3 August 2016 8:45:27.330 AM PRAXIS_PRB FORTRAN90 version Test the PRAXIS library. BEALE_TEST The Beale function. Initial point: 1 0.10000000 2 0.10000000 Function value = 12.9910 Computed minimizer: 1 3.0000000 2 0.50000000 Function value = 0.369857E-25 BOX_TEST The Box function. Initial point: 1 0.0000000 2 10.000000 3 20.000000 Function value = 1031.15 Computed minimizer: 1 1.0000000 2 10.000000 3 1.0000000 Function value = 0.194198E-25 CHEBYQUAD_TEST The Chebyquad function. Initial point: 1 0.11111111 2 0.22222222 3 0.33333333 4 0.44444444 5 0.55555556 6 0.66666667 7 0.77777778 8 0.88888889 Function value = 0.386177E-01 Computed minimizer: 1 0.43152699E-01 2 0.19309075 3 0.26632869 4 0.50000006 5 0.49999989 6 0.73367126 7 0.80690919 8 0.95684732 Function value = 0.351687E-02 CUBE_TEST The Cube function. Initial point: 1 -1.2000000 2 -1.0000000 Function value = 57.8384 Computed minimizer: 1 1.0000000 2 1.0000000 Function value = 0.868265E-21 HELIX_TEST The Fletcher-Powell Helix function. Initial point: 1 -1.0000000 2 0.0000000 3 0.0000000 Function value = 10000.0 Computed minimizer: 1 1.0000000 2 0.27378912E-09 3 0.43379194E-09 Function value = 0.199308E-18 HILBERT_TEST The Hilbert function. Initial point: 1 1.0000000 2 1.0000000 3 1.0000000 4 1.0000000 5 1.0000000 6 1.0000000 7 1.0000000 8 1.0000000 9 1.0000000 10 1.0000000 Function value = 13.3754 Computed minimizer: 1 -0.64423362E-06 2 0.59753831E-04 3 -0.13313527E-02 4 0.12515949E-01 5 -0.61271770E-01 6 0.17196341 7 -0.28694199 8 0.28120433 9 -0.14937973 10 0.33182686E-01 Function value = 0.245811E-13 POWELL3D_TEST The Powell 3D function. Initial point: 1 0.0000000 2 1.0000000 3 2.0000000 Function value = 1.50000 Computed minimizer: 1 1.0000000 2 1.0000000 3 1.0000000 Function value = 0.00000 ROSENBROCK_TEST The Rosenbrock function. Initial point: 1 -1.2000000 2 -1.2000000 Function value = 701.800 Computed minimizer: 1 1.0000000 2 1.0000000 Function value = 0.573253E-21 SINGULAR_TEST The Powell Singular function. Initial point: 1 3.0000000 2 -1.0000000 3 0.0000000 4 1.0000000 Function value = 215.000 Computed minimizer: 1 0.15015271E-05 2 -0.15015271E-06 3 0.13856459E-05 4 0.13856469E-05 Function value = 0.777949E-22 TRIDIAGONAL_TEST The Tridiagonal function. Initial point: 1 0.0000000 2 0.0000000 3 0.0000000 4 0.0000000 Function value = 0.00000 Computed minimizer: 1 4.0000000 2 3.0000000 3 2.0000000 4 1.0000000 Function value = -4.00000 WATSON_TEST The Watson function. Initial point: 1 0.0000000 2 0.0000000 3 0.0000000 4 0.0000000 5 0.0000000 6 0.0000000 Function value = 30.0000 Computed minimizer: 1 -0.15725086E-01 2 1.0124349 3 -0.23299162 4 1.2604301 5 -1.5137290 6 0.99299645 Function value = 0.228767E-02 WOOD_TEST The Wood function. Initial point: 1 -3.0000000 2 -1.0000000 3 -3.0000000 4 -1.0000000 Function value = 19192.0 Computed minimizer: 1 1.0000000 2 1.0000000 3 1.0000000 4 1.0000000 Function value = 0.486832E-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 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 0.500000 -0.577350 0.500000 -0.288675 2 0.500000 -0.500000 0.240746E-15 0.500000 -0.500000 3 -0.577350 0.190820E-15 0.577350 -0.359110E-15 -0.577350 4 0.500000 0.500000 0.607563E-16 -0.500000 -0.500000 5 -0.288675 -0.500000 -0.577350 -0.500000 -0.288675 The singular values D: 1 3.7320508 2 3.0000000 3 2.0000000 4 1.0000000 5 0.26794919 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 2.00000 -1.00000 -0.492661E-15 -0.943690E-15 -0.163064E-15 2 -1.00000 2.00000 -1.00000 0. -0.735523E-15 3 -0.388578E-15 -1.00000 2.00000 -1.00000 -0.402456E-15 4 -0.943690E-15 -0.111022E-15 -1.00000 2.00000 -1.00000 5 -0.166533E-15 -0.735523E-15 -0.291434E-15 -1.00000 2.00000 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 11.0000 12.0000 13.0000 14.0000 15.0000 21.0000 22.0000 23.0000 24.0000 25.0000 31.0000 32.0000 33.0000 34.0000 35.0000 41.0000 42.0000 43.0000 44.0000 45.0000 51.0000 52.0000 53.0000 54.0000 55.0000 After sorting D and rearranging V: 0.956318 0.829509 0.561695 0.415307 0.218418 12.0000 13.0000 14.0000 15.0000 11.0000 22.0000 23.0000 24.0000 25.0000 21.0000 32.0000 33.0000 34.0000 35.0000 31.0000 42.0000 43.0000 44.0000 45.0000 41.0000 52.0000 53.0000 54.0000 55.0000 51.0000 PRAXIS_PRB Normal end of execution. 3 August 2016 8:45:27.340 AM