test_interp_nd

test_interp_nd, a MATLAB 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:

• the function, f(x);
• the derivative with respect to any coordinate, dfdx(i);
• the integral of f(x) over the unit hypercube;

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:

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

Languages:

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 MATLAB 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 MATLAB code which contains many utility routines using double precision real (r8) arithmetic.

rbf_interp_nd, a MATLAB code which defines and evaluates radial basis function (rbf) interpolants to multidimensional data.

shepard_interp_nd, a MATLAB code which defines and evaluates shepard interpolants to multidimensional data, based on inverse distance weighting.

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

spinterp, a MATLAB code 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 MATLAB code which defines test problems for interpolation of data y(x), depending on a 2d argument.

test_interp_2d, a MATLAB code which defines test problems for interpolation of data z(x,y), depending on a 2d argument.

test_interp_nd_test

Reference:

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:

• csevl.m, evaluates a Chebyshev series.
• inits.m, initializes a Chebyshev series.
• p00_cw.m, returns a random C parameter vector for any problem.
• p00_d.m, returns a derivative component of any function.
• p00_f.m, returns the value of any function.
• p00_prob_num.m, returns the number of test functions available.
• p00_q.m, returns the integral of any function.
• p00_title.m, returns the title for any function.
• p00_cw.m, returns a random W parameter vector for any problem.
• p01_d.m, evaluates a derivative component for problem p01.
• p01_f.m, evaluates the function for problem p01.
• p01_q.m, returns the integral for problem p01.
• p01_title.m, returns the name of problem p01.
• p02_d.m, evaluates a derivative component for problem p02.
• p02_f.m, evaluates the function for problem p02.
• p02_q.m, returns the integral for problem p02.
• p02_title.m, returns the title of problem p02.
• p03_d.m, evaluates a derivative component for problem p03.
• p03_f.m, evaluates the function for problem p03.
• p03_q.m, returns the integral for problem p03.
• p03_title.m, returns the title of problem p03.
• p04_d.m, evaluates a derivative component for problem p04.
• p04_f.m, evaluates the function for problem p04.
• p04_q.m, returns the integral for problem p04.
• p04_title.m, returns the title of problem p04.
• p05_d.m, evaluates a derivative component for problem p05.
• p05_f.m, evaluates the function for problem p05.
• p05_q.m, returns the integral for problem p05.
• p05_title.m, returns the title of problem p05.
• p06_d.m, evaluates a derivative component for problem p06.
• p06_f.m, evaluates the function for problem p06.
• p06_q.m, returns the integral for problem p06.
• p06_title.m, returns the title of problem p06.
• r8_error.m, evaluates the error function of an R8 argument.
• r8_errorc.m, evaluates the co-error function of an R8 argument.
• r8_mach.m, returns double precision real machine-dependent constants.
• tuple_next.m, computes the next element of a tuple space.