(cell.components) if c in Exyz], 0 ) +# f=0.0j*np.ones(cell.slice_dims) +# for nc,c in enumerate(cell.components): +# if c not in Exyz: +# continue +# f+=EH_forward[nc]*EH_adjoint[nc] + return project_basis(self.basis,cell.xyzw,f) + + ######################################################### + ######################################################### + ######################################################### + def run_until_converged(self, case='forward'): + + last_source_time = self.sim.sources[0].src.swigobj.last_time_max() + verbose = (adjoint_options['verbosity'] == 'verbose') + reltol = adjoint_options['dft_reltol'] + max_time = adjoint_options['dft_timeout']*last_source_time + check_interval = adjoint_options['dft_interval']*last_source_time + names = self.bnames if case=='adjoint' else self.fqnames + + # register DFT cells + self.sim.init_sim() + [cell.register(self.sim) for cell in self.dft_cells] + + #update_plot(self.sim, which='Geometry') + if self.vis: + self.vis.update(self.sim,'Geometry') + + # construct field-animation step function if requested + step_funcs = [] + acs = adjoint_options['animate_components'] + if acs is not None: + ivl=adjoint_options['animate_interval'] + step_funcs = [ plot_field_components(self.sim, components=acs, interval=ivl) ] + + log("Beginning {} timestepping run...".format(case)) + self.sim.run(*step_funcs, until=self.sim.fields.last_source_time()) + + if self.vis: + self.vis.update(self.sim,'ForwardFD') + + # now continue timestepping with periodic convergence checks until + # we converge or timeout + last_vals = np.inf*np.ones(len(names)) + max_rel_delta=np.inf + next_check_time=self.sim.round_time() + while True: + self.sim.run(*step_funcs, until=next_check_time) + next_check_time = min(next_check_time + check_interval, max_time) + + vals = self.eval_gradf() if case=='adjoint' else self.eval_fq() + + rel_delta = [rel_diff(v,last_v) for v,last_v in zip(vals,last_vals)] + last_vals = vals + max_rel_delta=max(rel_delta) + + log(' ** t={} MRD={} ** '.format(self.sim.round_time(),max_rel_delta)) + if verbose: + [log('{:10s}: {:+.4e}({:.1e})'.format(n,v,e)) for n,v,e in zip(names,vals,rel_delta)] + [log('')] + + if max_rel_delta<=reltol or self.sim.round_time()>=max_time: + return vals + + + ############################################################## + ############################################################## + ############################################################## + def place_adjoint_sources(self, qweights): + + # extract temporal envelope of forward sources from existing simulation + envelope = self.sim.sources[0].src + freq = envelope.frequency + omega = 2.0*np.pi*freq + factor = 2.0j*omega + if callable(getattr(envelope, "fourier_transform", None)): + factor /= envelope.fourier_transform(freq) + + ################################################## + # loop over all objective quantities, adding + # appropriately-weighted adjoint sources for each + # quantity + ################################################## + self.sim.reset_meep() + self.sim.change_sources([]) + nf=0 + for qr, qw in zip(self.obj_func.qrules, qweights): + + if qw==0.0: + continue + + code, mode, cell=qr.code, qr.mode, self.dft_cells[qr.ncell] + EH = cell.get_EH_slices(nf=nf, label='forward') if mode==0 \ + else cell.get_eigenfield_slices(mode=mode, nf=0) + + components = cell.components + x, y, z, w = cell.xyzw[0], cell.xyzw[1], cell.xyzw[2], cell.xyzw[3] + shape = [np.shape(q)[0] for q in [x,y,z]] + + if code in 'PM': + sign = 1.0 if code=='P' else -1.0 + signs=[+1.0,-1.0,+1.0*sign,-1.0*sign] + self.sim.sources+=[mp.Source(envelope, cell.components[3-nc], + cell.center, cell.size, + amplitude=signs[nc]*factor*qw, + amp_data=np.reshape(np.conj(EH[nc]),shape) + ) for nc in range(len(components)) + ] + + self.sim.force_complex_fields=True + + ######################################################## + ######################################################## + ######################################################## + def solve(self, need_gradient=False): + + # forward run + fq=self.run_until_converged(case='forward') + + if self.vis: + self.vis.update(self.sim,'ForwardFD') + + if need_gradient==False: + return fq[0], 0 + + for cell in self.dft_cells: + cell.save_fields('forward') + + # adjoint run(s) + qweights=self.obj_func.get_partials() + self.place_adjoint_sources(qweights) + gradf=self.run_until_converged(case='adjoint') + if self.vis: + self.vis.update(self.sim,'AdjointFD') + + return fq[0], gradf + + ######################################################## + ######################################################## + ######################################################## + def get_gradq(self, qname): + qweights=[1.0 if qn==qname else 0.0 for qn in self.obj_func.qnames] + self.place_adjoint_sources(qweights) + return self.run_until_converged(case='adjoint') diff --git a/python/adjoint/OptimizationProblem.py b/python/adjoint/OptimizationProblem.py new file mode 100644 index 000000000..b456b5c05 --- /dev/null +++ b/python/adjoint/OptimizationProblem.py @@ -0,0 +1,351 @@ +import sys +import os +import argparse +import pickle +import datetime + +import numpy as np + +import matplotlib.pyplot as plt + +import meep as mp +from . import ObjectiveFunction +from . import Visualization +from . import Basis + +from .ObjectiveFunction import (adjoint_options, xHat, yHat, zHat, origin, + EHTransverse, Exyz, Hxyz, EHxyz, GridInfo, + abs2, unit_vector, rel_diff, FluxLine, + DFTCell, ObjectiveFunction, AdjointSolver, + global_dft_cell_names) + +from .Visualization import visualize_sim, AdjointVisualizer, set_plot_default + +###################################################################### +# invoke python's 'abstract base class' formalism in a version-agnostic way +###################################################################### +from abc import ABCMeta, abstractmethod +ABC = ABCMeta('ABC', (object,), {'__slots__': ()}) # compatible with Python 2 *and* 3: + +###################################################################### +# OptimizationProblem is an abstract base class from which classes +# describing specific optimization problems should inherit +###################################################################### +class OptimizationProblem(ABC): + + ###################################################################### + # pure virtual methods that must be overridden by child + ###################################################################### + @abstractmethod + def init_problem(self, args): + raise NotImplementedError("derived class must implement init_problem() method") + + + @abstractmethod + def create_sim(self, betavector, vacuum=False): + raise NotImplementedError("derived class must implement create_sim() method") + + + ###################################################################### + # virtual methods that *may* optionally be overridden by child + ###################################################################### + def add_args(self, args): + pass + + ###################################################################### + ###################################################################### + ###################################################################### + def __init__(self): + + # define command-line arguments + parser = self.init_args() # general args + self.add_args(parser) # problem-specific arguments + self.args = args = parser.parse_args() + + # parse arguments and do problem-specific initialization first... + fstr, objective_regions, extra_regions, design_region, self.basis \ + = self.init_problem(self.args) + + # ...and now do some general initialization + fcen, df, nfreq = args.fcen, args.df, args.nfreq + #self.grid = FDGrid(size=self.cell_size, res=self.args.res) + global_dft_cell_names = [] + self.objective_cells = [ DFTCell(region=v, fcen=fcen, df=df, nfreq=nfreq) for v in objective_regions ] + self.extra_cells = [ DFTCell(region=v, fcen=fcen, df=df, nfreq=nfreq) for v in extra_regions ] if args.full_dfts else [] + self.design_cell = DFTCell(region=design_region, fcen=fcen, df=df, nfreq=nfreq, name='design_fields') + self.dft_cells = self.objective_cells + self.extra_cells + [self.design_cell] + + self.obj_func = ObjectiveFunction(fstr=fstr) + + self.dimension = len(self.basis()) # dimension of optimization problem = number of design variables + self.beta_vector = self.init_beta_vector() + + self.sim = None + + self.filebase = args.filebase if args.filebase else self.__class__.__name__ + + adjoint_options['dft_reltol'] = args.dft_reltol + adjoint_options['dft_timeout'] = args.dft_timeout + adjoint_options['dft_interval'] = args.dft_interval + adjoint_options['verbosity'] = 'verbose' if args.verbose \ + else 'concise' if args.concise \ + else adjoint_options['verbosity'] + adjoint_options['logfile'] = args.logfile + + self.vis = None if not args.visualize \ + else AdjointVisualizer(label_source_regions=args.label_source_regions) + adjoint_options['animate_components'] = args.animate_component + adjoint_options['animate_interval'] = args.animate_interval + + ###################################################################### + # constructor helper method that initializes the command-line parser + # with general-purpose (problem-independent) arguments + ###################################################################### + def init_args(self): + parser = argparse.ArgumentParser() + + #-------------------------------------------------- + # parameters affecting geometry and sources + #-------------------------------------------------- + parser.add_argument('--res', type=float, default=20, help='resolution') + parser.add_argument('--dpml', type=float, default=-1.0, help='PML thickness (-1 --> autodetermined)') + parser.add_argument('--fcen', type=float, default=0.5, help='center frequency') + parser.add_argument('--df', type=float, default=0.25, help='frequency width') + parser.add_argument('--source_mode', type=int, default=1, help='mode index of eigenmode source') + + #-------------------------------------------------- + # initial values for basis-function coefficients + #-------------------------------------------------- + parser.add_argument('--betafile', type=str, default='', help='file of expansion coefficients') + parser.add_argument('--beta', nargs=2, default=[], action='append', help='set value of expansion coefficient') + + #-------------------------------------------------- + # options describing the calculation to be done + #-------------------------------------------------- + # do a single calculation of the objective function, optionally with gradient + parser.add_argument('--eval_objective', dest='eval_objective', action='store_true', help='evaluate objective function value') + parser.add_argument('--eval_gradient', dest='eval_gradient', action='store_true', help='evaluate objective function value and gradient') + parser.add_argument('--gradient_qname', type=str, default=None, help='name of objective quantity to differentiate via adjoint method') + + # compute finite-difference approximation to derivative for test purposes + parser.add_argument('--fd_order', type=int, default=0, help='finite-difference order (0,1,2)') + parser.add_argument('--fd_index', default=[], action='append', help='index of differentiation variable') + parser.add_argument('--fd_rel_delta', type=float, default=1.0e-2, help='relative finite-difference delta') + + # run the full iterative optimization + parser.add_argument('--optimize', dest='optimize', help='perform automated design optimization') + + #-------------------------------------------------- + # flags affecting the simulation run + #-------------------------------------------------- + parser.add_argument('--nfreq', type=int, default=1, help='number of output frequencies') + parser.add_argument('--full_dfts', dest='full_dfts', action='store_true', help='compute DFT fields over full volume') + parser.add_argument('--complex_fields', dest='complex_fields', action='store_true', help='force complex fields') + parser.add_argument('--filebase', type=str, default=self.__class__.__name__, help='base name of output files') + + #-------------------------------------------------- + # flags configuring adjoint-solver options + #--------------------------------------------------l + parser.add_argument('--dft_reltol', type=float, default=adjoint_options['dft_reltol'], help='convergence threshold for end of timestepping') + parser.add_argument('--dft_timeout', type=float, default=adjoint_options['dft_timeout'], help='max runtime in units of last_source_time') + parser.add_argument('--dft_interval', type=float, default=adjoint_options['dft_interval'], help='meep time DFT convergence checks in units of last_source_time') + parser.add_argument('--verbose', dest='verbose', action='store_true', help='produce more output') + parser.add_argument('--concise', dest='concise', action='store_true', help='produce less output') + parser.add_argument('--visualize', dest='visualize', action='store_true', help='produce visualization graphics') + parser.add_argument('--label_source_regions', dest='label_source_regions', action='store_true', help='label source regions in visualization plots') + parser.add_argument('--logfile', type=str, default=None, help='log file name') + parser.add_argument('--animate_component', action='append', help='plot time-domain field component') + parser.add_argument('--animate_interval', type=float, default=1.0, help='meep time between animation frames') + + return parser + + ###################################################################### + # constructor helper method to process command-line arguments for + # initializing the vector of design variables + ###################################################################### + def init_beta_vector(self): + + # default: beta_0 (constant term) = 1, all other coefficients=0 + beta_vector=unit_vector(0,self.dimension) + + # if a --betafile was specified, try to parse it in the form + # beta_0 \n beta_1 \n ... (if single column) + # or + # i1 beta_i1 \n i2 beta_i2 \n (if two columns) + if self.args.betafile: + fb = np.loadtxt(self.args.betafile) # 'file beta' + if np.ndim(fb)==1: + indices,vals = range(len(fb)), fb + elif np.ndim(fb)==2 and np.shape(fb)[1] == 2: + indices,vals = fb[:,0], fb[:,1] + else: + raise ValueError("{}: invalid file format".format(self.args.betafile)) + for i,v in zip(indices,vals): beta_vector[i]=v + + # parse arguments of the form --beta index value + for ivpair in self.args.beta: # loop over (index,value) pairs + beta_vector[int(ivpair[0])]=ivpair[1] + + # this step ensures that epsilon(x) never falls below 1.0, assuming + # (a) the 0th basis function is the constant 1 + # (b) all other basis functions (b_1, ... b_{D-1}) take values in [-1:1] + # (c) coefficients (\beta_1, ..., \beta_{D-1}) are nonnegative. + eps_min=beta_vector[0] - np.sum(beta_vector[1:]) + if eps_min<1.0: + beta_vector[0] += 1.0-eps_min + return beta_vector + + ###################################################################### + # the 'run' class method of OptimizationProblem, which is where control + # passes after __init__ if we were executed as a script, looks at + # command-line flags to determine whether to (a) launch a full + # iterative optimization of the design variables or (b) study + # the geometry for just the one given set of design variables + ###################################################################### + def run(self): + + #-------------------------------------------------------------- + # if --optimize is present, run iterative design optimization + #-------------------------------------------------------------- + args=self.args + if args.optimize: + self.optimize() + return 0 + + #-------------------------------------------------------------- + # if no computation was requested, just plot the geometry + #-------------------------------------------------------------- + if not(args.eval_gradient or args.eval_objective or args.fd_order>0): + sim = self.create_sim(self.beta_vector) + sim.init_sim() + [cell.register(sim) for cell in self.dft_cells] + vis = self.vis if self.vis else AdjointVisualizer() + vis.update(sim,'Geometry') + return 0 + + #-------------------------------------------------------------- + #-------------------------------------------------------------- + #-------------------------------------------------------------- + fq,gradf=self.eval_fq(self.beta_vector, need_gradient=args.eval_gradient, vis=self.vis) + + fqnames=['f'] + self.obj_func.qnames + self.output([],[],actions=['begin']) + self.output(['res','fcen','df','source_mode'], [args.res,args.fcen,args.df,args.source_mode]) + [self.output(['beta'+str(n)],[beta]) for (n,beta) in enumerate(self.beta_vector)] + [self.output([fqn], [fqv]) for (fqn,fqv) in zip(fqnames,fq)] + if args.eval_gradient: + [self.output( ['df/db'+str(n)], [g]) for n,g in enumerate(gradf)] + + #-------------------------------------------------------------- + # calculate the objective function value, optionally its gradient, + # and optionally the finite-difference approximation to the + # derivative of a single objective quantity + #-------------------------------------------------------------- + indices = [] if args.fd_order==0 else [int(index) for index in args.fd_index] + for index in indices: + dbeta = args.fd_rel_delta*(1.0 if self.beta_vector[index]==0 else np.abs(self.beta_vector[index])) + beta_hat = unit_vector(index,self.dimension) + fqp, _ = self.eval_fq(self.beta_vector + dbeta*beta_hat) + d1fq = (fqp - fq) / dbeta + if args.fd_order==2 and self.beta_vector[index]!=0.0: + fqm, _ = self.eval_fq(self.beta_vector - dbeta*beta_hat) + d2fq = (fqp - fqm) / (2.0*dbeta) + elif args.fd_order==2 and self.beta_vector[index]==0.0: + fqpp, _ = self.eval_fq(self.beta_vector + 2*dbeta*beta_hat) + d2fq = (4*fqp - fqpp - 3.0*fq) / (2.0*dbeta) + for i,fqn in enumerate(fqnames): + nlist = ['d{}/db{}__O{}__'.format(fqn,index,ord+1) for ord in range(args.fd_order)] + vlist = [ d1fq[i] ] + ([d2fq[i]] if args.fd_order==2 else[]) + [self.output(nlist, vlist)] + + self.output([],[],actions=['end']) + + #f = open('store.pckl', 'wb') + # pickle.dump(obj, f) + #f.close() + #f = open('store.pckl', 'rb') + #obj = pickle.load(f) + #f.close() + + ###################################################################### + ###################################################################### + ###################################################################### + def output(self, names, values, actions=[]): + + if 'begin' in actions: + self.nout = 1 # running index of output quantity + self.legend = open(self.filebase + '.legend','w') + self.digest = open(self.filebase + '.digest','a') + self.outfile = open(self.filebase + '.out','a') + dt=datetime.datetime.now().strftime('%D::%T ') + for f in [sys.stdout,self.digest]: + f.write('\n\n** {} ran {} \n'.format(dt,self.__class__.__name__)) + f.write('** with args {}'.format(' '.join(sys.argv[1:]))) + f.write('\n**') + + #-------------------------------------------------------------- + #- inline utility functions for real/complex numerical output + #-------------------------------------------------------------- + def myangle(z): + theta=np.angle(z,deg=True) + return theta if theta>=0.0 else theta+360.0 + + def pretty_print(val,for_file=False,polar=False): + fmt='{:+.8e} ' if for_file else '{:+.4e}' + if not np.iscomplex(val): + return fmt.format(np.real(val)) + (v1,v2)=(np.abs(val),myangle(val)) if polar else (np.real(val), np.imag(val)) + if for_file: + return (fmt + fmt).format(v1,v2) + elif polar: + return (fmt + '@' + '{:.0e}').format(v1,v2) + else: + return ('(' + fmt + ',' + fmt + ')').format(v1,v2) + + namestrs, valstrs = '', '' + for name,val in zip(names, values): + + namestrs += (' ,' if namestrs else '') + name + valstrs += (' ,' if valstrs else '') + pretty_print(val) + if np.iscomplex(val): + valstrs += '(' + pretty_print(val,polar=True) + ') ' + + self.outfile.write(pretty_print(val, for_file=True)) + + idxstr=str(self.nout) + (','+str(self.nout+1) if np.iscomplex(val) else '') + self.legend.write('{}: {}\n'.format(idxstr,name)) + self.nout += (2 if np.iscomplex(val) else 1) + + for f in [sys.stdout,self.digest]: + f.write('{:30s}: {}\n'.format(namestrs,valstrs)) + + if 'end' in actions: + self.outfile.write('\n') + self.outfile.close() + self.digest.close() + self.legend.close() + + ###################################################################### + ###################################################################### + ###################################################################### + def optimize(self): + print("Running optimization...") + sys.exit(0) + + ###################################################################### + # compute the objective function, plus possibly its gradient (via + # adjoints), at a single point in design space + ###################################################################### + def eval_objective(self, beta_vector, need_gradient=False, vis=None): + sim = self.create_sim(beta_vector) + solver = AdjointSolver(self.obj_func, self.dft_cells, self.basis, sim, vis=vis) + self.sim=sim # save a copy for debugging; not strictly necessary + return solver.solve(need_gradient=need_gradient) + + ################################################## + ################################################## + ################################################## + def eval_fq(self, beta_vector, need_gradient=False, vis=None): + f,gradf = self.eval_objective(beta_vector, need_gradient=need_gradient, vis=vis) + fq = np.array( [f] + list(self.obj_func.qvals) ) + return fq, gradf diff --git a/python/adjoint/Visualization.py b/python/adjoint/Visualization.py new file mode 100644 index 000000000..1f6b59674 --- /dev/null +++ b/python/adjoint/Visualization.py @@ -0,0 +1,962 @@ +###################################################extent +# visualize.py -- various routines for visualizing +# the inputs and outputs of pymeep calculations in +# simple standardized ways +################################################### +import warnings +import numpy as np +import sympy +from collections import namedtuple +import time +import datetime +from multiprocessing import Process, Pipe +from matplotlib import ticker + +import matplotlib +matplotlib.use('qt5agg') +import matplotlib.pyplot as plt +from mpl_toolkits.mplot3d import axes3d + +from matplotlib.collections import PolyCollection, LineCollection +from mpl_toolkits.mplot3d.art3d import Poly3DCollection + +import meep as mp + +from .ObjectiveFunction import global_dft_cell_names +from .Basis import fl_basis_names + +######################################################## +# the next few routines are some of my older general-purpose +# utilities for working with DFT cells; for that purpose +# they have been rendered obsolete by the DFTCell class +# in the adjoint module, but I reproduce them in this +# visualization module just so it can be independent of +# the adjoint innards. +######################################################## +EHTransverse=[ [mp.Ey, mp.Ez, mp.Hy, mp.Hz], + [mp.Ez, mp.Ex, mp.Hz, mp.Hx], + [mp.Ex, mp.Ey, mp.Hx, mp.Hy] ] +Exyz=[mp.Ex, mp.Ey, mp.Ez] +Hxyz=[mp.Hx, mp.Hy, mp.Hz] +EHxyz=Exyz + Hxyz +origin=mp.Vector3() + +def abs2(z): + return np.real(np.conj(z)*z) + +def dft_cell_type(cell): + return 'flux' if isinstance(cell, mp.simulation.DftFlux) else 'fields' + +def dft_cell_name(nc): + try: + name=global_dft_cell_names[nc] + if name.endswith('_flux'): + name=name[0:-5] + if name.endswith('_fields'): + name=name[0:-7] + return name.replace('_','\_') + except NameError: + return 'flux_' + str(nc) + +def is_flux_cell(cell): + return dft_cell_type(cell)=='flux' + + +def add_dft_cell(sim, region, fcen, df=0, nfreq=1): + if hasattr(region,"direction"): + return sim.add_flux(fcen,df,nfreq,region) + return sim.add_dft_fields(EHxyz, fcen, df,nfreq, where=region) + + +def flux_line(x0, y0, length, dir): + size=length*(xhat if dir is mp.Y else yhat) + return mp.FluxRegion(center=mp.Vector3(x0,y0), size=size, direction=dir) + + +def tangential_components(normal_dir): + if normal_dir in range(mp.X, mp.Z+1): + return EHTransverse[normal_dir-mp.X] + raise ValueError("invalid normal_dir={} in tangential_components".format(normal_dir)) + + +# return a list of the field components stored in a DFT cell +def dft_cell_components(cell): + if dft_cell_type(cell)=='flux': + return tangential_components(cell.normal_direction) + elif cell.num_components==6: + return EHxyz + elif cell.num_components==3: + return Exyz + else: + raise ValueError("internal error in dft_cell_components") + + +# like get_dft_array, but 'zero-padded:' when the DFT cell +# does not have data for the requested component (perhaps +# because it vanishes identically by symmetry), this routine +# returns an array of the expected dimensions with all zero +# entries, instead of a rank-0 array that prints out as a +# single nonsensical floating-point number which is the +# not-very-user-friendly behavior of core pymeep. +def get_dft_array_zp(sim, cell, c, nf=0, w=None): + array = sim.get_dft_array(cell, c, nf) + if len(np.shape(array))==0: + if w is None: + _,_,_,w = sim.get_dft_array_metadata(dft_cell=cell) + array=np.zeros(np.shape(w)) + return array + + +def unpack_dft_cell(sim,cell,nf=0): + (x,y,z,w)=sim.get_dft_array_metadata(dft_cell=cell) + cEH = dft_cell_components(cell) + EH = [ get_dft_array_zp(sim, cell, c, nf, w) for c in cEH ] + return x, y, z, w, cEH, EH + + +def unpack_dft_fields(sim,cell,nf=0): + _,_,_,_,_,EH=unpack_dft_cell(sim,cell,nf=nf) + return EH + +################################################### +################################################### +################################################### +def eigenfield_tag(ncell, mode, freq): + return "C{}.M{}.F{:.6f}".format(ncell,mode,freq) + +def lookup_eigenfields(ncell, mode, freq, eigencache): + tag=eigenfield_tag(ncell, mode, freq) + if eigencache and tag in eigencache: + return eigencache[tag] + raise ValueError("eigenfields for tag {} not found in cache".format(tag)) + +def get_eigenfields(sim, dft_cells, ncell, mode, nf=0, eigencache=None): + + # look for data in cache + cell=dft_cells[ncell] + +######################################################## +# this routine configures some global matplotlib settings +# (as distinct from the plot-specific settings handled +# by the plot_options dicts). if you intend to set your +# own values of these parameters, pass set_rmecParams=False +# to visualize_sim. +######################################################## +def set_meep_rcParams(): + plt.rc('xtick') + plt.rc('ytick') + plt.rc('font', size=40) + plt.rc('text', usetex=True) + matplotlib.rcParams['axes.labelsize']='large' + matplotlib.rcParams['axes.titlesize']='large' + matplotlib.rcParams['axes.titlepad']=20 + +######################################################## +# general-purpose default option values, customized for +# specific types of plots below, and everything settable +# via set_plot_option +######################################################## +def_plot_options={ 'line_color' : [1.0,0.0,1.0], + 'line_width' : 4.0, + 'line_style' : '-', + 'boundary_width' : 2.0, + 'boundary_color' : [0.0,1.0,0.0], + 'boundary_style' : '--', + 'z_offset' : 0.0, + 'zmin' : 0.60, + 'zmax' : 1.00, + 'fill_color' : 'none', + 'alpha' : 1.0, + 'cmap' : matplotlib.cm.plasma, + 'fontsize' : 40, + 'colorbar_shrink': 0.60, + 'colorbar_pad' : 0.04, + 'num_contours' : 100 + } + +#-------------------------------------------------- +# options for permittivity plots +#-------------------------------------------------- +def_eps_options={ **def_plot_options, + 'cmap':matplotlib.cm.Blues, + 'line_width': 0.00, 'colorbar_shrink':0.75, + 'plot_method':'contourf', # or 'pcolormesh' or 'imshow' + 'num_contours':100 + } + +def_src_options={ **def_plot_options, + 'line_width':4.0, 'line_color':[0.0,1.0,1.0], + 'fontsize':0, 'zmin':0.0, 'zmax':0.0 + } + +def_pml_options={ **def_plot_options, + 'boundary_color':'none', 'boundary_width':0.0, + 'fill_color': 0.75*np.ones(3), 'alpha':0.25 + } + +def_flux_options={ **def_plot_options, + 'boundary_color':[0.0,0.0,0.0], 'boundary_width':2.0, + 'boundary_style':'--', + 'line_color': [1.0,0.0,1.0], 'line_width':4.0 + } + +def_field_options={ **def_plot_options, + 'line_width': 0.0, 'alpha': 0.5, 'z_offset':0.5 + } + +def_dft_options={ **def_plot_options } + + +def set_plot_default(option, value, type=None): + which= def_eps_options if type=='eps' \ + else def_src_options if type=='src' \ + else def_pml_optionss if type=='pml' \ + else def_flux_options if type=='flux' \ + else def_fields_options if type=='fields' \ + else def_plot_options + which[option]=value + + +################################################### +################################################### +################################################### +def get_text_size(fig, label, fontsize): + r = fig.canvas.get_renderer() + t = plt.text(0.5, 0.5, label, fontsize=fontsize) + bb = t.get_window_extent(renderer=r) + return bb.width, bb.height + +################################################### +# visualize epsilon distribution. eps_min, eps_max +# are optional upper and lower clipping bounds. +# If we are in 3D, the permittivity is plotted using +# plot_surface. +# Otherwise, the permittivity is plotted using +# imshow (if use_imshow==True) or using pcolormesh +# (by default). +################################################### +def plot_eps(sim, eps_min=None, eps_max=None, options=None, plot3D=False, fig=None): + + options = options if options else def_eps_options + cmap = options['cmap'] + edgecolors = options['line_color'] + linewidth = options['line_width'] + alpha = options['alpha'] + fontsize = options['fontsize'] + plot_method = options['plot_method'] + num_contours = options['num_contours'] + shading = 'gouraud' if linewidth==0.0 else 'none' + interpolation = 'gaussian' if linewidth==0.0 else 'none' + + eps=np.transpose(sim.get_epsilon()) + if eps_min is not None or eps_max is not None: + eps=np.clip(eps,eps_min,eps_max) + eps_min, eps_max=np.min(eps), np.max(eps) + (x,y,z,w)=sim.get_array_metadata() + extent=(min(x), max(x), min(y), max(y)) + + if fig is None: + fig = plt.gcf() + ax = fig.gca(projection='3d') if plot3D else fig.gca() + else: + ax = fig.gca() + cb = None + if plot3D: # check if 3D plot + X, Y = np.meshgrid(x, y) + zmin = 0.0 + zmax = max(sim.cell_size.x, sim.cell_size.y) + Z0 = zmin + options['z_offset']*(zmax-zmin) + img = ax.contourf(X, Y, eps, num_contours, zdir='z', offset=Z0, + vmin=eps_min, vmax=eps_max, cmap=cmap, alpha=alpha) + ax.set_zlim3d(zmin, zmax) + ax.set_zticks([]) + pad=options['colorbar_pad'] + shrink=options['colorbar_shrink'] + cb=fig.colorbar(img, shrink=shrink, pad=pad) + elif plot_method=='imshow': + img = plt.imshow(np.transpose(eps), extent=extent, cmap=cmap, + interpolation=interpolation, alpha=alpha) + elif plot_method=='pcolormesh': + img = plt.pcolormesh(x,y,np.transpose(eps), cmap=cmap, shading=shading, + edgecolors=edgecolors, linewidth=linewidth, alpha=alpha) + else: + X, Y = np.meshgrid(x, y) + img = ax.contourf(X, Y, eps, num_contours, vmin=eps_min, vmax=eps_max, + cmap=cmap, alpha=alpha) + + ax.set_xlabel(r'$x$', fontsize=fontsize, labelpad=0.25*fontsize) + ax.set_ylabel(r'$y$', fontsize=fontsize, labelpad=fontsize, rotation=0) + ax.tick_params(axis='both', labelsize=0.75*fontsize) + cb=cb if cb else fig.colorbar(img) + cb.set_label(r'$\epsilon$',fontsize=1.5*fontsize,rotation=0,labelpad=0.5*fontsize) + cb.ax.tick_params(labelsize=0.75*fontsize) + cb.locator = ticker.MaxNLocator(nbins=5) + cb.update_ticks() + +################################################## +# plot_volume() adds a polygon representing a given +# mp.Volume to the current 2D or 3D plot. +################################################## +def plot_volume(sim, vol=None, center=None, size=None, + options=None, plot3D=False, label=None): + + options = options if options else def_plot_options + + fig=plt.gcf() + ax=fig.gca(projection='3d') if plot3D else fig.gca() + + if vol: + center, size = vol.center, vol.size + v0=np.array([center.x, center.y]) + dx,dy=np.array([0.5*size.x,0.0]), np.array([0.0,0.5*size.y]) + if plot3D: + zmin,zmax = ax.get_zlim3d() + z0 = zmin + options['z_offset']*(zmax-zmin) + + ################################################## + # add polygon(s) to the plot to represent the volume + ################################################## + def add_to_plot(c): + ax.add_collection3d(c,zs=z0,zdir='z') if plot3D else ax.add_collection(c) + + if size.x==0.0 or size.y==0.0: # zero thickness, plot as line + polygon = [ v0+dx+dy, v0-dx-dy ] + add_to_plot( LineCollection( [polygon], colors=options['line_color'], + linewidths=options['line_width'], + linestyles=options['line_style'] + ) + ) + else: + if options['fill_color'] is not 'none': # first copy: faces, no edges + polygon = np.array([v0+dx+dy, v0-dx+dy, v0-dx-dy, v0+dx-dy]) + pc=PolyCollection( [polygon], linewidths=0.0) + pc.set_color(options['fill_color']) + pc.set_alpha(options['alpha']) + add_to_plot(pc) + if options['boundary_width']>0.0: # second copy: edges, no faces + closed_polygon = np.array([v0+dx+dy, v0-dx+dy, v0-dx-dy, v0+dx-dy, v0+dx+dy]) + lc=LineCollection([closed_polygon]) + lc.set_linestyle(options['boundary_style']) + lc.set_linewidth(options['boundary_width']) + lc.set_edgecolor(options['boundary_color']) + add_to_plot(lc) + + ###################################################################### + # attempt to autodetermine text rotation and alignment + ###################################################################### + if label: + x0, y0, r, h, v = np.mean(ax.get_xlim()),np.mean(ax.get_ylim()), 0, 'center', 'center' + if size.y==0.0: + v = 'top' if center.y>y0 else 'bottom' + elif size.x==0.0: + r, h = (270,'left') if center.x>x0 else (90,'right') + if plot3D: + ax.text(center.x, center.y, z0, label, rotation=r, + fontsize=options['fontsize'], color=options['line_color'], + horizontalalignment=h, verticalalignment=v) + else: + ax.text(center.x, center.y, label, rotation=r, + fontsize=options['fontsize'], color=options['line_color'], + horizontalalignment=h, verticalalignment=v) + + +################################################## +# Plot one or more curves, +################################################## +def plot_data_curves(sim,center=None,size=None,superpose=True, + data=None, labels=None, options=None, + dmin=None, dmax=None): + + if size.x>0 and size.y>0: + msg="plot_data_curves: expected zero-width region, got {}x{} (skipping)" + warnings.warn(msg.format(size.x,size.y),RuntimeWarning) + return + if np.ndim(data[0])!=1: + msg="plot_data_curves: expected 1D data arrays, got {} (skipping)" + warnings.warn(msg.format(np.shape(data[0])),RuntimeWarning) + return + + options=options if options else def_flux_options + lw=options['line_width'] + lc=options['line_color'] + zeta_min=options['zmin'] + zeta_max=options['zmax'] + draw_baseline=(options['boundary_width']>0.0) + + kwargs=dict() + if 'line_color' in options: + kwargs['color']=options['line_color'] + if 'line_width' in options: + kwargs['linewidth']=options['line_width'] + if 'line_style' in options: + kwargs['linestyle']=options['line_style'] + + # construct horizontal axis + ii=1 if size.x==0 else 0 + hstart,hend = (center-0.5*size).__array__()[0:2], (center+0.5*size).__array__()[0:2] + hmin,hmax=hstart[ii],hend[ii] + haxis = np.linspace(hmin, hmax, len(data[0])) + + # if we are superposing the curves onto a simulation-geometry + # visualization plot, construct the appropriate mapping that + # squeezes the full vertical extent of the curve into the + # z-axis interval [zmin, zmax] + if superpose: + ax=plt.gcf().gca(projection='3d') + (zfloor,zceil)=ax.get_zlim() + zmin=zfloor + zeta_min*(zceil-zfloor) + zmax=zfloor + zeta_max*(zceil-zfloor) + z0,dz=0.5*(zmax+zmin),(zmax-zmin) + dmin=dmin if dmin else np.min(data) + dmax=dmax if dmax else np.max(data) + d0,dd=0.5*(dmax+dmin),(dmax-dmin) + zs = center[1-ii] + zdir='x' if size.x==0 else 'y' + if draw_baseline: + lc=LineCollection( [[hstart,hend]], colors=options['boundary_color'], + linewidths=options['boundary_width'], + linestyles=options['boundary_style'] + ) + ax.add_collection3d(lc,zs=z0,zdir='z') + + for n in range(len(data)): + kwargs['label']=None if not labels else labels[n] + if superpose: + ax.plot(haxis,z0+(data[n]-d0)*dz/dd, zs=zs, zdir=zdir, **kwargs) + else: + plt.plot(haxis,data[n],**kwargs) + +################################################## +################################################## +################################################## +def visualize_source_distribution(sim, superpose=True, options=None): + + if not mp.am_master(): + return + options=options if options else def_src_options + + for ns,s in enumerate(sim.sources): + sc,ss=s.center,s.size + J2=sum([abs2(sim.get_source_slice(c,center=sc,size=ss)) for c in Exyz]) +# M2=sum([abs2(sim.get_source_slice(c,center=sc,size=ss)) for c in Hxyz]) + if superpose==False: + if ns==0: + plt.ion() + plt.figure() + plt.title('Source regions') + fig.subplot(len(sim.sources),1,ns+1) + fig.title('Currents in source region {}'.format(ns)) +# plot_data_curves(sim,superpose,[J2,M2],labels=['||J||','||M||'], +# styles=['bo-','rs-'],center=sc,size=ssu + plot_data_curves(sim,center=sc,size=ss, superpose=superpose, + data=[J2], labels=['J'], options=options) + +################################################## +################################################## +################################################## +def visualize_dft_flux(sim, superpose=True, flux_cells=[], + options=None, nf=0): + + if not mp.am_master(): + return + options=options if options else def_flux_options + + # first pass to get arrays of poynting flux strength for all cells + if len(flux_cells)==0: + flux_cells=[cell for cell in sim.dft_objects if is_flux_cell(cell)] + flux_arrays=[] + for cell in flux_cells: # first pass to compute flux data + (x,y,z,w,c,EH)=unpack_dft_cell(sim,cell,nf=nf) + flux_arrays.append( 0.25*np.real(w*(np.conj(EH[0])*EH[3] - np.conj(EH[1])*EH[2])) ) + + # second pass to plot + for n, cell in enumerate(flux_cells): # second pass to plot + if superpose==False: + if n==0: + plt.figure() + plt.title('Poynting flux') + plt.subplot(len(flux_cells),1,n) + plt.gca().set_title('Flux cell {}'.format(n)) + cn,sz=mp.get_center_and_size(cell.where) + max_flux=np.amax(flux_arrays) + plot_data_curves(sim, center=cn, size=sz, data=[flux_arrays[n]], + superpose=superpose, options=options, + labels=['flux through cell {}'.format(n)], + dmin=-max_flux,dmax=max_flux) + +################################################## +################################################## +################################################## +def fc_name(c,which): + name=mp.component_name(c) + return name if which=='scattered' else str(name[0].upper())+str(name[1]) + +def field_func_array(fexpr,x,y,z,w,cEH,EH): + if fexpr=='re(Ex)': + return np.real(EH[0]) + if fexpr=='im(Ex)': + return np.imag(EH[0]) + if fexpr=='re(Ey)': + return np.real(EH[1]) + if fexpr=='im(Ey)': + return np.imag(EH[1]) + if fexpr=='re(Ez)': + return np.real(EH[2]) + if fexpr=='im(Ez)': + return np.imag(EH[2]) + if fexpr=='re(Hx)': + return np.real(EH[3]) + if fexpr=='im(Hx)': + return np.imag(EH[3]) + if fexpr=='re(Hy)': + return np.real(EH[4]) + if fexpr=='im(Hy)': + return np.imag(EH[4]) + if fexpr=='re(Hz)': + return np.real(EH[5]) + if fexpr=='im(Hz)': + return np.imag(EH[5]) + if fexpr=='abs2(H)': + return abs2(EH[3]) + abs2(EH[4]) + abs2(EH[5]) + if True: # fexpr=='abs2(E)': + return abs2(EH[0]) + abs2(EH[1]) + abs2(EH[2]) + +################################################## +# this routine intended to be called by +# visualize_dft_fields, not directly by user +################################################## +def plot_dft_fields(sim, field_cells=[], options=None, nf=0): + + options = options if options else def_field_options + cmap = options['cmap'] + alpha = options['alpha'] + num_contours = options['num_contours'] + fontsize = options['fontsize'] + + for ncell, cell in enumerate(field_cells): + (x,y,z,w,cEH,EH)=unpack_dft_cell(sim,cell,nf=nf) + X, Y = np.meshgrid(x, y) + plt.figure() + plt.suptitle('DFT cell {}'.format(ncell+1)) + ops=['Re', 'Im', 'Abs'] + rows,cols=len(cEH),len(ops) + for row, c in enumerate(cEH): + for col, op in enumerate(ops): + plt.subplot(rows, cols, row*cols + col + 1) + ax=plt.gca() + ax.set_title('{}({})'.format(op,mp.component_name(c))) + ax.set_xlabel(r'$x$', fontsize=fontsize, labelpad=fontsize) + ax.set_ylabel(r'$y$', fontsize=fontsize, labelpad=fontsize, rotation=0) + ax.tick_params(axis='both', labelsize=0.75*fontsize) + data=np.real(EH[row]) if op=='Re' else np.imag(EH[row]) if op=='Im' else np.abs(EH[row]) + img = ax.contourf(X,Y,np.transpose(data),num_contours, cmap=cmap,alpha=alpha) + plt.colorbar(img) + #cb.set_label(r'$\epsilon$',fontsize=1.5*fontsize,rotation=0,labelpad=0.5*fontsize) + #cb.ax.tick_params(labelsize=0.75*fontsize) + + plt.show(False) + plt.draw() + return 0 + +################################################## +################################################## +################################################## +def visualize_dft_fields(sim, superpose=True, field_cells=[], + field_funcs=None, z_offsets=None, options=None, nf=0): + + if not mp.am_master(): + return + + if len(field_cells)==0: + field_cells=[cl for cl in sim.dft_objects if dft_cell_type(cl)=='fields'] + if len(field_cells)==0: + return + + if superpose and not isinstance(plt.gcf().gca(),axes3d.Axes3D): + warnings.warn("visualize_dft_fields: non-3D plot, can't superpose.") + superpose=False + + if not superpose: + return plot_dft_fields(sim, field_cells, options, nf=nf) + + # the remainder of this routine is for the superposition case + + options = options if options else def_field_options + cmap = options['cmap'] + alpha = options['alpha'] + num_contours = options['num_contours'] + fontsize = options['fontsize'] + + if field_funcs is None: + field_funcs, z_offsets = ['abs2(E)'], [options['z_offset']] + + for n, cell in enumerate(field_cells): + + # skip if cell is entirely contained in another field_cell + Contained=False + for m, parent in enumerate(field_cells): + if m!=n and parent.where.contains(cell.where): + Contained=True + if Contained: + continue + + (x,y,z,w,cEH,EH)=unpack_dft_cell(sim,cell,nf=nf) + X, Y = np.meshgrid(x, y) + fig = plt.gcf() + ax = fig.gca(projection='3d') + (zmin,zmax)=ax.get_zlim() + for f,z in zip(field_funcs,z_offsets): + data=field_func_array(f,x,y,z,w,cEH,EH) + Z0=zmin + z*(zmax-zmin) + img = ax.contourf(X, Y, np.transpose(data), num_contours, + cmap=cmap, alpha=alpha, zdir='z', offset=Z0) + pad=options['colorbar_pad'] + shrink=options['colorbar_shrink'] + cb=fig.colorbar(img, shrink=shrink, pad=pad, orientation='horizontal') + #cb.set_label(r'$|\mathbf{E}|^2$',fontsize=1.0*fontsize,rotation=0,labelpad=0.5*fontsize) + cb.set_label(f,fontsize=1.0*fontsize,rotation=0,labelpad=0.5*fontsize) + cb.ax.tick_params(labelsize=0.75*fontsize) + cb.locator = ticker.MaxNLocator(nbins=5) + cb.update_ticks() + + plt.show(False) + plt.draw() + +################################################## +################################################## +################################################## +def visualize_sim(sim, fig=None, plot3D=None, + eps_min=0.0, eps_max=None, + eps_options=None, src_options=None, + pml_options=None, dft_options=None, + flux_options=None, field_options=None, + set_rcParams=True, plot_dft_data=None): + + if not mp.am_master(): + return + + # if plot3D not specified, set it automatically: false + # if we are plotting only the geometry (at the beginning + # of a simulation), true if we are also plotting results + # (at the end of a simulation). + sources_finished = sim.round_time() > sim.fields.last_source_time() + if plot3D is None: + plot3D=sources_finished + + ###################################################### + # create figure and set some global parameters, unless + # the caller asked us not to + ###################################################### + if fig is None: + plt.ion + fig=plt.gcf() + fig.clf() + if set_rcParams: + set_meep_rcParams() + ax = axes3d.Axes3D(fig) if plot3D else fig.gca() + + if not plot3D: + ax.set_aspect('equal') + plt.tight_layout() + + ################################################## + # plot permittivity + ################################################## + eps_options = eps_options if eps_options else def_eps_options + plot_eps(sim, eps_min=eps_min, eps_max=eps_max, options=eps_options, plot3D=plot3D) + + ################################################### + ## plot source regions and optionally source amplitudes + ################################################### + src_options = src_options if src_options else def_src_options + for ns,s in enumerate(sim.sources): + plot_volume(sim, center=s.center, size=s.size, + options=src_options, plot3D=plot3D, + label=( None if src_options['fontsize']==0 + else 'src' + ( '\_'+str(ns) if len(sim.sources)>1 else '')) + ) + if src_options['zmin']!=src_options['zmax']: + visualize_source_distribution(sim, standalone=not plot3D, options=src_options) + + ################################################### + ## plot PML regions + ################################################### + def_options=def_pml_options + if pml_options is None: + pml_options = { **def_pml_options, + 'fill_color' : (0.25 if plot3D else 0.75)*np.ones(3) + } + if sim.boundary_layers and hasattr(sim.boundary_layers[0],'thickness'): + dpml = sim.boundary_layers[0].thickness + sx, sy = sim.cell_size.x, sim.cell_size.y + y0, x0 = mp.Vector3(0.0, 0.5*(sy-dpml)), mp.Vector3(0.5*(sx-dpml), 0.0) + ns, ew = mp.Vector3(sx-2*dpml, dpml), mp.Vector3(dpml,sy) + centers = [ y0, -1*y0, x0, -1*x0 ] # north, south, east, west + sizes = [ ns, ns, ew, ew ] + for c,s in zip(centers,sizes): + plot_volume(sim, center=c, size=s, + options=pml_options, plot3D=plot3D) + + ###################################################################### + # plot DFT cell regions, with labels for flux cells. + ###################################################################### + dft_options = dft_options if dft_options else def_dft_options + for nc, c in enumerate(sim.dft_objects): + plot_volume(sim,center=c.regions[0].center,size=c.regions[0].size, + options=dft_options, plot3D=plot3D, + label=dft_cell_name(nc) if dft_cell_type(c)=='flux' else None) + + ################################################### + ################################################### + ################################################### + if plot_dft_data is None: + plot_dft_data=sources_finished + + if plot_dft_data: + visualize_dft_flux(sim, superpose=True, options=flux_options) + visualize_dft_fields(sim, superpose=True, options=field_options) + + plt.show(False) + plt.draw() + return fig + +###################################################################### +###################################################################### +###################################################################### +def plot_basis(opt_prob): + + x0=opt_prob.dft_cells[-1].center + xyzw=opt_prob.dft_cells[-1].xyzw + x,y,z,w = xyzw[0],xyzw[1],xyzw[2],xyzw[3] + xyz=[mp.Vector3(xx,yy,zz) for xx in x for yy in y for zz in z] + bm=np.zeros(np.shape(w)) + + blen=len(opt_prob.basis()) + cols=5 + rows=blen//5 + fig, axes = plt.subplots(rows,cols) + extent=(min(x), max(x), min(y), max(y)) + + bfnames=fl_basis_names(opt_prob.args.nr_max, opt_prob.args.kphi_max) + for nb in range(blen): + fig.sca(axes.flat[nb]) + axes.flat[nb].set_title('b{}: {}'.format(nb,bfnames[nb])) + it=np.nditer(w,flags=['f_index','multi_index']) + while not it.finished: + n, nn = it.index, it.multi_index + bm[nn] = opt_prob.basis(xyz[n]-x0)[nb] + it.iternext() + img=plt.imshow(np.transpose(bm),extent=extent,cmap=matplotlib.cm.Blues) + fig.colorbar(img) + + plt.show(False) + plt.draw() + + +###################################################################### +###################################################################### +###################################################################### +LogFile='/tmp/PFCServer.log' +def message(msg): + dt=datetime.datetime.now().strftime("%T ") + with open(LogFile,'a') as f: + f.write("{} {}\n".format(dt,msg)) + #os.system('zenity --info --text "{} {}" &'.format(dt,msg)) + +PFCRequest = namedtuple('PFCRequest', 't flist') + +###################################################################### +###################################################################### +###################################################################### +class PFCServer(object): + + def __init__(self, x, y, clist, cumulative=True, + poll_interval=None, options=None): + self.X, self.Y = np.meshgrid(x, y) + self.extent = (min(x), max(x), min(y), max(y)) + self.clist = clist + self.cumulative = cumulative + self.poll_interval = poll_interval if poll_interval else 500 + self.options = options if options else def_field_options + self.num_contours = self.options['num_contours'] + self.cmap = self.options['cmap'] + + ###################################################################### + ###################################################################### + ###################################################################### + def __call__(self, pipe): + self.pipe = pipe + self.fig, self.axes = plt.subplots(1,len(self.clist)) + self.imgs, self.cbs=[],[] + for n, ax in enumerate(self.axes): + self.fig.sca(ax) + ax.set_title(mp.component_name(self.clist[n])) + img = ax.contourf(self.X,self.Y,np.zeros(np.shape(self.X)), + self.num_contours, cmap=self.cmap) +# img=plt.imshow(np.zeros(np.shape(np.transpose(self.X))), cmap=self.cmap, +# extent=self.extent) +# extent=self.extent) + cb=self.fig.colorbar(img) + self.imgs.append(img) + self.cbs.append(cb) + + timer=self.fig.canvas.new_timer(interval=self.poll_interval) + timer.add_callback(self.make_callback()) + timer.start() + plt.show() + + ###################################################################### + ###################################################################### + ###################################################################### + def make_callback(self): + + def callback(): + request = self.pipe.recv() + if request is None: + return False + self.fig.suptitle('t={:.8f}'.format(request.t)) + for n,f in enumerate(request.flist): + ax=self.axes[n] + self.fig.sca(ax) + plt.cla() + ax.set_title(mp.component_name(self.clist[n])) + vmin, vmax = np.amin(f), np.amax(f) + if self.cumulative: + lvmin,lvmax = self.cbs[n].get_clim() + vmin, vmax = min(vmin,lvmin), max(vmax,lvmax) +# self.imgs[n].set_data(np.transpose(f)) +# self.imgs[n].set_clim(vmin,vmax) + img = ax.contourf(self.X,self.Y,np.transpose(f), + self.num_contours, cmap=self.cmap, + vmin=vmin,vmax=vmax) + #img.set_clim(vmin,vmax) + self.cbs[n]=self.fig.colorbar(img, cax=self.cbs[n].ax) + self.cbs[n].set_clim(vmin,vmax) + self.cbs[n].draw_all() + # self.cbs[n].update_bruteforce(img) + #self.cbs[n].remove() + #self.cbs[n]=self.fig.colorbar(img) + #self.cbs[n].draw_all() + #self.cbs[n].update_bruteforce(img) + #self.cbs[n]. + #self.cbs[n].set_clim(vmin=vmin,vmax=vmax) + #self.cbs[n].update + #self.cbs[n].draw_all() + #self.cbs[n].remove() + #self.cbs[n]=self.fig.colorbar(img) + self.fig.canvas.draw() + return True + + return callback + +################################################## +################################################## +################################################## +def str_to_component(s): + for c in EHxyz: + if mp.component_name(c)==s.lower(): + return c + raise ValueError("unknown field component " + s) + +###################################################################### +###################################################################### +###################################################################### +def plot_field_components(sim, components, vol=None, size=None, center=origin, + interval=1.0, options=None): + + clist=[str_to_component(c) if isinstance(c,str) else c for c in components] + + ################################################## + # initialization: launch server process + ################################################## + closure = { 'next_plot_time': interval } + if vol is None: + vol=mp.Volume(center=center, size=(size if size else sim.cell_size) ) + (x,y,z,w)=sim.get_array_metadata(vol=vol) + + pipe_to_server, pipe_from_client = Pipe() + server=PFCServer(x,y,clist,options=options) + server_process = Process(target=server, args=(pipe_from_client,), daemon=True) + server_process.start() + + def _step_func(sim, todo): + if todo=='step' and sim.round_time() Date: Sat, 16 Mar 2019 19:25:43 -0400 Subject: [PATCH 09/16] updates --- python/adjoint/Basis.py | 213 ++++++++++++------ python/adjoint/ObjectiveFunction.py | 6 +- python/adjoint/Visualization.py | 36 +-- python/adjoint/__init__.py | 3 +- .../adjoint_optimization/HoleyWaveguide.py | 5 +- 5 files changed, 169 insertions(+), 94 deletions(-) diff --git a/python/adjoint/Basis.py b/python/adjoint/Basis.py index 9579a4cf1..4d958cfc1 100644 --- a/python/adjoint/Basis.py +++ b/python/adjoint/Basis.py @@ -4,6 +4,7 @@ # of basis functions, plus predefined implementations of # some simple basis sets for common cases ###################################################################### +from __future__ import division import numpy as np import meep as mp @@ -12,7 +13,7 @@ ################################################## def parameterized_dielectric(center, basis, beta): def _eps_func(p): - return np.dot(beta,basis( (p-center).__array__())) + return np.dot(beta,basis( (p-center) ) ) return _eps_func @@ -26,12 +27,71 @@ def sinusoid(k,u): arg = 2.0*np.pi*np.floor((k+1)/2)*u return np.sin(arg) if (k%2) else np.cos(arg) -def sinusoid_names(arg,kmax): - sinusoid_names=['1'] - for nu in range(1,kmax+1): - sinusoid_names.append('sin({}{})'.format('' if nu==1 else str(nu),arg)) - sinusoid_names.append('cos({}{})'.format('' if nu==1 else str(nu),arg)) - return sinusoid_names +def sinusoid_names(arg,kmax,tex=False): + c='\\' if tex else '' + SC=[c+'sin',c+'cos'] + return ['1'] + [ SC[p]+'({}{})'.format('' if k is 1 else k,arg) for k in range(1,kmax+1) for p in [0,1]] + +def product_name(f1,f2,tex=False): + pname = f1 if f2=='1' else f2 if f1=='1' else f1 + '*' + f2 + return pname if not tex else '$' + pname.replace('*','') + '$' + +###################################################################### +# invoke python's 'abstract base class' formalism in a version-agnostic way +###################################################################### +from abc import ABCMeta, abstractmethod +ABC = ABCMeta('ABC', (object,), {'__slots__': ()}) # compatible with Python 2 *and* 3: + +###################################################################### +# Basis is the abstract base class from which classes describing specific +# basis sets should inherit +###################################################################### +class Basis(ABC): + + # derived classes must override __call__, which inputs the coordinates + # of an evaluation point and returns a np.array of basis-function values + @abstractmethod + def __call__(self, p=[0.0,0.0]): + raise NotImplementedError("derived class must implement __call__() method") + + def __init__(self, dim): + self.dim=dim + + @property + def dimension(self): + return self.dim + + # derived classes may override shape() and names(), for which + # + @property + def shape(self): + return (self.dim,1) + + @property + def names(self): + return ['b{}'.format(d) for d in range(self.dim)] + + #########################################################j + # project an arbitrary function f(x) onto the basis, i.e. + # return the vector of normalized overlap integrals + # / + ########################################################## + def project(self,f,xyzw): + (x,y,z,w)=xyzw[0],xyzw[1],xyzw[2],xyzw[3] + ffunc = f if callable(f) else None + fmatrix = f if not callable(f) and np.shape(f)==np.shape(w) else None + if ffunc is None and fmatrix is None: + raise ValueError("invalid function specification in {}.project()".format(self.__class__.__name__)) + f_dot_b, b_dot_b = 1.0j*np.zeros(self.dim), np.zeros(self.dim) + xyz=[mp.Vector3(xx,yy,zz) for xx in x for yy in y for zz in z] + it=np.nditer(w,flags=['f_index','multi_index']) + while not it.finished: + n, nn = it.index, it.multi_index + ww, bb, ff = w[nn], self(xyz[n]), ffunc(xyz[n]) if ffunc else fmatrix[nn] + f_dot_b += (ww*ff)*bb + b_dot_b += ww*bb*bb + it.iternext() + return np.array( [ fdb/bdb for (fdb,bdb) in zip(f_dot_b,b_dot_b)] ) ################################################## @@ -45,79 +105,88 @@ def sinusoid_names(arg,kmax): # # The size of the basis is (2*kx_max+1)*(2*ky_max+1) ################################################## -def plane_wave_basis(lx, ly, kx_max=0, ky_max=0): +class PlaneWaveBasis(Basis): - def _get_bf_vector(p=[0.0,0.0]): - b=np.zeros( (2*kx_max+1)*(2*ky_max+1) ) - for kx in range(0,2*kx_max+1): - for ky in range(0,2*ky_max+1): - b[ kx*(2*ky_max+1) + ky ] = sinusoid(kx,p[0]/lx)*sinusoid(ky,p[1]/ly) - return b + def __init__(self, lx, ly, kx_max=0, ky_max=0): + self.l = [lx,ly] + self.kmax = [kx_max, ky_max] + self.nn = range(2*kx_max+1), range(2*ky_max+1) + fxnames,fynames = [sinusoid_names(arg,kmax) for (arg,kmax) in zip('xy',self.kmax)] + self.fnames = [product_name(fxn,fyn) for fxn in fxnames for fyn in fynames] + super().__init__(len(self.fnames)) - return _get_bf_vector + @property + def shape(self): + return ( len(self.nn[0]) , len(self.nn[1]) ) + @property + def names(self): + return self.fnames + + def __call__(self, p=[0.0,0.0]): + u=[pi/li for pi,li in zip(p,self.l)] + return np.array([ sinusoid(nx,u[0])*sinusoid(ny,u[1]) for nx in self.nn[0] for ny in self.nn[1] ]) -################################################## -# basis of expansion functions f{m,n}(rho,phi) for -# a disc or annulus. -# -# f(rho,phi) = (legendre polynomial in rho) * (sinusoid in phi) -# -# f_{nr, 0} = L_{nr}(u) -# f_{nr, 2*k-1} = L_{nr}(u) * sin(k*phi) -# f_{nr, 2*k} = L_{nr}(u) * cos(k*phi) -# -# for nr=[0,...,nr_max], k=[0,1,...,kphi_max] -# -# Here u is a rescaled version of rho that runs over [-1:1] -# as rho runs over [inner_radius:outer_radius]. -# -# The size of the basis is (nr_max+1)*(2*kphiMax+1) -################################################## -def fourier_legendre_basis(radius=None, outer_radius=None, inner_radius=0.0, - nr_max=0, kphi_max=0): - num_radial=nr_max+1 - num_angular=(2*kphi_max+1) - outer_radius=radius if outer_radius is None else outer_radius +################################################### +## basis of expansion functions f{m,n}(r,phi) for +## a disc or annulus. +## +## f(r,phi) = (legendre polynomial in ur) * (sinusoid in phi) +## +## f_{nr, 0} = L_{nr}(ur) +## f_{nr, 2*k-1} = L_{nr}(ur) * sin(k*phi) +## f_{nr, 2*k} = L_{nr}(ur) * cos(k*phi) +## +## for nr=[0,...,nr_max], k=[0,1,...,kphi_max] +## +## Here ur is a rescaled version of r that runs over [-1:1] +## as rho runs over [inner_radius:outer_radius]. +## +## The size of the basis is (nr_max+1)*(2*kphiMax+1) +################################################### +class FourierLegendreBasis(Basis): - def _get_bf_vector(p=[0.0,0.0]): - b=np.zeros( num_radial*num_angular ) + def __init__(self, radius=None, outer_radius=None, inner_radius=0.0, + nr_max=0, kphi_max=0): + + self.nrphi = (nr_max+1, 2*kphi_max+1) + self.outer_radius = radius if outer_radius is None else outer_radius + self.inner_radius = 0.0 if inner_radius is None else inner_radius + self.radial_span = self.outer_radius - self.inner_radius + frnames = ['1'] + ['P_{}(u)'.format(n) for n in range(1,nr_max+1)] + fpnames = sinusoid_names('theta',kphi_max) + self.fnames = [product_name(fr,fp) for fr in frnames for fp in fpnames] + frnames = ['1'] + ['P_{'+str(n)+'}(\overline{r})' for n in range(1,nr_max+1)] + fpnames = sinusoid_names('\\theta',kphi_max,tex=True) + self.tex_fnames = [product_name(fr,fp,tex=True) for fr in frnames for fp in fpnames] + super().__init__(len(self.fnames)) + + @property + def shape(self): + return (self.nrphi[0],self.nrphi[1]) + + @property + def tex_names(self): + return self.tex_fnames + + @property + def names(self): + return self.fnames + + + def __call__(self, p=[0.0,0.0]): + b=np.zeros( self.nrphi[0] * self.nrphi[1] ) r=np.sqrt(p[0]*p[0] + p[1]*p[1]) - if router_radius: + if rself.outer_radius: b[0]=1.0; return b - u = -1.0 + 2.0*(r-inner_radius)/(outer_radius-inner_radius) - phi=np.arctan2(p[1],p[0]) - (Lm1, L)=(0.0,1.0) - for nr in range(0,num_radial): - for nphi in range(0,num_angular): - b[ nr*num_angular + nphi ] = L*sinusoid(nphi,phi/(2.0*np.pi)) + ur = -1.0 + 2.0*(r-self.inner_radius)/self.radial_span + uphi = np.arctan2(p[1],p[0])/(2.0*np.pi) + (Lm1, L)=(0.0,1.0) # initialize Legendre recursion + for nr in range(self.nrphi[0]): + for nphi in range(self.nrphi[1]): + b[ nr*self.nrphi[1] + nphi ] = L*sinusoid(nphi,uphi) (Lm2,Lm1)=(Lm1,L) - L = ( (2*nr+1)*u*Lm1 - nr*Lm2 )/(nr+1) # Legendre recursion + L = ( (2*nr+1)*ur*Lm1 - nr*Lm2 )/(nr+1) # Legendre recursion return b - - return _get_bf_vector - -def fl_basis_names(nr_max, kphi_max): - snames=sinusoid_names('phi',kphi_max) - flb_names=snames[:] - for nr in range(1,nr_max+1): - flb_names += ['L{}(r)'.format(nr) + ('' if s=='1' else s) for s in snames] - return flb_names - -######################################################### -# utility routine to project an arbitrary function f(x) -# onto a basis set {b_n(x)}, i.e. computes the N-vector -# of overlap integrals -######################################################### -def project_basis(basis,xyzw,f): - projection=1.0j*np.zeros(len(basis())) - (x,y,z,w)=xyzw[0],xyzw[1],xyzw[2],xyzw[3] - xyz=[mp.Vector3(xx,yy,zz) for xx in x for yy in y for zz in z] - it=np.nditer(w,flags=['f_index','multi_index']) - while not it.finished: - n, nn = it.index, it.multi_index - projection+=w[nn]*basis(xyz[n])*f[nn] - it.iternext() - return projection diff --git a/python/adjoint/ObjectiveFunction.py b/python/adjoint/ObjectiveFunction.py index 41e6fc7a7..29342ab57 100644 --- a/python/adjoint/ObjectiveFunction.py +++ b/python/adjoint/ObjectiveFunction.py @@ -10,8 +10,6 @@ import meep as mp -from .Basis import project_basis - ###################################################################### # various global options affecting the adjoint solver, user-tweakable # via command-line arguments or set_adjoint_option() @@ -495,7 +493,7 @@ def __init__(self, obj_func, dft_cells, basis, sim, vis=None): # prefetch names of outputs computed by forward and # adjoint solves, for use in writing log files self.fqnames = ['f'] + obj_func.qnames - self.bnames = ['b'+str(n) for n in range(len(self.basis()))] + self.bnames = basis.names ######################################################### ######################################################### @@ -515,7 +513,7 @@ def eval_gradf(self, nf=0): # if c not in Exyz: # continue # f+=EH_forward[nc]*EH_adjoint[nc] - return project_basis(self.basis,cell.xyzw,f) + return self.basis.project(f,cell.xyzw) ######################################################### ######################################################### diff --git a/python/adjoint/Visualization.py b/python/adjoint/Visualization.py index 1f6b59674..d3385889c 100644 --- a/python/adjoint/Visualization.py +++ b/python/adjoint/Visualization.py @@ -1,4 +1,4 @@ -###################################################extent +################################################### # visualize.py -- various routines for visualizing # the inputs and outputs of pymeep calculations in # simple standardized ways @@ -23,7 +23,6 @@ import meep as mp from .ObjectiveFunction import global_dft_cell_names -from .Basis import fl_basis_names ######################################################## # the next few routines are some of my older general-purpose @@ -721,7 +720,10 @@ def visualize_sim(sim, fig=None, plot3D=None, return fig ###################################################################### -###################################################################### +# useful options: +# +# matplotlib.rcParams['axes.titlesize']='medium' +# plt.rc('font',size=20) ###################################################################### def plot_basis(opt_prob): @@ -729,24 +731,32 @@ def plot_basis(opt_prob): xyzw=opt_prob.dft_cells[-1].xyzw x,y,z,w = xyzw[0],xyzw[1],xyzw[2],xyzw[3] xyz=[mp.Vector3(xx,yy,zz) for xx in x for yy in y for zz in z] - bm=np.zeros(np.shape(w)) + bmatrix=np.zeros(np.shape(w)) - blen=len(opt_prob.basis()) - cols=5 - rows=blen//5 + rows,cols=opt_prob.basis.shape fig, axes = plt.subplots(rows,cols) + plt.tight_layout() extent=(min(x), max(x), min(y), max(y)) - bfnames=fl_basis_names(opt_prob.args.nr_max, opt_prob.args.kphi_max) - for nb in range(blen): - fig.sca(axes.flat[nb]) - axes.flat[nb].set_title('b{}: {}'.format(nb,bfnames[nb])) + usetex=matplotlib.rcParams['text.usetex'] + + if usetex: + titles=['$b_{' + str(n) + '}: ' + bn[1:] for n,bn in enumerate(opt_prob.basis.tex_names)] + else: + titles=['b{}: {}'.format(n,bn) for n,bn in enumerate(opt_prob.basis.names)] + + + for d in range(len(titles)): + fig.sca(axes.flat[d]) + axes.flat[d].set_title(titles[d]) + axes.flat[d].set_aspect('equal') + print('titles[d]={}'.format(titles[d])) it=np.nditer(w,flags=['f_index','multi_index']) while not it.finished: n, nn = it.index, it.multi_index - bm[nn] = opt_prob.basis(xyz[n]-x0)[nb] + bmatrix[nn] = opt_prob.basis(xyz[n]-x0)[d] it.iternext() - img=plt.imshow(np.transpose(bm),extent=extent,cmap=matplotlib.cm.Blues) + img=plt.imshow(np.transpose(bmatrix),extent=extent,cmap=matplotlib.cm.Blues) fig.colorbar(img) plt.show(False) diff --git a/python/adjoint/__init__.py b/python/adjoint/__init__.py index 75c53ebbe..2cb21387a 100644 --- a/python/adjoint/__init__.py +++ b/python/adjoint/__init__.py @@ -84,8 +84,7 @@ def create_sim(self,beta_vector,vacuum=False): abs2, unit_vector, rel_diff, FluxLine, DFTCell, ObjectiveFunction, AdjointSolver) -from .Basis import (plane_wave_basis, fourier_legendre_basis, project_basis, - parameterized_dielectric, fl_basis_names) +from .Basis import (parameterized_dielectric, PlaneWaveBasis, FourierLegendreBasis) from .Visualization import (set_plot_default, plot_basis, plot_field_components, visualize_sim, AdjointVisualizer) diff --git a/python/examples/adjoint_optimization/HoleyWaveguide.py b/python/examples/adjoint_optimization/HoleyWaveguide.py index e1313c368..25183bc16 100644 --- a/python/examples/adjoint_optimization/HoleyWaveguide.py +++ b/python/examples/adjoint_optimization/HoleyWaveguide.py @@ -5,7 +5,7 @@ from meep.adjoint import (OptimizationProblem, DFTCell, adjoint_options, xHat, yHat, zHat, origin, FluxLine, - parameterized_dielectric, fourier_legendre_basis) + parameterized_dielectric, FourierLegendreBasis) ################################################## ################################################## @@ -81,8 +81,7 @@ def init_problem(self, args): #---------------------------------------- # basis set #---------------------------------------- - basis = fourier_legendre_basis(radius=args.r_disc, - nr_max=args.nr_max, kphi_max=args.kphi_max) + basis = FourierLegendreBasis(radius=args.r_disc, nr_max=args.nr_max, kphi_max=args.kphi_max) #---------------------------------------- #- source location From 77395d6072af9c83c56d9ba0c4fd7993a9160738 Mon Sep 17 00:00:00 2001 From: Homer Reid Date: Sat, 16 Mar 2019 20:58:48 -0400 Subject: [PATCH 10/16] updates --- python/adjoint/Basis.py | 17 +++++++++++++++++ 1 file changed, 17 insertions(+) diff --git a/python/adjoint/Basis.py b/python/adjoint/Basis.py index 4d958cfc1..10ec73640 100644 --- a/python/adjoint/Basis.py +++ b/python/adjoint/Basis.py @@ -93,6 +93,23 @@ def project(self,f,xyzw): it.iternext() return np.array( [ fdb/bdb for (fdb,bdb) in zip(f_dot_b,b_dot_b)] ) + #########################################################j + ########################################################## + def gram_matrix(self,xyzw): + (x,y,z,w)=xyzw[0],xyzw[1],xyzw[2],xyzw[3] + xyz=[mp.Vector3(xx,yy,zz) for xx in x for yy in y for zz in z] + it=np.nditer(w,flags=['f_index','multi_index']) + dim=self.dim + gram=0.0*np.zeros([dim,dim]) + while not it.finished: + n, nn = it.index, it.multi_index + bvec = self(xyz[n]) + ww = w[nn] + for dr in range(dim): + for dc in range(dim): + gram[dr,dc]+=ww*bvec[dr]*bvec[dc] + it.iternext() + return gram ################################################## # Plane-wave basis for a rectangular region. From be23dbb685465481bcceb91cfc6339718b346854 Mon Sep 17 00:00:00 2001 From: Homer Reid Date: Fri, 22 Mar 2019 02:45:42 -0400 Subject: [PATCH 11/16] updates --- python/Makefile.am | 23 +- python/adjoint/Basis.py | 99 +++- python/adjoint/ObjectiveFunction.py | 91 ++-- python/adjoint/OptimizationProblem.py | 81 ++- python/adjoint/Visualization.py | 496 +++++++++++------- python/adjoint/__init__.py | 5 +- .../adjoint_optimization/HoleCloak.py | 14 +- .../adjoint_optimization/HoleyWaveguide.py | 16 +- 8 files changed, 503 insertions(+), 322 deletions(-) diff --git a/python/Makefile.am b/python/Makefile.am index 98c58a4a9..5435f06f6 100644 --- a/python/Makefile.am +++ b/python/Makefile.am @@ -105,7 +105,7 @@ if WITH_MPB EXTRA_DIST += solver.py mpb_data.py MPB_LA = _mpb.la pympbdir = $(pkgpythondir)/mpb - pympb_DATA = mpb.py solver.py mpb_data.py + pympb_PYTHON = mpb.py solver.py mpb_data.py pympb_LTLIBRARIES = _mpb.la _mpb_la_SOURCES = mpb-python.cxx _mpb_la_LIBADD = $(PYTHON_LIBS) $(top_builddir)/libpympb/libpympb.la @@ -146,7 +146,6 @@ if WITH_MPB MPB_SWIG_SRC = mpb.i mpb-python.cxx: $(MPB_SWIG_SRC) $(top_srcdir)/libpympb/pympb.hpp $(SWIG) -Wextra $(AM_CPPFLAGS) $(PYMPBINCLUDE) -outdir $(builddir) -c++ -python -o $@ $(srcdir)/mpb.i - mpb.py: mpb-python.cxx MPB_PY = mpb.py endif # WITH_MPB @@ -179,12 +178,6 @@ endif # MAINTAINER_MODE ###################################################################### # specification of python source files to be byte-compiled at installation -# time. Note that files in `pkgpython_PYTHON` are both byte-compiled and -# installed in the 'meep' subdirectory of the python site-packages -# installation. The `nodist` version does the byte-compiling but omits the -# installation, so we can install the files to a custom destination. -# note: previously the pympb source files were excluded from this; was -# that intentional? ###################################################################### HL_IFACE = \ $(srcdir)/geom.py \ @@ -194,14 +187,12 @@ HL_IFACE = \ pkgpython_PYTHON = __init__.py $(HL_IFACE) -adjointdir = $(pkgpythondir)/adjoint -adjoint_DATA = $(srcdir)/adjoint/__init__.py \ - $(srcdir)/adjoint/Basis.py \ - $(srcdir)/adjoint/ObjectiveFunction.py \ - $(srcdir)/adjoint/OptimizationProblem.py \ - $(srcdir)/adjoint/Visualization.py - -nodist_python_PYTHON = $(adjoint_DATA) $(pympb_DATA) +adjointdir = $(pkgpythondir)/adjoint +adjoint_PYTHON = $(srcdir)/adjoint/__init__.py \ + $(srcdir)/adjoint/Basis.py \ + $(srcdir)/adjoint/ObjectiveFunction.py \ + $(srcdir)/adjoint/OptimizationProblem.py \ + $(srcdir)/adjoint/Visualization.py ###################################################################### # finally, specification of what gets installed in the meep python diff --git a/python/adjoint/Basis.py b/python/adjoint/Basis.py index 10ec73640..047e3cdd6 100644 --- a/python/adjoint/Basis.py +++ b/python/adjoint/Basis.py @@ -1,5 +1,4 @@ ###################################################################### -# Basis.py -- general support for spatially-varying permittivity # functions described by expansions in user-defined sets # of basis functions, plus predefined implementations of # some simple basis sets for common cases @@ -7,14 +6,27 @@ from __future__ import division import numpy as np import meep as mp +import fenics ################################################# -################################################# +# ideally the following should be passable to meep +# as an epsilon_function, but the typemaps in +# typemap_utils.cpp don't seem to allow it ################################################## -def parameterized_dielectric(center, basis, beta): - def _eps_func(p): - return np.dot(beta,basis( (p-center) ) ) - return _eps_func +#class ParameterizedDielectric(object): +# +# def __init__(self, center, basis, beta_vector): +# self.center, self.basis = center, basis +# self.basis.set_coefficients(beta_vector) +# +# def __call__(p): +# return self.basis.eval_expansion( p-self.center ) + +def ParameterizedDielectric(center, basis, beta_vector): + basis.set_coefficients(beta_vector) + def eps_func(p): + return basis.eval_expansion( p-center ) + return eps_func ################################################## @@ -48,21 +60,27 @@ def product_name(f1,f2,tex=False): ###################################################################### class Basis(ABC): - # derived classes must override __call__, which inputs the coordinates - # of an evaluation point and returns a np.array of basis-function values - @abstractmethod - def __call__(self, p=[0.0,0.0]): - raise NotImplementedError("derived class must implement __call__() method") - def __init__(self, dim): self.dim=dim + self.beta_vector=np.zeros(dim) @property def dimension(self): return self.dim - # derived classes may override shape() and names(), for which - # + # derived classes must override __call__, which returns the full + # vector of basis-function values at a given evaluation point + @abstractmethod + def __call__(self, p=[0.0,0.0]): + raise NotImplementedError("derived class must implement __call__() method") + + def set_coefficients(self,beta_vector): + self.beta_vector[:]=beta_vector[:] + + def eval_expansion(self, p=[0.0,0.0]): + return np.dot(self.beta_vector, self.__call__(p) ) + + # derived classes may override shape(), names(), texnames() @property def shape(self): return (self.dim,1) @@ -71,6 +89,10 @@ def shape(self): def names(self): return ['b{}'.format(d) for d in range(self.dim)] + @property + def texnames(self): + return [r'$b_{}$'.format(d) for d in range(self.dim)] + #########################################################j # project an arbitrary function f(x) onto the basis, i.e. # return the vector of normalized overlap integrals @@ -130,6 +152,8 @@ def __init__(self, lx, ly, kx_max=0, ky_max=0): self.nn = range(2*kx_max+1), range(2*ky_max+1) fxnames,fynames = [sinusoid_names(arg,kmax) for (arg,kmax) in zip('xy',self.kmax)] self.fnames = [product_name(fxn,fyn) for fxn in fxnames for fyn in fynames] + fxnames,fynames = [sinusoid_names(arg,kmax,tex=True) for (arg,kmax) in zip(['\\overline{x}','\\overline{y}'],self.kmax)] + self.tex_fnames = [product_name(fx,fy,tex=True) for fx in fxnames for fy in fynames] super().__init__(len(self.fnames)) @property @@ -140,11 +164,14 @@ def shape(self): def names(self): return self.fnames + @property + def tex_names(self): + return self.tex_fnames + def __call__(self, p=[0.0,0.0]): u=[pi/li for pi,li in zip(p,self.l)] return np.array([ sinusoid(nx,u[0])*sinusoid(ny,u[1]) for nx in self.nn[0] for ny in self.nn[1] ]) - ################################################### ## basis of expansion functions f{m,n}(r,phi) for ## a disc or annulus. @@ -207,3 +234,45 @@ def __call__(self, p=[0.0,0.0]): (Lm2,Lm1)=(Lm1,L) L = ( (2*nr+1)*ur*Lm1 - nr*Lm2 )/(nr+1) # Legendre recursion return b + +################################################### +## basis of 2D finite-element functions over a rectangle or disc +################################################### +class FiniteElementBasis(Basis): + + def __init__(self, N=4, lx=None, ly=None, radius=None, + fe_type='Lagrange', fe_order=1): + + try: + import fenics + except ImportError: + raise ImportError('failed to load fenics module (needed for FiniteElementBasis)') + + if lx is not None and ly is not None: + mesh=fenics.RectangleMesh(fenics.Point(-0.5*lx,-0.5*ly), + fenics.Point(+0.5*lx,+0.5*ly), + int(np.ceil(N*lx)),int(np.ceil(N*ly))) + elif radius is not None: + mesh=fenics.SphereMesh(fenics.Point(0.0,0.0),radius,1.0/N) + else: + raise ValueError('invalid parameters in FiniteElementBasis') + + self.fs = fenics.FunctionSpace(mesh,fe_type,fe_order) + self.f = fenics.Function(self.fs) + super().__init__( self.fs.dim() ) + + # FIXME + self.bfs = [] + for n in range(self.fs.dim()): + bf=fenics.Function(self.fs) + bf.vector()[n]=1.0 + self.bfs.append(bf) + + def __call__(self, p=[0.0,0.0]): + return np.array( [bf(p[0],p[1]) for bf in self.bfs] ) + + def set_coefficients(self, beta_vector): + self.f.vector().set_local(beta_vector) + + def eval_expansion(self, p=[0.0,0.0]): + return 1.0 + self.f(p[0],p[1]) diff --git a/python/adjoint/ObjectiveFunction.py b/python/adjoint/ObjectiveFunction.py index 29342ab57..4f7b87e8b 100644 --- a/python/adjoint/ObjectiveFunction.py +++ b/python/adjoint/ObjectiveFunction.py @@ -1,4 +1,4 @@ -############################################### +################################################## # ObjectiveFunction.py --- routines for evaluating # objective quantities and objective functions for # adjoint-based optimization in meep @@ -8,7 +8,12 @@ import numpy as np import sympy +import matplotlib.cm + import meep as mp +import meep.adjoint + +#from Visualization import (AFEClient, def_field_options) ###################################################################### # various global options affecting the adjoint solver, user-tweakable @@ -21,7 +26,7 @@ 'verbosity': 'default', 'visualize': False, 'logfile': None, - 'plot_pause': 0.01, + 'plot_pause': 0.1, 'animate_components': None, 'animate_interval': 1.0 } @@ -146,26 +151,29 @@ def FluxLine(x0,y0,length,dir,name=None): # Note: for now, all arrays are stored in memory. For large calculations with # many DFT frequencies this may become impractical. TODO: disk caching. ###################################################################### -global_dft_cell_names=[] class DFTCell(object): -# Why does this not work?! I would have thought DFTCell.DFTCellNames would -# be globally accessible like a static member of a C++ class, and in fact it -# **is** accessible from most code, but seems to go out of scope when we're -# in the body of a method of some other class. -# DFTCellNames=[] -# @classmethod -# def get_index(cls, region_name): -# cell_name = region_name + '_flux' -# if cell_name in cls.DFTCellNames: -# return cls.DFTCellNames.index(cell_name) -# raise ValueError("reference to nonexistent DFT cell {}",region_name) + cell_names=[] + + @classmethod + def get_cell_names(cls): + return cls.cell_names + + @classmethod + def add_cell_name(cls,cell_name): + cls.cell_names.append(cell_name) + + @classmethod + def reset_cell_names(cls): + cls.cell_names=[] + @classmethod def get_index(cls, region_name): - cell_name = region_name + '_flux' - if cell_name in global_dft_cell_names: - return global_dft_cell_names.index(cell_name) - raise ValueError("reference to nonexistent DFT cell {}",region_name) + if region_name + '_flux' in cls.cell_names: + return cls.cell_names.index(region_name + '_flux') + if region_name + '_fields' in cls.cell_names: + return cls.cell_names.index(region_name + '_fields') + raise ValueError("reference to nonexistent DFT cell {}".format(region_name)) ###################################################################### @@ -204,10 +212,8 @@ def __init__(self, grid_info=None, region=None, center=origin, size=None, elif grid_info and self.size==grid_info.size: self.name = 'fullgrid_{}'.format(self.celltype) else: - self.name = '{}_{}'.format(self.celltype, len(global_dft_cell_names)) -# self.name = '{}_{}'.format(self.celltype, len(self.DFTCellNames)) -# self.DFTCellNames.append(self.name) - global_dft_cell_names.append(self.name) + self.name = '{}_{}'.format(self.celltype, len(self.get_cell_names())) + self.add_cell_name(self.name) # FIXME At present the 'xyzw' metadata cannot be computed until a mp.simulation / meep::fields # object has been created, but in fact the metadata only depend on the GridInfo @@ -361,7 +367,7 @@ def qname_to_qrule(qname): pieces=qname.split('_') codemode, cellstr = pieces[0], '_'.join(pieces[1:]) - ncell=int(cellstr) if cellstr.isdigit() else DFTCell.get_index(cellstr) + ncell=int(cellstr) if cellstr.isdigit() else meep.adjoint.DFTCell.get_index(cellstr) if codemode.upper()=='S': return qrule(codemode, 0, ncell) elif codemode[0] in 'PM': @@ -489,6 +495,7 @@ def __init__(self, obj_func, dft_cells, basis, sim, vis=None): self.basis = basis self.sim = sim self.vis = vis + self.dfdEps = 0.0j*np.zeros(self.dft_cells[-1].slice_dims) # prefetch names of outputs computed by forward and # adjoint solves, for use in writing log files @@ -502,18 +509,13 @@ def eval_fq(self, nf=0): return self.obj_func.get_fq(self.dft_cells,nf=nf) def eval_gradf(self, nf=0): - gradient=0.0j*np.zeros(len(self.basis())) + gradient=0.0j*np.zeros(self.basis.dim) cell=self.dft_cells[-1] # design cell EH_forward=cell.get_EH_slices(nf,label='forward') EH_adjoint=cell.get_EH_slices(nf) # no label->current simulation - f=np.sum( [EH_forward[nc]*EH_adjoint[nc] - for nc,c in enumerate(cell.components) if c in Exyz], 0 ) -# f=0.0j*np.ones(cell.slice_dims) -# for nc,c in enumerate(cell.components): -# if c not in Exyz: -# continue -# f+=EH_forward[nc]*EH_adjoint[nc] - return self.basis.project(f,cell.xyzw) + self.dfdEps=np.sum( [EH_forward[nc]*EH_adjoint[nc] + for nc,c in enumerate(cell.components) if c in Exyz], 0 ) + return self.basis.project(self.dfdEps,cell.xyzw) ######################################################### ######################################################### @@ -531,23 +533,25 @@ def run_until_converged(self, case='forward'): self.sim.init_sim() [cell.register(self.sim) for cell in self.dft_cells] - #update_plot(self.sim, which='Geometry') if self.vis: self.vis.update(self.sim,'Geometry') # construct field-animation step function if requested step_funcs = [] - acs = adjoint_options['animate_components'] - if acs is not None: + clist = adjoint_options['animate_components'] + if clist is not None: ivl=adjoint_options['animate_interval'] - step_funcs = [ plot_field_components(self.sim, components=acs, interval=ivl) ] - + ivl=0.5 + options = dict(def_field_options) +# options['cmap']=matplotlib.cm.RdGy +# options['clim']=(-0.5,0.5) + step_funcs = [ AFEClient(self.sim, clist, interval=ivl, field_options=options) ] + + import time + time.sleep(10) log("Beginning {} timestepping run...".format(case)) self.sim.run(*step_funcs, until=self.sim.fields.last_source_time()) - if self.vis: - self.vis.update(self.sim,'ForwardFD') - # now continue timestepping with periodic convergence checks until # we converge or timeout last_vals = np.inf*np.ones(len(names)) @@ -566,7 +570,8 @@ def run_until_converged(self, case='forward'): log(' ** t={} MRD={} ** '.format(self.sim.round_time(),max_rel_delta)) if verbose: [log('{:10s}: {:+.4e}({:.1e})'.format(n,v,e)) for n,v,e in zip(names,vals,rel_delta)] - [log('')] + if self.vis: + self.vis.update(self.sim,'Forward') if case=='forward' else self.vis.update(self.sim,'Adjoint',dfdEps=self.dfdEps) if max_rel_delta<=reltol or self.sim.round_time()>=max_time: return vals @@ -627,7 +632,7 @@ def solve(self, need_gradient=False): fq=self.run_until_converged(case='forward') if self.vis: - self.vis.update(self.sim,'ForwardFD') + self.vis.update(self.sim,'Forward') if need_gradient==False: return fq[0], 0 @@ -640,7 +645,7 @@ def solve(self, need_gradient=False): self.place_adjoint_sources(qweights) gradf=self.run_until_converged(case='adjoint') if self.vis: - self.vis.update(self.sim,'AdjointFD') + self.vis.update(self.sim,'Adjoint',dfdEps=self.dfdEps) return fq[0], gradf diff --git a/python/adjoint/OptimizationProblem.py b/python/adjoint/OptimizationProblem.py index b456b5c05..8fc5cc4f4 100644 --- a/python/adjoint/OptimizationProblem.py +++ b/python/adjoint/OptimizationProblem.py @@ -16,10 +16,9 @@ from .ObjectiveFunction import (adjoint_options, xHat, yHat, zHat, origin, EHTransverse, Exyz, Hxyz, EHxyz, GridInfo, abs2, unit_vector, rel_diff, FluxLine, - DFTCell, ObjectiveFunction, AdjointSolver, - global_dft_cell_names) + DFTCell, ObjectiveFunction, AdjointSolver) -from .Visualization import visualize_sim, AdjointVisualizer, set_plot_default +from .Visualization import (visualize_sim, AdjointVisualizer, set_plot_default) ###################################################################### # invoke python's 'abstract base class' formalism in a version-agnostic way @@ -57,19 +56,19 @@ def add_args(self, args): ###################################################################### def __init__(self): - # define command-line arguments + # define and parse command-line arguments parser = self.init_args() # general args self.add_args(parser) # problem-specific arguments self.args = args = parser.parse_args() - # parse arguments and do problem-specific initialization first... + # call subclass for problem-specific initialization first... fstr, objective_regions, extra_regions, design_region, self.basis \ = self.init_problem(self.args) # ...and now do some general initialization fcen, df, nfreq = args.fcen, args.df, args.nfreq - #self.grid = FDGrid(size=self.cell_size, res=self.args.res) - global_dft_cell_names = [] + + DFTCell.reset_cell_names() self.objective_cells = [ DFTCell(region=v, fcen=fcen, df=df, nfreq=nfreq) for v in objective_regions ] self.extra_cells = [ DFTCell(region=v, fcen=fcen, df=df, nfreq=nfreq) for v in extra_regions ] if args.full_dfts else [] self.design_cell = DFTCell(region=design_region, fcen=fcen, df=df, nfreq=nfreq, name='design_fields') @@ -84,6 +83,7 @@ def __init__(self): self.filebase = args.filebase if args.filebase else self.__class__.__name__ + # miscellaneous general options affecting the solver adjoint_options['dft_reltol'] = args.dft_reltol adjoint_options['dft_timeout'] = args.dft_timeout adjoint_options['dft_interval'] = args.dft_interval @@ -92,8 +92,12 @@ def __init__(self): else adjoint_options['verbosity'] adjoint_options['logfile'] = args.logfile - self.vis = None if not args.visualize \ - else AdjointVisualizer(label_source_regions=args.label_source_regions) + # miscellaneous general options affecting visualization + self.vis = None + + if args.label_source_regions: + set_plot_default('fontsize',def_plot_options['fontsize'], 'src') + adjoint_options['animate_components'] = args.animate_component adjoint_options['animate_interval'] = args.animate_interval @@ -154,6 +158,7 @@ def init_args(self): parser.add_argument('--visualize', dest='visualize', action='store_true', help='produce visualization graphics') parser.add_argument('--label_source_regions', dest='label_source_regions', action='store_true', help='label source regions in visualization plots') parser.add_argument('--logfile', type=str, default=None, help='log file name') + parser.add_argument('--pickle_data', dest='pickle_data', action='store_true', help='save state to binary data file') parser.add_argument('--animate_component', action='append', help='plot time-domain field component') parser.add_argument('--animate_interval', type=float, default=1.0, help='meep time between animation frames') @@ -190,11 +195,29 @@ def init_beta_vector(self): # (a) the 0th basis function is the constant 1 # (b) all other basis functions (b_1, ... b_{D-1}) take values in [-1:1] # (c) coefficients (\beta_1, ..., \beta_{D-1}) are nonnegative. - eps_min=beta_vector[0] - np.sum(beta_vector[1:]) - if eps_min<1.0: - beta_vector[0] += 1.0-eps_min + #eps_min=beta_vector[0] - np.sum(beta_vector[1:]) + #if eps_min<1.0: + # beta_vector[0] += 1.0-eps_min return beta_vector + ###################################################################### + # terminate script without exiting the (i)python console or notebook + ###################################################################### + def terminate(self, msg): + raise Exception(msg) + + ###################################################################### + ###################################################################### + ###################################################################### + def plot_geometry(self): + sim = self.create_sim(self.beta_vector) + sim.init_sim() + [cell.register(sim) for cell in self.dft_cells] + vis = AdjointVisualizer(cases=['Geometry']) + vis.update(sim,'Geometry') + self.sim,self.vis = sim,vis # save copies for debugging; not strictly necessary + self.terminate("Finished visualization") + ###################################################################### # the 'run' class method of OptimizationProblem, which is where control # passes after __init__ if we were executed as a script, looks at @@ -210,23 +233,23 @@ def run(self): args=self.args if args.optimize: self.optimize() - return 0 #-------------------------------------------------------------- # if no computation was requested, just plot the geometry #-------------------------------------------------------------- if not(args.eval_gradient or args.eval_objective or args.fd_order>0): - sim = self.create_sim(self.beta_vector) - sim.init_sim() - [cell.register(sim) for cell in self.dft_cells] - vis = self.vis if self.vis else AdjointVisualizer() - vis.update(sim,'Geometry') - return 0 + self.plot_geometry() #-------------------------------------------------------------- #-------------------------------------------------------------- #-------------------------------------------------------------- - fq,gradf=self.eval_fq(self.beta_vector, need_gradient=args.eval_gradient, vis=self.vis) + vis = None + if args.visualize: + cases=['Geometry','Forward'] + (['Adjoint'] if args.eval_gradient else []) + vis=AdjointVisualizer(cases=cases) + self.vis = vis # save copy for debugging; not strictly necessary + + fq,gradf=self.eval_fq(self.beta_vector, need_gradient=args.eval_gradient, vis=vis) fqnames=['f'] + self.obj_func.qnames self.output([],[],actions=['begin']) @@ -260,12 +283,12 @@ def run(self): self.output([],[],actions=['end']) - #f = open('store.pckl', 'wb') - # pickle.dump(obj, f) - #f.close() - #f = open('store.pckl', 'rb') - #obj = pickle.load(f) - #f.close() + if args.pickle_data: + f = open(self.filebase + '.pickle', 'wb') + pickle.dump(self,f) + f.close() + + self.terminate("Completed single-point calculation") ###################################################################### ###################################################################### @@ -329,8 +352,10 @@ def pretty_print(val,for_file=False,polar=False): ###################################################################### ###################################################################### def optimize(self): + args=self.args print("Running optimization...") - sys.exit(0) + vis = AdjointVisualizer() if args.visualize else None # cases=ALL_CASES + self.terminate("Finished optimization") ###################################################################### # compute the objective function, plus possibly its gradient (via @@ -339,7 +364,7 @@ def optimize(self): def eval_objective(self, beta_vector, need_gradient=False, vis=None): sim = self.create_sim(beta_vector) solver = AdjointSolver(self.obj_func, self.dft_cells, self.basis, sim, vis=vis) - self.sim=sim # save a copy for debugging; not strictly necessary + self.sim, self.solver=sim,solver # save copies for debugging; not strictly necessary return solver.solve(need_gradient=need_gradient) ################################################## diff --git a/python/adjoint/Visualization.py b/python/adjoint/Visualization.py index d3385889c..86631cbc3 100644 --- a/python/adjoint/Visualization.py +++ b/python/adjoint/Visualization.py @@ -22,8 +22,6 @@ import meep as mp -from .ObjectiveFunction import global_dft_cell_names - ######################################################## # the next few routines are some of my older general-purpose # utilities for working with DFT cells; for that purpose @@ -48,14 +46,14 @@ def dft_cell_type(cell): def dft_cell_name(nc): try: - name=global_dft_cell_names[nc] + name=meep.adjoint.DFTCell.get_cell_names()[nc] if name.endswith('_flux'): name=name[0:-5] if name.endswith('_fields'): name=name[0:-7] return name.replace('_','\_') except NameError: - return 'flux_' + str(nc) + return 'flux' + str(nc) def is_flux_cell(cell): return dft_cell_type(cell)=='flux' @@ -138,39 +136,41 @@ def get_eigenfields(sim, dft_cells, ncell, mode, nf=0, eigencache=None): # this routine configures some global matplotlib settings # (as distinct from the plot-specific settings handled # by the plot_options dicts). if you intend to set your -# own values of these parameters, pass set_rmecParams=False -# to visualize_sim. +# own values of these parameters, pass set_rcParams=False +# to e.g. visualize_sim and AdjointVisualizer ######################################################## def set_meep_rcParams(): plt.rc('xtick') plt.rc('ytick') - plt.rc('font', size=40) +# plt.rc('font', size=20) plt.rc('text', usetex=True) - matplotlib.rcParams['axes.labelsize']='large' - matplotlib.rcParams['axes.titlesize']='large' + matplotlib.rcParams['axes.labelsize']='medium' + matplotlib.rcParams['axes.titlesize']='medium' matplotlib.rcParams['axes.titlepad']=20 ######################################################## # general-purpose default option values, customized for # specific types of plots below, and everything settable -# via set_plot_option +# via set_plot_default ######################################################## -def_plot_options={ 'line_color' : [1.0,0.0,1.0], - 'line_width' : 4.0, - 'line_style' : '-', - 'boundary_width' : 2.0, - 'boundary_color' : [0.0,1.0,0.0], - 'boundary_style' : '--', - 'z_offset' : 0.0, - 'zmin' : 0.60, - 'zmax' : 1.00, - 'fill_color' : 'none', - 'alpha' : 1.0, - 'cmap' : matplotlib.cm.plasma, - 'fontsize' : 40, - 'colorbar_shrink': 0.60, - 'colorbar_pad' : 0.04, - 'num_contours' : 100 +def_plot_options={ 'line_color' : [1.0,0.0,1.0], + 'line_width' : 4.0, + 'line_style' : '-', + 'boundary_width' : 2.0, + 'boundary_color' : [0.0,1.0,0.0], + 'boundary_style' : '--', + 'zrel' : 0.0, + 'zrel_min' : 0.60, + 'zrel_max' : 1.00, + 'fill_color' : 'none', + 'alpha' : 1.0, + 'cmap' : matplotlib.cm.plasma, + 'fontsize' : 20, + 'colorbar_shrink' : 0.60, + 'colorbar_pad' : 0.04, + 'colorbar_cannibalize' : True, + 'num_contours' : 100, + 'plot_delay' : 0.1, } #-------------------------------------------------- @@ -183,24 +183,37 @@ def set_meep_rcParams(): 'num_contours':100 } +#-------------------------------------------------- +# options for source region visualization (default: cyan line, no label) +#-------------------------------------------------- def_src_options={ **def_plot_options, 'line_width':4.0, 'line_color':[0.0,1.0,1.0], - 'fontsize':0, 'zmin':0.0, 'zmax':0.0 + 'fontsize':0, 'zrel_min':0.0, 'zrel_max':0.0 } +#-------------------------------------------------- +# options for PML visualization (default: grey semitransparent blocks) +#-------------------------------------------------- def_pml_options={ **def_plot_options, 'boundary_color':'none', 'boundary_width':0.0, 'fill_color': 0.75*np.ones(3), 'alpha':0.25 } +#-------------------------------------------------- +# options for flux monitor visualization (default: magenta line with label) +#-------------------------------------------------- def_flux_options={ **def_plot_options, 'boundary_color':[0.0,0.0,0.0], 'boundary_width':2.0, 'boundary_style':'--', 'line_color': [1.0,0.0,1.0], 'line_width':4.0 } +#-------------------------------------------------- +# options for dft_field cell visualization (default: green dashed border, not filled) +#-------------------------------------------------- def_field_options={ **def_plot_options, - 'line_width': 0.0, 'alpha': 0.5, 'z_offset':0.5 + 'line_width': 0.0, 'alpha': 0.5, 'plot_method': 'contourf', + 'zrel_min':0.4, 'zrel_max':0.6 } def_dft_options={ **def_plot_options } @@ -211,10 +224,12 @@ def set_plot_default(option, value, type=None): else def_src_options if type=='src' \ else def_pml_optionss if type=='pml' \ else def_flux_options if type=='flux' \ - else def_fields_options if type=='fields' \ + else def_field_options if type=='fields' \ else def_plot_options which[option]=value +def plot_pause(): + plt.pause(def_eps_options['plot_delay']) ################################################### ################################################### @@ -264,7 +279,7 @@ def plot_eps(sim, eps_min=None, eps_max=None, options=None, plot3D=False, fig=No X, Y = np.meshgrid(x, y) zmin = 0.0 zmax = max(sim.cell_size.x, sim.cell_size.y) - Z0 = zmin + options['z_offset']*(zmax-zmin) + Z0 = zmin + options['zrel']*(zmax-zmin) img = ax.contourf(X, Y, eps, num_contours, zdir='z', offset=Z0, vmin=eps_min, vmax=eps_max, cmap=cmap, alpha=alpha) ax.set_zlim3d(zmin, zmax) @@ -283,7 +298,7 @@ def plot_eps(sim, eps_min=None, eps_max=None, options=None, plot3D=False, fig=No img = ax.contourf(X, Y, eps, num_contours, vmin=eps_min, vmax=eps_max, cmap=cmap, alpha=alpha) - ax.set_xlabel(r'$x$', fontsize=fontsize, labelpad=0.25*fontsize) + ax.set_xlabel(r'$x$', fontsize=fontsize, labelpad=0.50*fontsize) ax.set_ylabel(r'$y$', fontsize=fontsize, labelpad=fontsize, rotation=0) ax.tick_params(axis='both', labelsize=0.75*fontsize) cb=cb if cb else fig.colorbar(img) @@ -294,7 +309,8 @@ def plot_eps(sim, eps_min=None, eps_max=None, options=None, plot3D=False, fig=No ################################################## # plot_volume() adds a polygon representing a given -# mp.Volume to the current 2D or 3D plot. +# mp.Volume to the current 2D or 3D plot, with an +# optional text label. ################################################## def plot_volume(sim, vol=None, center=None, size=None, options=None, plot3D=False, label=None): @@ -310,7 +326,7 @@ def plot_volume(sim, vol=None, center=None, size=None, dx,dy=np.array([0.5*size.x,0.0]), np.array([0.0,0.5*size.y]) if plot3D: zmin,zmax = ax.get_zlim3d() - z0 = zmin + options['z_offset']*(zmax-zmin) + z0 = zmin + options['zrel']*(zmax-zmin) ################################################## # add polygon(s) to the plot to represent the volume @@ -346,7 +362,7 @@ def add_to_plot(c): if label: x0, y0, r, h, v = np.mean(ax.get_xlim()),np.mean(ax.get_ylim()), 0, 'center', 'center' if size.y==0.0: - v = 'top' if center.y>y0 else 'bottom' + v = 'bottom' if center.y>y0 else 'top' elif size.x==0.0: r, h = (270,'left') if center.x>x0 else (90,'right') if plot3D: @@ -378,8 +394,8 @@ def plot_data_curves(sim,center=None,size=None,superpose=True, options=options if options else def_flux_options lw=options['line_width'] lc=options['line_color'] - zeta_min=options['zmin'] - zeta_max=options['zmax'] + zrel_min=options['zrel_min'] + zrel_max=options['zrel_max'] draw_baseline=(options['boundary_width']>0.0) kwargs=dict() @@ -403,8 +419,8 @@ def plot_data_curves(sim,center=None,size=None,superpose=True, if superpose: ax=plt.gcf().gca(projection='3d') (zfloor,zceil)=ax.get_zlim() - zmin=zfloor + zeta_min*(zceil-zfloor) - zmax=zfloor + zeta_max*(zceil-zfloor) + zmin=zfloor + zrel_min*(zceil-zfloor) + zmax=zfloor + zrel_max*(zceil-zfloor) z0,dz=0.5*(zmax+zmin),(zmax-zmin) dmin=dmin if dmin else np.min(data) dmax=dmax if dmax else np.max(data) @@ -477,7 +493,7 @@ def visualize_dft_flux(sim, superpose=True, flux_cells=[], plt.subplot(len(flux_cells),1,n) plt.gca().set_title('Flux cell {}'.format(n)) cn,sz=mp.get_center_and_size(cell.where) - max_flux=np.amax(flux_arrays) + max_flux=np.amax([np.amax(fa) for fa in flux_arrays]) plot_data_curves(sim, center=cn, size=sz, data=[flux_arrays[n]], superpose=superpose, options=options, labels=['flux through cell {}'.format(n)], @@ -524,34 +540,59 @@ def field_func_array(fexpr,x,y,z,w,cEH,EH): # this routine intended to be called by # visualize_dft_fields, not directly by user ################################################## -def plot_dft_fields(sim, field_cells=[], options=None, nf=0): +def plot_dft_fields(sim, field_cells=[], field_funcs=None, ff_arrays=None, options=None, nf=0): options = options if options else def_field_options cmap = options['cmap'] + edgecolors = options['line_color'] + linewidth = options['line_width'] alpha = options['alpha'] - num_contours = options['num_contours'] fontsize = options['fontsize'] + plot_method = options['plot_method'] + num_contours = options['num_contours'] + shading = 'gouraud' if linewidth==0.0 else 'none' + interpolation = 'gaussian' if linewidth==0.0 else 'none' for ncell, cell in enumerate(field_cells): (x,y,z,w,cEH,EH)=unpack_dft_cell(sim,cell,nf=nf) X, Y = np.meshgrid(x, y) - plt.figure() - plt.suptitle('DFT cell {}'.format(ncell+1)) - ops=['Re', 'Im', 'Abs'] - rows,cols=len(cEH),len(ops) - for row, c in enumerate(cEH): - for col, op in enumerate(ops): - plt.subplot(rows, cols, row*cols + col + 1) + if ff_arrays is None: + plt.figure() + plt.suptitle('DFT cell {}'.format(ncell+1)) + + if field_funcs==None: + ops=['Re', 'Im', 'Abs'] + field_funcs=['{}({})'.format(op,mp.component_name(c)) for c in cEH for op in ops] + rows,cols=len(cEH),len(ops) + else: + rows,cols=1,len(field_funcs) + + def op(F,index): + return np.real(F) if op=='Re' else np.imag(F) if op=='Im' else np.abs(F) + + for row in range(rows): + for col in range(cols): + nplot = row*cols + col + data = ff_arrays[nplot] if ff_arrays else op(EH[row],ops[col]) + plt.subplot(rows, cols, nplot+1) ax=plt.gca() - ax.set_title('{}({})'.format(op,mp.component_name(c))) - ax.set_xlabel(r'$x$', fontsize=fontsize, labelpad=fontsize) + ax.set_title(field_funcs[nplot]) + ax.set_xlabel(r'$x$', fontsize=fontsize, labelpad=0.5*fontsize) ax.set_ylabel(r'$y$', fontsize=fontsize, labelpad=fontsize, rotation=0) ax.tick_params(axis='both', labelsize=0.75*fontsize) - data=np.real(EH[row]) if op=='Re' else np.imag(EH[row]) if op=='Im' else np.abs(EH[row]) - img = ax.contourf(X,Y,np.transpose(data),num_contours, cmap=cmap,alpha=alpha) - plt.colorbar(img) - #cb.set_label(r'$\epsilon$',fontsize=1.5*fontsize,rotation=0,labelpad=0.5*fontsize) - #cb.ax.tick_params(labelsize=0.75*fontsize) + ax.set_aspect('equal') + plt.tight_layout() + if plot_method=='imshow': + img = plt.imshow(np.transpose(data), extent=(min(x), max(x), min(y), max(y)), + cmap=cmap, interpolation=interpolation, alpha=alpha) + elif plot_method=='pcolormesh': + img = plt.pcolormesh(x,y,np.transpose(data), cmap=cmap, shading=shading, + edgecolors=edgecolors, linewidth=linewidth, alpha=alpha) + else: + img = ax.contourf(X,Y,np.transpose(data),num_contours, cmap=cmap,alpha=alpha) + cb=plt.colorbar(img,shrink=options['colorbar_shrink'], pad=options['colorbar_pad']) + cb.locator = ticker.MaxNLocator(nbins=5) + cb.update_ticks() plt.show(False) plt.draw() @@ -560,14 +601,17 @@ def plot_dft_fields(sim, field_cells=[], options=None, nf=0): ################################################## ################################################## ################################################## -def visualize_dft_fields(sim, superpose=True, field_cells=[], - field_funcs=None, z_offsets=None, options=None, nf=0): +def visualize_dft_fields(sim, superpose=True, field_cells=[], field_funcs=None, + ff_arrays=None, zrels=None, options=None, nf=0): if not mp.am_master(): return if len(field_cells)==0: field_cells=[cl for cl in sim.dft_objects if dft_cell_type(cl)=='fields'] + full_cells=[cell for cell in field_cells if cell.regions[0].size==sim.cell_size] + field_cells=full_cells if full_cells else field_cells + if len(field_cells)==0: return @@ -576,7 +620,7 @@ def visualize_dft_fields(sim, superpose=True, field_cells=[], superpose=False if not superpose: - return plot_dft_fields(sim, field_cells, options, nf=nf) + return plot_dft_fields(sim, field_cells, field_funcs, ff_arrays, options, nf=nf) # the remainder of this routine is for the superposition case @@ -587,36 +631,34 @@ def visualize_dft_fields(sim, superpose=True, field_cells=[], fontsize = options['fontsize'] if field_funcs is None: - field_funcs, z_offsets = ['abs2(E)'], [options['z_offset']] + field_funcs = ['abs2(E)'] + if zrels is None: + zrel_min, zrel_max, nz = options['zrel_min'], options['zrel_max'], len(field_funcs) + zrels=[0.5*(zrel_min+zrel_max)] if nz==1 else np.linspace(zrel_min,zrel_max,nz) for n, cell in enumerate(field_cells): - - # skip if cell is entirely contained in another field_cell - Contained=False - for m, parent in enumerate(field_cells): - if m!=n and parent.where.contains(cell.where): - Contained=True - if Contained: - continue - (x,y,z,w,cEH,EH)=unpack_dft_cell(sim,cell,nf=nf) X, Y = np.meshgrid(x, y) fig = plt.gcf() ax = fig.gca(projection='3d') (zmin,zmax)=ax.get_zlim() - for f,z in zip(field_funcs,z_offsets): - data=field_func_array(f,x,y,z,w,cEH,EH) - Z0=zmin + z*(zmax-zmin) - img = ax.contourf(X, Y, np.transpose(data), num_contours, - cmap=cmap, alpha=alpha, zdir='z', offset=Z0) + for n,(ff,zrel) in enumerate(zip(field_funcs,zrels)): + data = ff_arrays[n] if ff_arrays else field_func_array(ff,x,y,z,w,cEH,EH) + z0 = zmin + zrel*(zmax-zmin) + img = ax.contourf(X, Y, np.transpose(data), num_contours, + cmap=cmap, alpha=alpha, zdir='z', offset=z0) pad=options['colorbar_pad'] shrink=options['colorbar_shrink'] - cb=fig.colorbar(img, shrink=shrink, pad=pad, orientation='horizontal') - #cb.set_label(r'$|\mathbf{E}|^2$',fontsize=1.0*fontsize,rotation=0,labelpad=0.5*fontsize) - cb.set_label(f,fontsize=1.0*fontsize,rotation=0,labelpad=0.5*fontsize) + if options['colorbar_cannibalize']: + cax=fig.axes[-1] + cb=plt.colorbar(img, cax=cax) + else: + cb=plt.colorbar(img, shrink=shrink, pad=pad, panchor=(0.0,0.5)) + cb.set_label(ff,fontsize=1.0*fontsize,rotation=0,labelpad=0.5*fontsize) cb.ax.tick_params(labelsize=0.75*fontsize) cb.locator = ticker.MaxNLocator(nbins=5) cb.update_ticks() + cb.draw_all() plt.show(False) plt.draw() @@ -674,7 +716,7 @@ def visualize_sim(sim, fig=None, plot3D=None, label=( None if src_options['fontsize']==0 else 'src' + ( '\_'+str(ns) if len(sim.sources)>1 else '')) ) - if src_options['zmin']!=src_options['zmax']: + if src_options['zrel_min']!=src_options['zrel_max']: visualize_source_distribution(sim, standalone=not plot3D, options=src_options) ################################################### @@ -711,8 +753,10 @@ def visualize_sim(sim, fig=None, plot3D=None, if plot_dft_data is None: plot_dft_data=sources_finished - if plot_dft_data: + if plot_dft_data==True or plot_dft_data=='flux': visualize_dft_flux(sim, superpose=True, options=flux_options) + + if plot_dft_data==True: visualize_dft_fields(sim, superpose=True, options=field_options) plt.show(False) @@ -776,38 +820,44 @@ def message(msg): PFCRequest = namedtuple('PFCRequest', 't flist') ###################################################################### +# 'AnimateFieldEvolution' server class ############################### ###################################################################### -###################################################################### -class PFCServer(object): +class AFEServer(object): - def __init__(self, x, y, clist, cumulative=True, - poll_interval=None, options=None): + def __init__(self, x, y, components, field_options=None, poll_interval=None): self.X, self.Y = np.meshgrid(x, y) self.extent = (min(x), max(x), min(y), max(y)) - self.clist = clist - self.cumulative = cumulative + self.components = components + self.cumulative = True; # cumulative self.poll_interval = poll_interval if poll_interval else 500 - self.options = options if options else def_field_options + self.options = field_options if field_options else def_field_options self.num_contours = self.options['num_contours'] + self.alpha = self.options['alpha'] self.cmap = self.options['cmap'] ###################################################################### ###################################################################### ###################################################################### def __call__(self, pipe): - self.pipe = pipe - self.fig, self.axes = plt.subplots(1,len(self.clist)) - self.imgs, self.cbs=[],[] + self.pipe = pipe + self.fig, self.axes = plt.subplots(1,len(self.components)) + if len(self.components)==1: + self.axes=[self.axes] + self.imgs, self.cbs = [], [] + self.fix_clim=True + self.clim=[0.0,0.025] for n, ax in enumerate(self.axes): self.fig.sca(ax) - ax.set_title(mp.component_name(self.clist[n])) - img = ax.contourf(self.X,self.Y,np.zeros(np.shape(self.X)), - self.num_contours, cmap=self.cmap) -# img=plt.imshow(np.zeros(np.shape(np.transpose(self.X))), cmap=self.cmap, -# extent=self.extent) -# extent=self.extent) - cb=self.fig.colorbar(img) - self.imgs.append(img) +# ax.set_title(mp.component_name(self.components[n])) + img = plt.contourf(self.X,self.Y,np.zeros(np.shape(self.X)), + self.num_contours, cmap=self.cmap) + ax.set_xlabel(r'$x$') + ax.set_ylabel(r'$y$') + cb = plt.colorbar(img) # , #orientation='horizontal', + cb.set_clim(self.clim[0],self.clim[1]) + cb.set_ticks(np.linspace(self.clim[0],self.clim[1],3)) + cb.draw_all() + ax.set_aspect('equal') self.cbs.append(cb) timer=self.fig.canvas.new_timer(interval=self.poll_interval) @@ -824,36 +874,30 @@ def callback(): request = self.pipe.recv() if request is None: return False - self.fig.suptitle('t={:.8f}'.format(request.t)) +# self.fig.suptitle('t={:.8f}'.format(request.t)) for n,f in enumerate(request.flist): ax=self.axes[n] self.fig.sca(ax) plt.cla() - ax.set_title(mp.component_name(self.clist[n])) - vmin, vmax = np.amin(f), np.amax(f) - if self.cumulative: - lvmin,lvmax = self.cbs[n].get_clim() - vmin, vmax = min(vmin,lvmin), max(vmax,lvmax) -# self.imgs[n].set_data(np.transpose(f)) -# self.imgs[n].set_clim(vmin,vmax) +# ax.set_title(mp.component_name(self.components[n]) + ' @ t={:.2f} ) + ax.set_title(r'$|E|^2, t={:.2f}$'.format(request.t)) + ax.set_xlabel(r'$x$') + ax.set_ylabel(r'$y$') +#mp.component_name(self.components[n]) + ' @ t={:.2f} ) +# cb=self.cbs[n] +# clim = cb.get_clim() + f=f*f + if not self.fix_clim: + self.clim[0] = min(self.clim[0],np.amin(f)) + self.clim[1] = max(self.clim[1],np.amax(f)) img = ax.contourf(self.X,self.Y,np.transpose(f), self.num_contours, cmap=self.cmap, - vmin=vmin,vmax=vmax) - #img.set_clim(vmin,vmax) + vmin=self.clim[0],vmax=self.clim[1]) + ax.set_aspect('equal') self.cbs[n]=self.fig.colorbar(img, cax=self.cbs[n].ax) - self.cbs[n].set_clim(vmin,vmax) + self.cbs[n].set_clim(self.clim[0],self.clim[1]) + self.cbs[n].set_ticks(np.linspace(self.clim[0],self.clim[1],3)) self.cbs[n].draw_all() - # self.cbs[n].update_bruteforce(img) - #self.cbs[n].remove() - #self.cbs[n]=self.fig.colorbar(img) - #self.cbs[n].draw_all() - #self.cbs[n].update_bruteforce(img) - #self.cbs[n]. - #self.cbs[n].set_clim(vmin=vmin,vmax=vmax) - #self.cbs[n].update - #self.cbs[n].draw_all() - #self.cbs[n].remove() - #self.cbs[n]=self.fig.colorbar(img) self.fig.canvas.draw() return True @@ -862,111 +906,163 @@ def callback(): ################################################## ################################################## ################################################## -def str_to_component(s): - for c in EHxyz: - if mp.component_name(c)==s.lower(): - return c - raise ValueError("unknown field component " + s) +def to_component(c): + if c in EHxyz: + return c + try: + EHxyz_names=['ex','ey','ez','hx','hy','hz'] + return EHxyz[EHxyz_names.index(c.lower())] + except: + return ValueError("unknown field component " + c) ###################################################################### +# AFEClient (where AFE stands for 'Animate Field Evolution') is a +# class whose constructor launches an AFEServer process, +# the __call__ method of AFEClient becomes a MEEP step function, +# each time it is hod of AFEClient becomes a MEEP step function; ###################################################################### -###################################################################### -def plot_field_components(sim, components, vol=None, size=None, center=origin, - interval=1.0, options=None): +class AFEClient(object): + + ################################################## + # the class constructor launches an AFEServer, + # which initiates a plot and then stands by + # awaiting updated field data + ################################################## + def __init__(self, sim, clist, interval=1.0, + vol=None, size=None, center=origin, + field_options=None): + + self.components=[to_component(c) for c in clist] + self.vol=vol if vol else mp.Volume(center=center, + size=(size if size else sim.cell_size) ) + (x,y,z,w)=sim.get_array_metadata(vol=self.vol) + self.interval=interval + self.next_plot_time=sim.round_time() + interval + + server=AFEServer(x,y,self.components,field_options=field_options) + self.pipe_to_server, pipe_from_client = Pipe() + Process(target=server,daemon=True, args=(pipe_from_client,)).start() + + # hack, explain and delete me + self.__code__ = namedtuple('gna_hack',['co_argcount']) + self.__code__.co_argcount=2 - clist=[str_to_component(c) if isinstance(c,str) else c for c in components] ################################################## - # initialization: launch server process + # the __call__ method has the appropriate prototype + # to allow an instance of AFECLient to serve as a + # meep step function; on each invocation it + # fetches arrays of the current instantaneous values + # of the time-domain MEEP fields and sends these to + # the server for visualization ################################################## - closure = { 'next_plot_time': interval } - if vol is None: - vol=mp.Volume(center=center, size=(size if size else sim.cell_size) ) - (x,y,z,w)=sim.get_array_metadata(vol=vol) - - pipe_to_server, pipe_from_client = Pipe() - server=PFCServer(x,y,clist,options=options) - server_process = Process(target=server, args=(pipe_from_client,), daemon=True) - server_process.start() - - def _step_func(sim, todo): - if todo=='step' and sim.round_time() Date: Fri, 22 Mar 2019 16:04:46 -0400 Subject: [PATCH 12/16] updates --- python/adjoint/OptimizationProblem.py | 56 ++++++++++--------- python/adjoint/ParallelDesignTester.py | 44 +++++++++++++++ .../adjoint_optimization/HoleyWaveguide.py | 2 +- 3 files changed, 75 insertions(+), 27 deletions(-) create mode 100644 python/adjoint/ParallelDesignTester.py diff --git a/python/adjoint/OptimizationProblem.py b/python/adjoint/OptimizationProblem.py index 8fc5cc4f4..5b17ee307 100644 --- a/python/adjoint/OptimizationProblem.py +++ b/python/adjoint/OptimizationProblem.py @@ -39,12 +39,10 @@ class OptimizationProblem(ABC): def init_problem(self, args): raise NotImplementedError("derived class must implement init_problem() method") - @abstractmethod def create_sim(self, betavector, vacuum=False): raise NotImplementedError("derived class must implement create_sim() method") - ###################################################################### # virtual methods that *may* optionally be overridden by child ###################################################################### @@ -54,12 +52,13 @@ def add_args(self, args): ###################################################################### ###################################################################### ###################################################################### - def __init__(self): + def __init__(self, cmdline=None): # define and parse command-line arguments parser = self.init_args() # general args self.add_args(parser) # problem-specific arguments - self.args = args = parser.parse_args() + argv=sys.argv[1:] if cmdline is None else cmdline.split(' ') + self.args = args = parser.parse_args(argv) # call subclass for problem-specific initialization first... fstr, objective_regions, extra_regions, design_region, self.basis \ @@ -218,6 +217,28 @@ def plot_geometry(self): self.sim,self.vis = sim,vis # save copies for debugging; not strictly necessary self.terminate("Finished visualization") + ###################################################################### + # compute the objective function, plus possibly its gradient (via + # adjoints), at a single point in design space + ###################################################################### + def eval_objective(self, beta_vector, need_gradient=False, vis=None): + sim = self.create_sim(beta_vector) + solver = AdjointSolver(self.obj_func, self.dft_cells, self.basis, sim, vis=vis) + self.sim, self.solver = sim, solver # save copies for debugging; not strictly necessary + retval=solver.solve(need_gradient=need_gradient) + if need_gradient and self.args.pickle_data: + with open(self.filebase + '.pickle','wb') as f: + pickle.dump(self.solver.dfdEps,f) + return retval + + ################################################## + ################################################## + ################################################## + def eval_fq(self, beta_vector, need_gradient=False, vis=None): + f,gradf = self.eval_objective(beta_vector, need_gradient=need_gradient, vis=vis) + fq = np.array( [f] + list(self.obj_func.qvals) ) + return fq, gradf + ###################################################################### # the 'run' class method of OptimizationProblem, which is where control # passes after __init__ if we were executed as a script, looks at @@ -283,10 +304,11 @@ def run(self): self.output([],[],actions=['end']) - if args.pickle_data: - f = open(self.filebase + '.pickle', 'wb') - pickle.dump(self,f) - f.close() +# if args.pickle_data: +# f = open(self.filebase + '.pickle', 'wb') + #pickle.dump(self,f) +# pickle.dump(self.dfdEps,f) +# f.close() self.terminate("Completed single-point calculation") @@ -356,21 +378,3 @@ def optimize(self): print("Running optimization...") vis = AdjointVisualizer() if args.visualize else None # cases=ALL_CASES self.terminate("Finished optimization") - - ###################################################################### - # compute the objective function, plus possibly its gradient (via - # adjoints), at a single point in design space - ###################################################################### - def eval_objective(self, beta_vector, need_gradient=False, vis=None): - sim = self.create_sim(beta_vector) - solver = AdjointSolver(self.obj_func, self.dft_cells, self.basis, sim, vis=vis) - self.sim, self.solver=sim,solver # save copies for debugging; not strictly necessary - return solver.solve(need_gradient=need_gradient) - - ################################################## - ################################################## - ################################################## - def eval_fq(self, beta_vector, need_gradient=False, vis=None): - f,gradf = self.eval_objective(beta_vector, need_gradient=need_gradient, vis=vis) - fq = np.array( [f] + list(self.obj_func.qvals) ) - return fq, gradf diff --git a/python/adjoint/ParallelDesignTester.py b/python/adjoint/ParallelDesignTester.py new file mode 100644 index 000000000..e44361860 --- /dev/null +++ b/python/adjoint/ParallelDesignTester.py @@ -0,0 +1,44 @@ +import os +from os import environ as env +import argparse +import multiprocessing +from multiprocessing import cpu_count as ncpus +from datetime import datetime as dt +from importlib import import_module as imp_mod + +###################################################################### +###################################################################### +###################################################################### +class ParallelDesignTester(object): + + def __init__(self, name, cmdlines): + self.name, self.cmdlines = name, cmdlines + + def __call__(self, n): + getattr(imp_mod(self.name),self.name)(self.cmdlines[n]).run() + + def launch(self, nproc): + + # create and cd to working directory, then launch servers and run jobs + wdir = '{}_{}'.format(self.name,dt.now().strftime("%m%d.%H%M%S")) + os.mkdir(wdir) + os.chdir(wdir) + multiprocessing.Pool(nproc).map(self,range(len(self.cmdlines))) + +###################################################################### +###################################################################### +###################################################################### +if __name__ == '__main__': + parser, nproc = argparse.ArgumentParser(), multiprocessing.cpu_count()//2 + parser.add_argument('--name', type=str, default=None, help='name of OptimizationProblem subclass') + parser.add_argument('--casefile', type=str, default=None, help='list of command-line strings') + parser.add_argument('--nproc', type=int, default=nproc, help='number of server processes to launch') + args=parser.parse_args() + + if args.name is None or not importlib.util.find_spec(args.name): + raise ValueError("missing or invalid class/module --name " + args.name if args.name else '') + if args.casefile is None or not os.path.isfile(args.casefile): + raise ValueError("missing or invalid list of command-line strings --casefile " + args.casefile if args.casefile else '') + with open(args.casefile) as f: + cmdlines=[l for l in [ln.strip(' \t\n') for ln in f.readlines()] if l and l[0]] + ParallelDesignTester(args.name,cmdlines).launch(args.nproc) diff --git a/python/examples/adjoint_optimization/HoleyWaveguide.py b/python/examples/adjoint_optimization/HoleyWaveguide.py index c80e4a9c7..d3cb35c11 100644 --- a/python/examples/adjoint_optimization/HoleyWaveguide.py +++ b/python/examples/adjoint_optimization/HoleyWaveguide.py @@ -86,7 +86,7 @@ def init_problem(self, args): #---------------------------------------- #- objective function #---------------------------------------- - fstr='P1_east+0.0*(P2_east+P1_west+P2_west+M1_east+M2_east+M1_west+M2_west+S_east+S_west)' + fstr='Abs(P1_east)**2+0.0*(P2_east+P1_west+P2_west+M1_east+M2_east+M1_west+M2_west+S_east+S_west)' #---------------------------------------- #- internal storage for variables needed later From e109bb65ee52fac9aff560bc496c1773e8491ae6 Mon Sep 17 00:00:00 2001 From: Homer Reid Date: Fri, 22 Mar 2019 17:45:54 -0400 Subject: [PATCH 13/16] updates --- python/adjoint/Basis.py | 6 +- python/adjoint/ObjectiveFunction.py | 2 - python/adjoint/OptimizationProblem.py | 3 +- python/adjoint/Visualization.py | 86 +++++++++++++++++++-------- 4 files changed, 68 insertions(+), 29 deletions(-) diff --git a/python/adjoint/Basis.py b/python/adjoint/Basis.py index 047e3cdd6..c1fb371d7 100644 --- a/python/adjoint/Basis.py +++ b/python/adjoint/Basis.py @@ -90,7 +90,7 @@ def names(self): return ['b{}'.format(d) for d in range(self.dim)] @property - def texnames(self): + def tex_names(self): return [r'$b_{}$'.format(d) for d in range(self.dim)] #########################################################j @@ -269,10 +269,14 @@ def __init__(self, N=4, lx=None, ly=None, radius=None, self.bfs.append(bf) def __call__(self, p=[0.0,0.0]): + if self.fs.mesh().bounding_box_tree().compute_collisions(fenics.Point(p[0],p[1])) == []: + return 0.0 return np.array( [bf(p[0],p[1]) for bf in self.bfs] ) def set_coefficients(self, beta_vector): self.f.vector().set_local(beta_vector) def eval_expansion(self, p=[0.0,0.0]): + if self.fs.mesh().bounding_box_tree().compute_collisions(fenics.Point(p[0],p[1])) == []: + return 0.0 return 1.0 + self.f(p[0],p[1]) diff --git a/python/adjoint/ObjectiveFunction.py b/python/adjoint/ObjectiveFunction.py index 4f7b87e8b..ef98c983a 100644 --- a/python/adjoint/ObjectiveFunction.py +++ b/python/adjoint/ObjectiveFunction.py @@ -13,8 +13,6 @@ import meep as mp import meep.adjoint -#from Visualization import (AFEClient, def_field_options) - ###################################################################### # various global options affecting the adjoint solver, user-tweakable # via command-line arguments or set_adjoint_option() diff --git a/python/adjoint/OptimizationProblem.py b/python/adjoint/OptimizationProblem.py index 8fc5cc4f4..7f1af7087 100644 --- a/python/adjoint/OptimizationProblem.py +++ b/python/adjoint/OptimizationProblem.py @@ -285,7 +285,8 @@ def run(self): if args.pickle_data: f = open(self.filebase + '.pickle', 'wb') - pickle.dump(self,f) + #pickle.dump(self,f) + pickle.dump(self.solver.dfdEps,f) f.close() self.terminate("Completed single-point calculation") diff --git a/python/adjoint/Visualization.py b/python/adjoint/Visualization.py index 86631cbc3..3f1e28516 100644 --- a/python/adjoint/Visualization.py +++ b/python/adjoint/Visualization.py @@ -4,24 +4,27 @@ # simple standardized ways ################################################### import warnings -import numpy as np -import sympy -from collections import namedtuple import time import datetime +from collections import namedtuple +import numpy as np +import sympy +import re from multiprocessing import Process, Pipe -from matplotlib import ticker import matplotlib matplotlib.use('qt5agg') import matplotlib.pyplot as plt +from matplotlib import ticker from mpl_toolkits.mplot3d import axes3d - +from mpl_toolkits.axes_grid1 import make_axes_locatable from matplotlib.collections import PolyCollection, LineCollection from mpl_toolkits.mplot3d.art3d import Poly3DCollection import meep as mp +from meep.adjoint import ObjectiveFunction + ######################################################## # the next few routines are some of my older general-purpose # utilities for working with DFT cells; for that purpose @@ -45,15 +48,13 @@ def dft_cell_type(cell): return 'flux' if isinstance(cell, mp.simulation.DftFlux) else 'fields' def dft_cell_name(nc): - try: - name=meep.adjoint.DFTCell.get_cell_names()[nc] - if name.endswith('_flux'): - name=name[0:-5] - if name.endswith('_fields'): - name=name[0:-7] - return name.replace('_','\_') - except NameError: - return 'flux' + str(nc) + name=ObjectiveFunction.DFTCell.get_cell_names()[nc] + if name.endswith('_flux'): + name=name[0:-5] + if name.endswith('_fields'): + name=name[0:-7] + return name.replace('_','\_') + def is_flux_cell(cell): return dft_cell_type(cell)=='flux' @@ -146,7 +147,7 @@ def set_meep_rcParams(): plt.rc('text', usetex=True) matplotlib.rcParams['axes.labelsize']='medium' matplotlib.rcParams['axes.titlesize']='medium' - matplotlib.rcParams['axes.titlepad']=20 + #matplotlib.rcParams['axes.titlepad']=20 ######################################################## # general-purpose default option values, customized for @@ -165,7 +166,7 @@ def set_meep_rcParams(): 'fill_color' : 'none', 'alpha' : 1.0, 'cmap' : matplotlib.cm.plasma, - 'fontsize' : 20, + 'fontsize' : 25, 'colorbar_shrink' : 0.60, 'colorbar_pad' : 0.04, 'colorbar_cannibalize' : True, @@ -212,7 +213,8 @@ def set_meep_rcParams(): # options for dft_field cell visualization (default: green dashed border, not filled) #-------------------------------------------------- def_field_options={ **def_plot_options, - 'line_width': 0.0, 'alpha': 0.5, 'plot_method': 'contourf', + 'line_width': 0.0, 'alpha': 0.5, + 'plot_method': 'contourf', 'zrel_min':0.4, 'zrel_max':0.6 } @@ -240,6 +242,15 @@ def get_text_size(fig, label, fontsize): bb = t.get_window_extent(renderer=r) return bb.width, bb.height +################################################### +# routine to produce proper colorbars even with subplots +# gleeped from https://joseph-long.com/writing/colorbars/ +################################################### +def happy_cb(img, axes): + divider = make_axes_locatable(axes) + cax = divider.append_axes("right", size="5%", pad=0.05) + return axes.figure.colorbar(img, cax=cax) + ################################################### # visualize epsilon distribution. eps_min, eps_max # are optional upper and lower clipping bounds. @@ -302,7 +313,8 @@ def plot_eps(sim, eps_min=None, eps_max=None, options=None, plot3D=False, fig=No ax.set_ylabel(r'$y$', fontsize=fontsize, labelpad=fontsize, rotation=0) ax.tick_params(axis='both', labelsize=0.75*fontsize) cb=cb if cb else fig.colorbar(img) - cb.set_label(r'$\epsilon$',fontsize=1.5*fontsize,rotation=0,labelpad=0.5*fontsize) + # cb.set_label(r'$\epsilon$',fontsize=1.5*fontsize,rotation=0,labelpad=0.5*fontsize) + cb.ax.set_xlabel(r'$\epsilon$',fontsize=1.5*fontsize,rotation=0,labelpad=0.5*fontsize) cb.ax.tick_params(labelsize=0.75*fontsize) cb.locator = ticker.MaxNLocator(nbins=5) cb.update_ticks() @@ -536,11 +548,27 @@ def field_func_array(fexpr,x,y,z,w,cEH,EH): if True: # fexpr=='abs2(E)': return abs2(EH[0]) + abs2(EH[1]) + abs2(EH[2]) +################################################## +################################################## +################################################## +def texify(expr): + expr=re.sub(r'([eEhH])([xyz])',r'\1_\2',expr) + expr=re.sub(r'e_','E_',expr) + expr=re.sub(r'H_','H_',expr) + expr=re.sub(r'abs\((.*)\)',r'|\1|',expr) + expr=re.sub(r'abs2\((.*)\)',r'|\1|^2',expr) + + loglike=['Re','Im'] + for s in loglike: + expr=re.sub(s,'\textrm{'+s+'}',expr) + return r'$'+expr+'$' + ################################################## # this routine intended to be called by # visualize_dft_fields, not directly by user ################################################## -def plot_dft_fields(sim, field_cells=[], field_funcs=None, ff_arrays=None, options=None, nf=0): +def plot_dft_fields(sim, field_cells=[], field_funcs=None, + ff_arrays=None, options=None, nf=0): options = options if options else def_field_options cmap = options['cmap'] @@ -561,8 +589,8 @@ def plot_dft_fields(sim, field_cells=[], field_funcs=None, ff_arrays=None, optio plt.suptitle('DFT cell {}'.format(ncell+1)) if field_funcs==None: - ops=['Re', 'Im', 'Abs'] - field_funcs=['{}({})'.format(op,mp.component_name(c)) for c in cEH for op in ops] + ops=['Re', 'Im', 'abs'] + field_funcs=[texify(op+'('+component_name(c)+')') for c in cEH for op in ops] rows,cols=len(cEH),len(ops) else: rows,cols=1,len(field_funcs) @@ -590,10 +618,13 @@ def op(F,index): edgecolors=edgecolors, linewidth=linewidth, alpha=alpha) else: img = ax.contourf(X,Y,np.transpose(data),num_contours, cmap=cmap,alpha=alpha) - cb=plt.colorbar(img,shrink=options['colorbar_shrink'], pad=options['colorbar_pad']) + #cb=plt.colorbar(img,shrink=options['colorbar_shrink'], pad=options['colorbar_pad']) + cb=happy_cb(img,ax) + #cb.ax.set_xlabel(ff,fontsize=1.5*fontsize,rotation=0,labelpad=0.5*fontsize) cb.locator = ticker.MaxNLocator(nbins=5) cb.update_ticks() + plt.tight_layout() plt.show(False) plt.draw() return 0 @@ -654,7 +685,8 @@ def visualize_dft_fields(sim, superpose=True, field_cells=[], field_funcs=None, cb=plt.colorbar(img, cax=cax) else: cb=plt.colorbar(img, shrink=shrink, pad=pad, panchor=(0.0,0.5)) - cb.set_label(ff,fontsize=1.0*fontsize,rotation=0,labelpad=0.5*fontsize) + #cb.set_label(ff,fontsize=1.0*fontsize,rotation=0,labelpad=0.5*fontsize) + cb.ax.set_xlabel(texify(ff),fontsize=1.5*fontsize,rotation=0,labelpad=0.5*fontsize) cb.ax.tick_params(labelsize=0.75*fontsize) cb.locator = ticker.MaxNLocator(nbins=5) cb.update_ticks() @@ -1056,13 +1088,17 @@ def update(self, sim, case, dfdEps=None): title=case if case=='Adjoint': + ffs=[r'Re$\left(\frac{\partial f}{\partial\epsilon}\right)$', + r'Im$\left(\frac{\partial f}{\partial\epsilon}\right)$', + r'$\left|\frac{\partial f}{\partial\epsilon}\right|$'] + plt.suptitle(title) visualize_dft_fields(sim,superpose=False,field_cells=[sim.dft_objects[-1]], - field_funcs=['Re(dfdEps)','Im(dfdEps)','Abs(dfdEps)'], + field_funcs=ffs, ff_arrays=[np.real(dfdEps),np.imag(dfdEps),np.abs(dfdEps)]) else: visualize_sim(sim,plot3D=plot3D,fig=fig,eps_options=self.eps_options,src_options=self.src_options, plot_dft_data=False if case=='Geometry' else True if case =='Forward' else 'flux') + plt.gcf().gca().set_title(title) - plt.gcf().gca().set_title(title) plt.draw() plot_pause() From 7cffdf227f5b0acd9d94b5f0755a4e9ab90b03c1 Mon Sep 17 00:00:00 2001 From: Homer Reid Date: Fri, 22 Mar 2019 22:05:54 -0400 Subject: [PATCH 14/16] updatesS --- python/Makefile.am | 1 + python/adjoint/ParallelDesignTester.py | 36 ++++++++ python/adjoint/__init__.py | 109 ++++++++----------------- 3 files changed, 72 insertions(+), 74 deletions(-) diff --git a/python/Makefile.am b/python/Makefile.am index 5435f06f6..6710a4b2d 100644 --- a/python/Makefile.am +++ b/python/Makefile.am @@ -192,6 +192,7 @@ adjoint_PYTHON = $(srcdir)/adjoint/__init__.py \ $(srcdir)/adjoint/Basis.py \ $(srcdir)/adjoint/ObjectiveFunction.py \ $(srcdir)/adjoint/OptimizationProblem.py \ + $(srcdir)/adjoint/ParallelDesignTester.py \ $(srcdir)/adjoint/Visualization.py ###################################################################### diff --git a/python/adjoint/ParallelDesignTester.py b/python/adjoint/ParallelDesignTester.py index e44361860..277698cbb 100644 --- a/python/adjoint/ParallelDesignTester.py +++ b/python/adjoint/ParallelDesignTester.py @@ -1,3 +1,39 @@ +###################################################################### +# ParallelDesignTester is a simple facility for running large numbers +# of single-design-point calculations on a meep.adjoint optimization +# problem, using a multi-process server pool to allow multiple jobs +# to be run simultaneously. +# +# ** Usage as a command-line script: +# +# % python ParallelDesignTester.py [ --nproc XX ] --name MyProb.py --casefile CaseFile +# +# where: +# +# -- MyProb.py is a python script describing a meep.adjoint +# optimization problem, which implements a class MyProb +# that inherits from meep.adjoint.OptimizationProblem +# +# -- CaseFile is a text file in which each line specifies +# a separate set of command-line arguments for MyProb.py, +# describing an objective-function evaluation at a single +# point in design space +# +# -- The optional --nproc argument specifies the number of +# server processes created, i.e. the number of simultaneous +# jobs that are run. The default value is half the number +# of CPU cores available on the machine. +# +# ** Usage from other scripts or a console/notebook interface: +# +# from meep.adjoint import ParallelDesignTester +# +# ParallelDesignTester('MyProb',command_lines).launch(nproc=nproc) +# +# (where command_lines=['command_line_1','command_line_2',...]) +# +# +###################################################################### import os from os import environ as env import argparse diff --git a/python/adjoint/__init__.py b/python/adjoint/__init__.py index e91c1516b..348e5686b 100644 --- a/python/adjoint/__init__.py +++ b/python/adjoint/__init__.py @@ -1,77 +1,36 @@ -""" Adjoint-based sensitivity-analysis submodule for the MEEP python module. - -Docmentation: -http://https://meep.readthedocs.io/en/latest/Python_Tutorials/AdjointSolver.md - -The code is structured as follows: - - __init__.py: formal definitions - - OptimizationProblem.py: abstract base class from which user-supplied - classes describing specific optimization - geometries should inherit; implements a high-level - notion of a differentiable objective function - depending on one or more input variables, which we - call "objective quantities." - - ObjectiveFunction.py: lower-level routines for carrying out MEEP timestepping - calculations to compute objective quantities and their - adjoint derivatives. - - Basis.py: general support for spatially-varying permittivity - functions described by expansions in user-defined sets - of basis functions, plus implementations of simple basis sets - for some common cases - - Visualization.py: routines for visualizing MEEP input geometries - and computational results. - -Minimal example: - -import meep as mp -import mp.adjoint as adj - -class MyOptProblem(adj.OptimizationProblem): - - ################################################## - # define problem-specific command-line options and - # problem-specific default values for general - # command-line optionsj - ################################################## - def add_args(self, parser): - parser.add_argument('--radius', type=float, default=1.0, help='radius') - parser.add_argument('--depth', type=float, default=0.5, help='depth') - - parser.set_defaults(fcen=0.5) - parser.set_defaults(df=0.1) - - - ################################################## - # routine called just once, before any calculations - # or optimization, to define aspects of the simulation - # geometry that remain constant independent of the - # values of design variables. - ################################################## - def initialize(self,args): - ... - ... - ... - return f_expr, objective_regions, design_regions, extra_regions, basis - - ################################################## - # routine called many times over the course of an - # iterative simulation process to instantiate a - # MEEP simulation for a given set of values of - # the design variables - ################################################## - def create_sim(self,beta_vector,vacuum=False): - ... - ... - ... - return sim - -""" - +# Adjoint-based sensitivity-analysis submodule for the MEEP python module. +# +#Documentation: +#http://https://meep.readthedocs.io/en/latest/Python_Tutorials/AdjointSolver.md +# +#The code is structured as follows: +# +# __init__.py: formal definitions +# +# OptimizationProblem.py: abstract base class from which user-supplied +# classes describing specific optimization +# geometries should inherit; implements a high-level +# notion of a differentiable objective function +# depending on one or more input variables, which we +# call "objective quantities." +# +# ObjectiveFunction.py: lower-level routines for carrying out MEEP timestepping +# calculations to compute objective quantities and their +# adjoint derivatives. +# +# ParallelDesignTester.py: simple module to spawn a multiprocessor server +# pool to run large numbers of objective-function +# calculations in parallel +# +# Basis.py: general support for spatially-varying permittivity +# functions described by expansions in user-defined sets +# of basis functions, plus implementations of simple basis sets +# for some common cases +# +# Visualization.py: routines for visualizing MEEP input geometries +# and computational results. +# +# #__all__ = [ 'OptimizationProblem', 'DFTCell', 'adjoint_options', 'update_plot', # 'EHTransverse', 'Exyz', 'Hxyz', 'EHxyz', # 'xHat', 'yHat', 'zHat', 'origin', 'FluxLine', @@ -84,6 +43,8 @@ def create_sim(self,beta_vector,vacuum=False): abs2, unit_vector, rel_diff, FluxLine, DFTCell, ObjectiveFunction, AdjointSolver) +from .ParallelDesignTester import ParallelDesignTester + from .Basis import (ParameterizedDielectric, PlaneWaveBasis, FourierLegendreBasis, FiniteElementBasis) From 6e2c3ce42108509657f6eaf8cdd16b89b6c2b702 Mon Sep 17 00:00:00 2001 From: Homer Reid Date: Fri, 29 Mar 2019 18:26:29 -0400 Subject: [PATCH 15/16] updates --- .../Python_Tutorials/AdjointQuickStart.md | 292 ++++++++++++++++ doc/docs/images/Ez2WithHoleMovie.h264 | Bin 0 -> 2935456 bytes doc/docs/images/Ez2WithoutHoleMovie.h264 | Bin 0 -> 1359420 bytes mkdocs.yml | 1 + python/Makefile.am | 2 +- python/adjoint/Basis.py | 330 +++++++++++++----- .../{ObjectiveFunction.py => Objective.py} | 99 +++--- python/adjoint/OptimizationProblem.py | 319 +++++++++++------ python/adjoint/ParallelDesignTester.py | 7 +- python/adjoint/Visualization.py | 115 +++--- python/adjoint/__init__.py | 11 +- .../AsymmetricSplitter.py | 172 +++++++++ .../adjoint_optimization/CrossRouter.py | 170 +++++++++ .../adjoint_optimization/HoleyWaveguide.py | 4 +- src/loop_in_chunks.cpp | 3 +- 15 files changed, 1216 insertions(+), 309 deletions(-) create mode 100644 doc/docs/Python_Tutorials/AdjointQuickStart.md create mode 100644 doc/docs/images/Ez2WithHoleMovie.h264 create mode 100644 doc/docs/images/Ez2WithoutHoleMovie.h264 rename python/adjoint/{ObjectiveFunction.py => Objective.py} (92%) create mode 100644 python/examples/adjoint_optimization/AsymmetricSplitter.py create mode 100644 python/examples/adjoint_optimization/CrossRouter.py diff --git a/doc/docs/Python_Tutorials/AdjointQuickStart.md b/doc/docs/Python_Tutorials/AdjointQuickStart.md new file mode 100644 index 000000000..cf68a3b97 --- /dev/null +++ b/doc/docs/Python_Tutorials/AdjointQuickStart.md @@ -0,0 +1,292 @@ +# MEEP adjoint module quickstart + +## `tl;dr`: I already know all about adjoint optimizers, just show me an example. + +This is the `CrossRouter.py` example included in the +`python/examples/adjoint_optimization` subdirectory of your MEEP installation: + +[Full automated optimization of a cross-router device](https://homerreid.github.io/meep-adjoint-documentation/AdjointSolver/ExampleGallery/#full-automated-optimization-of-a-cross-router-device) + +## What does this module do? + +At the lowest level, it implements an adjoint method for computing +the derivatives of an objective function with respect to the permittivity +at each spatial point in a subregion. This amounts to just a MEEP timestepping +calculation with a special type of source distribution and a certain +type of postprocessing applied to the results; it is implemented entirely +in high-level python code and doesn't require tweaks to the `libmeep` +core library. + +At a higher level, the module implements functionality for wrapping +a numerical optimizer around the gradient computation to allow +users to execute automated design automation with a minimum of +effort. + +## How do I use it? + +1. You write a python script implementing a subclass of + the `OptimizationProblem` virtual base class defined by `meep.adjoint.` + Your subclass must provide overrides for the virtual + class methods `init_problem` and `create_sim`. + +2. Then you execute your python scripts with command-line options + specifying various calculations to perform, which range + in complexity from **(a)** evaluating an objective function and its + gradient for a single design (a *single-point calculation*) + to **(b)** full iterative optimization in which the design is + repeatedly evaluated and tweaked automatically based on the + gradient computation. + +## What is this `init_problem` method that my subclass must override? + +It inputs an `args` structure containing the parsed values of +command-line options, performs any necessary internal initialization, +and returns a 5-tuple +```py3 + fstr, objective_regions, design_region, extra_regions, basis +``` +describing your optimization problem, where + ++ `fstr` is a string specifying your objective function ++ `objective_regions` is a list of regions over which to compute + frequency-domain (DFT) fields needed to evaluate the quantities + on which your objective function depends ++ `extra_regions` is a list of additional regions over which to compute + DFT fields for post-processing or visualization; it will often be + just the empty list ++ `design_region` is a region encompassing the variable-permittivity + region of your geometry ++ `basis` is a specification of the set of basis functions used to + expand the permittivity. This is a subclass of the `Basis` base class + defined by `meep.adjoint`; you may implement your own arbitrary + basis, or use one of several predefined bases provided by `meep.adjoint.` + +## How can I add my own problem-specific command-line options, or specify problem-specific values for [built-in options?](https://homerreid.github.io/meep-adjoint-documentation/AdjointSolver/ReferenceManual#4-built-in-command-line-options) + +By overriding the `add_args` method of `OptimizationProblem.` See the examples +in the `python/examples/adjoint_optimization` subdirectory of your MEEP installation. + +## Show me some examples of `fstr` strings defining objective functions. + ++ Maximize power flux through the first DFT flux region in your `objective_regions` list: + +```py3 + fstr = 'S_0' +``` + ++ Minimize the difference between the power fluxes through the DFT flux regions labeled 'north' and 'south': + +```py3 + fstr = '-(S_north - S_south)^2' +``` + ++ Maximize the squared magnitude of the eigenmode coefficient for the forward-traveling component + of eigenmode 3 at the 'east' flux region: + +```py3 + fstr = 'Abs2(P3_east)^2' +``` + +## What do I return as the `basis` field in the 5-tuple returned by `init_problem`? + +For most purposes, the simplest answer is to use the build-in `FiniteElementBasis` +class, which describes a localized basis of functions over a rectangular +domain with a variable resolution, i.e. + +```py3 + basis=FiniteElementBasis(design_region_width, design_region_height, density=3) +``` + +Here `density` specifies the number of finite-element subdivisions +per unit length. + +## What is this `create_sim` method that my subclass must override? + +In inputs a vector `beta_vector` of basis expansion coefficients and returns +a pymeep `simulation` describing your geometry with the corresponding +spatially-varying permittivity in the design region. The simplest way +to do this is simply to include in your `geometry` list an object +whose spatial extent coincides with the `design_region` returned +by your `init_problem` and whose `epsilon_func` is an instance +of the `ParameterizedDielectric` class defined by `meep.adjoint`. +See the examples in the `python/examples/adjoint_optimization` +subdirectory of your MEEP installation. + +## Aside from overriding `init_problem` and `create_sim`, is there any other code to include in my python script? + +If you want to be able to run your script as an executable from the shell, copy and paste the +following boilerplate code verbatim into bottom of your script: + +```py3 +###################################################################### +# if executed as a script, we look at our own filename to figure out +# the name of the class above, create an instance of this class called +# op, and call its run() method. +###################################################################### +if __name__ == '__main__': + op=globals()[__file__.split('/')[-1].split('.')[0]]() + op.run() +``` + + +## Once I have written my python script subclassing `OptimizationProblem`, how do I run calculations on it? + +Assuming your python script is called `MyOptimizationProblem.py`: + +### Plot the geometry, with all options set to default values + +```bash + % python MyOptimizationProblem.py +``` + +### Plot the geometry with a given functional form for the initial design permittivity + +```bash + % python MyOptimizationProblem.py --eps_design '1.0+5.0*(1.0+sin(x)*cos(2.0*y))' +``` + +### Compute the objective function at the initial design point: + +```bash + % python MyOptimizationProblem.py --eval_objective +``` + +### Compute the objective function and gradient at the initial design point + +```bash + % python MyOptimizationProblem.py --eval_objective +``` + +### Run full iterative optimization + +```bash + % python MyOptimizationProblem.py --optimize +``` + +## What other command-line options are available? + +The full list is documented [here.](https://homerreid.github.io/meep-adjoint-documentation/AdjointSolver/ReferenceManual#4-built-in-command-line-options) + +## Does the `meep.adjoint` module offer any general functionality that is useful for general (non-adjoint) MEEP calculations? + +### `ParallelDesignTester` + +The standalone module `meep.adjoint.ParallelDesignTester` offers an extremely +painless way to parallelize a large number of runs of a python script with +different command-line options. Thus, supose you want to run +a script named `MyScript.py` with 100 different sets of command-line options, +i.e. you want to achieve the effect of running the following sequence +of shell commands: + +```bash + % python MyScript.py '--x 1.0 --name x1' + % python MyScript.py '--x 2.0 --name x1' + % ... + % python MyScript.py '--x 100.0 --name x100' +``` + +The following script will launch a pool of N servers +and run N of your jobs at a time, yielding a painless N-fold speedup: + +``` +from meep.adjoint import ParallelDesignTester + +cmdlines=[ +'--x 0 1.0 --name x1', +'--x 0 2.0 --name x2', +... +'--x 0 100.0 --name x100'] + +ParallelDesignTester(MyScript,cmdlines).launch() +``` + +The number N of server processes launched is chosen by default +to be 1/2 the number of CPU cores on your machine, but may +be set to e.g. 4 by saying `launch(nproc=4)`. + +### Visualization module + +The `meep.adjoint.visualization` module is an attempt at +providing simple standardized routines for visualization of +MEEP simulations. + +#### Visualizing simulation geometries + +Call `visualize_sim()` after initializing a `simulation` +(just before timestepping) to get a visual depiction of +the geometry, PML layers, source regions, and DFT regions. + +```py3 +from meep.adjoint import visualize_sim + +sim=mp.simulation(...) + +# code to add DFT cells goes here + +visualize_sim(sim) +``` + +#### Visualizing simulation results: Frequency-domain fields + +Call the *same* routine `visualize_sim()` after timestepping +to get a visual depiction of DFT fields superposed over the geometry + +```py3 +sim.run(...) +visualize_sim(sim) +``` + +This routine is designed for quick-and-easy visualization of +**any MEEP geometry** without the need to configure a bunch +of customization options. For example, here's what it does +before and after timestepping on the +[`bend-flux` example](https://github.com/NanoComp/meep/blob/master/python/examples/bend-flux.py): + ++ **Before timestepping:** + +![](../images/BentFluxGeometryVisualization.png) + ++ **After timestepping:** + +![](../images/BentFluxFieldsVisualization.png) + +See the [Adjoint solver documentation](https://homerreid.github.io/meep-adjoint-documentation) +for many more examples of pre- and post-timestepping visualizations generated +by `meep.adjoint.Visualization.` + +Note: Although `visualize_sim` is designed to do something useful on any +geometry with no command-line options, it also offers copious +options for customizing the visualization; see the +[`meep.adjoint.Visualization` documentation](https://homerreid.github.io/meep-adjoint-documentation/Visualization) +for more details. + +#### Real-time visualization of time-domain fields + +`meep.adjoint.Visualization` also offers functionality for easy +*real-time* visualization of time-domain fields. More specifically, +the module provides a new [step function](https://meep.readthedocs.io/en/latest/Scheme_User_Interface/#run-and-step-functions) +named `AFEClient` that intermittently updates a plot of time-domain field-components while +a simulation is ongoing. (More specifically, `AFEClient` is a *class* implemented by +`meep.adjoint` that accepts initialization options and may then subsequently be called +as a step function via its `__call__` method; behind the scenes, it implements +the client side of a client-server visualization protocol in which the heavy lifting +of the visualization is done by a separate process to offload that computational +burden from the MEEP timestepping process. See the `AFE_Client` and `AFE_Server` +functions in the `Visualization.py` file in the `meep.adjoint` implementation.) + +For example, to update a plot of the *z*-component of the electric field +every 2 timesteps (in MEEP time), you could go like this: + +```py3 + step_funcs = [ AFEClient(sim, ['Ez'], interval=2) ] + sim.fun(*stepfuncs, until=200) +``` + +Here are movies of what this produces for the +[holey waveguide](Overview#the-holey-waveguide) geometry, +showing an incident eigenmode field propagating across a waveguide +with and without a hole in it. + ++ Without hole: [Ez2WithoutHole.h264](http://127.0.0.1:8000/AdjointSolver/images/Ez2WithoutHole.h264) + ++ With hole: [Ez2WithHole.h264](http://127.0.0.1:8000/AdjointSolver/images/Ez2WithHole.h264) diff --git a/doc/docs/images/Ez2WithHoleMovie.h264 b/doc/docs/images/Ez2WithHoleMovie.h264 new file mode 100644 index 0000000000000000000000000000000000000000..f1a5744f3bf5183c2c46cbdfc698896d789b4c48 GIT binary patch literal 2935456 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zxG}5EVjw(DSwWoA%%f(updhfMZ-_WxWySp|{o5uiP)VzWHLnx$f7B`d+8g{I;V*nZ zU-cjJe+-_Bz$NFu$dv(EJ6S-B-=fcbZyFWZ25&=(u z. + # xyzw = array metadata for the region over which to integrate. + # f may be a function that inputs a mp.Vector3 (coordinates of + # eval point) and returns a floating-point number, or a + # matrix of the same dimension as w, or a constant, or a string expression + # defining a function of x,y, and z. + ###################################################################### + def overlap(self,f,xyzw, subtract_one=False): + p,w = [mp.Vector3(xx,yy,zz) for xx in xyzw[0] for yy in xyzw[1] for zz in xyzw[2]], xyzw[3].flatten() + fn = GridFunc(f,p,np.shape(xyzw[-1])) + f_dot_b = 0.0*fn(0)*np.zeros(self.dim) + offset=1.0 if subtract_one else 0.0 + for n,(pp,ww) in enumerate(zip(p,w)): + f_dot_b += ww*self(pp)*(fn(n) - offset) + return f_dot_b - @property - def tex_names(self): - return [r'$b_{}$'.format(d) for d in range(self.dim)] - - #########################################################j - # project an arbitrary function f(x) onto the basis, i.e. - # return the vector of normalized overlap integrals - # / ########################################################## - def project(self,f,xyzw): - (x,y,z,w)=xyzw[0],xyzw[1],xyzw[2],xyzw[3] - ffunc = f if callable(f) else None - fmatrix = f if not callable(f) and np.shape(f)==np.shape(w) else None - if ffunc is None and fmatrix is None: - raise ValueError("invalid function specification in {}.project()".format(self.__class__.__name__)) - f_dot_b, b_dot_b = 1.0j*np.zeros(self.dim), np.zeros(self.dim) - xyz=[mp.Vector3(xx,yy,zz) for xx in x for yy in y for zz in z] - it=np.nditer(w,flags=['f_index','multi_index']) - while not it.finished: - n, nn = it.index, it.multi_index - ww, bb, ff = w[nn], self(xyz[n]), ffunc(xyz[n]) if ffunc else fmatrix[nn] - f_dot_b += (ww*ff)*bb - b_dot_b += ww*bb*bb - it.iternext() - return np.array( [ fdb/bdb for (fdb,bdb) in zip(f_dot_b,b_dot_b)] ) - - #########################################################j + # return the matrix of basis-function inner products, + # gram_{ij} = , by brute-force numerical quadrature. ########################################################## - def gram_matrix(self,xyzw): + def gram_matrix_bf(self,xyzw): (x,y,z,w)=xyzw[0],xyzw[1],xyzw[2],xyzw[3] xyz=[mp.Vector3(xx,yy,zz) for xx in x for yy in y for zz in z] it=np.nditer(w,flags=['f_index','multi_index']) @@ -133,6 +190,30 @@ def gram_matrix(self,xyzw): it.iternext() return gram + ########################################################## + # default implementation of gram_matrix is to use + # numerical quadrature, but subclasses should override this + # with more efficient methods. + ########################################################## + def gram_matrix(self,xyzw): + return self.gram_matrix_bf(xyzw) + + ###################################################################### + # derived classes may override shape(), names(), texnames(), which are + # used for plotting the basis + ###################################################################### + @property + def shape(self): + return (self.dim,1) + + @property + def names(self): + return ['b{}'.format(d) for d in range(self.dim)] + + @property + def tex_names(self): + return [r'$b_{}$'.format(d) for d in range(self.dim)] + ################################################## # Plane-wave basis for a rectangular region. # @@ -236,47 +317,124 @@ def __call__(self, p=[0.0,0.0]): return b ################################################### -## basis of 2D finite-element functions over a rectangle or disc +## basis of 2D finite-element functions over a rectangle or disc, +## implemented using the FENICS finite-element package; this is +## temporarily shelved pending an assessment of how limiting it +## may be to have a FENICS dependency. Instead, the routine +## below implements a baby version supporting only first-order +## Lagrange functions on a rectangular domain. ################################################### -class FiniteElementBasis(Basis): +#class FiniteElementBasis(Basis): +# +# def __init__(self, N=4, lx=None, ly=None, radius=None, +# fe_type='Lagrange', fe_order=1): +# +# try: +# import fenics +# except ImportError: +# raise ImportError('failed to load fenics module (needed for FiniteElementBasis)') +# +# if lx is not None and ly is not None: +# mesh=fenics.RectangleMesh(fenics.Point(-0.5*lx,-0.5*ly), +# fenics.Point(+0.5*lx,+0.5*ly), +# int(np.ceil(N*lx)),int(np.ceil(N*ly))) +# elif radius is not None: +# mesh=fenics.SphereMesh(fenics.Point(0.0,0.0),radius,1.0/N) +# else: +# raise ValueError('invalid parameters in FiniteElementBasis') +# +# self.fs = fenics.FunctionSpace(mesh,fe_type,fe_order) +# self.f = fenics.Function(self.fs) +# super().__init__( self.fs.dim() ) +# +# # FIXME +# self.bfs = [] +# for n in range(self.fs.dim()): +# bf=fenics.Function(self.fs) +# bf.vector()[n]=1.0 +# self.bfs.append(bf) +# +# def __call__(self, p=[0.0,0.0]): +# if self.fs.mesh().bounding_box_tree().compute_collisions(fenics.Point(p[0],p[1])) == []: +# return 0.0 +# return np.array( [bf(p[0],p[1]) for bf in self.bfs] ) +# +# def set_coefficients(self, beta_vector): +# self.f.vector().set_local(beta_vector) +# +# def eval_expansion(self, p=[0.0,0.0]): +# if self.fs.mesh().bounding_box_tree().compute_collisions(fenics.Point(p[0],p[1])) == []: +# return 0.0 +# return 1.0 + self.f(p[0],p[1]) - def __init__(self, N=4, lx=None, ly=None, radius=None, - fe_type='Lagrange', fe_order=1): +###################################################################### +## finite-element basis for a rectangle. +## density is the number of basis functions per unit length. +## +## (This is a somewhat simplistic implementation that supports only +## first-order elements over triangles, possibly to be replaced +## eventually by something more sophisticated from the many available +## choices of python FEM codes.) +## +## How it works: The sides of an (lx x ly) rectangle are divided in to +## segments at a resolution of `density` functions per unit length. +## To each node in the resulting (NX+1)*(NY+1) grid of nodes we assign +## a single basis function. The basis function associated with node #n +## is only supported on those triangles naving node #n as a vertex; +## it takes the value 1 at node #n and falls linearly to zero at +## the neighboring nodes. Indexing: The node with grid coordinates +## (nx,ny) (0 \le ni \le N_i) is assigned index nx*(NY+1) + ny, +## following the convention MEEP scheme for grid indexing. +###################################################################### +class FiniteElementBasis(Basis): - try: - import fenics - except ImportError: - raise ImportError('failed to load fenics module (needed for FiniteElementBasis)') + def __init__(self, lx, ly, density=4): + self.l=[lx,ly] + self.N=[int(np.ceil(density*ll)) for ll in self.l] + self.d=[ll/(1.0*NN) for ll,NN in zip(self.l,self.N)] + super().__init__( (self.N[0]+1)*(self.N[1]+1) ) - if lx is not None and ly is not None: - mesh=fenics.RectangleMesh(fenics.Point(-0.5*lx,-0.5*ly), - fenics.Point(+0.5*lx,+0.5*ly), - int(np.ceil(N*lx)),int(np.ceil(N*ly))) - elif radius is not None: - mesh=fenics.SphereMesh(fenics.Point(0.0,0.0),radius,1.0/N) - else: - raise ValueError('invalid parameters in FiniteElementBasis') + def in_grid(self, n, ofs=[0,0]): + return np.all([nn+oo in range(0,NN+1) for(nn,oo,NN) in zip(n,ofs,self.N)]) - self.fs = fenics.FunctionSpace(mesh,fe_type,fe_order) - self.f = fenics.Function(self.fs) - super().__init__( self.fs.dim() ) + # scalar index of basis function associated with node n + optional offset + def bindex(self, n, ofs=[0,0]): + return -1 if not self.in_grid(n,ofs) else (n[0]+ofs[0])*(self.N[1]+1) + (n[1]+ofs[1]) - # FIXME - self.bfs = [] - for n in range(self.fs.dim()): - bf=fenics.Function(self.fs) - bf.vector()[n]=1.0 - self.bfs.append(bf) + @property + def shape(self): + return (self.N[0]+1,self.N[1]+1) + + ############################################################## + # on input, p[0,1] are the x,y coordinates of an evaluation + # point in the grid. The return value is a list of + # (bindex,bvalue) pairs giving the index and value of all + # basis functions supported at p. + ############################################################## + def contributors(self, p): + pshift = [ pp + 0.5*ll for pp,ll in zip(p,self.l) ] + node = [ int(np.floor(pp/dd)) for pp,dd in zip(pshift,self.d) ] + xi = [ (pp-nn*dd)/(1.0*dd) for (pp,nn,dd) in zip(pshift,node,self.d) ] + xisum, lower = xi[0]+xi[1], xi[0] <= (1.0-xi[1]) + indices = [self.bindex(node,ofs) for ofs in [(1,0), (0,1), (0,0) if lower else (1,1)]] + vals = [xi[0], xi[1], 1.0-xisum] if lower else [1.0-xi[1],1.0-xi[0],xisum-1.0] + return [ (i,v) for i,v in zip(indices,vals) if i!= -1 ] def __call__(self, p=[0.0,0.0]): - if self.fs.mesh().bounding_box_tree().compute_collisions(fenics.Point(p[0],p[1])) == []: - return 0.0 - return np.array( [bf(p[0],p[1]) for bf in self.bfs] ) - - def set_coefficients(self, beta_vector): - self.f.vector().set_local(beta_vector) + b=np.zeros(self.dim) + for idx,val in self.contributors(p): + b[idx]=val + return b - def eval_expansion(self, p=[0.0,0.0]): - if self.fs.mesh().bounding_box_tree().compute_collisions(fenics.Point(p[0],p[1])) == []: - return 0.0 - return 1.0 + self.f(p[0],p[1]) + def eval(self, p=[0.0,0.0], beta_vector=None): + bv = beta_vector if beta_vector else self.beta_vector + return sum( [ bv[idx]*val for idx,val in self.contributors(p) ] ) + + def gram_matrix(self, xyzw): + diag,off_diag=np.array([1.0/2.0,1.0/12.0]) * (self.d[0]*self.d[1]) + gm = diag*np.identity(self.dim) + offsets=[(dx,dy) for dx in [-1,0,1] for dy in [-1,0,1] if dx!=dy ] + for (i,n) in enumerate([(nx,ny) for nx in range(0,self.N[0]+1) for ny in range(0,self.N[1]+1)]): + for j in [ self.bindex(n,ofs) for ofs in offsets if self.in_grid(n,ofs) ]: + gm[i,j]=gm[j,i]=(diag if i==j else off_diag) + return gm diff --git a/python/adjoint/ObjectiveFunction.py b/python/adjoint/Objective.py similarity index 92% rename from python/adjoint/ObjectiveFunction.py rename to python/adjoint/Objective.py index ef98c983a..dac98b02f 100644 --- a/python/adjoint/ObjectiveFunction.py +++ b/python/adjoint/Objective.py @@ -1,17 +1,14 @@ -################################################## +##################################################### # ObjectiveFunction.py --- routines for evaluating # objective quantities and objective functions for # adjoint-based optimization in meep ##################################################### -import datetime from collections import namedtuple +from datetime import datetime as dt2 import numpy as np import sympy -import matplotlib.cm - import meep as mp -import meep.adjoint ###################################################################### # various global options affecting the adjoint solver, user-tweakable @@ -73,9 +70,9 @@ def rel_diff(a,b): def log(msg): if not mp.am_master() or adjoint_options['logfile'] is None: return - dt=datetime.datetime.now().strftime("%T ") + tm=dt2.now().strftime("%T ") with open(adjoint_options['logfile'],'a') as f: - f.write("{} {}\n".format(dt,msg)) + f.write("{} {}\n".format(tm,msg)) ##################################################################### # A FluxLine is essentially a 2D mp.FluxRegion with a convenient constructor @@ -149,6 +146,18 @@ def FluxLine(x0,y0,length,dir,name=None): # Note: for now, all arrays are stored in memory. For large calculations with # many DFT frequencies this may become impractical. TODO: disk caching. ###################################################################### + +# I find the scoping rules surrounding python modules, classes, and +# functions to be completely inscrutable and do not understand +# why the static class method DFTCell.get_cell_names() appears to +# be available in some external contexts and not others. after +# many weeks and hours trying various combinations of imports +# and periods and etcetera, I throw my hands up and declare a +# global function to achieve the same purpose. +global_dft_cell_names=[] +def get_dft_cell_names(): + return global_dft_cell_names + class DFTCell(object): cell_names=[] @@ -160,10 +169,12 @@ def get_cell_names(cls): @classmethod def add_cell_name(cls,cell_name): cls.cell_names.append(cell_name) + global_dft_cell_names.append(cell_name) @classmethod def reset_cell_names(cls): cls.cell_names=[] + global_dft_cell_names=[] @classmethod def get_index(cls, region_name): @@ -189,8 +200,8 @@ def __init__(self, grid_info=None, region=None, center=origin, size=None, self.nHat = region.direction if hasattr(region,'direction') else None self.celltype = 'flux' if self.nHat is not None else 'fields' # TODO extend to other cases - self.components = components if components is not None \ - else EHTransverse[self.nHat] if self.celltype is 'flux' \ + self.components = components if components is not None \ + else EHTransverse[self.nHat] if self.celltype=='flux' \ else EHxyz self.fcen = fcen self.df = df if nfreq>1 else 0.0 @@ -288,10 +299,14 @@ def subtract_incident_fields(self, EHT, nf=0): # for purposes of future retrieval. ###################################################################### def save_fields(self, label): - if label in self.EH_cache: - raise ValueError("DFTCell {}: data for label {} has already been saved in cache".format(self.name,label)) + #if label in self.EH_cache: + # raise ValueError("DFTCell {}: data for label {} has already been saved in cache".format(self.name,label)) self.EH_cache[label] = [self.get_EH_slices(nf=nf) for nf in range(len(self.freqs))] + def purge_fields(self, label): + if label in self.EH_cache: + del self.EH_cache[label] + ###################################################################### # Return a 1D array (list) of arrays of field amplitudes for all # tangential E,H components at a single frequency---just like @@ -365,7 +380,7 @@ def qname_to_qrule(qname): pieces=qname.split('_') codemode, cellstr = pieces[0], '_'.join(pieces[1:]) - ncell=int(cellstr) if cellstr.isdigit() else meep.adjoint.DFTCell.get_index(cellstr) + ncell=int(cellstr) if cellstr.isdigit() else DFTCell.get_index(cellstr) if codemode.upper()=='S': return qrule(codemode, 0, ncell) elif codemode[0] in 'PM': @@ -486,14 +501,14 @@ class AdjointSolver(object): ######################################################### ######################################################### ######################################################### - def __init__(self, obj_func, dft_cells, basis, sim, vis=None): + def __init__(self, obj_func, dft_cells, basis, sim=None, vis=None): self.obj_func = obj_func self.dft_cells = dft_cells self.basis = basis self.sim = sim self.vis = vis - self.dfdEps = 0.0j*np.zeros(self.dft_cells[-1].slice_dims) + self.dfdEps = None #0.0j*np.zeros(self.dft_cells[-1].slice_dims) # prefetch names of outputs computed by forward and # adjoint solves, for use in writing log files @@ -507,13 +522,12 @@ def eval_fq(self, nf=0): return self.obj_func.get_fq(self.dft_cells,nf=nf) def eval_gradf(self, nf=0): - gradient=0.0j*np.zeros(self.basis.dim) cell=self.dft_cells[-1] # design cell EH_forward=cell.get_EH_slices(nf,label='forward') EH_adjoint=cell.get_EH_slices(nf) # no label->current simulation self.dfdEps=np.sum( [EH_forward[nc]*EH_adjoint[nc] for nc,c in enumerate(cell.components) if c in Exyz], 0 ) - return self.basis.project(self.dfdEps,cell.xyzw) + return self.basis.overlap(self.dfdEps,cell.xyzw) ######################################################### ######################################################### @@ -536,14 +550,11 @@ def run_until_converged(self, case='forward'): # construct field-animation step function if requested step_funcs = [] - clist = adjoint_options['animate_components'] - if clist is not None: - ivl=adjoint_options['animate_interval'] - ivl=0.5 - options = dict(def_field_options) -# options['cmap']=matplotlib.cm.RdGy -# options['clim']=(-0.5,0.5) - step_funcs = [ AFEClient(self.sim, clist, interval=ivl, field_options=options) ] +# clist = adjoint_options['animate_components'] +# if clist is not None: +# ivl=adjoint_options['animate_interval'] +# ivl=0.5 +# step_funcs = [ AFEClient(self.sim, clist, interval=ivl) ] import time time.sleep(10) @@ -552,10 +563,11 @@ def run_until_converged(self, case='forward'): # now continue timestepping with periodic convergence checks until # we converge or timeout - last_vals = np.inf*np.ones(len(names)) + vals = last_vals = np.inf*np.ones(len(names)) max_rel_delta=np.inf next_check_time=self.sim.round_time() - while True: + while max_rel_delta>reltol and self.sim.round_time()=max_time: - return vals - + return vals ############################################################## ############################################################## @@ -622,33 +633,27 @@ def place_adjoint_sources(self, qweights): self.sim.force_complex_fields=True ######################################################## + # the adjoint solve is assumed always to take place + # immediately following a forward solve on the same + # geometry ######################################################## - ######################################################## - def solve(self, need_gradient=False): - - # forward run - fq=self.run_until_converged(case='forward') - - if self.vis: - self.vis.update(self.sim,'Forward') - - if need_gradient==False: - return fq[0], 0 + def forward_solve(self): + return self.run_until_converged(case='forward') # returns fq + def adjoint_solve(self): for cell in self.dft_cells: cell.save_fields('forward') - - # adjoint run(s) qweights=self.obj_func.get_partials() self.place_adjoint_sources(qweights) - gradf=self.run_until_converged(case='adjoint') - if self.vis: - self.vis.update(self.sim,'Adjoint',dfdEps=self.dfdEps) + return self.run_until_converged(case='adjoint') # returns gradf - return fq[0], gradf + def solve(self, need_gradient=False): + fq = self.forward_solve() + gradf = self.adjoint_solve() if need_gradient else 0 + return fq, gradf ######################################################## - ######################################################## + # compute the adjoint-based gradient of a single objective quantity ######################################################## def get_gradq(self, qname): qweights=[1.0 if qn==qname else 0.0 for qn in self.obj_func.qnames] diff --git a/python/adjoint/OptimizationProblem.py b/python/adjoint/OptimizationProblem.py index 8e8d0792e..b6cb3bc36 100644 --- a/python/adjoint/OptimizationProblem.py +++ b/python/adjoint/OptimizationProblem.py @@ -1,24 +1,16 @@ -import sys import os +import sys import argparse import pickle -import datetime +from datetime import datetime as dt2 +from collections import namedtuple import numpy as np -import matplotlib.pyplot as plt - -import meep as mp -from . import ObjectiveFunction -from . import Visualization -from . import Basis +from .Objective import (adjoint_options, unit_vector, log, + DFTCell, ObjectiveFunction, AdjointSolver) -from .ObjectiveFunction import (adjoint_options, xHat, yHat, zHat, origin, - EHTransverse, Exyz, Hxyz, EHxyz, GridInfo, - abs2, unit_vector, rel_diff, FluxLine, - DFTCell, ObjectiveFunction, AdjointSolver) - -from .Visualization import (visualize_sim, AdjointVisualizer, set_plot_default) +from .Visualization import (AdjointVisualizer, set_plot_default, def_plot_options) ###################################################################### # invoke python's 'abstract base class' formalism in a version-agnostic way @@ -54,35 +46,39 @@ def add_args(self, args): ###################################################################### def __init__(self, cmdline=None): + # define and parse command-line arguments parser = self.init_args() # general args self.add_args(parser) # problem-specific arguments - argv=sys.argv[1:] if cmdline is None else cmdline.split(' ') + + # set options from cmdline parameter (if present) or sys.argv + argv = [ a for a in cmdline.split(' ') if a ] if cmdline \ + else sys.argv[1:] if len(sys.argv)>1 else [] + self.cmdline = ' '.join(argv) self.args = args = parser.parse_args(argv) # call subclass for problem-specific initialization first... fstr, objective_regions, extra_regions, design_region, self.basis \ = self.init_problem(self.args) - # ...and now do some general initialization + # and now do some general initialization of basic data fields: + # DFT cells fcen, df, nfreq = args.fcen, args.df, args.nfreq - DFTCell.reset_cell_names() self.objective_cells = [ DFTCell(region=v, fcen=fcen, df=df, nfreq=nfreq) for v in objective_regions ] self.extra_cells = [ DFTCell(region=v, fcen=fcen, df=df, nfreq=nfreq) for v in extra_regions ] if args.full_dfts else [] self.design_cell = DFTCell(region=design_region, fcen=fcen, df=df, nfreq=nfreq, name='design_fields') self.dft_cells = self.objective_cells + self.extra_cells + [self.design_cell] + # objective function self.obj_func = ObjectiveFunction(fstr=fstr) + self.fqnames = ['f'] + self.obj_func.qnames - self.dimension = len(self.basis()) # dimension of optimization problem = number of design variables + # design variables + self.dim = self.basis.dim self.beta_vector = self.init_beta_vector() - self.sim = None - - self.filebase = args.filebase if args.filebase else self.__class__.__name__ - - # miscellaneous general options affecting the solver + # options affecting meep calculations adjoint_options['dft_reltol'] = args.dft_reltol adjoint_options['dft_timeout'] = args.dft_timeout adjoint_options['dft_interval'] = args.dft_interval @@ -90,9 +86,12 @@ def __init__(self, cmdline=None): else 'concise' if args.concise \ else adjoint_options['verbosity'] adjoint_options['logfile'] = args.logfile + self.filebase = args.filebase if args.filebase else self.__class__.__name__ + + # options controlling the optimizer + adjoint_options['logfile'] = args.logfile # miscellaneous general options affecting visualization - self.vis = None if args.label_source_regions: set_plot_default('fontsize',def_plot_options['fontsize'], 'src') @@ -100,27 +99,43 @@ def __init__(self, cmdline=None): adjoint_options['animate_components'] = args.animate_component adjoint_options['animate_interval'] = args.animate_interval + # other data structures that are initialized on a just-in-time basis + self.solver = self.sim = self.vis = self.dfdEps = None + ###################################################################### # constructor helper method that initializes the command-line parser # with general-purpose (problem-independent) arguments ###################################################################### def init_args(self): + parser = argparse.ArgumentParser() #-------------------------------------------------- - # parameters affecting geometry and sources + # parameters affecting meep computations #-------------------------------------------------- - parser.add_argument('--res', type=float, default=20, help='resolution') - parser.add_argument('--dpml', type=float, default=-1.0, help='PML thickness (-1 --> autodetermined)') - parser.add_argument('--fcen', type=float, default=0.5, help='center frequency') - parser.add_argument('--df', type=float, default=0.25, help='frequency width') - parser.add_argument('--source_mode', type=int, default=1, help='mode index of eigenmode source') + parser.add_argument('--res', type=float, default=20, help='resolution') + parser.add_argument('--dpml', type=float, default=-1.0, help='PML thickness (-1 --> autodetermined)') + parser.add_argument('--fcen', type=float, default=0.5, help='center frequency') + parser.add_argument('--df', type=float, default=0.25, help='frequency width') + parser.add_argument('--source_mode', type=int, default=1, help='mode index of eigenmode source') + parser.add_argument('--dft_reltol', type=float, default=adjoint_options['dft_reltol'], help='convergence threshold for end of timestepping') + parser.add_argument('--dft_timeout', type=float, default=adjoint_options['dft_timeout'], help='max runtime in units of last_source_time') + parser.add_argument('--dft_interval', type=float, default=adjoint_options['dft_interval'], help='meep time DFT convergence checks in units of last_source_time') + + #-------------------------------------------------- + # flags affecting outputs from meep computations + #-------------------------------------------------- + parser.add_argument('--nfreq', type=int, default=1, help='number of output frequencies') + parser.add_argument('--full_dfts', dest='full_dfts', action='store_true', help='compute DFT fields over full volume') + parser.add_argument('--complex_fields', dest='complex_fields', action='store_true', help='force complex fields') + parser.add_argument('--filebase', type=str, default=self.__class__.__name__, help='base name of output files') #-------------------------------------------------- # initial values for basis-function coefficients #-------------------------------------------------- - parser.add_argument('--betafile', type=str, default='', help='file of expansion coefficients') - parser.add_argument('--beta', nargs=2, default=[], action='append', help='set value of expansion coefficient') + parser.add_argument('--betafile', type=str, default='', help='file of expansion coefficients') + parser.add_argument('--beta', nargs=2, default=[], action='append', help='set value of expansion coefficient') + parser.add_argument('--eps_design', type=str, default=None, help='functional expression for initial design permittivity') #-------------------------------------------------- # options describing the calculation to be done @@ -136,22 +151,22 @@ def init_args(self): parser.add_argument('--fd_rel_delta', type=float, default=1.0e-2, help='relative finite-difference delta') # run the full iterative optimization - parser.add_argument('--optimize', dest='optimize', help='perform automated design optimization') + parser.add_argument('--optimize', dest='optimize', action='store_true', help='perform automated design optimization') #-------------------------------------------------- - # flags affecting the simulation run + #- options affecting optimization --------------- #-------------------------------------------------- - parser.add_argument('--nfreq', type=int, default=1, help='number of output frequencies') - parser.add_argument('--full_dfts', dest='full_dfts', action='store_true', help='compute DFT fields over full volume') - parser.add_argument('--complex_fields', dest='complex_fields', action='store_true', help='force complex fields') - parser.add_argument('--filebase', type=str, default=self.__class__.__name__, help='base name of output files') + parser.add_argument('--alpha', type=float, default=1.0, help='gradient descent relaxation parameter') + parser.add_argument('--min_alpha', default=1.0e-3, help='minimum value of alpha') + parser.add_argument('--max_alpha', default=10.0, help='maximum value of alpha') + parser.add_argument('--boldness', default=1.25, help='sometimes you just gotta live a little') + parser.add_argument('--timidity', default=0.75, help='can\'t be too careful in this dangerous world') + parser.add_argument('--max_iters', type=int, default=100, help='max number of optimization iterations') + parser.add_argument('--overlap_dfdEps', dest='overlap_dfdEps', action='store_true') #-------------------------------------------------- # flags configuring adjoint-solver options #--------------------------------------------------l - parser.add_argument('--dft_reltol', type=float, default=adjoint_options['dft_reltol'], help='convergence threshold for end of timestepping') - parser.add_argument('--dft_timeout', type=float, default=adjoint_options['dft_timeout'], help='max runtime in units of last_source_time') - parser.add_argument('--dft_interval', type=float, default=adjoint_options['dft_interval'], help='meep time DFT convergence checks in units of last_source_time') parser.add_argument('--verbose', dest='verbose', action='store_true', help='produce more output') parser.add_argument('--concise', dest='concise', action='store_true', help='produce less output') parser.add_argument('--visualize', dest='visualize', action='store_true', help='produce visualization graphics') @@ -169,13 +184,14 @@ def init_args(self): ###################################################################### def init_beta_vector(self): - # default: beta_0 (constant term) = 1, all other coefficients=0 - beta_vector=unit_vector(0,self.dimension) + beta_vector=np.zeros(self.dim) + ####################################################################### # if a --betafile was specified, try to parse it in the form # beta_0 \n beta_1 \n ... (if single column) # or # i1 beta_i1 \n i2 beta_i2 \n (if two columns) + ####################################################################### if self.args.betafile: fb = np.loadtxt(self.args.betafile) # 'file beta' if np.ndim(fb)==1: @@ -186,17 +202,23 @@ def init_beta_vector(self): raise ValueError("{}: invalid file format".format(self.args.betafile)) for i,v in zip(indices,vals): beta_vector[i]=v + ####################################################################### # parse arguments of the form --beta index value + ####################################################################### for ivpair in self.args.beta: # loop over (index,value) pairs beta_vector[int(ivpair[0])]=ivpair[1] - # this step ensures that epsilon(x) never falls below 1.0, assuming - # (a) the 0th basis function is the constant 1 - # (b) all other basis functions (b_1, ... b_{D-1}) take values in [-1:1] - # (c) coefficients (\beta_1, ..., \beta_{D-1}) are nonnegative. - #eps_min=beta_vector[0] - np.sum(beta_vector[1:]) - #if eps_min<1.0: - # beta_vector[0] += 1.0-eps_min + ####################################################################### + # if a functional form for --eps_design was specified, project that + # function onto the basis and use this as the initial design point + ####################################################################### + if np.count_nonzero(beta_vector)==0: + eps_design=self.args.eps_design if self.args.eps_design else 1.0 + sim = self.create_sim(beta_vector) + sim.init_sim() + xyzw=sim.get_dft_array_metadata(center=self.dft_cells[-1].center, size=self.dft_cells[-1].size) + beta_vector=self.basis.expand(eps_design,xyzw,cache=True,subtract_one=True) + return beta_vector ###################################################################### @@ -215,29 +237,115 @@ def plot_geometry(self): vis = AdjointVisualizer(cases=['Geometry']) vis.update(sim,'Geometry') self.sim,self.vis = sim,vis # save copies for debugging; not strictly necessary - self.terminate("Finished visualization") + return + + ###################################################################### + ###################################################################### + ###################################################################### + def update_design_variables(self, beta_vector): + if self.solver==None: + self.solver=AdjointSolver(self.obj_func, self.dft_cells, self.basis) + self.solver.sim=self.create_sim(beta_vector) ###################################################################### # compute the objective function, plus possibly its gradient (via # adjoints), at a single point in design space ###################################################################### def eval_objective(self, beta_vector, need_gradient=False, vis=None): - sim = self.create_sim(beta_vector) - solver = AdjointSolver(self.obj_func, self.dft_cells, self.basis, sim, vis=vis) - self.sim, self.solver = sim, solver # save copies for debugging; not strictly necessary - retval=solver.solve(need_gradient=need_gradient) - if need_gradient and self.args.pickle_data: - with open(self.filebase + '.pickle','wb') as f: - pickle.dump(self.solver.dfdEps,f) - return retval - - ################################################## - ################################################## - ################################################## - def eval_fq(self, beta_vector, need_gradient=False, vis=None): - f,gradf = self.eval_objective(beta_vector, need_gradient=need_gradient, vis=vis) - fq = np.array( [f] + list(self.obj_func.qvals) ) - return fq, gradf + self.update_design_variables(beta_vector) + self.solver.vis=vis + return self.solver.solve(need_gradient=need_gradient) + + ###################################################################### + # an OptState stores the current state of an optimization problem. + ###################################################################### + OptState = namedtuple('OptState', 'n alpha beta fq gradf dfdEps') + + ###################################################################### + ###################################################################### + ###################################################################### + def log_state(self, state, substate=None): + + ts=dt2.now().strftime('%T') + with open(self.iterfile,'a') as f: + if substate: + f.write('{}: Subiter {}.{}: '.format(ts,state.n,substate.n)) + f.write('f={}, alpha={}\n'.format(substate.fq[0],substate.alpha)) + return + + dfdEps_avg=np.sum(self.dft_cells[-1].xyzw[3] * state.dfdEps) + f.write('\n\n{}: Iter {}: f={}, alpha={} dfdeAve={}\n' + .format(ts,state.n,state.fq[0],state.alpha,dfdEps_avg)) + [f.write('#{} {} = {}\n'.format(state.n,nn,qq)) for nn,qq in zip(self.fqnames[1:], state.fq[1:]) ] + [f.write('#{} b{} = {}\n'.format(state.n,n,b)) for n,b in enumerate(state.beta)] + f.write('\n\n') + self.annals.append(state) + + ###################################################################### + ###################################################################### + ###################################################################### + def line_search(self,state): + + self.log_state(state) + cease_file = '/tmp/terminate.{}'.format(os.getpid()) + + bs, xyzw, ovrlp = self.basis, self.dft_cells[-1].xyzw, self.args.overlap_dfdEps + dbeta = bs.overlap(state.dfdEps, xyzw) if ovrlp else bs.expand(state.dfdEps, xyzw) + + alpha, iter, subiter = state.alpha, state.n, 0 + while alpha>self.args.min_alpha: + + beta = state.beta + alpha*np.real(dbeta) + for n in range(len(beta)): + beta[n] = max(0.0, beta[n]) + self.update_design_variables(beta) + fq = self.solver.forward_solve() + + substate = self.OptState(subiter,alpha,beta,fq,0,0) + self.log_state(state,substate) + + if fq[0] > state.fq[0]: # found a new optimum, declare victory and a new iteration + gradf = self.solver.adjoint_solve() + alpha = min(alpha*self.args.boldness,self.args.max_alpha) + return self.OptState(iter+1, alpha, beta, fq, gradf, self.solver.dfdEps) + + if os.path.isfile(cease_file): # premature termination requested by user + os.remove(cease_file) + return None + + alpha*=self.args.timidity + + return None # unable to improve objective by proceeding any distance in given direction + + ###################################################################### + ###################################################################### + ###################################################################### + def optimize(self): + + ss = int( dt2.now().strftime("%s") ) - 1553607629 + self.iterfile = '{}.{}.iters'.format(self.filebase,ss) + with open(self.iterfile,'w') as f: + f.write('#{} ran'.format(self.__class__.__name__)) + f.write(dt2.now().strftime(' %D::%T\n')) + f.write('# with args {}\n\n'.format(self.cmdline)) + self.annals=[] + + ###################################################################### + # initialize AdjointSolver and get objective function value and gradient + # at the initial design point + ###################################################################### + alpha = self.args.alpha + beta = self.beta_vector + self.update_design_variables(beta) + fq,gradf = self.solver.solve(need_gradient=True) + dfdEps = self.solver.dfdEps + + state = self.OptState(1,alpha,beta,fq,gradf,dfdEps) + + while state and state.n0): self.plot_geometry() + return #-------------------------------------------------------------- #-------------------------------------------------------------- @@ -268,15 +378,13 @@ def run(self): if args.visualize: cases=['Geometry','Forward'] + (['Adjoint'] if args.eval_gradient else []) vis=AdjointVisualizer(cases=cases) - self.vis = vis # save copy for debugging; not strictly necessary - fq,gradf=self.eval_fq(self.beta_vector, need_gradient=args.eval_gradient, vis=vis) + fq,gradf=self.eval_objective(self.beta_vector, need_gradient=args.eval_gradient, vis=vis) - fqnames=['f'] + self.obj_func.qnames - self.output([],[],actions=['begin']) + self.output([],[],actions=['begin'],msg='{} {}'.format(self.filebase,self.cmdline)) self.output(['res','fcen','df','source_mode'], [args.res,args.fcen,args.df,args.source_mode]) [self.output(['beta'+str(n)],[beta]) for (n,beta) in enumerate(self.beta_vector)] - [self.output([fqn], [fqv]) for (fqn,fqv) in zip(fqnames,fq)] + [self.output([fqn], [fqv]) for (fqn,fqv) in zip(self.fqnames,fq)] if args.eval_gradient: [self.output( ['df/db'+str(n)], [g]) for n,g in enumerate(gradf)] @@ -288,16 +396,16 @@ def run(self): indices = [] if args.fd_order==0 else [int(index) for index in args.fd_index] for index in indices: dbeta = args.fd_rel_delta*(1.0 if self.beta_vector[index]==0 else np.abs(self.beta_vector[index])) - beta_hat = unit_vector(index,self.dimension) - fqp, _ = self.eval_fq(self.beta_vector + dbeta*beta_hat) + beta_hat = unit_vector(index,self.dim) + fqp, _ = self.eval_objective(self.beta_vector + dbeta*beta_hat) d1fq = (fqp - fq) / dbeta if args.fd_order==2 and self.beta_vector[index]!=0.0: - fqm, _ = self.eval_fq(self.beta_vector - dbeta*beta_hat) + fqm, _ = self.eval_objective(self.beta_vector - dbeta*beta_hat) d2fq = (fqp - fqm) / (2.0*dbeta) elif args.fd_order==2 and self.beta_vector[index]==0.0: - fqpp, _ = self.eval_fq(self.beta_vector + 2*dbeta*beta_hat) + fqpp, _ = self.eval_objective(self.beta_vector + 2*dbeta*beta_hat) d2fq = (4*fqp - fqpp - 3.0*fq) / (2.0*dbeta) - for i,fqn in enumerate(fqnames): + for i,fqn in enumerate(self.fqnames): nlist = ['d{}/db{}__O{}__'.format(fqn,index,ord+1) for ord in range(args.fd_order)] vlist = [ d1fq[i] ] + ([d2fq[i]] if args.fd_order==2 else[]) [self.output(nlist, vlist)] @@ -306,31 +414,37 @@ def run(self): if args.pickle_data: f = open(self.filebase + '.pickle', 'wb') - #pickle.dump(self,f) pickle.dump(self.solver.dfdEps,f) f.close() - self.terminate("Completed single-point calculation") + return ###################################################################### + # 'lcdoi' = legend, console, digest, output, iterations ###################################################################### - ###################################################################### - def output(self, names, values, actions=[]): + def output(self, names, values, actions=[], msg=None, files='lcdoi'): if 'begin' in actions: self.nout = 1 # running index of output quantity - self.legend = open(self.filebase + '.legend','w') - self.digest = open(self.filebase + '.digest','a') - self.outfile = open(self.filebase + '.out','a') - dt=datetime.datetime.now().strftime('%D::%T ') - for f in [sys.stdout,self.digest]: - f.write('\n\n** {} ran {} \n'.format(dt,self.__class__.__name__)) - f.write('** with args {}'.format(' '.join(sys.argv[1:]))) - f.write('\n**') + self.legend = open(self.filebase + '.legend','w') if 'l' in files else None + self.digest = open(self.filebase + '.digest','a') if 'd' in files else None + self.outfile = open(self.filebase + '.out','a') if 'o' in files else None + self.iterlog = open(self.filebase + '.iters','a') if 'i' in files else None + + msgfiles = [sys.stdout] if 'c' in files else [] + msgfiles += [self.digest] if 'd' in files else [] + if msg is not None: + tm=dt2.now().strftime('%D::%T ') + for f in msgfiles: + f.write('\n\n** {} {}\n**'.format(tm,msg)) #-------------------------------------------------------------- #- inline utility functions for real/complex numerical output #-------------------------------------------------------------- + def fw(f,s=None): + if f is not None: + f.write(s) if s is not None else f.close() + def myangle(z): theta=np.angle(z,deg=True) return theta if theta>=0.0 else theta+360.0 @@ -353,28 +467,19 @@ def pretty_print(val,for_file=False,polar=False): namestrs += (' ,' if namestrs else '') + name valstrs += (' ,' if valstrs else '') + pretty_print(val) if np.iscomplex(val): - valstrs += '(' + pretty_print(val,polar=True) + ') ' + valstrs += '(' + pretty_print(val,polar=True) + ' ' - self.outfile.write(pretty_print(val, for_file=True)) + fw(self.outfile,pretty_print(val, for_file=True)) idxstr=str(self.nout) + (','+str(self.nout+1) if np.iscomplex(val) else '') - self.legend.write('{}: {}\n'.format(idxstr,name)) - self.nout += (2 if np.iscomplex(val) else 1) + fw(self.legend,'{}: {}\n'.format(idxstr,name)) + self.nout += (2 if np.iscomplex(val) else 1) if self.legend else 0 - for f in [sys.stdout,self.digest]: + for f in msgfiles: f.write('{:30s}: {}\n'.format(namestrs,valstrs)) if 'end' in actions: - self.outfile.write('\n') - self.outfile.close() - self.digest.close() - self.legend.close() - - ###################################################################### - ###################################################################### - ###################################################################### - def optimize(self): - args=self.args - print("Running optimization...") - vis = AdjointVisualizer() if args.visualize else None # cases=ALL_CASES - self.terminate("Finished optimization") + fw(self.outfile,'\n') + fw(self.outfile) + fw(self.digest) + fw(self.legend) diff --git a/python/adjoint/ParallelDesignTester.py b/python/adjoint/ParallelDesignTester.py index 277698cbb..82a289660 100644 --- a/python/adjoint/ParallelDesignTester.py +++ b/python/adjoint/ParallelDesignTester.py @@ -40,6 +40,8 @@ import multiprocessing from multiprocessing import cpu_count as ncpus from datetime import datetime as dt +import importlib +from importlib import util from importlib import import_module as imp_mod ###################################################################### @@ -53,12 +55,13 @@ def __init__(self, name, cmdlines): def __call__(self, n): getattr(imp_mod(self.name),self.name)(self.cmdlines[n]).run() - def launch(self, nproc): + def launch(self, nproc=None): # create and cd to working directory, then launch servers and run jobs wdir = '{}_{}'.format(self.name,dt.now().strftime("%m%d.%H%M%S")) os.mkdir(wdir) os.chdir(wdir) + nproc=nproc if nproc else max(ncpus()//2,1) multiprocessing.Pool(nproc).map(self,range(len(self.cmdlines))) ###################################################################### @@ -72,7 +75,7 @@ def launch(self, nproc): args=parser.parse_args() if args.name is None or not importlib.util.find_spec(args.name): - raise ValueError("missing or invalid class/module --name " + args.name if args.name else '') + raise ValueError("missing or invalid class/module --name " + args.name if args.name else '') if args.casefile is None or not os.path.isfile(args.casefile): raise ValueError("missing or invalid list of command-line strings --casefile " + args.casefile if args.casefile else '') with open(args.casefile) as f: diff --git a/python/adjoint/Visualization.py b/python/adjoint/Visualization.py index 3f1e28516..1c1d4a435 100644 --- a/python/adjoint/Visualization.py +++ b/python/adjoint/Visualization.py @@ -4,11 +4,9 @@ # simple standardized ways ################################################### import warnings -import time -import datetime +from datetime import datetime as dt2 from collections import namedtuple import numpy as np -import sympy import re from multiprocessing import Process, Pipe @@ -19,11 +17,12 @@ from mpl_toolkits.mplot3d import axes3d from mpl_toolkits.axes_grid1 import make_axes_locatable from matplotlib.collections import PolyCollection, LineCollection -from mpl_toolkits.mplot3d.art3d import Poly3DCollection +import matplotlib.cm import meep as mp -from meep.adjoint import ObjectiveFunction +from .Objective import get_dft_cell_names +#from . get_dft_cell_names ######################################################## # the next few routines are some of my older general-purpose @@ -33,13 +32,16 @@ # visualization module just so it can be independent of # the adjoint innards. ######################################################## +xHat=mp.Vector3(1.0,0.0,0.0) +yHat=mp.Vector3(0.0,1.0,0.0) +zHat=mp.Vector3(0.0,0.0,1.0) +origin=mp.Vector3() EHTransverse=[ [mp.Ey, mp.Ez, mp.Hy, mp.Hz], [mp.Ez, mp.Ex, mp.Hz, mp.Hx], [mp.Ex, mp.Ey, mp.Hx, mp.Hy] ] Exyz=[mp.Ex, mp.Ey, mp.Ez] Hxyz=[mp.Hx, mp.Hy, mp.Hz] EHxyz=Exyz + Hxyz -origin=mp.Vector3() def abs2(z): return np.real(np.conj(z)*z) @@ -48,7 +50,11 @@ def dft_cell_type(cell): return 'flux' if isinstance(cell, mp.simulation.DftFlux) else 'fields' def dft_cell_name(nc): - name=ObjectiveFunction.DFTCell.get_cell_names()[nc] +# name=DFTCell.get_cell_names()[nc] + dft_cell_names=get_dft_cell_names() + if len(dft_cell_names) <= nc: + return 'flux{}'.format(nc) + name=get_dft_cell_names()[nc] if name.endswith('_flux'): name=name[0:-5] if name.endswith('_fields'): @@ -67,7 +73,7 @@ def add_dft_cell(sim, region, fcen, df=0, nfreq=1): def flux_line(x0, y0, length, dir): - size=length*(xhat if dir is mp.Y else yhat) + size=length*(xHat if dir is mp.Y else yHat) return mp.FluxRegion(center=mp.Vector3(x0,y0), size=size, direction=dir) @@ -116,23 +122,6 @@ def unpack_dft_fields(sim,cell,nf=0): _,_,_,_,_,EH=unpack_dft_cell(sim,cell,nf=nf) return EH -################################################### -################################################### -################################################### -def eigenfield_tag(ncell, mode, freq): - return "C{}.M{}.F{:.6f}".format(ncell,mode,freq) - -def lookup_eigenfields(ncell, mode, freq, eigencache): - tag=eigenfield_tag(ncell, mode, freq) - if eigencache and tag in eigencache: - return eigencache[tag] - raise ValueError("eigenfields for tag {} not found in cache".format(tag)) - -def get_eigenfields(sim, dft_cells, ncell, mode, nf=0, eigencache=None): - - # look for data in cache - cell=dft_cells[ncell] - ######################################################## # this routine configures some global matplotlib settings # (as distinct from the plot-specific settings handled @@ -224,7 +213,7 @@ def set_meep_rcParams(): def set_plot_default(option, value, type=None): which= def_eps_options if type=='eps' \ else def_src_options if type=='src' \ - else def_pml_optionss if type=='pml' \ + else def_pml_options if type=='pml' \ else def_flux_options if type=='flux' \ else def_field_options if type=='fields' \ else def_plot_options @@ -354,7 +343,7 @@ def add_to_plot(c): ) ) else: - if options['fill_color'] is not 'none': # first copy: faces, no edges + if options['fill_color'] != 'none': # first copy: faces, no edges polygon = np.array([v0+dx+dy, v0-dx+dy, v0-dx-dy, v0+dx-dy]) pc=PolyCollection( [polygon], linewidths=0.0) pc.set_color(options['fill_color']) @@ -404,7 +393,7 @@ def plot_data_curves(sim,center=None,size=None,superpose=True, return options=options if options else def_flux_options - lw=options['line_width'] + #lw=options['line_width'] lc=options['line_color'] zrel_min=options['zrel_min'] zrel_max=options['zrel_max'] @@ -471,8 +460,8 @@ def visualize_source_distribution(sim, superpose=True, options=None): plt.ion() plt.figure() plt.title('Source regions') - fig.subplot(len(sim.sources),1,ns+1) - fig.title('Currents in source region {}'.format(ns)) + plt.fig().subplot(len(sim.sources),1,ns+1) + plt.fig().title('Currents in source region {}'.format(ns)) # plot_data_curves(sim,superpose,[J2,M2],labels=['||J||','||M||'], # styles=['bo-','rs-'],center=sc,size=ssu plot_data_curves(sim,center=sc,size=ss, superpose=superpose, @@ -590,7 +579,7 @@ def plot_dft_fields(sim, field_cells=[], field_funcs=None, if field_funcs==None: ops=['Re', 'Im', 'abs'] - field_funcs=[texify(op+'('+component_name(c)+')') for c in cEH for op in ops] + field_funcs=[texify(op+'('+mp.component_name(c)+')') for c in cEH for op in ops] rows,cols=len(cEH),len(ops) else: rows,cols=1,len(field_funcs) @@ -749,16 +738,11 @@ def visualize_sim(sim, fig=None, plot3D=None, else 'src' + ( '\_'+str(ns) if len(sim.sources)>1 else '')) ) if src_options['zrel_min']!=src_options['zrel_max']: - visualize_source_distribution(sim, standalone=not plot3D, options=src_options) + visualize_source_distribution(sim, superpose=plot3D, options=src_options) ################################################### ## plot PML regions ################################################### - def_options=def_pml_options - if pml_options is None: - pml_options = { **def_pml_options, - 'fill_color' : (0.25 if plot3D else 0.75)*np.ones(3) - } if sim.boundary_layers and hasattr(sim.boundary_layers[0],'thickness'): dpml = sim.boundary_layers[0].thickness sx, sy = sim.cell_size.x, sim.cell_size.y @@ -767,8 +751,8 @@ def visualize_sim(sim, fig=None, plot3D=None, centers = [ y0, -1*y0, x0, -1*x0 ] # north, south, east, west sizes = [ ns, ns, ew, ew ] for c,s in zip(centers,sizes): - plot_volume(sim, center=c, size=s, - options=pml_options, plot3D=plot3D) + plot_volume(sim, center=c, size=s, plot3D=plot3D, + options=pml_options if pml_options else def_pml_options) ###################################################################### # plot DFT cell regions, with labels for flux cells. @@ -844,9 +828,9 @@ def plot_basis(opt_prob): ###################################################################### LogFile='/tmp/PFCServer.log' def message(msg): - dt=datetime.datetime.now().strftime("%T ") + tm=dt2.now().strftime("%T ") with open(LogFile,'a') as f: - f.write("{} {}\n".format(dt,msg)) + f.write("{} {}\n".format(tm,msg)) #os.system('zenity --info --text "{} {}" &'.format(dt,msg)) PFCRequest = namedtuple('PFCRequest', 't flist') @@ -1004,32 +988,37 @@ def __call__(self, sim, todo): # series of plot windows. It relies on the 'screeninfo' module # available from pypl. ##################################################################### -################################################## -################################################## -################################################## def set_figure_geometry(index): + + window, n = plt.get_current_fig_manager().window, index+1 +###################################################################### + xmax, ymax, dx, dy=5120, 1440, 840, 670 + window.setGeometry(xmax-n*dx,ymax-dy,dx,dy) + return +###################################################################### + try: # attempt to fetch size of monitor from screeninfo import get_monitors - w0, h0=get_monitors()[0].width, get_monitors()[0].height + xmax, ymax=get_monitors()[0].width, get_monitors()[0].height except: warnings.warn('could not find screeninfo module; run % pip install screeninfo') return # failed to fetch current monitor size # attempt to fetch size of current window - window, n = plt.get_current_fig_manager().window, index+1 if callable(getattr(window,'winfo_width',None)): # Tkagg - w,h=window.winfo_width(),window.winfo_height() - window.wm_geometry('+{}+{}'.format(w0-n*w,h0-h)) + dx,dy=window.winfo_width(),window.winfo_height() + window.wm_geometry('+{}+{}'.format(xmax-n*dx,ymax-dy)) elif callable(getattr(window,'width',None)): # qt{4,5}agg - w,h=window.width(), window.height() - window.setGeometry(w0-n*w,h0-h,w,h) + dx,dy=window.width(), window.height() + window.setGeometry(xmax-n*dx,ymax-dy,dx,dy) elif getattr(window,'Size',None): # works for wxagg - w,h=window.Size - window.Move(w0-n*w, h0-h) + dx,dy=window.Size + window.Move(xmax-n*dx, ymax-dy) else: warnings.warn('failed to auto-position matplotlib windows: unknown backend') + ###################################################################### # AdjointVisualizer is an entity that knows how to create and update # various types of MEEP simulation visualizations that are useful @@ -1088,17 +1077,27 @@ def update(self, sim, case, dfdEps=None): title=case if case=='Adjoint': - ffs=[r'Re$\left(\frac{\partial f}{\partial\epsilon}\right)$', - r'Im$\left(\frac{\partial f}{\partial\epsilon}\right)$', - r'$\left|\frac{\partial f}{\partial\epsilon}\right|$'] - plt.suptitle(title) + + ff_ria= [ r'Re $\left(\frac{\partial f}{\partial\epsilon}\right)$', + r'Im $\left(\frac{\partial f}{\partial\epsilon}\right)$', + r' $\left|\frac{\partial f}{\partial\epsilon}\right|$'] + fa_ria= [ np.real(dfdEps), np.imag(dfdEps), np,abs(dfdEps) ] + + plot_ria = False; # -->True to plot real, imag, abs components + if plot_ria: + plt.suptitle(title) + ffs, fas = ff_ria, fa_ria + else: + ffs, fas = [ff_ria[0] + ',' + title], [fa_ria[0]] visualize_dft_fields(sim,superpose=False,field_cells=[sim.dft_objects[-1]], - field_funcs=ffs, - ff_arrays=[np.real(dfdEps),np.imag(dfdEps),np.abs(dfdEps)]) + field_funcs = ffs, ff_arrays=fas) else: visualize_sim(sim,plot3D=plot3D,fig=fig,eps_options=self.eps_options,src_options=self.src_options, plot_dft_data=False if case=='Geometry' else True if case =='Forward' else 'flux') plt.gcf().gca().set_title(title) + if case=='Geometry': + plt.tight_layout() + plt.draw() plot_pause() diff --git a/python/adjoint/__init__.py b/python/adjoint/__init__.py index 348e5686b..de2bcb8e9 100644 --- a/python/adjoint/__init__.py +++ b/python/adjoint/__init__.py @@ -14,7 +14,7 @@ # depending on one or more input variables, which we # call "objective quantities." # -# ObjectiveFunction.py: lower-level routines for carrying out MEEP timestepping +# Objective.py lower-level routines for carrying out MEEP timestepping # calculations to compute objective quantities and their # adjoint derivatives. # @@ -38,10 +38,11 @@ from .OptimizationProblem import OptimizationProblem -from .ObjectiveFunction import (adjoint_options, xHat, yHat, zHat, origin, - EHTransverse, Exyz, Hxyz, EHxyz, GridInfo, - abs2, unit_vector, rel_diff, FluxLine, - DFTCell, ObjectiveFunction, AdjointSolver) +from .Objective import (adjoint_options, xHat, yHat, zHat, origin, + EHTransverse, Exyz, Hxyz, EHxyz, GridInfo, + abs2, unit_vector, rel_diff, FluxLine, + DFTCell, ObjectiveFunction, AdjointSolver, + get_dft_cell_names) from .ParallelDesignTester import ParallelDesignTester diff --git a/python/examples/adjoint_optimization/AsymmetricSplitter.py b/python/examples/adjoint_optimization/AsymmetricSplitter.py new file mode 100644 index 000000000..cb006718c --- /dev/null +++ b/python/examples/adjoint_optimization/AsymmetricSplitter.py @@ -0,0 +1,172 @@ +import sys +import argparse +import numpy as np +import meep as mp + +from meep.adjoint import (OptimizationProblem, DFTCell, adjoint_options, + xHat, yHat, zHat, origin, FluxLine, + ParameterizedDielectric, FiniteElementBasis) + +################################################## +################################################## +################################################## +class Splitter12(OptimizationProblem): + + ################################################## + ################################################## + ################################################## + def add_args(self, parser): + + # add new problem-specific arguments + parser.add_argument('--dair', type=float, default=-1.0, help='') + parser.add_argument('--w_in', type=float, default=1.0, help='width of input waveguide') + parser.add_argument('--w_out1', type=float, default=0.5, help='width of output waveguide 1') + parser.add_argument('--w_out2', type=float, default=0.5, help='width of output waveguide 2') + parser.add_argument('--l_stub', type=float, default=3.0, help='length of waveguide input/output stub') + parser.add_argument('--l_design', type=float, default=2.0, help='length of design region') + parser.add_argument('--h_design', type=float, default=6.0, help='height of design region') + parser.add_argument('--eps_in', type=float, default=6.0, help='input waveguide permittivity') + parser.add_argument('--eps_out1', type=float, default=2.0, help='output waveguide 1 permittivity') + parser.add_argument('--eps_out2', type=float, default=12.0, help='output waveguide 2 permittivity') + parser.add_argument('--nfe', type=int, default=2, help='number of finite elements per unit length') + + # set problem-specific defaults for existing (general) arguments + parser.set_defaults(fcen=0.5) + parser.set_defaults(df=0.2) + parser.set_defaults(dpml=1.0) + + ################################################## + ################################################## + ################################################## + def init_problem(self, args): + + #---------------------------------------- + # size of computational cell + #---------------------------------------- + lcen = 1.0/args.fcen + dpml = 0.5*lcen if args.dpml==-1.0 else args.dpml + dair = 0.5*args.w_in if args.dair==-1.0 else args.dair + sx = dpml + args.l_stub + args.l_design + args.l_stub + dpml + sy = dpml + dair + args.h_design + dair + dpml + cell_size = mp.Vector3(sx, sy, 0.0) + + #---------------------------------------- + #- design region + #---------------------------------------- + design_center = origin + design_size = mp.Vector3(args.l_design, args.h_design, 0.0) + design_region = mp.Volume(center=design_center, size=design_size) + + #---------------------------------------- + #- objective regions + #---------------------------------------- + x_in = -0.5*(args.l_design + args.l_stub) + x_out = +0.5*(args.l_design + args.l_stub) + y_out1 = +0.25*args.h_design + y_out2 = -0.25*args.h_design + + flux_in = FluxLine(x_in, 0.0, 2.0*args.w_in, mp.X, 'in') + flux_out1 = FluxLine(x_out, y_out1, 2.0*args.w_out1, mp.X, 'out1') + flux_out2 = FluxLine(x_out, y_out2, 2.0*args.w_out2, mp.X, 'out2') + + objective_regions = [flux_in, flux_out1, flux_out2] + + #---------------------------------------- + #- optional extra regions for visualization if the --full-dfts options is present. + #---------------------------------------- + extra_regions = [mp.Volume(center=origin, size=cell_size)] if args.full_dfts else [] + + #---------------------------------------- + # forward source region + #---------------------------------------- + source_center = (x_in - 0.25*args.l_stub)*xHat + source_size = 2.0*args.w_in*yHat + + #---------------------------------------- + # basis set + #---------------------------------------- + basis = FiniteElementBasis(args.l_design, args.h_design, args.nfe) + + #---------------------------------------- + #- objective function + #---------------------------------------- + fstr = ( 'Abs(P1_out1)**2' + + '+0.0*(P1_out1 + M1_out1)' + + '+0.0*(P1_out2 + M1_out2)' + + '+0.0*(P1_in + M1_in + S_out1 + S_out2 + S_in)' + ) + + #---------------------------------------- + #- internal storage for variables needed later + #---------------------------------------- + self.args = args + self.dpml = dpml + self.cell_size = cell_size + self.basis = basis + self.design_center = origin + self.design_size = design_size + self.source_center = source_center + self.source_size = source_size + + return fstr, objective_regions, extra_regions, design_region, basis + + ############################################################## + ############################################################## + ############################################################## + def create_sim(self, beta_vector, vacuum=False): + + args=self.args + sx=self.cell_size.x + + x_in = -0.5*(args.l_design + args.l_stub) + x_out = +0.5*(args.l_design + args.l_stub) + y_out1 = +0.25*args.h_design + y_out2 = -0.25*args.h_design + + wvg_in = mp.Block( center=mp.Vector3(x_in,0.0), + size=mp.Vector3(args.l_stub,args.w_in), + material=mp.Medium(epsilon=args.eps_in)) + wvg_out1 = mp.Block( center=mp.Vector3(x_out,y_out1), + size=mp.Vector3(args.l_stub,args.w_out1), + material=mp.Medium(epsilon=args.eps_out1)) + wvg_out2 = mp.Block( center=mp.Vector3(x_out,y_out2), + size=mp.Vector3(args.l_stub,args.w_out2), + material=mp.Medium(epsilon=args.eps_out2)) + design = mp.Block( center=origin, + size=mp.Vector3(args.l_design,args.h_design), + epsilon_func=ParameterizedDielectric(self.design_center, + self.basis, + beta_vector) + ) + + geometry=[wvg_in, wvg_out1, wvg_out2, design] + + envelope = mp.GaussianSource(args.fcen,fwidth=args.df) + amp=1.0 + if callable(getattr(envelope, "fourier_transform", None)): + amp /= envelope.fourier_transform(args.fcen) + sources=[mp.EigenModeSource(src=envelope, + center=self.source_center, + size=self.source_size, + eig_band=self.args.source_mode, + amplitude=amp + ) + ] + + sim=mp.Simulation(resolution=args.res, cell_size=self.cell_size, + boundary_layers=[mp.PML(args.dpml)], geometry=geometry, + sources=sources) + + if args.complex_fields: + sim.force_complex_fields=True + + return sim + +###################################################################### +# if executed as a script, we look at our own filename to figure out +# the name of the class above, create an instance of this class called +# opt_prob, and call its run() method. +###################################################################### +if __name__ == '__main__': + opt_prob=globals()[__file__.split('/')[-1].split('.')[0]]() + opt_prob.run() diff --git a/python/examples/adjoint_optimization/CrossRouter.py b/python/examples/adjoint_optimization/CrossRouter.py new file mode 100644 index 000000000..9701024ac --- /dev/null +++ b/python/examples/adjoint_optimization/CrossRouter.py @@ -0,0 +1,170 @@ +import numpy as np +import meep as mp + +from meep.adjoint import (OptimizationProblem, FluxLine, + xHat, yHat, zHat, origin, + ParameterizedDielectric, FiniteElementBasis) + +################################################## +################################################## +################################################## +class CrossRouter(OptimizationProblem): + + ################################################## + ################################################## + ################################################## + def add_args(self, parser): + + # add new problem-specific arguments + parser.add_argument('--wh', type=float, default=1.5, help='width of horizontal waveguide') + parser.add_argument('--wv', type=float, default=1.5, help='width of vertical waveguide') + parser.add_argument('--l_stub', type=float, default=3.0, help='waveguide input/output stub length') + parser.add_argument('--eps', type=float, default=6.0, help='waveguide permittivity') + parser.add_argument('--r_design', type=float, default=0.0, help='design region radius') + parser.add_argument('--l_design', type=float, default=4.0, help='design region side length') + parser.add_argument('--nfe', type=int, default=2, help='number of finite elements per unit length') + + # the following three quantities are weighting prefactors assigned to + # the north, south, and east power fluxes in the objective function + parser.add_argument('--n_weight', type=float, default=1.00, help='') + parser.add_argument('--s_weight', type=float, default=0.00, help='') + parser.add_argument('--e_weight', type=float, default=0.00, help='') + + # set problem-specific defaults for existing (general) arguments + parser.set_defaults(fcen=0.5) + parser.set_defaults(df=0.2) + parser.set_defaults(dpml=1.0) + parser.set_defaults(epsilon_design=6.0) + + ################################################## + ################################################## + ################################################## + def init_problem(self, args): + + #---------------------------------------- + # size of computational cell + #---------------------------------------- + lcen = 1.0/args.fcen + dpml = 0.5*lcen if args.dpml == -1.0 else args.dpml + design_length = 2.0*args.r_design if args.r_design > 0.0 else args.l_design + sx = sy = dpml + args.l_stub + design_length + args.l_stub + dpml + cell_size = mp.Vector3(sx, sy, 0.0) + + #---------------------------------------- + #- design region bounding box + #---------------------------------------- + design_center = origin + design_size = mp.Vector3(design_length, design_length) + design_region = mp.Volume(center=design_center, size=design_size) + + #---------------------------------------- + #- objective and source regions + #---------------------------------------- + gap = args.l_stub/6.0 # gap between source region and flux monitor + d_flux = 0.5*(design_length + args.l_stub) # distance from origin to NSEW flux monitors + d_source = d_flux + gap # distance from origin to source + d_flx2 = d_flux + 2.0*gap + l_flux_NS = 2.0*args.wv + l_flux_EW = 2.0*args.wh + north = FluxLine(0.0, +d_flux, l_flux_NS, mp.Y, 'north') + south = FluxLine(0.0, -d_flux, l_flux_NS, mp.Y, 'south') + east = FluxLine(+d_flux, 0.0, l_flux_EW, mp.X, 'east') + west1 = FluxLine(-d_flux, 0.0, l_flux_EW, mp.X, 'west1') + west2 = FluxLine(-d_flx2, 0.0, l_flux_EW, mp.X, 'west2') + + objective_regions = [north, south, east, west1, west2] + + source_center = mp.Vector3(-d_source, 0.0) + source_size = mp.Vector3(0.0,l_flux_EW) + + #---------------------------------------- + #- optional extra regions for visualization + #---------------------------------------- + extra_regions = [mp.Volume(center=origin, size=cell_size)] if args.full_dfts else [] + + #---------------------------------------- + # basis set + #---------------------------------------- + basis = FiniteElementBasis(lx=args.l_design, ly=args.l_design, density=args.nfe) + + #---------------------------------------- + #- objective function + #---------------------------------------- + fstr=( ' {:s}*Abs(P1_north)**2'.format('0.0' if args.n_weight==0.0 else '{}'.format(args.n_weight)) + + ' + {:s}*Abs(M1_south)**2'.format('0.0' if args.s_weight==0.0 else '{}'.format(args.s_weight)) + + ' + {:s}*Abs(P1_east)**2'.format('0.0' if args.e_weight==0.0 else '{}'.format(args.e_weight)) + + ' + 0.0*(P1_north + M1_south + P1_east + P1_west1 + P1_west2)' + + ' + 0.0*(M1_north + M1_south + M1_east + M1_west1 + M1_west2)' + + ' + 0.0*(S_north + S_south + S_east + S_west1 + S_west2)' + ) + + #---------------------------------------- + #- internal storage for variables needed later + #---------------------------------------- + self.args = args + self.dpml = dpml + self.cell_size = cell_size + self.basis = basis + self.design_center = design_center + self.design_size = design_size + self.source_center = source_center + self.source_size = source_size + + if args.eps_design is None: + args.eps_design = args.eps + + return fstr, objective_regions, extra_regions, design_region, basis + + ############################################################## + ############################################################## + ############################################################## + def create_sim(self, beta_vector, vacuum=False): + + args=self.args + + hwvg=mp.Block(center=origin, material=mp.Medium(epsilon=args.eps), + size=mp.Vector3(self.cell_size.x,args.wh)) + vwvg=mp.Block(center=origin, material=mp.Medium(epsilon=args.eps), + size=mp.Vector3(args.wv,self.cell_size.y)) + + if args.r_design>0.0: + router=mp.Cylinder(center=self.design_center, radius=args.r_design, + epsilon_func=ParameterizedDielectric(self.design_center, + self.basis, + beta_vector)) + else: + router=mp.Block(center=self.design_center, size=self.design_size, + epsilon_func=ParameterizedDielectric(self.design_center, + self.basis, + beta_vector)) + geometry=[hwvg, vwvg, router] + + envelope = mp.GaussianSource(args.fcen,fwidth=args.df) + amp=1.0 + if callable(getattr(envelope, "fourier_transform", None)): + amp /= envelope.fourier_transform(args.fcen) + sources=[mp.EigenModeSource(src=envelope, + center=self.source_center, + size=self.source_size, + eig_band=args.source_mode, + amplitude=amp + ) + ] + + sim=mp.Simulation(resolution=args.res, cell_size=self.cell_size, + boundary_layers=[mp.PML(self.dpml)], geometry=geometry, + sources=sources) + + if args.complex_fields: + sim.force_complex_fields=True + + return sim + +###################################################################### +# if executed as a script, we look at our own filename to figure out +# the name of the class above, create an instance of this class called +# op, and call its run() method. +###################################################################### +if __name__ == '__main__': + op=globals()[__file__.split('/')[-1].split('.')[0]]() + op.run() diff --git a/python/examples/adjoint_optimization/HoleyWaveguide.py b/python/examples/adjoint_optimization/HoleyWaveguide.py index d3cb35c11..5dab0a772 100644 --- a/python/examples/adjoint_optimization/HoleyWaveguide.py +++ b/python/examples/adjoint_optimization/HoleyWaveguide.py @@ -46,7 +46,7 @@ def init_problem(self, args): L = max(L,Lmin) sx = dpml+L+dpml sy = dpml+dair+args.w_wvg+dair+dpml - cell_size = mp.Vector3(sx, sy, 0.0) + cell_size = mp.Vector3(sx,sy) #---------------------------------------- #- design region @@ -146,4 +146,4 @@ def create_sim(self, beta_vector, vacuum=False): ###################################################################### if __name__ == '__main__': opt_prob=globals()[__file__.split('/')[-1].split('.')[0]]() - opt_prob.run() + diff --git a/src/loop_in_chunks.cpp b/src/loop_in_chunks.cpp index ea4e15bdf..834e3e7fe 100644 --- a/src/loop_in_chunks.cpp +++ b/src/loop_in_chunks.cpp @@ -518,7 +518,8 @@ void fields::loop_in_chunks(field_chunkloop chunkloop, void *chunkloop_data, con /* should have length 1. */ /***************************************************************/ void fields::get_array_metadata(const volume &where, double *xtics, double *ytics, double *ztics, - double *weights, bool collapse_empty_dimensions) { + double *weights, bool collapse_empty_dimensions) +{ // mimic what is done in `loop_in_chunks` to initialize a loop // over grid points in `where` component 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