04 March 2022 01:09:08 PM

PRAXIS_TEST
  C++ version
  Test the PRAXIS library.

BEALE_TEST
  The Beale function.

  Initial point:

         0:            0.1
         1:            0.1
  Function value = 12.991

  Computed minimizer:

         0:              3
         1:            0.5
  Function value = 3.70308e-26

BOX_TEST
  The Box function.

  Initial point:

         0:              0
         1:             10
         2:             20
  Function value = 1031.15

  Computed minimizer:

         0:              1
         1:             10
         2:              1
  Function value = 1.94198e-26

CHEBYQUAD_TEST
  The Chebyquad function.

  Initial point:

         0:       0.111111
         1:       0.222222
         2:       0.333333
         3:       0.444444
         4:       0.555556
         5:       0.666667
         6:       0.777778
         7:       0.888889
  Function value = 0.0386177

  Computed minimizer:

         0:      0.0431527
         1:       0.193091
         2:       0.266329
         3:            0.5
         4:            0.5
         5:       0.733671
         6:       0.806909
         7:       0.956847
  Function value = 0.00351687

CUBE_TEST
  The Cube function.

  Initial point:

         0:           -1.2
         1:             -1
  Function value = 57.8384

  Computed minimizer:

         0:              1
         1:              1
  Function value = 8.68265e-22

HELIX_TEST
  The Fletcher-Powell Helix function.

  Initial point:

         0:             -1
         1:              0
         2:              0
  Function value = 10000

  Computed minimizer:

         0:              1
         1:    2.73789e-10
         2:    4.33792e-10
  Function value = 1.99308e-19

HILBERT_TEST
  The Hilbert function.

  Initial point:

         0:              1
         1:              1
         2:              1
         3:              1
         4:              1
         5:              1
         6:              1
         7:              1
         8:              1
         9:              1
  Function value = 13.3754

  Computed minimizer:

         0:   -1.34882e-10
         1:    8.82905e-09
         2:   -1.26442e-07
         3:    7.14152e-07
         4:   -1.86151e-06
         5:    1.94693e-06
         6:    7.24941e-07
         7:   -3.57163e-06
         8:    3.01855e-06
         9:   -8.53612e-07
  Function value = 1.1713e-21

POWELL3D_TEST
  The Powell 3D function.

  Initial point:

         0:              0
         1:              1
         2:              2
  Function value = 1.5

  Computed minimizer:

         0:              1
         1:              1
         2:              1
  Function value = 0

ROSENBROCK_TEST
  The Rosenbrock function.

  Initial point:

         0:           -1.2
         1:              1
  Function value = 24.2

  Computed minimizer:

         0:              1
         1:              1
  Function value = 4.46274e-24

SINGULAR_TEST
  The Powell Singular function.

  Initial point:

         0:              3
         1:             -1
         2:              0
         3:              1
  Function value = 215

  Computed minimizer:

         0:   -3.79004e-06
         1:    3.79004e-07
         2:   -8.18762e-07
         3:   -8.18766e-07
  Function value = 8.65468e-22

TRIDIAGONAL_TEST
  The Tridiagonal function.

  Initial point:

         0:              0
         1:              0
         2:              0
         3:              0
  Function value = 0

  Computed minimizer:

         0:              4
         1:              3
         2:              2
         3:              1
  Function value = -4

WATSON_TEST
  The Watson function.

  Initial point:

         0:              0
         1:              0
         2:              0
         3:              0
         4:              0
         5:              0
  Function value = 30

  Computed minimizer:

         0:     -0.0157251
         1:        1.01243
         2:      -0.232992
         3:        1.26043
         4:       -1.51373
         5:       0.992996
  Function value = 0.00228767

WOOD_TEST
  The Wood function.

  Initial point:

         0:             -3
         1:             -1
         2:             -3
         3:             -1
  Function value = 19192

  Computed minimizer:

         0:              1
         1:              1
         2:              1
         3:              1
  Function value = 2.14612e-19

MINFIT_TEST
  MINFIT computes part of the SVD of a matrix A.
    SVD: A = U * D * V'
  MINFIT is given A, and returns the diagonal D
  and the orthogonal matrix V.

  The matrix A:

  Col:          0             1             2             3             4       
  Row

    0:            2            -1             0             0             0  
    1:           -1             2            -1             0             0  
    2:            0            -1             2            -1             0  
    3:            0             0            -1             2            -1  
    4:            0             0             0            -1             2  

  The vector V:

  Col:          0             1             2             3             4       
  Row

    0:    -0.288675           0.5      -0.57735           0.5     -0.288675  
    1:          0.5          -0.5   2.40746e-16           0.5          -0.5  
    2:     -0.57735    1.9082e-16       0.57735   -3.5911e-16      -0.57735  
    3:          0.5           0.5   6.07563e-17          -0.5          -0.5  
    4:    -0.288675          -0.5      -0.57735          -0.5     -0.288675  

  The singular values D:

         0:        3.73205
         1:              3
         2:              2
         3:              1
         4:       0.267949

  Because A is positive definite symmetric,
  we can reconstruct it as A = V * D * V'

  The product A2 = V * D * V'

  Col:          0             1             2             3             4       
  Row

    0:            2            -1  -4.92661e-16   -9.4369e-16  -1.63064e-16  
    1:           -1             2            -1             0  -7.35523e-16  
    2: -3.88578e-16            -1             2            -1  -4.02456e-16  
    3:  -9.4369e-16  -1.11022e-16            -1             2            -1  
    4: -1.66533e-16  -7.35523e-16  -2.91434e-16            -1             2  

SVSORT_TEST
  SVSORT sorts a vector D, and the corresponding columns
  of a matrix V.

  First row = entries of D.
  Corresponding columns of V below.

      0.218418      0.956318      0.829509      0.561695      0.415307

            11            12            13            14            15
            21            22            23            24            25
            31            32            33            34            35
            41            42            43            44            45
            51            52            53            54            55

  After sorting D and rearranging V:

      0.956318      0.829509      0.561695      0.415307      0.218418

            12            13            14            15            11
            22            23            24            25            21
            32            33            34            35            31
            42            43            44            45            41
            52            53            54            55            51

PRAXIS_TEST
  Normal end of execution.

04 March 2022 01:09:08 PM