Wed Oct 8 07:49:39 2025 hankel_cholesky_test(): python version: 3.10.12 numpy version: 1.26.4 Test hankel_cholesky(). hankel_cholesky_upper_test(): hankel_cholesky_upper() is given a Hankel matrix H and computes an upper triangular matrix R such that H = R' * R The Hankel matrix H: Col: 0 1 2 3 4 Row 0 : 0.0990257 0.0558276 0.962937 0.930582 10.3178 1 : 0.0558276 0.962937 0.930582 10.3178 13.2878 2 : 0.962937 0.930582 10.3178 13.2878 112.461 3 : 0.930582 10.3178 13.2878 112.461 178.061 4 : 10.3178 13.2878 112.461 178.061 1238.29 R computed by NUMPY.LINALG.CHOLESKY: Col: 0 1 2 3 4 Row 0 : 0.314683 0.177409 3.06002 2.9572 32.7878 1 : 0 0.965124 0.401718 10.147 7.74095 2 : 0 0 0.890322 0.182499 10.1311 3 : 0 0 0 0.848742 0.829538 4 : 0 0 0 0 0.0663776 R computed by r8mat_cholesky_factor_upper(): Col: 0 1 2 3 4 Row 0 : 0.314683 0.177409 3.06002 2.9572 32.7878 1 : 0 0.965124 0.401718 10.147 7.74095 2 : 0 0 0.890322 0.182499 10.1311 3 : 0 0 0 0.848742 0.829538 4 : 0 0 0 0 0.0663776 R computed by hankel_cholesky_upper(): Col: 0 1 2 3 4 Row 0 : 0.314683 0.177409 3.06002 2.9572 32.7878 1 : 0 0.965124 0.401718 10.147 7.74095 2 : 0 0 0.890322 0.182499 10.1311 3 : 0 0 0 0.848742 0.829538 4 : 0 0 0 0 0.0663776 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 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 : 0.509998 0 0 0 0 1 : 0.615324 0.221235 0 0 0 2 : 0.838371 0.777081 0.676234 0 0 3 : 1.34861 4.2226 0.613824 0.0421891 0 4 : 3.45886 12.1984 11.3107 0.187099 0.762149 The Hankel matrix H = L * L': Col: 0 1 2 3 4 Row 0 : 0.260098 0.313814 0.427568 0.687787 1.76401 1 : 0.313814 0.427568 0.687787 1.76401 4.82702 2 : 0.427568 0.687787 1.76401 4.82702 20.0276 3 : 0.687787 1.76401 4.82702 20.0276 63.1241 4 : 1.76401 4.82702 20.0276 63.1241 289.312 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 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 hankel_cholesky_test(): Normal end of execution. Wed Oct 8 07:49:39 2025