TEST_INTERP_ND is a FORTRAN90 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:
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.
The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.
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 FORTRAN90 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 FORTRAN90 library which contains many utility routines using double precision real (R8) arithmetic.
RBF_INTERP_ND, a FORTRAN90 library which defines and evaluates radial basis function (RBF) interpolants to multidimensional data.
SHEPARD_INTERP_ND, a FORTRAN90 library which defines and evaluates Shepard interpolants to multidimensional data, based on inverse distance weighting.
SPARSE_INTERP_ND a FORTRAN90 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 FORTRAN90 library which defines test problems for interpolation of data y(x), depending on a 1D argument.
TEST_INTERP_2D, a FORTRAN90 library which defines test problems for interpolation of data z(x,y)), depending on a 2D argument.
TOMS526, a FORTRAN90 library which interpolates scattered bivariate data. This is a FORTRAN90 version of ACM TOMS algorithm 526, by Hiroshi Akima;
TOMS660, a FORTRAN90 library which takes scattered 2D data and produces an interpolating function F(X,Y). This is a FORTRAN90 version of ACM TOMS algorithm 660, called qshep2d, by Robert Renka.
TOMS661, a FORTRAN90 library which takes scattered 3D data and produces an interpolating function F(X,Y,Z). This is a FORTRAN90 version of ACM TOMS algorithm 661, called qshep3d, by Robert Renka.
TOMS790, a FORTRAN90 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 a FORTRAN90 version of ACM TOMS algorithm 790.
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.
You can go up one level to the FORTRAN90 source codes.