Tue Oct 19 11:53:12 2021 hankel_spd_test(): Python version: 3.6.9 Test hankel_spd(). hankel_spd_cholesky_lower_test01 hankel_spd_cholesky_lower computes a lower Cholesky matrix L such that the matrix H = L * L' is a symmetric positive definite (SPD) 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 : 0.591329 0 0 0 0 1 : 0.444794 0.17786 0 0 0 2 : 0.388068 0.561008 0.483551 0 0 3 : 0.460642 2.7789 0.205239 0.48285 0 4 : 1.18233 7.37149 7.47693 0.485055 0.890395 The Hankel matrix H = L * L': Col: 0 1 2 3 4 Row 0 : 0.34967 0.263019 0.229476 0.272391 0.699148 1 : 0.263019 0.229476 0.272391 0.699148 1.83699 2 : 0.229476 0.272391 0.699148 1.83699 8.20977 3 : 0.272391 0.699148 1.83699 8.20977 22.7981 4 : 0.699148 1.83699 8.20977 22.7981 112.669 hankel_spd_cholesky_lower_test02 hankel_spd_cholesky_lower computes a lower Cholesky matrix L such that the matrix H = L * L' is a symmetric positive definite (SPD) 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: 3.6.9 r8mat_cholesky_factor determines the lower triangular Cholesky factorization of a symmetric positive definite 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. hankel_spd_test(): Normal end of execution. Tue Oct 19 11:53:12 2021