Wed Apr 3 23:34:24 2024 test_matrix_test(): python version: 3.10.12 numpy version: 1.26.4 scipy version: 1.8.0 test_matrix() defines various matrices with known properties. test_condition() Compute the L1 condition number of test matrices Title N COND COND COND Reported by Norms np.linalg.cond() aegerter 5 24 24 24 antisummation 5 80 80 80 bab 5 8.37602 8.37602 8.37602 bauer 6 8.52877e+06 8.52877e+06 8.52877e+06 bernstein 5 6400 6400 480 bis 5 126.906 126.906 126.906 biw 5 59.9171 59.9171 59.9171 bodewig 4 10.4366 10.4366 10.4366 boothroyd 5 1.002e+06 1.002e+06 1.002e+06 combin 3 12.245 12.245 12.245 companion 5 16.4082 16.4082 16.4082 conex1 4 131.942 131.942 131.942 conex2 3 17.7237 17.7237 17.7237 conex3 5 80 80 80 conex4 4 4488 4488 4488 daub2 4 2 2 2 daub4 8 2.79904 2.79904 2.79904 daub6 12 3.44146 3.44146 3.44146 daub8 16 3.47989 3.47989 3.47989 daub10 20 4.00375 4.00375 4.00375 daub12 24 4.80309 4.80309 4.80309 diagonal 5 10.2813 10.2813 10.2813 dif2 5 18 18 18 downshift 5 1 1 1 exchange 5 1 1 1 fibonacci2 5 15 15 15 gfpp 5 20.8689 20.8689 20.8689 golub 5 4.68521e+08 4.68521e+08 4.68521e+08 hankel_n 5 5.8368 5.8368 5.8368 hanowa 6 3.85026 3.85026 3.85026 harman 8 77.069 77.069 77.069 hartley 5 5 5 5 helmert 5 4.63951 4.63951 4.63951 herndon 5 24 24 24 hilbert 5 943656 943656 943656 identity 5 1 1 1 ill3 3 216775 216775 216775 jordan 5 3.89232 3.89232 3.89232 kahan 5 48.0606 48.0606 48.0606 kershaw 4 49 49 49 lietzke 5 38 38 38 maxij 5 100 100 100 minij 5 60 60 60 moler3 5 1539 1539 1539 orthogonal_symmetric 5 4.39765 4.39765 4.39765 oto 5 18 18 18 pascal1 5 100 100 100 pascal3 5 62.0925 62.0925 62.0925 pei 5 6.09348 6.09348 6.09348 rodman 5 1.43569 1.43569 1.43569 rutis1 4 15 15 15 rutis2 4 11.44 11.44 11.44 rutis3 4 6 6 6 rutis4 5 4006.75 4006.75 4006.75 rutis5 4 62608 62608 62608 summation 5 10 10 10 sweet1 6 16.9669 16.9669 16.9669 sweet2 6 49.2227 49.2227 49.2227 sweet3 6 24.7785 24.7785 24.7785 sweet4 13 51.1709 51.1709 51.1709 tri_upper 5 13611.4 13611.4 13611.4 upshift 5 1 1 1 wilk03 3 2.6e+10 2.6e+10 2.6e+10 wilk04 4 2.45892e+16 2.45889e+16 2.45889e+16 wilk05 5 7.93703e+06 7.93703e+06 7.93703e+06 wilson 4 4488 4488 4488 test_determinant(): Compute the determinants of an example of each test matrix compare with the determinant routine, if available. Print the matrix Frobenius norm for an estimate of magnitude. Title N Determ Determ ||A|| a123 3 0 0 17 aegerter 5 -25 -25 9.4 antisummation 5 1 1 3.9 antisymmetric_random 5 0 0 4 antisymmetric_random 6 6.52877 6.52877 4.8 bab 5 1.94549 1.94549 4.2 bauer 6 1 1 1.9e+02 bernstein 5 96 2500 68 bimarkov_random 5 -0.0529543 1.6 bis 5 -0.169415 -0.169415 1.8 biw 5 0.0547223 0.0547223 2.4 bodewig 4 568 568 13 boothroyd 5 1 1 8.9e+02 borderband 5 -0.328125 -0.328125 2.8 carry 5 2.86797e-10 2.86797e-10 1.4 cauchy 5 1.86146 1.86146 10 cheby_diff1 5 -5.32907e-14 13 cheby_diff1 6 -8.52651e-13 21 cheby_t 5 64 64 13 cheby_u 5 1024 1024 22 cheby_van1 5 18 4.3 cheby_van2 2 -2 -2 2 cheby_van2 3 -1.41421 -1.41421 2 cheby_van2 4 1 1 2.1 cheby_van2 5 0.707107 0.707107 2.2 cheby_van2 6 -0.5 -0.5 2.3 cheby_van2 7 -0.353553 -0.353553 2.4 cheby_van2 8 0.25 0.25 2.5 cheby_van2 9 0.176777 0.176777 2.6 cheby_van2 10 -0.125 -0.125 2.7 cheby_van3 5 13.9754 13.9754 3.9 chow 5 -5089.34 -5089.34 18 clement1 5 0 0 6.3 clement1 6 -225 -225 8.4 clement2 5 0 0 6.3 clement2 6 1294.7 1294.7 12 combin 5 -2022.28 -2022.28 27 companion 5 0.91442 0.91442 4.2 complex_i 2 1 1 1.4 conex1 4 1.93709 1.93709 6.9 conex2 3 -2.73668 -2.73668 7.9 conex3 5 -1 -1 3.9 conex4 4 -0.365406 -1 31 conference 6 -125 -125 5.5 creation 5 0 0 5.5 daub2 4 1 1 2 daub4 8 -1 -1 2.8 daub6 12 1 1 3.5 daub8 16 -1 -1 4 daub10 20 1 1 4.5 daub12 24 -1 -1 4.9 defective 2 1 1 1.7 diagonal 5 2.10323 2.10323 6.7 dif1 5 0 0 2.8 dif1 6 1 1 3.2 dif1cyclic 5 0 0 3.2 dif2 5 6 6 5.3 dif2cyclic 5 0 0 5.5 dorr 5 2.00809e+09 2.00809e+09 2.7e+02 downshift 5 1 1 2.2 eberlein 5 0 0 36 eulerian 5 1 1 77 exchange 5 1 1 2.2 fibonacci1 5 0 -9.80048e-43 96 fibonacci2 5 -1 -1 3 fibonacci3 5 8 8 3.6 fiedler 5 197.578 197.578 16 forsythe 5 2.85065 2.85065 3.5 fourier_cosine 5 1 1 2.2 fourier_sine 5 1 1 2.2 frank 5 1 1 12 gfpp 5 11.4618 11.4618 4 givens 5 16 16 21 gk323 5 32 32 10 gk324 5 -58.1864 -58.1864 9.9 golub 5 1 1 4.7e+02 grcar 5 16 4.4 hankel 5 -6049.79 14 hankel_n 5 3125 3125 15 hanowa 6 37.1781 37.1781 5.3 harman 8 0.000954779 0.000954779 5.1 hartley 5 55.9017 55.9017 5 hartley 6 -216 -216 6 hartley 7 907.493 -907.493 7 hartley 8 -4096 -4096 8 helmert 5 1 1 2.2 helmert2 5 1 2.2 hermite 5 1024 1024 54 herndon 5 -0.04 -0.04 1.8 hilbert 5 3.7493e-12 3.7493e-12 1.6 householder 5 -1 -1 2.2 idempotent_random 5 0 0 2 identity 5 1 1 2.2 ijfact1 5 7.16636e+09 7.16636e+09 3.7e+06 ijfact2 5 1.4948e-21 1.4948e-21 0.56 ill3 3 6 6 8.2e+02 integration 5 1 1 6.3 involutory 5 -1 -1 1.9e+03 involutory_random 5 -1 2.2 jacobi 5 0 0 1.5 jacobi 6 -0.021645 -0.021645 1.7 jordan 5 226.788 226.788 6.9 kahan 5 0.0426464 0.0426464 1.8 kershaw 4 1 1 8.2 kershawtri 5 -47.9498 -47.9498 8.3 kms 5 250444 250444 8.1e+02 laguerre 5 0.00347222 0.00347222 6.9 legendre 5 16.4062 16.4063 6.8 lehmer 5 0.065625 0.065625 3.3 leslie 4 0.605244 0.605244 1.8 lesp 5 -42300 -42300 22 lietzke 5 48 48 18 line_adj 5 0 0 2.8 line_adj 6 -1 -1 3.2 line_loop_adj 5 0 0 3.6 lotkin 5 1.87465e-11 1.87465e-11 2.5 markov_random 5 0.00138409 1.2 maxij 5 5 5 20 milnes 5 49.9736 49.9736 11 minij 5 1 1 12 moler1 5 1 1 75 moler2 5 0 0 1e+05 moler3 5 1 1 8.7 moler4 4 1 1 2.8 neumann 25 0 0.000830873 23 one 5 0 0 5 ortega 5 -45.393 -45.393 1.5e+02 orthogonal_random 5 1 -1 2.2 orthogonal_symmetric 5 1 1 2.2 oto 5 6 6 5.3 parter 5 131.917 131.917 6.3 pascal1 5 1 1 9.9 pascal2 5 1 1 92 pascal3 5 1 1 2.3e+02 pei 5 86.0441 86.0441 5.5 permutation_random 5 -1 -1 2.2 plu 5 -1.93261e+07 -1.93261e+07 1.5e+02 poisson 25 3.25655e+13 3.25655e+13 22 projection_random 5 1 1 2.2 projection_random 5 0 0 1.7 redheffer 5 -2 -2 3.7 reflection_random 5 -1 -1 2.2 ring_adj 1 1 1 1 ring_adj 2 -1 -1 1.4 ring_adj 3 2 2 2.4 ring_adj 4 0 0 2.8 ring_adj 5 2 2 3.2 ring_adj 6 -4 -4 3.5 ring_adj 7 2 2 3.7 ring_adj 8 0 0 4 ris 5 4.12239 4.12239 3.2 rodman 5 11.8718 11.8718 9.5 rosser1 8 0 -4138.53 2.5e+03 routh 5 -25.9629 25.9629 5.5 rutis1 4 -375 -375 17 rutis2 4 100 100 11 rutis3 4 624 624 14 rutis4 5 216 216 59 rutis5 4 1 1 24 schur_block 5 1.35233 1.35233 2.7 spd_random 5 0.0109431 0.0109431 1.6 spline 5 -1245.4 -1245.4 18 stirling 5 1 1 68 summation 5 1 1 3.9 sweet1 6 -2.04682e+07 -2.04682e+07 70 sweet2 6 9562.52 9562.52 30 sweet3 6 -5.40561e+07 -5.40561e+07 73 sweet4 13 -6.46348e+16 -6.46348e+16 1.2e+02 sylvester_kac 5 0 0 7.7 sylvester_kac 6 -225 -225 10 symmetric_random 5 -714.283 -714.283 8.9 toeplitz 5 13.4001 4.9 tournament_random 7 0 0 6.5 tournament_random 8 9 9 7.5 transition_random 5 0.000939813 1.2 tri_upper 5 1 1 5.6 tris 5 1455.85 1455.85 12 triv 5 -1058.7 -1058.7 11 triw 5 1 1 3.3 upshift 5 1 1 2.2 vand1 5 -892.575 -892.575 96 vand2 5 -5291.67 -5291.67 2.8e+02 wathen 96 2.06724e+289 3.7e+04 wilk03 3 9e-21 9e-21 1.4 wilk04 4 4.42923e-17 4.42923e-17 1.9 wilk05 5 3.7995e-15 3.79947e-15 1.5 wilk12 12 1 1 54 wilk20 20 7.59709e+24 1e+02 wilk21 21 -4.15825e+12 -4.15825e+12 28 wilson 4 1 1 31 zero 5 0 0 0 test_eigen_left(): Compute the Frobenius norm of the left eigensystem error: X * A - LAMBDA * X given K left eigenvectors X and eigenvalues lambda. Title N K ||A|| ||X*A-LAMBDA*X|| a123 3 3 16.8819 1.23246e-14 carry 5 5 1.40861 3.63804e-15 chow 5 5 991.113 1.6161e-13 diagonal 5 5 5.85374 0 rosser1 8 8 2482.26 2.61994e-11 symmetric_random 5 5 4.92329 9.96728e-16 test_eigen_right(): Compute the Frobenius norm of the right eigensystem error: A * X - X * lambda given K right eigenvectors X and eigenvalues lambda. Title N K ||A|| ||A*X-X*LAMBDA|| a123 3 3 16.8819 1.33427e-14 bab 5 5 14.9997 4.44584e-15 bodewig 4 4 12.7279 9.17346e-15 carry 5 5 1.40933 8.90533e-16 chow 5 5 11.1115 1.22427e-14 combin 5 5 15.0679 3.97205e-15 dif2 5 5 5.2915 1.07099e-15 exchange 5 5 2.23607 0 fibonacci2 5 5 3 1.46869e-16 idempotent_random 5 5 1.73205 8.12125e-16 identity 5 5 2.23607 0 ill3 3 3 817.763 1.62356e-11 kershaw 4 4 8.24621 4.80549e-15 kms 5 5 2.23635 1.54903e-09 line_adj 5 5 2.82843 8.99223e-16 line_loop_adj 5 5 3.60555 9.99459e-16 one 5 5 5 0 ortega 5 5 79.0819 3.87896e-13 oto 5 5 5.2915 1.07099e-15 pei 5 5 6.73348 0 reflection_random 5 5 2.23607 8.25459e-16 rodman 5 5 9.04982 0 rosser1 8 8 2482.26 2.61994e-11 rutis1 4 4 16.6132 0 rutis2 4 4 11.4018 0 rutis5 4 4 23.7697 1.46286e-14 spd_random 5 5 1.61724 7.06846e-16 sylvester_kac 5 5 7.74597 0 symmetric_random 5 5 6.50358 2.47822e-15 tribonacci2 5 5 3.31662 5.50739e-07 wilk12 12 12 53.591 1.01528e-07 wilson 4 4 30.545 2.48731e-14 zero 5 5 0 0 test_inverse() A = a test matrix of order N B = inverse as computed by a routine. C = inverse as computed by the numpy.linalg.inv() function. ||A|| = Frobenius norm of A. ||C|| = Frobenius norm of C. ||I-AC|| = Frobenius norm of I-A*C. ||I-AB|| = Frobenius norm of I-A*B. Title N ||A|| ||C|| ||I-AC|| ||I-AB|| aegerter 5 9.4 1.8 7.8e-16 7.1e-16 antisummation 5 3.9 11 0 0 bab 5 8.9 3.5 3.7e-15 3.3e-15 bauer 6 1.9e+02 2.1e+04 1.3e-10 0 bernstein 5 68 3.6 4.2e-15 8.2e+03 bis 5 3.7 5e+04 0 7.1e-15 biw 5 2.4 26 3e-15 1e-15 bodewig 4 13 0.68 1.1e-15 7.1e-16 boothroyd 5 8.9e+02 8.9e+02 4.4e-11 0 borderband 5 2.8 6.8 0 0 carry 5 1.4 3.9e+05 1.4e-10 4.9e-11 cauchy 5 46 3.1 1.2e-14 2e-15 cheby_t 5 13 1.9 0 0 cheby_u 5 22 1.2 0 0 cheby_van2 5 2.2 2.5 5.2e-16 5.9e-16 cheby_van3 5 3.9 1.3 6.5e-16 7.5e-16 chow 5 1.6e+03 18 1.2e-12 1.2e-12 clement1 6 8.4 1.5 6.1e-16 0 clement2 6 7.9 3.5 1.2e-15 4.9e-16 combin 5 11 1.1 1.2e-15 2.1e-15 companion 5 6.4 2.2 3.6e-16 0 complex_i 2 1.4 1.4 0 0 conex1 4 13 8.4 1e-15 2e-15 conex2 3 2.7 3.4 0 2.2e-16 conex3 5 3.9 11 0 0 conex4 4 31 99 1.9e-13 0 conference 6 5.5 1.1 7.4e-16 0 daub2 4 2 2 0 8.9e-16 daub4 8 2.8 2.8 2.9e-16 2.1e-15 daub6 12 3.5 3.5 1.2e-15 1.4e-15 daub8 16 4 4 1.7e-15 4.6e-15 daub10 20 4.5 4.5 1.6e-15 8.7e-15 daub12 24 4.9 4.9 1.6e-15 2e-14 diagonal 5 7.2 0.86 0 0 dif1 6 3.2 3.5 0 0 dif2 5 5.3 3.9 1.1e-15 6.9e-16 dorr 5 1e+02 0.22 1.3e-15 1.4e-15 downshift 5 2.2 2.2 0 0 eulerian 5 77 7.8e+02 4.8e-13 0 exchange 5 2.2 2.2 0 0 fibonacci2 5 3 3.5 0 0 fibonacci3 5 3.6 1.6 1.6e-16 0 fiedler 7 23 15 1.2e-13 1.6e-14 forsythe 5 6.4 1 1e-15 1.1e-15 fourier_cosine 5 2.2 2.2 6.2e-16 1e-15 fourier_sine 5 2.2 2.2 6e-16 1.8e-15 frank 5 12 59 3.4e-14 0 gfpp 5 15 0.96 9.7e-16 6.2e-14 givens 5 21 2.7 0 0 gk323 5 10 2.3 0 0 gk324 5 7.2 14 3.6e-15 2.5e-15 golub 5 4.7e+02 9.1e+05 5.1e-09 4.3e-09 hankel 5 3.7 1.7 7.5e-16 8.8e-16 hankel_n 5 15 0.55 4.7e-16 0 hanowa 6 6.6 1 1.9e-16 3.1e-16 harman 8 5.1 15 6.1e-15 1.1e-14 hartley 5 5 1 7.6e-16 2.8e-15 helmert 5 2.2 2.2 6.2e-16 8.2e-16 helmert2 5 2.2 2.2 5.1e-16 5.9e-16 hermite 5 54 1.8 0 0 herndon 5 1.8 9.4 1.2e-15 7.1e-16 hilbert 5 1.6 3e+05 4.3e-11 7.3e-12 householder 5 2.2 2.2 6.4e-16 9.4e-16 identity 5 2.2 2.2 0 0 ill3 3 8.2e+02 3.4e+02 1.1e-11 0 integration 5 5.8 26 1.8e-15 3.8e-15 involutory 5 1.9e+03 1.9e+03 1.1e-10 7.3e-12 jacobi 6 1.7 6.5 5.3e-16 0 jordan 5 6.1 0.93 5.4e-16 5.4e-16 kahan 5 1.8 11 1.1e-15 1.8e-15 kershaw 4 8.2 8.2 5.3e-16 0 kershawtri 5 6.6 2.9 7.5e-16 1.9e-15 kms 5 4.7e+02 2.1 9.6e-14 5.4e-15 laguerre 5 6.9 2e+02 2e-15 0 legendre 5 6.8 1.9 2.5e-16 2.7e-16 lehmer 5 3.3 7.7 1.5e-15 1.4e-15 lesp 5 22 0.32 4.1e-16 7.6e-16 lietzke 5 18 2.4 2.9e-15 7e-16 line_adj 6 3.2 3.5 0 0 lotkin 5 2.5 2.4e+05 3.4e-11 0 maxij 5 20 4.7 1.4e-14 0 milnes 5 6.2 8.9 4e-15 7.5e-16 minij 5 12 5 0 0 moler1 5 93 1e+05 2.1e-10 1.6e-10 moler3 5 8.7 1.2e+02 0 0 ortega 5 3.8e+02 37 2.3e-12 1.8e-12 orthogonal_random 5 2.2 2.2 5e-16 1.7e-15 orthogonal_symmetric 5 2.2 2.2 1.1e-15 2.2e-15 oto 5 5.3 3.9 1.1e-15 6.9e-16 parter 5 6.3 0.94 3.6e-16 7e-17 pascal1 5 9.9 9.9 0 0 pascal2 5 92 92 0 0 pascal3 5 18 18 1.3e-14 6.5e-15 pei 5 6.3 2 1.1e-15 8.3e-16 permutation_random 5 2.2 2.2 0 0 plu 5 1.5e+02 0.14 1.2e-15 1.3e-15 reflection_random 5 2.2 2.2 8.6e-16 3.3e-16 ris 5 3.2 1.9 3.5e-16 8.4e-17 rodman 5 9.9 0.65 1.2e-15 1e-15 rutis1 4 17 1 1.6e-15 1.1e-15 rutis2 4 11 1.1 2.8e-16 6.8e-16 rutis3 4 14 0.58 1.2e-15 6e-16 rutis4 4 51 18 7.9e-14 9.1e-14 rutis5 4 24 1.9e+03 4.4e-12 0 schur_block 5 10 0.83 2.5e-16 3.5e-16 spd_random 5 1.6 36 3.9e-15 1.2e-14 spline 5 10 3.4 2.4e-16 7.5e-16 stirling 5 68 32 3e-14 0 summation 5 3.9 3 0 0 sweet1 6 70 0.26 1.8e-15 1.1e-13 sweet2 6 30 1.4 7.6e-15 3.4e-14 sweet3 6 73 0.34 1e-15 1.4e-13 sweet4 13 1.2e+02 0.38 4e-15 2.6e-13 sylvester_kac 6 10 2.5 0 0 symmetric_random 5 6.9 2.3 1.3e-15 4.3e-15 toeplitz 5 4.5 3.3 1.3e-15 1.7e-15 tri_upper 5 3.8 3 0 7.9e-17 tris 5 11 0.61 5.5e-16 7.7e-16 triv 5 12 36 2.5e-14 4e-14 triw 5 2.2 2.2 0 0 upshift 5 2.2 2.2 0 0 vand1 5 4.6e+02 2 1.1e-14 5.2e-14 vand2 5 1.5e+02 11 1.2e-13 2.3e-14 wilk03 3 1.4 1.8e+10 9.5e-07 6.7e-07 wilk04 4 1.9 1.2e+16 0.0002 11 wilk05 5 1.5 3.1e+06 3.6e-10 1.2e-09 wilk21 21 28 4.3 1.6e-15 3.8e-15 wilson 4 31 99 1.6e-13 0 test_llt(): A = a test matrix of order M by M L is an M by N lower triangular Cholesky factor. ||A|| = Frobenius norm of A. ||A-LLT|| = Frobenius norm of A-L*L'. Title M N ||A|| ||A-LLT|| dif2 5 5 5.2915 8.88178e-16 givens 5 5 20.6155 4.23634e-15 kershaw 4 4 8.24621 2.57035e-15 lehmer 5 5 3.28041 2.07704e-16 minij 5 5 12.4499 0 moler1 5 5 97.7856 1.2307e-14 moler3 5 5 8.66025 0 oto 5 5 5.2915 7.36439e-16 pascal2 5 5 92.4608 0 wilson 4 4 30.545 5.25453e-15 test_lu(): A = a test matrix of order M by N L, U are the LU factors. ||A|| = Frobenius norm of A. ||A-LU|| = Frobenius norm of A-L*U. Title M N ||A|| ||A-LU|| bodewig 4 4 12.7279 7.4476e-15 borderband 5 5 2.76699 0 dif2 5 5 5.2915 0 fibonacci2 5 5 3 0 gfpp 5 5 4.3589 0 givens 5 5 20.6155 0 golub 5 5 467.882 0 kms 5 5 30.0167 0 lehmer 5 5 3.28041 0 minij 5 5 12.4499 0 moler1 5 5 40.0625 0 moler3 5 5 8.66025 0 oto 5 5 5.2915 0 pascal2 5 5 92.4608 0 vand2 5 5 712.488 8.76972e-14 test_null_left(): A = a test matrix of order M by N x = an M vector, candidate for a left null vector. ||A|| = Frobenius norm of A. ||x|| = L2 norm of x. ||A*x||/||x|| = L2 norm of A'*x over L2 norm of x. Title M N ||A|| ||x|| ||A'*x||/||x|| a123 3 3 16.8819 2.44949 0 cheby_diff1 5 5 13.4722 3.74166 5.1e-16 creation 5 5 5.47723 1 0 dif1 5 5 2.82843 1.73205 0 dif1cyclic 5 5 3.16228 2.23607 0 dif2cyclic 5 5 5.47723 2.23607 0 eberlein 5 5 26.8206 2.23607 1.8e-15 fibonacci1 5 5 72.0404 1.73205 0 lauchli 6 5 6.5747 3.55603 0 line_adj 7 7 3.4641 2 0 moler2 5 5 101035 263.82 0 one 5 5 5 1.41421 0 ring_adj 12 12 4.89898 3.4641 0 rosser1 8 8 2482.26 22.3607 0 zero 5 5 0 2.23607 0 test_null_right(): A = a test matrix of order M by N x = an N vector, candidate for a right null vector. ||A|| = Frobenius norm of A. ||x|| = L2 norm of x. ||A*x||/||x|| = L2 norm of A*x over L2 norm of x. Title M N ||A|| ||x|| ||A*x||/||x|| a123 3 3 16.8819 2.44949 0 archimedes 7 8 93.397 1.87697e+07 0 cheby_diff1 5 5 13.4722 2.23607 8.9e-16 creation 5 5 5.47723 1 0 dif1 5 5 2.82843 1.73205 0 dif1cyclic 5 5 3.16228 2.23607 0 dif2cyclic 5 5 5.47723 2.23607 0 fibonacci1 5 5 97.8939 1.73205 0 hamming 5 31 8.94427 2.44949 0 line_adj 7 7 3.4641 2 0 moler2 5 5 101035 1016.3 0 neumann 25 25 23.2379 5 0 one 5 5 5 1.41421 0 ring_adj 12 12 4.89898 3.4641 0 rosser1 8 8 2482.26 22.3607 0 zero 5 5 0 2.23607 0 test_plu(): A = a test matrix of order M by N P, L, U are the PLU factors. ||A|| = Frobenius norm of A. ||A-PLU|| = Frobenius norm of A-P*L*U. Title M N ||A|| ||A-PLU|| a123 3 3 16.8819 6.8798e-15 bodewig 4 4 12.7279 4.1243e-15 borderband 5 5 2.76699 0 dif2 5 5 5.2915 0 gfpp 5 5 6.57575 0 givens 5 5 20.6155 0 golub 5 5 467.882 4.92278e-14 kms 5 5 671.23 8.40046e-12 lehmer 5 5 3.28041 1.11022e-16 maxij 5 5 19.8746 0 minij 5 5 12.4499 0 moler1 5 5 156.48 0 moler3 5 5 8.66025 0 oto 5 5 5.2915 0 pascal2 5 5 92.4608 0 plu 5 5 152.462 0 vand2 4 4 74.513 3.66205e-15 wilson 4 4 30.545 7.32411e-15 test_solution(): Compute the Frobenius norm of the solution error: A * X - B given MxN matrix A, NxK solution X, MxK right hand side B. Title M N K ||A|| ||A*X-B|| a123 3 3 1 16.8819 0 bodewig 4 4 1 12.7279 0 dif2 10 10 2 7.61577 0 frank 10 10 2 38.6652 0 poisson 20 20 1 19.5448 0 wilk03 3 3 1 1.39284 6.7435e-07 wilk04 4 4 1 1.89545 3.95105e-05 wilson 4 4 1 30.545 0 test_matrix_test(): Normal end of execution. Wed Apr 3 23:34:24 2024