TEST_INTERP_ND
Test Functions for Multidimensional Interpolation

TEST_INTERP_ND is a FORTRAN77 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:

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

Languages:

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:

LAGRANGE_INTERP_ND, a FORTRAN77 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 FORTRAN77 library which contains many utility routines using double precision real (R8) arithmetic.

RBF_INTERP_ND, a FORTRAN77 library which defines and evaluates radial basis function (RBF) interpolants to multidimensional data.

SHEPARD_INTERP_ND, a FORTRAN77 library which defines and evaluates Shepard interpolants to multidimensional data, based on inverse distance weighting.

SPARSE_INTERP_ND a FORTRAN77 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 FORTRAN77 library which defines test problems for interpolation of data y(x), depending on a 1D argument.

TEST_INTERP_2D, a FORTRAN77 library which defines test problems for interpolation of data z(x,y)), depending on a 2D argument.

TOMS526, a FORTRAN77 library which interpolates scattered bivariate data. This is ACM TOMS algorithm 526, by Hiroshi Akima;

TOMS660, a FORTRAN77 library which takes scattered 2D data and produces an interpolating function F(X,Y). This is ACM TOMS algorithm 660, called qshep2d, by Robert Renka.

TOMS661, a FORTRAN77 library which takes scattered 3D data and produces an interpolating function F(X,Y,Z). This is ACM TOMS algorithm 661, called qshep3d, by Robert Renka.

TOMS790, a FORTRAN77 library which computes an interpolating function to a set of scattered data in the plane, by Robert Renka; this library is commonly called cshep2d; this is ACM TOMS algorithm 790.

Reference:

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:

• test_interp_nd.f, the source code.
• test_interp_nd.sh, BASH commands to compile the source code.

Examples and Tests:

• test_interp_nd_prb.f, a sample calling program.
• test_interp_nd_prb.sh, BASH commands to compile and run the sample program.
• test_interp_nd_prb_output.txt, the output file.

List of Routines:

• CSEVL evaluates a Chebyshev series.
• I4VEC_SUM returns the sum of 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_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-dependent constants.
• TUPLE_NEXT computes the next element of a tuple space.

You can go up one level to the FORTRAN77 source codes.