08-Jan-2022 09:45:55

sparse_interp_nd_test():
  MATLAB/Octave version 9.8.0.1380330 (R2020a) Update 2
  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  2.522725e-02
   1         3  5.062799e-04
   2         5  1.631396e-06
   3         9  2.037762e-12
   4        17  2.048961e-17
   5        33  3.487766e-17
   6        65  3.392992e-17
   7       129  4.254838e-17
   8       257  6.818169e-17
   9       513  4.246672e-15

Elapsed time is 0.728660 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  1.953485e-02
   1         7  6.473906e-03
   2        25  5.995136e-04
   3        67  7.488308e-04
   4       161  2.369064e-04
   5       371  7.620782e-05
   6       837  2.287569e-05
   7      1863  1.329944e-05
   8      4105  1.258689e-06
   9      8971  7.530324e-07

Elapsed time is 4.405118 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  1.668699e-02
   1        10  6.463606e-03
   2        52  2.448000e-03
   3       195  3.217250e-04
   4       609  6.641054e-04
   5      1710  3.150076e-04
   6      4502  1.408414e-04
   7     11369  6.275155e-05
   8     27887  3.375686e-05
   9     66936  8.420761e-06

Elapsed time is 25.243910 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  1.363654e-02
   1        13  5.663999e-03
   2        87  1.780058e-03
   3       411  7.507483e-04
   4      1573  1.649774e-04
   5      5257  2.399414e-04
   6     16035  2.645979e-04
   7     45879  1.931831e-04

Elapsed time is 18.756200 seconds.

sparse_interp_nd_test():
  Normal end of execution.

08-Jan-2022 09:46:45