Thu Sep 13 12:59:34 2018 PRAXIS_TEST Python version: 3.6.5 Test the PRAXIS library. BEALE_TEST Python version: 3.6.5 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 BEALE_TEST: Normal end of execution. BOX_TEST Python version: 3.6.5 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 = 1.86586e-26 BOX_TEST: Normal end of execution. CHEBYQUAD_TEST Python version: 3.6.5 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 CHEBYQUAD_TEST: Normal end of execution. CUBE_TEST Python version: 3.6.5 The Cube function. Initial point: 0: -1.2 1: -1 Function value = 57.8384 Computed minimizer: 0: 1 1: 1 Function value = 2.9475e-25 CUBE_TEST: Normal end of execution. HELIX_TEST Python version: 3.6.5 The Fletcher-Powell Helix function. Initial point: 0: -1 1: 0 2: 0 Function value = 10000 Computed minimizer: 0: 1 1: 1.56759e-09 2: 2.48566e-09 Function value = 6.47992e-18 HELIX_TEST: Normal end of execution. HILBERT_TEST Python version: 3.6.5 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: 4.69862e-07 1: -4.12104e-05 2: 0.000882944 3: -0.00806313 4: 0.0386016 5: -0.10644 6: 0.175078 7: -0.169551 8: 0.0891712 9: -0.0196397 Function value = 8.81956e-15 HILBERT_TEST: Normal end of execution. POWELL3D_TEST Python version: 3.6.5 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 POWELL3D_TEST: Normal end of execution. ROSENBROCK_TEST Python version: 3.6.5 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 ROSENBROCK_TEST: Normal end of execution. SINGULAR_TEST Python version: 3.6.5 The Powell Singular function. Initial point: 0: 3 1: -1 2: 0 3: 1 Function value = 215 Computed minimizer: 0: 2.61381e-06 1: -2.61381e-07 2: -1.66163e-06 3: -1.6616e-06 Function value = 6.01228e-21 SINGULAR_TEST: Normal end of execution. TRIDIAGONAL_TEST Python version: 3.6.5 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 TRIDIAGONAL_TEST: Normal end of execution. WATSON_TEST Python version: 3.6.5 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 WATSON_TEST: Normal end of execution. WOOD_TEST Python version: 3.6.5 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 = 1.84968e-21 WOOD_TEST: Normal end of execution. MINFIT_TEST Python version: 3.6.5 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 MINFIT_TEST: Normal end of execution. SVSORT_TEST Python version: 3.6.5 SVSORT sorts a vector D, and the corresponding columns of a matrix V. First row = entries of D. Corresponding columns of V below. 0.0458309 0.548504 0.839205 0.885236 0.382575 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: 0.885236 0.839205 0.548504 0.382575 0.0458309 14 13 12 15 11 24 23 22 25 21 34 33 32 35 31 44 43 42 45 41 54 53 52 55 51 SVSORT_TEST: Normal end of execution. PRAXIS_TEST: Normal end of execution. Thu Sep 13 12:59:34 2018