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


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:

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.

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”}

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

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

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


Last revised on 29 August 2012.