Thu Sep 13 09:51:22 2018 HANKEL_PDS_TEST Python version: 3.6.5 Test the HANKEL_PDS library. HANKEL_PDS_CHOLESKY_LOWER_TEST01 HANKEL_PDS_CHOLESKY_LOWER computes a lower Cholesky matrix L such that the matrix H = L * L' is a positive definite (symmetric) Hankel matrix. The Cholesky factor L: Col: 0 1 2 3 4 Row 0 : 1 0 0 0 0 1 : 1 1 0 0 0 2 : 2 1 1 0 0 3 : 3 3 1 1 0 4 : 6 4 4 1 1 The Hankel matrix H = L * L': Col: 0 1 2 3 4 Row 0 : 1 1 2 3 6 1 : 1 2 3 6 10 2 : 2 3 6 10 20 3 : 3 6 10 20 35 4 : 6 10 20 35 70 The Cholesky factor L: Col: 0 1 2 3 4 Row 0 : 1 0 0 0 0 1 : 4 2 0 0 0 2 : 20 3 3 0 0 3 : 86 37 2 4 0 4 : 418 82.5 59.1667 1 5 The Hankel matrix H = L * L': Col: 0 1 2 3 4 Row 0 : 1 4 20 86 418 1 : 4 20 86 418 1837 2 : 20 86 418 1837 8785 3 : 86 418 1837 8785 39122.8 4 : 418 1837 8785 39122.8 185057 The Cholesky factor L: Col: 0 1 2 3 4 Row 0 : 0.218418 0 0 0 0 1 : 0.0661187 0.956318 0 0 0 2 : 4.20713 0.257578 0.829509 0 0 3 : 2.40134 19.1313 0.109957 0.561695 0 4 : 84.4911 9.97088 16.9598 0.043829 0.415307 The Hankel matrix H = L * L': Col: 0 1 2 3 4 Row 0 : 0.0477066 0.0144415 0.918915 0.524497 18.4544 1 : 0.0144415 0.918915 0.524497 18.4544 15.1218 2 : 0.918915 0.524497 18.4544 15.1218 372.102 3 : 0.524497 18.4544 15.1218 372.102 395.538 4 : 18.4544 15.1218 372.102 395.538 7525.98 HANKEL_PDS_CHOLESKY_LOWER_TEST02 HANKEL_PDS_CHOLESKY_LOWER computes a lower Cholesky matrix L such that the matrix H = L * L' is a positive definite (symmetric) Hankel matrix. The Cholesky factor L: Col: 0 1 2 3 4 Row 0 : 1 0 0 0 0 1 : 1 1 0 0 0 2 : 2 1 1 0 0 3 : 3 3 1 1 0 4 : 6 4 4 1 1 The Hankel matrix H = L * L': Col: 0 1 2 3 4 Row 0 : 1 1 2 3 6 1 : 1 2 3 6 10 2 : 2 3 6 10 20 3 : 3 6 10 20 35 4 : 6 10 20 35 70 The Cholesky factor L2 of H: Col: 0 1 2 3 4 Row 0 : 1 0 0 0 0 1 : 1 1 0 0 0 2 : 2 1 1 0 0 3 : 3 3 1 1 0 4 : 6 4 4 1 1 The Hankel matrix H2 = L2 * L2': Col: 0 1 2 3 4 Row 0 : 1 1 2 3 6 1 : 1 2 3 6 10 2 : 2 3 6 10 20 3 : 3 6 10 20 35 4 : 6 10 20 35 70 R8MAT_CHOLESKY_FACTOR_TEST Python version: 3.6.5 R8MAT_CHOLESKY_FACTOR determines the lower triangular Cholesky factorization of a positive definite symmetric matrix, Matrix to be factored: 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 Cholesky factor L: Col: 0 1 2 3 4 Row 0 : 1.41421 0 0 0 0 1 : -0.707107 1.22474 0 0 0 2 : 0 -0.816497 1.1547 0 0 3 : 0 0 -0.866025 1.11803 0 4 : 0 0 0 -0.894427 1.09545 Product L * L': 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 R8MAT_CHOLESKY_FACTOR_TEST: Normal end of execution. R8MAT_PRINT_TEST Python version: 3.6.5 R8MAT_PRINT prints an R8MAT. Here is an R8MAT: Col: 0 1 2 3 4 Row 0 : 11 12 13 14 15 1 : 21 22 23 24 25 2 : 31 32 33 34 35 3 : 41 42 43 44 45 Col: 5 Row 0 : 16 1 : 26 2 : 36 3 : 46 R8MAT_PRINT_TEST: Normal end of execution. R8MAT_PRINT_SOME_TEST Python version: 3.6.5 R8MAT_PRINT_SOME prints some of an R8MAT. Here is an R8MAT: Col: 3 4 5 Row 0 : 14 15 16 1 : 24 25 26 2 : 34 35 36 R8MAT_PRINT_SOME_TEST: Normal end of execution. R8VEC_PRINT_TEST Python version: 3.6.5 R8VEC_PRINT prints an R8VEC. Here is an R8VEC: 0: 123.456 1: 5e-06 2: -1e+06 3: 3.14159 R8VEC_PRINT_TEST: Normal end of execution. R8VEC_UNIFORM_01_TEST Python version: 3.6.5 R8VEC_UNIFORM_01 computes a random R8VEC. Initial seed is 123456789 Random R8VEC: 0: 0.218418 1: 0.956318 2: 0.829509 3: 0.561695 4: 0.415307 5: 0.0661187 6: 0.257578 7: 0.109957 8: 0.043829 9: 0.633966 R8VEC_UNIFORM_01_TEST: Normal end of execution. HANKEL_PDS_TEST Normal end of execution. Thu Sep 13 09:51:23 2018