16-May-2025 05:10:13

sparse_interp_nd_test():
  MATLAB/Octave version 6.4.0
  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  2.650471e-02
   1         3  5.021894e-04
   2         5  1.511436e-06
   3         9  1.767895e-12
   4        17  1.505350e-17
   5        33  3.906956e-17
   6        65  3.483156e-17
   7       129  5.538826e-17
   8       257  7.665579e-17
   9       513  1.279867e-16

Elapsed time is 2.5844 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  1.920178e-02
   1         7  5.849170e-03
   2        25  5.563061e-04
   3        67  5.900751e-04
   4       161  1.884623e-04
   5       371  7.935749e-05
   6       837  2.350688e-05
   7      1863  9.981339e-06
   8      4105  1.030734e-06
   9      8971  7.978116e-07

Elapsed time is 25.9212 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  1.687677e-02
   1        10  5.923433e-03
   2        52  1.780810e-03
   3       195  2.693566e-04
   4       609  3.944768e-04
   5      1710  2.918790e-04
   6      4502  1.289213e-04
   7     11369  3.356685e-05
   8     27887  2.090216e-05
   9     66936  1.003140e-05

Elapsed time is 160.273 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  1.387132e-02
   1        13  6.036795e-03
   2        87  1.950224e-03
   3       411  8.166899e-04
   4      1573  1.337687e-04
   5      5257  2.910391e-04
   6     16035  2.606718e-04
   7     45879  1.536706e-04

Elapsed time is 127.244 seconds.

sparse_interp_nd_test():
  Normal end of execution.

16-May-2025 05:15:29