04-Jul-2023 16:54:30

sparse_interp_nd_test():
  MATLAB/Octave version 5.2.0
  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  2.456574e-02
   1         3  4.993937e-04
   2         5  1.645560e-06
   3         9  2.147429e-12
   4        17  1.663780e-17
   5        33  3.221914e-17
   6        65  4.877147e-17
   7       129  5.426915e-17
   8       257  8.527596e-17
   9       513  2.323085e-16

Elapsed time is 4.54718 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  2.024158e-02
   1         7  6.618112e-03
   2        25  5.384518e-04
   3        67  7.446342e-04
   4       161  2.474966e-04
   5       371  9.156419e-05
   6       837  2.590482e-05
   7      1863  1.386365e-05
   8      4105  1.017629e-06
   9      8971  7.009862e-07

Elapsed time is 49.1559 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  1.610001e-02
   1        10  5.557536e-03
   2        52  1.959519e-03
   3       195  2.727117e-04
   4       609  4.706581e-04
   5      1710  2.088684e-04
   6      4502  1.243270e-04
   7     11369  4.493041e-05
   8     27887  1.852853e-05
   9     66936  6.359041e-06

Elapsed time is 316.37 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  1.241507e-02
   1        13  5.134260e-03
   2        87  1.555106e-03
   3       411  6.158439e-04
   4      1573  1.258538e-04
   5      5257  1.970597e-04
   6     16035  1.818317e-04
   7     45879  9.881760e-05

Elapsed time is 247.883 seconds.

sparse_interp_nd_test():
  Normal end of execution.

04-Jul-2023 17:04:48