sparse_interp_nd_test
21-Mar-2019 11:50:59

sparse_interp_nd_test
  MATLAB version.
  Test sparse_interp_nd.
  The R8LIB library is also required.

SPARSE_INTERP_ND_TEST01:
  Sparse interpolation for a function f(x) of M-dimensional argument.
  Use a sequence of sparse grids of levels 0 through SPARSE_MAX.
  Invoke a general Lagrange interpolant function to do this.

  Compare the exact function and the interpolants at a grid of points.

  The "order" is the sum of the orders of all the product grids
  used to make a particular sparse grid.

  Spatial dimension M = 1
  Maximum sparse grid level = 9
  Number of interpolation points is NI = 100

   L     Order    ApproxError

   0         1  2.660252e-02
   1         3  5.080240e-04
   2         5  1.576667e-06
   3         9  2.199063e-12
   4        17  1.703618e-17
   5        33  3.794612e-17
   6        65  3.401266e-17
   7       129  4.435931e-17
   8       257  7.631459e-17
   9       513  1.757716e-16

Elapsed time is 0.748841 seconds.

SPARSE_INTERP_ND_TEST01:
  Sparse interpolation for a function f(x) of M-dimensional argument.
  Use a sequence of sparse grids of levels 0 through SPARSE_MAX.
  Invoke a general Lagrange interpolant function to do this.

  Compare the exact function and the interpolants at a grid of points.

  The "order" is the sum of the orders of all the product grids
  used to make a particular sparse grid.

  Spatial dimension M = 2
  Maximum sparse grid level = 9
  Number of interpolation points is NI = 100

   L     Order    ApproxError

   0         1  2.114102e-02
   1         7  7.377220e-03
   2        25  5.919883e-04
   3        67  5.899332e-04
   4       161  2.200918e-04
   5       371  9.366517e-05
   6       837  3.088292e-05
   7      1863  1.310471e-05
   8      4105  4.490183e-06
   9      8971  1.976692e-06

Elapsed time is 5.166904 seconds.

SPARSE_INTERP_ND_TEST01:
  Sparse interpolation for a function f(x) of M-dimensional argument.
  Use a sequence of sparse grids of levels 0 through SPARSE_MAX.
  Invoke a general Lagrange interpolant function to do this.

  Compare the exact function and the interpolants at a grid of points.

  The "order" is the sum of the orders of all the product grids
  used to make a particular sparse grid.

  Spatial dimension M = 3
  Maximum sparse grid level = 9
  Number of interpolation points is NI = 100

   L     Order    ApproxError

   0         1  1.525544e-02
   1        10  5.641203e-03
   2        52  2.188606e-03
   3       195  2.464865e-04
   4       609  4.722710e-04
   5      1710  1.991416e-04
   6      4502  9.841563e-05
   7     11369  3.049995e-05
   8     27887  1.509040e-05
   9     66936  7.432038e-06

Elapsed time is 30.344988 seconds.

SPARSE_INTERP_ND_TEST01:
  Sparse interpolation for a function f(x) of M-dimensional argument.
  Use a sequence of sparse grids of levels 0 through SPARSE_MAX.
  Invoke a general Lagrange interpolant function to do this.

  Compare the exact function and the interpolants at a grid of points.

  The "order" is the sum of the orders of all the product grids
  used to make a particular sparse grid.

  Spatial dimension M = 4
  Maximum sparse grid level = 7
  Number of interpolation points is NI = 100

   L     Order    ApproxError

   0         1  1.418816e-02
   1        13  6.078180e-03
   2        87  2.433122e-03
   3       411  1.242241e-03
   4      1573  1.268313e-04
   5      5257  4.149993e-04
   6     16035  2.114153e-04
   7     45879  1.553052e-04

Elapsed time is 22.703017 seconds.

sparse_interp_nd_test
  Normal end of execution.

21-Mar-2019 11:51:59

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