19-Jun-2023 07:20:21

praxis_test():
  MATLAB/Octave version 5.2.0
  Test praxis()

beale_test():
  beale() evaluates the Beale function.

  Initial point:

     1:          0.1
     2:          0.1
  Function value = 12.991

  Computed minimizer:

     1:            3
     2:          0.5
  Function value = 3.72204e-26

box_test()
  box() evaluates the Box function.

  Initial point:

     1:            0
     2:           10
     3:           20
  Function value = 1031.15

  Computed minimizer:

     1:            1
     2:           10
     3:            1
  Function value = 3.09179e-26

chebyquad_test():
  chebyquad() evaluates the Chebyquad function.

  Initial point:

     1:     0.111111
     2:     0.222222
     3:     0.333333
     4:     0.444444
     5:     0.555556
     6:     0.666667
     7:     0.777778
     8:     0.888889
  Function value = 0.196514

  Computed minimizer:

     1:    0.0431528
     2:     0.193091
     3:     0.266329
     4:          0.5
     5:          0.5
     6:     0.733671
     7:     0.806909
     8:     0.956847
  Function value = 0.0593032

cube_test():
  cube() evaluates the Cube function.

  Initial point:

     1:         -1.2
     2:           -1
  Function value = 57.8384

  Computed minimizer:

     1:            1
     2:            1
  Function value = 7.13076e-27

helix_test()
  helix() evaluates the Fletcher-Powell Helix function.

  Initial point:

     1:           -1
     2:            0
     3:            0
  Function value = 10000

  Computed minimizer:

     1:            1
     2:  9.98714e-13
     3:  1.58482e-12
  Function value = 3.62547e-23

hilbert_test():
  hilbert() evaluates the Hilbert function.

  Initial point:

     1:            1
     2:            1
     3:            1
     4:            1
     5:            1
     6:            1
     7:            1
     8:            1
     9:            1
    10:            1
  Function value = 13.3754

  Computed minimizer:

     1:  1.01779e-06
     2:  -8.7757e-05
     3:   0.00186422
     4:   -0.0168983
     5:    0.0803691
     6:    -0.220325
     7:     0.360546
     8:    -0.347579
     9:     0.182062
    10:   -0.0399533
  Function value = 3.73913e-14

powell3d_test()
  powell_3d() evaluates the Powell 3D function.

  Initial point:

     1:            0
     2:            1
     3:            2
  Function value = 1.5

  Computed minimizer:

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

rosenbrock_test():
  rosenbrock() evaluates the Rosenbrock function.

  Initial point:

     1:         -1.2
     2:            1
  Function value = 24.2

  Computed minimizer:

     1:            1
     2:            1
  Function value = 4.48935e-24

singular_test():
  singular() evaluates the Powell Singular function.

  Initial point:

     1:            3
     2:           -1
     3:            0
     4:            1
  Function value = 215

  Computed minimizer:

     1: -5.75851e-06
     2:  5.75851e-07
     3: -2.61728e-06
     4: -2.61728e-06
  Function value = 2.11768e-21

tridiagonal_test():
  tridiagonal() evaluates the Tridiagonal function.

  Initial point:

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

  Computed minimizer:

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

watson_test():
  watson() evaluates the Watson function.

  Initial point:

     1:            0
     2:            0
     3:            0
     4:            0
     5:            0
     6:            0
  Function value = 30

  Computed minimizer:

     1:   -0.0157251
     2:      1.01243
     3:    -0.232992
     4:      1.26043
     5:     -1.51373
     6:     0.992996
  Function value = 0.00228767

wood_test():
  wood() evaluates the Wood function.

  Initial point:

     1:           -3
     2:           -1
     3:           -3
     4:           -1
  Function value = 19192

  Computed minimizer:

     1:            1
     2:            1
     3:            1
     4:            1
  Function value = 1.12313e-18

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:       1             2             3             4             5       
  Row
      1 :           2            -1             0             0             0  
      2 :          -1             2            -1             0             0  
      3 :           0            -1             2            -1             0  
      4 :           0             0            -1             2            -1  
      5 :           0             0             0            -1             2  

  The vector V:

  Col:       1             2             3             4             5       
  Row
      1 :   -0.288675           0.5      -0.57735           0.5     -0.288675  
      2 :         0.5          -0.5   2.44073e-16           0.5          -0.5  
      3 :    -0.57735   1.59595e-16       0.57735   -3.0807e-16      -0.57735  
      4 :         0.5           0.5  -6.39419e-17          -0.5          -0.5  
      5 :   -0.288675          -0.5      -0.57735          -0.5     -0.288675  

  The singular values D:

     1:      3.73205
     2:            3
     3:            2
     4:            1
     5:     0.267949

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

  The product A2 = V * D * V'

  Col:       1             2             3             4             5       
  Row
      1 :           2            -1  -4.30211e-16  -8.04912e-16   4.71845e-16  
      2 :          -1             2            -1   4.57967e-16  -3.33067e-16  
      3 :-5.41234e-16            -1             2            -1  -2.84495e-16  
      4 :-8.04912e-16   3.46945e-16            -1             2            -1  
      5 : 4.71845e-16  -2.22045e-16  -2.84495e-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.

      0.940633      0.794954      0.778209      0.779173      0.514634

            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:

      0.940633      0.794954      0.779173      0.778209      0.514634

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

praxis_test():
  Normal end of execution.

19-Jun-2023 07:20:25