rbf_interp_nd, a FORTRAN90 code which defines and evaluates radial basis function (RBF) interpolants to multidimensional data.
A radial basis interpolant is a useful, but expensive, technique for definining a smooth function which interpolates a set of function values specified at an arbitrary set of data points.
Given nd multidimensional points xd with function values fd, and a basis function phi(r), the form of the interpolant is
f(x) = sum ( 1 <= i <= nd ) w(i) * phi(||x-xd(i)||)where the weights w have been precomputed by solving
sum ( 1 <= i <= nd ) w(i) * phi(||xd(j)-xd(i)||) = fd(j)
Four families of radial basis functions are provided.
The code needs 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
rbf_interp_nd is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version.
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_1D, a FORTRAN90 code which defines and evaluates radial basis function (RBF) interpolants to 1D data.
RBF_INTERP_2D, a FORTRAN90 code which defines and evaluates radial basis function (RBF) interpolants to 2D data.
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SPARSE_INTERP_ND a FORTRAN90 code 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_ND, a FORTRAN90 code which defines test problems for interpolation of data z(x), depending on an M-dimensional argument.