4 April 2024 3:34:00.691 PM test_matrix_test(): Fortran90 version test_matrix() defines a number of test matrices with known properties. test_analyze(): Analyze a matrix. a123 Not (unit) upper triangular Not (unit) lower triangular No band matrix structure detected. Cyclic tridiagonal. Diagonality = 5 Relative sparseness = 0.00000 Irreducible. Not property A. Not a permutation matrix Not symmetric Not antisymmetric Not a Tournament matrix Not a transition matrix Not persymmetric Not antipersymmetric Not centrosymmetric Not symmetric positive (semi)-definite Not circulant Not anticirculant Positive Not negative or nonpositive Not (strictly) row diagonally dominant. Not (strictly) column diagonally dominant. Matrix rows do not have unit Euclidean norm. Matrix columns do not all have unit Euclidean norm. Not row orthogonal Not column orthogonal Not orthogonal Integer matrix. Not a zero/one matrix Not row scalar Not column scalar Not diagonal scalar Not antidiagonal scalar (Hankel) Row sum is not constant Column sum is not constant Not magic, stochastic or biMarkov Not an adjacency matrix. Not (reduced) row echelon form Not normal. Not an M matrix Spectral norm = 16.1168 L1 norm = 18.0000 L2 norm = 16.8481 Loo norm = 24.0000 Frobenius norm = 16.8819 EISPACK norm = 45.0000 test_condition(): Compute the L1 condition number of an example of each test matrix Title N COND COND Reported Computed aegerter 5 24.0000 24.0000 antisummation 5 80.0000 80.0000 bab 5 21.4321 21.4321 bauer 6 0.852877E+07 0.852877E+07 bernstein 5 160.000 160.000 bis 5 33.3308 33.3308 biw 5 59.9171 59.9171 bodewig 4 10.4366 10.4366 boothroyd 5 0.100200E+07 0.100200E+07 combin 5 5.31884 5.31884 companion 5 14.5786 14.5786 conex1 4 21.5406 21.5406 conex2 3 15.8028 15.8028 conex3 5 80.0000 80.0000 conex4 4 4488.00 4488.00 daub2 4 2.00000 2.00000 daub4 8 2.79904 2.79904 daub6 12 3.44146 3.44146 daub8 16 3.47989 3.47989 daub10 20 4.00375 4.00375 daub12 24 4.80309 4.80309 diagonal 5 7.39629 7.39629 dif2 5 18.0000 18.0000 downshift 5 1.00000 1.00000 exchange 5 1.00000 1.00000 fibonacci2 5 15.0000 15.0000 gfpp 5 17.6821 17.6821 givens 5 50.0000 50.0000 golub 5 0.176171E+10 0.176171E+10 hankel_n 5 5.83680 5.83680 hanowa 6 2.80386 2.80386 harman 8 77.0690 77.0690 hartley 5 5.00000 5.00000 helmert 5 4.63951 4.63951 herndon 5 24.0000 24.0000 hilbert 5 943656. 943656. identity 5 1.00000 1.00000 ill3 3 216775. 216775. jordan 5 2.62667 2.62667 kahan 5 5159.86 5159.86 kershaw 4 49.0000 49.0000 lietzke 5 38.0000 38.0000 maxij 5 100.000 100.000 minij 5 60.0000 60.0000 moler3 5 1539.00 1539.00 moler4 4 9.00000 9.00000 orthogonal_symmetric 5 4.39765 4.39765 oto 5 18.0000 18.0000 pascal1 5 100.000 100.000 pascal3 5 4716.17 4716.17 pei 5 2.70265 2.70265 rodman 5 5.26701 5.26701 rutis1 4 15.0000 15.0000 rutis2 4 11.4400 11.4400 rutis3 4 6.00000 6.00000 rutis4 5 4006.75 4006.75 rutis5 4 62608.0 62608.0 summation 5 10.0000 10.0000 sweet1 6 16.9669 16.9669 sweet2 6 49.2227 49.2227 sweet3 6 24.7785 24.7785 sweet4 13 51.1709 51.1709 tri_upper 5 329.526 329.526 upshift 5 1.00000 1.00000 wilk03 3 0.260000E+11 0.260000E+11 wilk04 4 0.245892E+17 0.285325E+17 wilk05 5 0.793703E+07 0.793703E+07 wilson 4 4488.00 4488.00 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|| Reported Computed a123 3 0.00000 0.666134E-15 16.8819 aegerter 5 -25.0000 -25.0000 9.43398 anticirculant 3 -235.484 -235.484 10.9008 anticirculant 4 1407.78 1407.78 12.6475 anticirculant 5 7148.67 7148.67 14.2666 antihadamard 5 1.00000 1.00000 3.31662 antisummation 5 1.00000 1.00000 3.87298 antisymmetric_random 5 0.394135E-16 2.68753 antisymmetric_random 6 0.524405E-01 3.09793 bab 5 -87.5191 -87.5191 7.40859 bauer 6 1.00000 1.00000 185.855 bernstein 5 96.0000 96.0000 25.2784 bimarkov_random 5 -0.557840E-01 1.53996 bis 5 736.719 736.719 8.52759 biw 5 0.547223E-01 0.547223E-01 2.36051 bodewig 4 568.000 568.000 12.7279 boothroyd 5 1.00000 1.00000 886.710 borderband 5 -0.328125 -0.328125 2.76699 carry 5 0.165382E-07 0.165382E-07 1.41391 cauchy 5 38.7671 38.7671 682.273 cheby_diff1 5 -0.213163E-13 13.4722 cheby_diff1 6 -0.511591E-12 20.7702 cheby_t 5 64.0000 64.0000 12.6886 cheby_u 5 1024.00 1024.00 22.4277 cheby_van1 5 18.0000 4.30116 cheby_van2 2 -2.00000 -2.00000 2.00000 cheby_van2 3 -1.41421 -1.41421 2.00000 cheby_van2 4 1.00000 1.00000 2.08167 cheby_van2 5 0.707107 0.707107 2.17945 cheby_van2 6 -0.500000 -0.500000 2.28035 cheby_van2 7 -0.353553 -0.353553 2.38048 cheby_van2 8 0.250000 0.250000 2.47848 cheby_van2 9 0.176777 0.176777 2.57391 cheby_van2 10 -0.125000 -0.125000 2.66667 cheby_van3 5 13.9754 13.9754 3.87298 chow 5 -371.932 -371.932 1190.00 circulant 5 7148.67 7148.67 14.2666 circulant2 3 18.0000 18.0000 6.48074 circulant2 4 -160.000 -160.000 10.9545 circulant2 5 1875.00 1875.00 16.5831 clement1 5 0.00000 0.00000 6.32456 clement1 6 -225.000 -225.000 8.36660 clement2 5 0.00000 0.00000 8.97900 clement2 6 -178.154 -178.154 10.1600 combin 5 961.248 961.248 10.3967 companion 5 -2.81582 -2.81582 6.68633 complex_i 2 1.00000 1.00000 1.41421 conex1 4 2.19062 2.19062 7.61262 conex2 3 0.438326 0.438326 2.65272 conex3 5 -1.00000 -1.00000 3.87298 conex4 4 -1.00000 -1.00000 30.5450 conference 6 -125.000 -125.000 5.47723 creation 5 0.00000 0.00000 5.47723 daub2 4 1.00000 1.00000 2.00000 daub4 8 -1.00000 -1.00000 2.82843 daub6 12 1.00000 1.00000 3.46410 daub8 16 -1.00000 -1.00000 4.00000 daub10 20 1.00000 1.00000 4.47214 daub12 24 -1.00000 -1.00000 4.89898 diagonal 5 22.1228 22.1228 6.38020 dif1 5 0.00000 0.00000 2.82843 dif1 6 1.00000 1.00000 3.16228 dif1cyclic 5 0.00000 0.00000 3.16228 dif2 5 6.00000 6.00000 5.29150 dif2cyclic 5 0.00000 0.00000 5.47723 dorr 5 0.837343E+12 0.837343E+12 898.453 downshift 5 1.00000 1.00000 2.23607 eberlein 5 0.00000 0.00000 18.3487 eulerian 5 1.00000 1.00000 77.2981 exchange 5 1.00000 1.00000 2.23607 fibonacci1 5 0.00000 0.297239E-43 136.601 fibonacci2 5 -1.00000 -1.00000 3.00000 fibonacci3 5 8.00000 8.00000 3.60555 fiedler 7 1332.21 1332.21 30.1350 forsythe 5 897.919 897.919 9.05024 forsythe 6 -0.247404 -0.247404 3.41934 fourier_cosine 5 1.00000 1.00000 2.23607 fourier_sine 5 1.00000 1.00000 2.23607 frank 5 1.00000 1.00000 11.6190 gfpp 5 146.228 146.228 8.38905 givens 5 16.0000 16.0000 20.6155 gk323 5 32.0000 32.0000 10.0000 gk324 5 11.9530 11.9530 11.4577 golub 5 1.00000 1.00000 483.360 grcar 5 15.0000 4.24264 hadamard 5 0.00000 4.00000 hankel 5 -2823.88 15.2126 hankel_n 5 3125.00 3125.00 15.0000 hanowa 6 704.058 704.058 7.53611 harman 8 0.954779E-03 0.954779E-03 5.05359 hartley 5 55.9017 55.9017 5.00000 hartley 6 -216.000 -216.000 6.00000 hartley 7 -907.493 -907.493 7.00000 hartley 8 -4096.00 -4096.00 8.00000 helmert 5 1.00000 1.00000 2.23607 helmert2 5 1.00000 2.23607 hermite 5 1024.00 1024.00 54.1941 herndon 5 -0.400000E-01 -0.400000E-01 1.77133 hilbert 5 0.374930E-11 0.374930E-11 1.58091 householder 5 -1.00000 -1.00000 2.23607 idempotent_random 5 0.00000 0.589429E-16 2.00000 identity 5 1.00000 1.00000 2.23607 ijfact1 5 0.716636E+10 0.716636E+10 0.366559E+07 ijfact2 5 0.149480E-20 0.149480E-20 0.557720 ill3 3 6.00000 6.00000 817.763 integration 6 1.00000 1.00000 5.15053 involutory 5 -1.00000 -1.00000 1942.46 involutory_random 5 1.00000 2.23607 jacobi 5 0.00000 0.00000 1.49071 jacobi 6 -0.216450E-01 -0.216450E-01 1.65145 jordan 6 2759.07 2759.07 9.44211 kahan 5 -0.736829E-02 -0.736829E-02 1.61179 kershaw 4 1.00000 1.00000 8.24621 kershawtri 5 1.00000 -270.772 8.52160 kms 5 886.063 886.063 69.6938 laguerre 5 0.347222E-02 0.347222E-02 6.85376 legendre_matrix 5 16.4062 16.4062 6.80762 lehmer 5 0.656250E-01 0.656250E-01 3.28041 leslie 4 0.605244 0.605244 1.78414 lesp 5 -42300.0 -42300.0 22.3487 lietzke 5 48.0000 48.0000 18.0278 lights_out 25 -0.325405E-29 10.2470 line_adj 5 0.00000 0.00000 2.82843 line_adj 6 -1.00000 -1.00000 3.16228 line_loop_adj 5 0.00000 -0.00000 3.60555 loewner 5 -12963.3 72.8555 lotkin 5 0.187465E-10 0.187465E-10 2.45676 markov_random 5 0.488558E-02 1.33584 maxij 5 5.00000 5.00000 19.8746 milnes 5 2.61868 2.61868 8.98492 minij 5 1.00000 1.00000 12.4499 moler1 5 1.00000 1.00000 150.314 moler2 5 0.00000 0.102538E-06 101035. moler3 5 1.00000 1.00000 8.66025 moler4 4 1.00000 1.00000 2.82843 neumann 25 0.00000 0.124631E-02 23.2379 one 5 0.00000 -0.00000 5.00000 ortega 5 65.4030 65.4030 37.7832 orthogonal_random 5 1.00000 1.00000 2.23607 orthogonal_symmetric 5 1.00000 1.00000 2.23607 oto 5 6.00000 6.00000 5.29150 parter 5 131.917 131.917 6.34077 pascal1 5 1.00000 1.00000 9.94987 pascal2 5 1.00000 1.00000 92.4608 pascal3 5 1.00000 1.00000 308.345 pei 5 1.76146 1.76146 4.49335 permutation_random 5 1.00000 1.00000 2.23607 plu 5 -0.193261E+08 -0.193261E+08 152.462 poisson 25 0.325655E+14 0.325655E+14 21.9089 prolate 5 -5.96289 3.22471 rectangle_adj 25 0.00000 0.00000 8.94427 redheffer 5 -2.00000 -2.00000 3.74166 ref_random 5 0.00000 0.00000 2.39924 ref_random 5 0.00000 0.00000 2.79973 riemann 5 96.0000 8.83176 ring_adj 1 1.00000 1.00000 1.00000 ring_adj 2 -1.00000 -1.00000 1.41421 ring_adj 3 2.00000 2.00000 2.44949 ring_adj 4 0.00000 0.00000 2.82843 ring_adj 5 2.00000 2.00000 3.16228 ring_adj 6 -4.00000 -4.00000 3.46410 ring_adj 7 2.00000 2.00000 3.74166 ring_adj 8 0.00000 0.00000 4.00000 ris 5 4.12239 4.12239 3.17039 rodman 5 7.83238 7.83238 9.08594 rosser1 8 0.00000 -9480.58 2482.26 routh 5 58.6269 58.6269 6.18616 rutis1 4 -375.000 -375.000 16.6132 rutis2 4 100.000 100.000 11.4018 rutis3 4 624.000 624.000 14.1421 rutis4 5 216.000 216.000 59.1270 rutis5 4 1.00000 1.00000 23.7697 schur_block 5 -587.226 -587.226 8.77163 skew_circulant 5 9142.63 9142.63 15.9061 spd_random 5 0.404187E-01 0.404187E-01 1.46230 spline 5 51.2851 51.2851 18.7288 stirling 5 1.00000 1.00000 67.9191 stripe 5 2112.00 14.8324 summation 5 1.00000 1.00000 3.87298 sweet1 6 -0.204682E+08 -0.204682E+08 70.1997 sweet2 6 9562.52 9562.52 30.1433 sweet3 6 -0.540561E+08 -0.540561E+08 73.4234 sweet4 13 -0.646348E+17 -0.646348E+17 119.704 sylvester 5 -1535.99 15.9018 sylvester_kac 5 0.00000 0.00000 7.74597 sylvester_kac 6 -225.000 -225.000 10.4881 symmetric_random 5 22.1228 22.1228 6.38020 toeplitz 5 -2823.88 15.2126 toeplitz_5diag 5 -51.4343 12.6457 toeplitz_5s 25 0.268454E+13 26.6839 toeplitz_spd 5 0.849362E-01 3.41573 tournament_random 5 0.00000 0.00000 4.47214 transition_random 5 0.486764E-02 1.32331 trench 5 26.2369 5.98375 tri_upper 5 1.00000 1.00000 15.0254 tribonacci2 5 1.00000 1.00000 3.31662 tris 5 -30.0629 -30.0629 7.63288 triv 5 -700.369 -700.369 11.1204 triw 5 1.00000 1.00000 8.10932 upshift 5 1.00000 1.00000 2.23607 vand1 5 133985. 133985. 466.164 vand2 5 133985. 133985. 466.164 wathen 96 0.129918+291 34082.8 wilk03 3 0.900000E-20 0.900000E-20 1.39284 wilk04 4 0.442923E-16 0.442923E-16 1.89545 wilk05 5 0.379950E-14 0.379947E-14 1.51485 wilk12 12 1.00000 1.00000 53.5910 wilk20 20 0.169247E+26 102.374 wilk21 21 -0.415825E+13 -0.415825E+13 28.4605 wilson 4 1.00000 1.00000 30.5450 zero 5 0.00000 0.00000 0.00000 zielke 5 424.513 20.1456 test_eigen_left(): Compute the Frobenius norm of the eigenvalue 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 0.123436E-13 carry 5 5 1.40898 0.362308E-14 chow 5 5 5.99579 0.361121E-14 diagonal 5 5 6.38020 0.00000 rosser1 8 8 2482.26 0.264201E-10 symmetric_random 5 5 6.38020 0.145703E-14 test_eigen_right(): Compute the Frobenius norm of the eigenvalue 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 0.144309E-13 bab 5 5 8.67824 0.651994E-15 bodewig 4 4 12.7279 0.952498E-14 carry 5 5 1.41391 0.101291E-14 chow 5 5 1190.00 0.399204E-11 combin 5 5 10.3967 0.00000 dif2 5 5 5.29150 0.111731E-14 exchange 5 5 2.23607 0.00000 fibonacci2 5 5 3.00000 0.146869E-15 idempotent_random 5 5 1.73205 0.497529E-15 identity 5 5 2.23607 0.00000 ill3 3 3 817.763 0.162358E-10 kershaw 4 4 8.24621 0.477470E-14 kms 5 5 4.13528 0.517440E-06 line_adj 5 5 2.82843 0.899223E-15 line_loop_adj 5 5 3.60555 0.959244E-15 one 5 5 5.00000 0.00000 ortega 5 5 244.268 0.334464E-12 oto 5 5 5.29150 0.111731E-14 pei 5 5 4.49335 0.00000 rodman 5 5 11.5809 0.00000 rosser1 8 8 2482.26 0.264201E-10 rutis1 4 4 16.6132 0.00000 rutis2 4 4 11.4018 0.00000 rutis3 4 4 14.1421 0.00000 rutis5 4 4 23.7697 0.145285E-13 spd_random 5 5 1.46230 0.530202E-15 sylvester_kac 5 5 7.74597 0.00000 symmetric_random 5 5 6.38020 0.147743E-14 tribonacci2 5 5 3.31662 0.387516E-14 wilk12 12 12 53.5910 0.387835E-12 wilson 4 4 30.5450 0.253131E-13 zero 5 5 0.00000 0.00000 test_inverse(): A = a test matrix of order N. B = inverse as computed by a routine. C = inverse as computed by R8MAT_INVERSE. ||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 0.75E-15 0.33E-15 antisummation 5 3.9 11. 0.0 0.0 bab 5 8.7 0.67 0.56E-15 0.74E-15 bauer 6 0.19E+03 0.21E+05 0.71E-10 0.0 bernstein 5 25. 3.2 0.0 0.0 bis 5 9.9 4.2 0.0 0.25E-14 biw 5 2.4 26. 0.39E-14 0.10E-14 bodewig 4 13. 0.68 0.86E-15 0.60E-15 boothroyd 5 0.89E+03 0.89E+03 0.51E-10 0.0 borderband 5 2.8 6.8 0.0 0.0 carry 5 1.4 0.58E+04 0.88E-12 0.71E-12 cauchy 5 0.68E+03 61. 0.18E-12 0.94E-13 cheby_t 5 13. 1.9 0.0 0.0 cheby_u 5 22. 1.2 0.0 0.0 cheby_van2 5 2.2 2.5 0.39E-15 0.55E-15 cheby_van3 5 3.9 1.3 0.91E-15 0.86E-15 chow 5 0.44E+03 25. 0.36E-13 0.37E-13 circulant 5 14. 0.41 0.73E-15 0.95E-15 circulant2 5 17. 0.64 0.11E-14 0.14E-14 clement1 6 8.4 1.5 0.66E-15 0.87E-16 clement2 6 10. 2.7 0.67E-15 0.89E-15 combin 5 14. 0.92 0.93E-15 0.11E-14 companion 5 6.7 2.9 0.86E-15 0.13E-15 complex_i 2 1.4 1.4 0.0 0.0 conex1 4 15. 9.9 0.0 0.0 conex2 3 2.7 2.8 0.56E-16 0.56E-16 conex3 5 3.9 11. 0.0 0.0 conex4 4 31. 99. 0.59E-12 0.0 conference 6 5.5 1.1 0.73E-15 0.0 daub2 4 2.0 2.0 0.0 0.89E-15 daub4 8 2.8 2.8 0.30E-15 0.19E-14 daub6 12 3.5 3.5 0.11E-14 0.57E-15 daub8 16 4.0 4.0 0.13E-14 0.47E-14 daub10 20 4.5 4.5 0.17E-14 0.86E-14 daub12 24 4.9 4.9 0.22E-14 0.20E-13 diagonal 5 6.4 2.1 0.0 0.0 dif1 6 3.2 3.5 0.0 0.0 dif2 5 5.3 3.9 0.10E-14 0.56E-15 dorr 5 0.30E+03 0.67E-01 0.14E-14 0.24E-14 downshift 5 2.2 2.2 0.0 0.0 eulerian 5 77. 0.78E+03 0.28E-12 0.0 exchange 5 2.2 2.2 0.0 0.0 fibonacci2 5 3.0 3.5 0.0 0.0 fibonacci3 5 3.6 1.6 0.16E-15 0.0 fiedler 7 30. 3.3 0.23E-13 0.49E-14 forsythe 5 4.8 2.2 0.67E-15 0.58E-15 fourier_cosine 5 2.2 2.2 0.11E-14 0.11E-14 fourier_sine 5 2.2 2.2 0.70E-15 0.19E-14 frank 5 12. 59. 0.45E-13 0.0 gfpp 5 13. 0.98 0.58E-15 0.79E-13 givens 5 21. 2.7 0.0 0.0 gk323 5 10. 2.3 0.0 0.0 gk324 5 11. 5.6 0.30E-14 0.28E-14 golub 5 0.48E+03 0.28E+07 0.29E-07 0.52E-07 hankel_n 5 15. 0.55 0.65E-15 0.11E-15 hanowa 6 7.7 0.83 0.35E-15 0.16E-15 harman 8 5.1 15. 0.71E-14 0.95E-06 hartley 5 5.0 1.0 0.97E-15 0.25E-14 helmert 5 2.2 2.2 0.59E-15 0.77E-15 helmert2 5 2.2 2.2 0.65E-15 0.49E-15 hermite 5 54. 1.8 0.0 0.0 herndon 5 1.8 9.4 0.16E-14 0.33E-15 hilbert 5 1.6 0.30E+06 0.28E-10 0.68E-11 householder 5 2.2 2.2 0.11E-14 0.88E-15 identity 5 2.2 2.2 0.0 0.0 ill3 3 0.82E+03 0.34E+03 0.16E-10 0.47E-10 integration 5 3.4 4.8 0.25E-15 0.25E-15 involutory 5 0.19E+04 0.19E+04 0.11E-09 0.73E-11 jacobi 6 1.7 6.5 0.60E-15 0.21E-15 jordan 5 5.5 1.1 0.97E-16 0.97E-16 kahan 5 2.2 2.2 0.38E-15 0.38E-15 kershaw 4 8.2 8.2 0.50E-14 0.0 kershawtri 5 8.7 0.69 0.37E-15 0.79E-15 kms 5 10. 6.8 0.83E-14 0.76E-14 laguerre 5 6.9 0.20E+03 0.0 0.0 legendre_matrix 5 6.8 1.9 0.25E-15 0.27E-15 lehmer 5 3.3 7.7 0.23E-14 0.15E-14 lesp 5 22. 0.32 0.49E-15 0.91E-15 lietzke 5 18. 2.4 0.49E-14 0.56E-15 line_adj 6 3.2 3.5 0.0 0.0 lotkin 5 2.5 0.24E+06 0.28E-10 0.29E-11 maxij 5 20. 4.7 0.29E-14 0.72E-15 milnes 5 11. 5.6 0.30E-14 0.28E-14 minij 5 12. 5.0 0.0 0.0 moler1 5 20. 0.10E+04 0.13E-11 0.13E-11 moler3 5 8.7 0.12E+03 0.0 0.0 ortega 5 0.24E+03 91. 0.98E-12 0.29E-11 orthogonal_symmetric 5 2.2 2.2 0.11E-14 0.25E-14 oto 5 5.3 3.9 0.10E-14 0.56E-15 parter 5 6.3 0.94 0.66E-15 0.10E-15 pascal1 5 9.9 9.9 0.0 0.0 pascal2 5 92. 92. 0.0 0.0 pascal3 5 0.16E+03 0.16E+03 0.48E-12 0.40E-13 pei 5 4.6 1.5 0.76E-15 0.77E-15 permutation_random 5 2.2 2.2 0.0 0.0 plu 5 0.15E+03 0.14 0.13E-14 0.14E-14 ris 5 3.2 1.9 0.65E-15 0.91E-16 rodman 5 3.9 1.3 0.65E-15 0.92E-15 rutis1 4 17. 1.0 0.15E-14 0.11E-14 rutis2 4 11. 1.1 0.59E-15 0.65E-15 rutis3 4 14. 0.58 0.80E-15 0.59E-15 rutis4 5 59. 52. 0.97E-12 0.21E-12 rutis5 4 24. 0.19E+04 0.49E-11 0.0 schur_block 5 8.4 0.65 0.79E-16 0.63E-15 spd_random 5 1.5 5.7 0.76E-15 0.30E-14 spline 5 21. 0.97 0.79E-15 0.12E-14 stirling 5 68. 32. 0.38E-13 0.0 summation 5 3.9 3.0 0.0 0.0 sweet1 6 70. 0.26 0.18E-14 0.11E-12 sweet2 6 30. 1.4 0.62E-14 0.34E-13 sweet3 6 73. 0.34 0.13E-14 0.14E-12 sweet4 13 0.12E+03 0.38 0.44E-14 0.26E-12 sylvester_kac 6 10. 2.5 0.11E-15 0.11E-15 symmetric_random 5 6.4 2.1 0.92E-15 0.22E-14 tri_upper 5 12. 89. 0.13E-13 0.13E-13 tris 5 10. 1.4 0.87E-15 0.77E-15 triv 5 11. 1.1 0.14E-14 0.96E-15 triw 5 7.0 0.13E+03 0.0 0.0 upshift 5 2.2 2.2 0.0 0.0 vand1 5 0.47E+03 1.3 0.87E-14 0.53E-14 vand2 5 0.47E+03 1.3 0.45E-13 0.54E-14 wilk03 3 1.4 0.18E+11 0.36E-06 0.36E-06 wilk04 4 1.9 0.12E+17 0.12E-03 11. wilk05 5 1.5 0.31E+07 0.80E-09 0.12E-08 wilk21 21 28. 4.3 0.18E-14 0.40E-14 wilson 4 31. 99. 0.66E-12 0.0 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 5.29150 0.800593E-15 givens 5 5 20.6155 0.329345E-14 kershaw 4 4 8.24621 0.252200E-14 lehmer 5 5 3.28041 0.157009E-15 minij 5 5 12.4499 0.00000 moler1 5 5 50.1922 0.00000 moler3 5 5 8.66025 0.00000 oto 5 5 5.29150 0.702167E-15 pascal2 5 5 92.4608 0.00000 wilson 4 4 30.5450 0.525453E-14 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 0.140433E-14 borderband 5 5 2.76699 0.00000 dif2 5 5 5.29150 0.00000 fibonacci2 5 5 3.00000 0.00000 gfpp 5 5 4.35890 0.00000 golub 5 5 483.360 0.00000 kms 5 5 30.0167 0.00000 lehmer 5 5 3.28041 0.111022E-15 minij 5 5 12.4499 0.00000 moler1 5 5 40.0625 0.00000 moler3 5 5 8.66025 0.00000 oto 5 5 5.29150 0.00000 pascal2 5 5 92.4608 0.00000 vand2 5 5 466.164 0.116305E-12 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. ||x'*A||/||x|| = L2 norm of x'A over L2 norm of x. Title M N ||A|| ||x|| ||x'*A||/||x|| a123 3 3 16.8819 2.44949 0.00000 cheby_diff1 5 5 13.4722 3.74166 0.507035E-15 creation 5 5 5.47723 1.00000 0.00000 dif1 5 5 2.82843 1.73205 0.00000 dif1cyclic 5 5 3.16228 2.23607 0.00000 dif2cyclic 5 5 5.47723 2.23607 0.00000 eberlein 5 5 38.4833 2.23607 0.158882E-14 fibonacci1 5 5 122.584 1.73205 0.00000 lauchli 6 5 10.7416 5.20350 0.00000 line_adj 7 7 3.46410 2.00000 0.00000 moler2 5 5 101035. 263.820 0.00000 one 5 5 5.00000 1.41421 0.00000 ring_adj 12 12 4.89898 3.46410 0.00000 rosser1 8 8 2482.26 22.3607 0.00000 zero 5 5 0.00000 2.23607 0.00000 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 0.00000 archimedes 7 8 93.3970 0.187697E+08 0.00000 cheby_diff1 5 5 13.4722 2.23607 0.649741E-15 creation 5 5 5.47723 1.00000 0.00000 dif1 5 5 2.82843 1.73205 0.00000 dif1cyclic 5 5 3.16228 2.23607 0.00000 dif2cyclic 5 5 5.47723 2.23607 0.00000 fibonacci1 5 5 82.9210 1.73205 0.00000 hamming 5 31 8.94427 2.44949 0.00000 line_adj 7 7 3.46410 2.00000 0.00000 moler2 5 5 101035. 1016.30 0.00000 neumann 25 25 23.2379 5.00000 0.00000 one 5 5 5.00000 1.41421 0.00000 ring_adj 12 12 4.89898 3.46410 0.00000 rosser1 8 8 2482.26 22.3607 0.00000 zero 5 5 0.00000 2.23607 0.00000 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 0.687980E-14 bodewig 4 4 12.7279 0.412430E-14 borderband 5 5 2.76699 0.00000 dif2 5 5 5.29150 0.00000 gfpp 5 5 10.1618 0.183103E-14 givens 5 5 20.6155 0.00000 golub 5 5 483.360 0.00000 kms 5 5 46.1798 0.392611E-13 lehmer 5 5 3.28041 0.111022E-15 maxij 5 5 19.8746 0.00000 minij 5 5 12.4499 0.00000 moler1 5 5 47.2172 0.502430E-14 moler3 5 5 8.66025 0.00000 oto 5 5 5.29150 0.00000 pascal2 5 5 92.4608 0.00000 plu 5 5 152.462 0.00000 vand2 4 4 107.076 0.163716E-13 wilson 4 4 30.5450 0.664652E-14 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 0.00000 bodewig 4 4 1 12.7279 0.00000 dif2 10 10 2 7.61577 0.00000 frank 10 10 2 38.6652 0.00000 poisson 20 20 1 19.5448 0.00000 wilk03 3 3 1 1.39284 0.360331E-06 wilk04 4 4 1 1.89545 0.129463E+17 wilson 4 4 1 30.5450 0.00000 test_type(): Test functions that query the type of a matrix. Title M N ||A|| ||transition Error|| bodewig 4 4 12.7279 0.100000E+31 snakes 101 101 5.92077 0.980522E-15 transition_random 5 5 1.32331 0.00000 test_matrix_test(): Normal end of execution. 4 April 2024 3:34:00.695 PM