test_interp_nd, a Fortran77 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:
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 information on this web page is 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 and an Octave version.
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.