08-Jan-2022 09:14:22

rbf_interp_nd_test():
  MATLAB/Octave version 9.8.0.1380330 (R2020a) Update 2
  Test rbf_interp_nd().
  The R8LIB library is also needed.

RBF_INTERP_ND_TEST01:
  RBF_WEIGHT computes weights for RBF interpolation.
  RBF_INTERP_ND evaluates the RBF interpolant.
  Use the multiquadratic basis function PHI1(R).

  The product points:

  Row:       1             2       
  Col
    1:           0           0
    2:         0.5           0
    3:           1           0
    4:         1.5           0
    5:           2           0
    6:           0         0.5
    7:         0.5         0.5
    8:           1         0.5
    9:         1.5         0.5
   10:           2         0.5
   11:           0           1
   12:         0.5           1
   13:           1           1
   14:         1.5           1
   15:           2           1
   16:           0         1.5
   17:         0.5         1.5
   18:           1         1.5
   19:         1.5         1.5
   20:           2         1.5
   21:           0           2
   22:         0.5           2
   23:           1           2
   24:         1.5           2
   25:           2           2
  Setting R0 = 0.4

  Scale factor R0 = 0.4

  Function data:

     1:            0
     2:            0
     3:            0
     4:            0
     5:            0
     6:            0
     7:       0.1947
     8:     0.303265
     9:     0.354275
    10:     0.367879
    11:            0
    12:     0.303265
    13:     0.367879
    14:     0.334695
    15:     0.270671
    16:            0
    17:     0.354275
    18:     0.334695
    19:     0.237148
    20:     0.149361
    21:            0
    22:     0.367879
    23:     0.270671
    24:     0.149361
    25:    0.0732626

  Weight vector:

     1:    -0.501359
     2:     0.300861
     3:      0.23295
     4:     0.369441
     5:     0.645573
     6:     0.300861
     7:    -0.155096
     8:    -0.367322
     9:    -0.407046
    10:     -1.30006
    11:      0.23295
    12:    -0.367322
    13:     0.182323
    14:     0.203404
    15:     0.514794
    16:     0.369441
    17:    -0.407046
    18:     0.203404
    19:     -0.12928
    20:   0.00990249
    21:     0.645573
    22:     -1.30006
    23:     0.514794
    24:   0.00990249
    25:    0.0666187

  L2 interpolation error averaged per interpolant node = 1.26424e-16

  L2 approximation error averaged per 1000 samples = 0.00298794

RBF_INTERP_ND_TEST02:
  RBF_WEIGHT computes weights for RBF interpolation.
  RBF_INTERP_ND evaluates the RBF interpolant.
  Use the multiquadratic basis function PHI2(R).

  The product points:

  Row:       1             2       
  Col
    1:           0           0
    2:         0.5           0
    3:           1           0
    4:         1.5           0
    5:           2           0
    6:           0         0.5
    7:         0.5         0.5
    8:           1         0.5
    9:         1.5         0.5
   10:           2         0.5
   11:           0           1
   12:         0.5           1
   13:           1           1
   14:         1.5           1
   15:           2           1
   16:           0         1.5
   17:         0.5         1.5
   18:           1         1.5
   19:         1.5         1.5
   20:           2         1.5
   21:           0           2
   22:         0.5           2
   23:           1           2
   24:         1.5           2
   25:           2           2

  Scale factor R0 = 0.4

  Function data:

     1:            0
     2:            0
     3:            0
     4:            0
     5:            0
     6:            0
     7:       0.1947
     8:     0.303265
     9:     0.354275
    10:     0.367879
    11:            0
    12:     0.303265
    13:     0.367879
    14:     0.334695
    15:     0.270671
    16:            0
    17:     0.354275
    18:     0.334695
    19:     0.237148
    20:     0.149361
    21:            0
    22:     0.367879
    23:     0.270671
    24:     0.149361
    25:    0.0732626

  Weight vector:

     1:   0.00455693
     2:    -0.044454
     3:   -0.0711033
     4:   -0.0829322
     5:    -0.121156
     6:    -0.044454
     7:    0.0524777
     8:    0.0753675
     9:      0.10031
    10:     0.184681
    11:   -0.0711033
    12:    0.0753675
    13:    0.0199836
    14:   0.00472747
    15:  -0.00972847
    16:   -0.0829322
    17:      0.10031
    18:   0.00472747
    19:   0.00968919
    20:   -0.0108128
    21:    -0.121156
    22:     0.184681
    23:  -0.00972847
    24:   -0.0108128
    25:   -0.0325387

  L2 interpolation error averaged per interpolant node = 2.22577e-17

  L2 approximation error averaged per 1000 samples = 0.0041942

RBF_INTERP_ND_TEST03:
  RBF_WEIGHT computes weights for RBF interpolation.
  RBF_INTERP_ND evaluates the RBF interpolant.
  Use the multiquadratic basis function PHI3(R).

  The product points:

  Row:       1             2       
  Col
    1:           0           0
    2:         0.5           0
    3:           1           0
    4:         1.5           0
    5:           2           0
    6:           0         0.5
    7:         0.5         0.5
    8:           1         0.5
    9:         1.5         0.5
   10:           2         0.5
   11:           0           1
   12:         0.5           1
   13:           1           1
   14:         1.5           1
   15:           2           1
   16:           0         1.5
   17:         0.5         1.5
   18:           1         1.5
   19:         1.5         1.5
   20:           2         1.5
   21:           0           2
   22:         0.5           2
   23:           1           2
   24:         1.5           2
   25:           2           2

  Scale factor R0 = 0.4

  Function data:

     1:            0
     2:            0
     3:            0
     4:            0
     5:            0
     6:            0
     7:       0.1947
     8:     0.303265
     9:     0.354275
    10:     0.367879
    11:            0
    12:     0.303265
    13:     0.367879
    14:     0.334695
    15:     0.270671
    16:            0
    17:     0.354275
    18:     0.334695
    19:     0.237148
    20:     0.149361
    21:            0
    22:     0.367879
    23:     0.270671
    24:     0.149361
    25:    0.0732626

  Weight vector:

     1:     0.433461
     2:    -0.204877
     3:   -0.0872454
     4:    -0.246184
     5:   -0.0676362
     6:    -0.204877
     7:   -0.0378926
     8:     0.133989
     9:     0.127043
    10:     0.441877
    11:   -0.0872454
    12:     0.133989
    13:   -0.0423124
    14:    -0.107041
    15:    -0.183447
    16:    -0.246184
    17:     0.127043
    18:    -0.107041
    19:   -0.0378467
    20:    -0.107503
    21:   -0.0676362
    22:     0.441877
    23:    -0.183447
    24:    -0.107503
    25:     0.141281

  L2 interpolation error averaged per interpolant node = 1.04779e-16

  L2 approximation error averaged per 1000 samples = 0.00258124

RBF_INTERP_ND_TEST04:
  RBF_WEIGHT computes weights for RBF interpolation.
  RBF_INTERP_ND evaluates the RBF interpolant.
  Use the multiquadratic basis function PHI4(R).

  The product points:

  Row:       1             2       
  Col
    1:           0           0
    2:         0.5           0
    3:           1           0
    4:         1.5           0
    5:           2           0
    6:           0         0.5
    7:         0.5         0.5
    8:           1         0.5
    9:         1.5         0.5
   10:           2         0.5
   11:           0           1
   12:         0.5           1
   13:           1           1
   14:         1.5           1
   15:           2           1
   16:           0         1.5
   17:         0.5         1.5
   18:           1         1.5
   19:         1.5         1.5
   20:           2         1.5
   21:           0           2
   22:         0.5           2
   23:           1           2
   24:         1.5           2
   25:           2           2

  Scale factor R0 = 0.4

  Function data:

     1:            0
     2:            0
     3:            0
     4:            0
     5:            0
     6:            0
     7:       0.1947
     8:     0.303265
     9:     0.354275
    10:     0.367879
    11:            0
    12:     0.303265
    13:     0.367879
    14:     0.334695
    15:     0.270671
    16:            0
    17:     0.354275
    18:     0.334695
    19:     0.237148
    20:     0.149361
    21:            0
    22:     0.367879
    23:     0.270671
    24:     0.149361
    25:    0.0732626

  Weight vector:

     1:    0.0247652
     2:   -0.0461165
     3:   -0.0818427
     4:   -0.0622022
     5:     -0.17306
     6:   -0.0461165
     7:    0.0838087
     8:     0.173681
     9:     0.128662
    10:      0.37891
    11:   -0.0818427
    12:     0.173681
    13:     0.051454
    14:    0.0737542
    15:   -0.0110253
    16:   -0.0622022
    17:     0.128662
    18:    0.0737542
    19:    0.0630212
    20:     0.076087
    21:     -0.17306
    22:      0.37891
    23:   -0.0110253
    24:     0.076087
    25:   -0.0125014

  L2 interpolation error averaged per interpolant node = 8.47965e-18

  L2 approximation error averaged per 1000 samples = 0.00400359

rbf_interp_nd_test():
  Normal end of execution.

08-Jan-2022 09:14:26