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<html>
<head>
<title>
TEST_INTERP_ND - Test Functions for Multidimensional Interpolation
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
TEST_INTERP_ND <br> Test Functions for Multidimensional Interpolation
</h1>
<hr>
<p>
<b>TEST_INTERP_ND</b>
is a C++ library which
provides test functions for multidimensional interpolation.
</p>
<p>
All the functions are defined over the unit hypercube [0,1]^M, for arbitrary
spatial dimension M. They include:
<ol>
<li>
Oscillatory;
</li>
<li>
Product Peak;
</li>
<li>
Corner Peak;
</li>
<li>
Gaussian;
</li>
<li>
Continuous;
</li>
<li>
Discontinuous;
</li>
</ol>
</p>
<p>
For each function, methods are provided to evaluate:
<ul>
<li>
the function, f(x);
</li>
<li>
the derivative with respect to any coordinate, dfdx(i);
</li>
<li>
the integral of f(x) over the unit hypercube;
</li>
</ul>
</p>
<p>
Most of the functions include a shift vector w whose entries can be
chosen randomly in the unit hypercube, and a coefficient vector c
whose entries should be positive, and for which the integration problem
becomes harder as the sum of the entries increases.
</p>
<p>
<b>TEST_INTERP_ND</b> requires access to 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_ND</b> is available in
<a href = "../../c_src/test_interp_nd/test_interp_nd.html">a C version</a> and
<a href = "../../cpp_src/test_interp_nd/test_interp_nd.html">a C++ version</a> and
<a href = "../../f77_src/test_interp_nd/test_interp_nd.html">a FORTRAN77 version</a> and
<a href = "../../f_src/test_interp_nd/test_interp_nd.html">a FORTRAN90 version</a> and
<a href = "../../m_src/test_interp_nd/test_interp_nd.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../cpp_src/lagrange_interp_nd/lagrange_interp_nd.html">
LAGRANGE_INTERP_ND</a>,
a C++ library which
defines and evaluates the Lagrange polynomial p(x)
which interpolates a set of data depending on a multidimensional argument x
that was evaluated on a product grid, so that p(x(i)) = z(i).
</p>
<p>
<a href = "../../cpp_src/r8lib/r8lib.html">
R8LIB</a>,
a C++ library which
contains many utility routines using double precision real (R8) arithmetic.
</p>
<p>
<a href = "../../cpp_src/rbf_interp_nd/rbf_interp_nd.html">
RBF_INTERP_ND</a>,
a C++ library which
defines and evaluates radial basis function (RBF) interpolants to multidimensional data.
</p>
<p>
<a href = "../../cpp_src/shepard_interp_nd/shepard_interp_nd.html">
SHEPARD_INTERP_ND</a>,
a C++ library which
defines and evaluates Shepard interpolants to multidimensional data,
based on inverse distance weighting.
</p>
<p>
<a href = "../../cpp_src/sparse_interp_nd/sparse_interp_nd.html">
SPARSE_INTERP_ND</a>
a C++ library which
can be used to define a sparse interpolant to a function f(x) of a
multidimensional argument.
</p>
<p>
<a href = "../../m_src/spinterp/spinterp.html">
SPINTERP</a>,
a MATLAB library which
carries out piecewise multilinear hierarchical sparse grid interpolation;
an earlier version of this software is ACM TOMS Algorithm 847,
by Andreas Klimke;
</p>
<p>
<a href = "../../cpp_src/test_interp_1d/test_interp_1d.html">
TEST_INTERP_1D</a>,
a C++ library which
defines test problems for interpolation of data y(x),
depending on a 1D argument.
</p>
<p>
<a href = "../../cpp_src/test_interp_2d/test_interp_2d.html">
TEST_INTERP_2D</a>,
a C++ library which
defines test problems for interpolation of data z(x,y)),
depending on a 2D argument.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Alan Genz,<br>
Testing Multidimensional Integration Routines,<br>
in Tools, Methods, and Languages for Scientific and
Engineering Computation,<br>
edited by B Ford, JC Rault, F Thomasset,<br>
North-Holland, 1984, pages 81-94,<br>
ISBN: 0444875700,<br>
LC: Q183.9.I53.
</li>
<li>
Alan Genz,<br>
A Package for Testing Multiple Integration Subroutines,<br>
in Numerical Integration:
Recent Developments, Software and Applications,<br>
edited by Patrick Keast, Graeme Fairweather,<br>
Reidel, 1987, pages 337-340,<br>
ISBN: 9027725144,<br>
LC: QA299.3.N38.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "test_interp_nd.cpp">test_interp_nd.cpp</a>, the source code.
</li>
<li>
<a href = "test_interp_nd.hpp">test_interp_nd.hpp</a>, the include file.
</li>
<li>
<a href = "test_interp_nd.sh">test_interp_nd.sh</a>,
BASH commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "test_interp_nd_prb.cpp">test_interp_nd_prb.cpp</a>,
a sample calling program.
</li>
<li>
<a href = "test_interp_nd_prb.sh">test_interp_nd_prb.sh</a>,
BASH commands to compile and run the sample program.
</li>
<li>
<a href = "test_interp_nd_prb_output.txt">test_interp_nd_prb_output.txt</a>,
the output file.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>CSEVL</b> evaluates a Chebyshev series.
</li>
<li>
<b>I4VEC_SUM</b> sums the entries of an I4VEC.
</li>
<li>
<b>INITS</b> initializes a Chebyshev series.
</li>
<li>
<b>P00_CW</b> computes a random C parameter vector for any problem.
</li>
<li>
<b>P00_D</b> returns a derivative component of any function.
</li>
<li>
<b>P00_F</b> returns the value of any function.
</li>
<li>
<b>P00_PROB_NUM</b> returns the number of test functions available.
</li>
<li>
<b>P00_Q</b> returns the integral of any function.
</li>
<li>
<b>P00_TITLE</b> returns the title for any function.
</li>
<li>
<b>P00_W</b> computes a random W parameter vector for any problem.
</li>
<li>
<b>P01_D</b> evaluates any derivative component for problem p01.
</li>
<li>
<b>P01_F</b> evaluates the function for problem p01.
</li>
<li>
<b>P01_Q</b> evaluates the integral for problem p01.
</li>
<li>
<b>P01_TITLE</b> returns the name of problem p01.
</li>
<li>
<b>P02_D</b> evaluates an derivative component for problem p02.
</li>
<li>
<b>P02_F</b> evaluates the function for problem p02.
</li>
<li>
<b>P02_Q</b> evaluates the integral for problem p02.
</li>
<li>
<b>P02_TITLE</b> returns the title of problem p02.
</li>
<li>
<b>P03_D</b> evaluates any derivative component for problem p03.
</li>
<li>
<b>P03_F</b> evaluates the function for problem p03.
</li>
<li>
<b>P03_Q</b> evaluates the integral for problem p03.
</li>
<li>
<b>P03_TITLE</b> returns the title of problem p03.
</li>
<li>
<b>P04_D</b> evaluates any derivative component for problem p04.
</li>
<li>
<b>P04_F</b> evaluates the function for problem p04.
</li>
<li>
<b>P04_Q</b> evaluates the integral for problem p04.
</li>
<li>
<b>P04_TITLE</b> returns the title of problem p04.
</li>
<li>
<b>P05_D</b> evaluates any derivative component for problem p05.
</li>
<li>
<b>P05_F</b> evaluates the function for problem p05.
</li>
<li>
<b>P05_Q</b> evaluates the integral for problem p05.
</li>
<li>
<b>P05_TITLE</b> returns the title of problem p05.
</li>
<li>
<b>P06_D</b> evaluates any derivative component for problem p06.
</li>
<li>
<b>P06_F</b> evaluates the function for problem p06.
</li>
<li>
<b>P06_Q</b> evaluates the integral for problem p06.
</li>
<li>
<b>P06_TITLE</b> returns the title of problem p06.
</li>
<li>
<b>R8_ABS</b> returns the absolute value of an R8.
</li>
<li>
<b>R8_ERROR</b> evaluates the error function of an R8 argument.
</li>
<li>
<b>R8_ERRORC</b> evaluates the co-error function of an R8 argument.
</li>
<li>
<b>R8_MACH</b> returns double precision real machine constants.
</li>
<li>
<b>TUPLE_NEXT</b> computes the next element of a tuple space.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../cpp_src.html">
the C++ source codes</a>.
</p>
<hr>
<i>
Last revised on 29 August 2012.
</i>
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