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TEST_INTERP_ND\ Test Functions for Multidimensional Interpolation {#test_interp_nd-test-functions-for-multidimensional-interpolation align=”center”} =================================================

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TEST_INTERP_ND is a C++ library which provides test functions for multidimensional interpolation.

All the functions are defined over the unit hypercube [0,1]\^M, for arbitrary spatial dimension M. They include:

1. Oscillatory;
2. Product Peak;
3. Corner Peak;
4. Gaussian;
5. Continuous;
6. Discontinuous;

For each function, methods are provided to evaluate:

• the function, f(x);
• the derivative with respect to any coordinate, dfdx(i);
• the integral of f(x) over the unit hypercube;

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.

TEST_INTERP_ND requires access to the R8LIB library.

Licensing: {#licensing align=”center”}

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Languages: {#languages align=”center”}

TEST_INTERP_ND is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs: {#related-data-and-programs align=”center”}

LAGRANGE_INTERP_ND, 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).

R8LIB, a C++ library which contains many utility routines using double precision real (R8) arithmetic.

RBF_INTERP_ND, a C++ library which defines and evaluates radial basis function (RBF) interpolants to multidimensional data.

SHEPARD_INTERP_ND, a C++ library which defines and evaluates Shepard interpolants to multidimensional data, based on inverse distance weighting.

SPARSE_INTERP_ND a C++ library which can be used to define a sparse interpolant to a function f(x) of a multidimensional argument.

SPINTERP, 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;

TEST_INTERP_1D, a C++ library which defines test problems for interpolation of data y(x), depending on a 1D argument.

TEST_INTERP_2D, a C++ library which defines test problems for interpolation of data z(x,y)), depending on a 2D argument.

Reference: {#reference align=”center”}

1. Alan Genz,\ Testing Multidimensional Integration Routines,\ in Tools, Methods, and Languages for Scientific and Engineering Computation,\ edited by B Ford, JC Rault, F Thomasset,\ North-Holland, 1984, pages 81-94,\ ISBN: 0444875700,\ LC: Q183.9.I53.
2. Alan Genz,\ A Package for Testing Multiple Integration Subroutines,\ in Numerical Integration: Recent Developments, Software and Applications,\ edited by Patrick Keast, Graeme Fairweather,\ Reidel, 1987, pages 337-340,\ ISBN: 9027725144,\ LC: QA299.3.N38.

Source Code: {#source-code align=”center”}

• test_interp_nd.cpp, the source code.
• test_interp_nd.hpp, the include file.

Examples and Tests: {#examples-and-tests align=”center”}

• test_interp_nd_prb.cpp, a sample calling program.
• test_interp_nd_prb_output.txt, the output file.

List of Routines: {#list-of-routines align=”center”}

• CSEVL evaluates a Chebyshev series.
• I4VEC_SUM sums the entries of an I4VEC.
• INITS initializes a Chebyshev series.
• P00_CW computes a random C parameter vector for any problem.
• P00_D returns a derivative component of any function.
• P00_F returns the value of any function.
• P00_PROB_NUM returns the number of test functions available.
• P00_Q returns the integral of any function.
• P00_TITLE returns the title for any function.
• P00_W computes a random W parameter vector for any problem.
• P01_D evaluates any derivative component for problem p01.
• P01_F evaluates the function for problem p01.
• P01_Q evaluates the integral for problem p01.
• P01_TITLE returns the name of problem p01.
• P02_D evaluates an derivative component for problem p02.
• P02_F evaluates the function for problem p02.
• P02_Q evaluates the integral for problem p02.
• P02_TITLE returns the title of problem p02.
• P03_D evaluates any derivative component for problem p03.
• P03_F evaluates the function for problem p03.
• P03_Q evaluates the integral for problem p03.
• P03_TITLE returns the title of problem p03.
• P04_D evaluates any derivative component for problem p04.
• P04_F evaluates the function for problem p04.
• P04_Q evaluates the integral for problem p04.
• P04_TITLE returns the title of problem p04.
• P05_D evaluates any derivative component for problem p05.
• P05_F evaluates the function for problem p05.
• P05_Q evaluates the integral for problem p05.
• P05_TITLE returns the title of problem p05.
• P06_D evaluates any derivative component for problem p06.
• P06_F evaluates the function for problem p06.
• P06_Q evaluates the integral for problem p06.
• P06_TITLE returns the title of problem p06.
• R8_ABS returns the absolute value of an R8.
• R8_ERROR evaluates the error function of an R8 argument.
• R8_ERRORC evaluates the co-error function of an R8 argument.
• R8_MACH returns double precision real machine constants.
• TUPLE_NEXT computes the next element of a tuple space.

You can go up one level to the C++ source codes.

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Last revised on 29 August 2012.