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<html>
<head>
<title>
TEST_INTERP - Interpolation Test Data
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
TEST_INTERP <br> Interpolation Test Data
</h1>
<hr>
<p>
<b>TEST_INTERP</b>
is a FORTRAN90 library which
defines data that may be used to test interpolation algorithms.
</p>
<p>
The following sets of data are available:
<ol>
<li>
<a href = "p01_plot.png">p01_plot.png</a>,
18 data points, 2 dimensions.
This example is due to Hans-Joerg Wenz.
It is an example of good data, which is dense enough in areas
where the expected curvature of the interpolant is large.
Good results can be expected with almost any reasonable
interpolation method.
</li>
<li>
<a href = "p02_plot.png">p02_plot.png</a>,
18 data points, 2 dimensions. This example is due to ETY Lee of Boeing.
Data near the corners is more dense than in regions of small curvature.
A local interpolation method will produce a more plausible
interpolant than a nonlocal interpolation method, such as
cubic splines.
</li>
<li>
<a href = "p03_plot.png">p03_plot.png</a>,
11 data points, 2 dimensions. This example is due to Fred Fritsch and Ralph Carlson.
This data can cause problems for interpolation methods.
There are sudden changes in direction, and at the same time,
sparsely-placed data. This can cause an interpolant to overshoot
the data in a way that seems implausible.
</li>
<li>
<a href = "p04_plot.png">p04_plot.png</a>,
8 data points, 2 dimensions. This example is due to Larry Irvine, Samuel Marin and Philip Smith.
This data can cause problems for interpolation methods.
There are sudden changes in direction, and at the same time,
sparsely-placed data. This can cause an interpolant to overshoot
the data in a way that seems implausible.
</li>
<li>
<a href = "p05_plot.png">p05_plot.png</a>,
9 data points, 2 dimensions. This example is due to Larry Irvine, Samuel Marin and Philip Smith.
This data can cause problems for interpolation methods.
There are sudden changes in direction, and at the same time,
sparsely-placed data. This can cause an interpolant to overshoot
the data in a way that seems implausible.
</li>
<li>
<a href = "p06_plot.png">p06_plot.png</a>,
49 data points, 2 dimensions. The data is due to deBoor and Rice.
The data represents a temperature dependent property of titanium.
The data has been used extensively as an example in spline
approximation with variably-spaced knots.
DeBoor considers two sets of knots:
(595,675,755,835,915,995,1075)
and
(595,725,850,910,975,1040,1075).
</li>
<li>
<a href = "p07_plot.png">p07_plot.png</a>,
4 data points, 2 dimensions. The data is a simple symmetric set of 4 points,
for which it is interesting to develop the Shepard interpolants
for varying values of the exponent p.
</li>
<li>
<a href = "p08_plot.png">p08_plot.png</a>,
12 data points, 2 dimensions. This is equally spaced data for y = x^2,
except for one extra point whose x value is close to another, but whose
y value is not so close. A small disagreement in nearby data can
become a disaster.
</li>
</ol>
</p>
<p>
<b>TEST_INTERP</b> requires access to a compiled copy of the R8LIB library.
</p>
<h3 align = "center">
Licensing:
</h3>
<p>
The computer code and data files described and made available on this web page
are distributed under
<a href = "../../txt/gnu_lgpl.txt">the GNU LGPL license.</a>
</p>
<h3 align = "center">
Languages:
</h3>
<p>
<b>TEST_INTERP</b> is available in
<a href = "../../c_src/test_interp/test_interp.html">a C version</a> and
<a href = "../../cpp_src/test_interp/test_interp.html">a C++ version</a> and
<a href = "../../f77_src/test_interp/test_interp.html">a FORTRAN77 version</a> and
<a href = "../../f_src/test_interp/test_interp.html">a FORTRAN90 version</a> and
<a href = "../../m_src/test_interp/test_interp.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../f_src/divdif/divdif.html">
DIVDIF</a>,
a FORTRAN90 library which
includes many routines to construct and evaluate divided difference
interpolants.
</p>
<p>
<a href = "../../f_src/hermite/hermite.html">
HERMITE</a>,
a FORTRAN90 library which
computes the Hermite interpolant, a polynomial that matches function values
and derivatives.
</p>
<p>
<a href = "../../f_src/interp/interp.html">
INTERP</a>,
a FORTRAN90 library which
can compute interpolants to data.
</p>
<p>
<a href = "../../datasets/interpolation/interpolation.html">
INTERPOLATION</a>,
a dataset directory which
contains datasets to be interpolated.
</p>
<p>
<a href = "../../f_src/lagrange_interp_1d/lagrange_interp_1d.html">
LAGRANGE_INTERP_1D</a>,
a FORTRAN90 library which
defines and evaluates the Lagrange polynomial p(x)
which interpolates a set of data, so that p(x(i)) = y(i).
</p>
<p>
<a href = "../../f_src/nearest_interp_1d/nearest_interp_1d.html">
NEAREST_INTERP_1D</a>,
a FORTRAN90 library which
interpolates a set of data using a piecewise constant interpolant
defined by the nearest neighbor criterion.
</p>
<p>
<a href = "../../f_src/pwl_interp_1d/pwl_interp_1d.html">
PWL_INTERP_1D</a>,
a FORTRAN90 library which
interpolates a set of data using a piecewise linear function.
</p>
<p>
<a href = "../../f_src/pppack/pppack.html">
PPPACK</a>,
a FORTRAN90 library which
implements Carl de Boor's piecewise polynomial functions,
including, particularly, cubic splines.
</p>
<p>
<a href = "../../f_src/r8lib/r8lib.html">
R8LIB</a>,
a FORTRAN90 library which
contains many utility routines using double precision real (R8) arithmetic.
</p>
<p>
<a href = "../../f_src/rbf_interp/rbf_interp.html">
RBF_INTERP</a>,
a FORTRAN90 library which
defines and evaluates radial basis interpolants to multidimensional data.
</p>
<p>
<a href = "../../f_src/spline/spline.html">
SPLINE</a>,
a FORTRAN90 library which
includes many routines to construct and evaluate spline
interpolants and approximants.
</p>
<p>
<a href = "../../f_src/test_approx/test_approx.html">
TEST_APPROX</a>,
a FORTRAN90 library which
defines tests for
approximation and interpolation algorithms.
</p>
<p>
<a href = "../../f_src/vandermonde_interp_1d/vandermonde_interp_1d.html">
VANDERMONDE_INTERP_1D</a>,
a FORTRAN90 library which
finds a polynomial interpolant to data y(x) of a 1D argument,
by setting up and solving a linear system for the polynomial coefficients,
involving the Vandermonde matrix.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Carl DeBoor, John Rice,<br>
Least-squares cubic spline approximation II - variable knots. <br>
Technical Report CSD TR 21, <br>
Purdue University, Lafayette, Indiana, 1968.
</li>
<li>
Carl DeBoor,<br>
A Practical Guide to Splines,<br>
Springer, 2001,<br>
ISBN: 0387953663,<br>
LC: QA1.A647.v27.
<li>
Fred Fritsch, Ralph Carlson,<br>
Monotone Piecewise Cubic Interpolation,<br>
SIAM Journal on Numerical Analysis,<br>
Volume 17, Number 2, April 1980, pages 238-246.
</li>
<li>
Larry Irvine, Samuel Marin, Philip Smith,<br>
Constrained Interpolation and Smoothing,<br>
Constructive Approximation,<br>
Volume 2, Number 1, December 1986, pages 129-151.
</li>
<li>
ETY Lee,<br>
Choosing Nodes in Parametric Curve Interpolation,<br>
Computer-Aided Design,<br>
Volume 21, Number 6, July/August 1989, pages 363-370.
</li>
<li>
Hans-Joerg Wenz,<br>
Interpolation of Curve Data by Blended Generalized Circles,<br>
Computer Aided Geometric Design,<br>
Volume 13, Number 8, November 1996, pages 673-680.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "test_interp.f90">test_interp.f90</a>, the source code.
</li>
<li>
<a href = "test_interp.sh">test_interp.sh</a>,
commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "test_interp_prb.f90">test_interp_prb.f90</a>,
a sample calling program.
</li>
<li>
<a href = "test_interp_prb.sh">test_interp_prb.sh</a>,
commands to compile and run the sample program.
</li>
<li>
<a href = "test_interp_prb_output.txt">test_interp_prb_output.txt</a>,
the output file.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>P00_DATA</b> returns the data for any problem.
</li>
<li>
<b>P00_DATA_NUM</b> returns the number of data points for any problem.
</li>
<li>
<b>P00_DIM_NUM</b> returns the spatial dimension for any problem.
</li>
<li>
<b>P00_PROB_NUM</b> returns the number of test problems.
</li>
<li>
<b>P00_STORY</b> prints the "story" for any problem.
</li>
<li>
<b>P01_DATA</b> returns the data for problem 01.
</li>
<li>
<b>P01_DATA_NUM</b> returns the number of data points for problem 01.
</li>
<li>
<b>P01_DIM_NUM</b> returns the spatial dimension for problem 01.
</li>
<li>
<b>P01_STORY</b> prints the "story" for problem 01.
</li>
<li>
<b>P02_DATA</b> returns the data for problem 02.
</li>
<li>
<b>P02_DATA_NUM</b> returns the number of data points for problem 02.
</li>
<li>
<b>P02_DIM_NUM</b> returns the spatial dimension for problem 02.
</li>
<li>
<b>P02_STORY</b> prints the "story" for problem 02.
</li>
<li>
<b>P03_DATA</b> returns the data for problem 03.
</li>
<li>
<b>P03_DATA_NUM</b> returns the number of data points for problem 03.
</li>
<li>
<b>P03_DIM_NUM</b> returns the spatial dimension for problem 03.
</li>
<li>
<b>P03_STORY</b> prints the "story" for problem 03.
</li>
<li>
<b>P04_DATA</b> returns the data for problem 04.
</li>
<li>
<b>P04_DATA_NUM</b> returns the number of data points for problem 04.
</li>
<li>
<b>P04_DIM_NUM</b> returns the spatial dimension for problem 04.
</li>
<li>
<b>P04_STORY</b> prints the "story" for problem 04.
</li>
<li>
<b>P05_DATA</b> returns the data for problem 05.
</li>
<li>
<b>P05_DATA_NUM</b> returns the number of data points for problem 05.
</li>
<li>
<b>P05_DIM_NUM</b> returns the spatial dimension for problem 05.
</li>
<li>
<b>P05_STORY</b> prints the "story" for problem 05.
</li>
<li>
<b>P06_DATA</b> returns the data for problem 06.
</li>
<li>
<b>P06_DATA_NUM</b> returns the number of data points for problem 06.
</li>
<li>
<b>P06_DIM_NUM</b> returns the spatial dimension for problem 06.
</li>
<li>
<b>P06_STORY</b> prints the "story" for problem 06.
</li>
<li>
<b>P07_DATA</b> returns the data for problem 07.
</li>
<li>
<b>P07_DATA_NUM</b> returns the number of data points for problem 07.
</li>
<li>
<b>P07_DIM_NUM</b> returns the spatial dimension for problem 07.
</li>
<li>
<b>P07_STORY</b> prints the "story" for problem 07.
</li>
<li>
<b>P08_DATA</b> returns the data for problem 08.
</li>
<li>
<b>P08_DATA_NUM</b> returns the number of data points for problem 08.
</li>
<li>
<b>P08_DIM_NUM</b> returns the spatial dimension for problem 08.
</li>
<li>
<b>P08_STORY</b> prints the "story" for problem 08.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../f_src.html">
the FORTRAN90 source codes</a>.
</p>
<hr>
<i>
Last revised on 04 October 2012.
</i>
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