spinterp_test

spinterp_test, MATLAB codes which call spinterp(), which is a powerful MATLAB code which uses sparse grids to carry out optimization, interpolation, and quadrature in higher dimensional spaces.

Licensing:

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

Languages:

spinterp_test is available in a MATLAB version.

Related Data and Programs:

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_ND, a MATLAB code which defines test problems for interpolation of data z(x), depending on an M-dimensional argument.

TOMS847, a MATLAB code which carries out piecewise multilinear hierarchical sparse grid interpolation; this library is commonly called SPINTERP (version 2.1); this is ACM TOMS Algorithm 847, by Andreas Klimke;

Reference:

1. Andreas Klimke, Barbara Wohlmuth,
   Algorithm 847: SPINTERP: Piecewise Multilinear Hierarchical Sparse Grid Interpolation in MATLAB,
   ACM Transactions on Mathematical Software,
   Volume 31, Number 4, December 2005, pages 561-579.
2. Andreas Klimke,
   SPINTERP V2.1: Piecewise multilinear hierarchical sparse grid interpolation in MATLAB: Documentation.
3. Andreas Klimke,
   SPINTERP V2.1: Examples: Reference Results.

Source Code:

• r8mat_print.m prints an R8MAT.
• r8mat_print_some.m prints some of an R8MAT.
• timestamp.m prints the YMDHMS date as a timestamp.

DISPLAY_GRID_TYPES shows examples in 2 dimensions of the level 0, 1 and 2 versions of the grid types available in SPINTERP, namely Chebyshev, Clenshaw-Curtis (not what you think!), Gauss-Patterson, Maximum, and NoBoundary.

• display_grid_types.m the code.
• display_grid_types.txt the output file.
• chebyshev_grid.png points for level 0/1/2 Chebyshev grids.
• clenshaw-curtis_grid.png points for level 0/1/2 Clenshaw-Curtis grids.
• default_grid.png points for level 0/1/2 default (=Clenshaw-Curtis) grids.
• gauss-patterson_grid.png points for level 0/1/2 Gauss-Patterson grids.
• maximum_grid.png points for level 0/1/2 Maximum grids.
• noboundary_grid.png points for level 0/1/2 No Boundary grids.

SINCOS seeks an interpolant of z(x,y)=sin(x)+cos(y).

• sincos_test.m creates an interpolant to z=sin(x)+cos(y) and displays it.
• sincos_test.txt creates an interpolant to z=sin(x)+cos(y) and displays it.
• sincos_f.m evaluates z=sin(x)+cos(y).
• sincos_grid.png an image of the grid.
• sincos_interp.png an image comparing the function and its interpolant.

TEST_ONE demonstrates how SPINTERP can be used to compute and evaluate an interpolant to a function of a multidimensional argument.

• test_one.m carries out the test.
• f_one.m the function to be interpolated.
• test_one.png a plot comparing the interpolant and the original function.
• test_one.txt the output file.

TEST_TWO demonstrates how SPINTERP can be used to estimate the integral of function of a multidimensional argument.

• test_two.m carries out the test.
• f_two.m the function to be integrated.
• test_two.txt the output file.

TEST_THREE demonstrates how SPINTERP can be used to optimize (in this case, minimize) a function of a multidimensional argument.

• test_three.m carries out the test.
• f_three.m the function to be minimized.
• g_three.m evaluates log ( f_three + 2 ), useful for plotting contour lines.
• test_three.png a contour plot of the function to be minimized.
• test_three.txt the output file.

TIMING estimates the amount of time required to set up a sparse grid for dimensions 1 through 20, and levels 0 through 5.

• timing_test.m carries out the test.
• timing_test.txt the output file.