16 April 2020 10:42:54 AM
 
SPARSE_INTERP_ND_TEST
  C++ version.
  Test the SPARSE_INTERP_ND library.
  The R8LIB library is also required.

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

   1         1  0.0266025
   2         3  0.000508024
   3         5  1.57667e-06
   4         9  2.19906e-12
   5        17  1.45153e-17
   6        33  3.24798e-17
   7        65  4.12282e-17
   8       129  5.0684e-17
   9       257  8.66074e-17
  10       513  1.34147e-16

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

   1         1  0.021141
   2         7  0.00737722
   3        25  0.000591988
   4        67  0.000589933
   5       161  0.000220092
   6       371  9.36652e-05
   7       837  3.08829e-05
   8      1863  1.31047e-05
   9      4105  4.49018e-06
  10      8971  1.97669e-06

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

   1         1  0.0152554
   2        10  0.0056412
   3        52  0.00218861
   4       195  0.000246487
   5       609  0.000472271
   6      1710  0.000199142
   7      4502  9.84156e-05
   8     11369  3.05e-05
   9     27887  1.50904e-05
  10     66936  7.43204e-06

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

   1         1  0.0141882
   2        13  0.00607818
   3        87  0.00243312
   4       411  0.00124224
   5      1573  0.000126831
   6      5257  0.000414999
   7     16035  0.000211415
   8     45879  0.000155305
 
SPARSE_INTERP_ND_TEST
  Normal end of execution.
 
16 April 2020 10:42:58 AM