# SPINTERP/EXAMPLES Piecewise multilinear hierarchical sparse grid interpolation

SPINTERP/EXAMPLES is a directory of MATLAB programs which demonstrate features of the SPINTERP toolbox.

### Examples and Tests:

• cmpgrids.m compares the maximum-norm-based grid, the no-boundary-nodes grid, the Clenshaw-Curtis grid, the Chebyshev grid and the Gauss-Patterson grid in d = 2 or d = 3 dimensions, level N. If N is omitted, N is taken to 4. If D is omitted, D is taken to 2.
• cmpgrids.png a PNG image of the plot created by the CMPGRIDS test program.
• spadaptanim.m, Illustrates the dimension-adaptive construction Illustrate process by means of a two-dimensional, separable function.
• spadaptdemo.m, a 2D-example for dimension-adaptive multi-linear sparse grid interpolation using the Chebyshev grid and vectorized processing of the model function.
• spadapterror.m compares the dimension-adaptive interpolation scheme to the non-adaptive one some simple test functions, for the Clenshaw- Curtis and the Chebyshev-Gauss-Lobatto grid.
• spcompare.m compares the multilinear sparse grid interpolation routines using the six test functions TESTFUNCTIONS of Genz.
• spcompare.png a PNG image of the plot created by the SPCOMPARE test program.
• spcomparederiv.m compare the achieved approximation quality of the derivatives for the multilinear Clenshaw-Curtis sparse grid (discontinuous and augmented continuous) and the Chebyshev grid.
• spcomparepoly.m compare the multilinear Clenshaw-Curtis sparse grid interpolation scheme to the polynomial interpotion scheme with the Chebyshev grid and the Gauss-Patterson grid.
• spdemo.m a 2D-example for multi-linear sparse grid interpolation using the Clenshaw-Curtis grid and vectorized processing of the function.
• spdemo.png a PNG image of the plot created by the SPDEMO test program.
• spdemovarout.m is a sparse grid interpolation demo for a function with multiple output parameters and non-vectorized processing. In this case, we use the Maximum-norm-based grid.
• spdemovarout.png a PNG image of the plot created by the SPDEMOVAROUT test program.
• testderivatives.m evaluates the derivatives of Genz's six test functions.
• testfunctions.m Genz's six test functions, typically used for testing multidimensional quadrature routines.
• timespderiv.m plot a graph showing the ratio of computing BOTH interpolated values AND gradients to computing interpolated values ONLY (at 100 points simultaneously). By default, the Clenshaw-Curtis-grid with sparse indices data is used. Alternatively, the Chebyshev grid and other options may be selected using an OPTIONS structure created with SPSET.
• timespinterp.m draw a graph showing the time to compute 1000 interpolated points with SPINTERP. By default, the Clenshaw-Curtis-grid is used. Other grid types can be selected using the SPSET method.
• timespinterp.png a PNG image of the plot created by the TIMESPINTERP test program.
• timespvals.m test the performance of the sparse grid interpolation routine SPVALS by measuring the required time to compute the hierarchical surpluses. By default, the Clenshaw-Curtis grid is used. Other grid types can be selected using the SPSET method.
• timespvals.png a PNG image of the plot created by the TIMESPVALS test program.
• timespvalsdct.m compares the performance of SPVALS for the Chebyshev-Gauss-Lobatto grid with and without the DCT-based grid construction algorithm.

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Last revised on 15 October 2009.