Wed Oct 8 08:47:23 2025 praxis_test() python version: 3.10.12 numpy version: 1.26.4 Test praxis(). beale_test(): Test praxis() with 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(): Test praxis() with 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 = 2.51413e-26 chebyquad_test(): Test praxis() with 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(): Test praxis() with the cube() function. Initial point: 0: -1.2 1: -1 Function value = 57.8384 Computed minimizer: 0: 1 1: 1 Function value = 6.87793e-27 helix_test(): Test praxis() with the Fletcher-Powell helix() function. Initial point: 0: -1 1: 0 2: 0 Function value = 10000 Computed minimizer: 0: 1 1: -4.4294e-09 2: -7.02969e-09 Function value = 4.96755e-17 hilbert_test(): Test praxis() with 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: 1.62286e-05 1: -0.00139703 2: 0.0300803 3: -0.276762 4: 1.33403 5: -3.69937 6: 6.11349 7: -5.94374 8: 3.13646 9: -0.692818 Function value = 1.08404e-11 powell3d_test(): Test praxis() with the powell3d() 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(): Test praxis() with 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(): Test praxis() with the Powell singular() function. Initial point: 0: 3 1: -1 2: 0 3: 1 Function value = 215 Computed minimizer: 0: 1.33581e-05 1: -1.33581e-06 2: 4.88398e-06 3: 4.88392e-06 Function value = 8.418e-20 tridiagonal_test(): Test praxis() with 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(): Test praxis() with 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(): Test praxis() with 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 = 2.45617e-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: 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. 0.172952 0.350095 0.49417 0.258224 0.0493318 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: 0.49417 0.350095 0.258224 0.172952 0.0493318 13 12 14 11 15 23 22 24 21 25 33 32 34 31 35 43 42 44 41 45 53 52 54 51 55 praxis_test(): Normal end of execution. Wed Oct 8 08:47:23 2025