test_interp_nd, a FORTRAN90 code 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.

The code requires access to the R8LIB library.


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


test_interp_nd is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

LAGRANGE_INTERP_ND, a FORTRAN90 code 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 FORTRAN90 code which contains many utility routines using double precision real (R8) arithmetic.

RBF_INTERP_ND, a FORTRAN90 code which defines and evaluates radial basis function (RBF) interpolants to multidimensional data.

SHEPARD_INTERP_ND, a FORTRAN90 code which defines and evaluates Shepard interpolants to multidimensional data, based on inverse distance weighting.

SPARSE_INTERP_ND a FORTRAN90 code which can be used to define a sparse interpolant to a function f(x) of a multidimensional argument.

TEST_INTERP_1D, a FORTRAN90 code which defines test problems for interpolation of data y(x), depending on a 1D argument.

TEST_INTERP_2D, a FORTRAN90 code which defines test problems for interpolation of data z(x,y)), depending on a 2D argument.


VANDERMONDE_INTERP_2D, a MATLAB library which finds a polynomial interpolant to data z(x,y) of a 2D argument by setting up and solving a linear system for the polynomial coefficients, involving the Vandermonde matrix.


  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:

Last revised on 03 September 2020.