01 April 2024 3:32:19.651 PM lapack_test(): Fortran90 version Test lapack(): dgbtrf_test(): dgbtrf() factors a general band matrix. dgbtrs() solves a factored system. For a double precision real matrix (D) in general band storage mode (GB): Bandwidth is 3 Partial solution (all should be 1) 1 1.0000000 2 1.0000000 3 1.0000000 4 1.0000000 5 1.0000000 DGECON_TEST DGECON computes the condition number of a factored matrix DGETRF computes the LU factorization; For a double precision real matrix (D) in general storage mode (GE): The matrix A: Col 1 2 3 Row 1 1. 2. 3. 2 4. 5. 6. 3 7. 8. 0. Matrix reciprocal condition number = 0.240000E-01 dgeev_test(): (D): for a double precision real matrix, (GE): in general storage mode, (EV): compute eigenvalues and eigenvectors. The matrix A: Col 1 2 3 4 5 Row 1 0. 2.44949 0. 0. 0. 2 2.44949 0. 3.16228 0. 0. 3 0. 3.16228 0. 3.46410 0. 4 0. 0. 3.46410 0. 3.46410 5 0. 0. 0. 3.46410 0. 6 0. 0. 0. 0. 3.16228 7 0. 0. 0. 0. 0. Col 6 7 Row 1 0. 0. 2 0. 0. 3 0. 0. 4 0. 0. 5 3.16228 0. 6 0. 2.44949 7 2.44949 0. The eigenvalues: 1 -6.00000 0.00000 2 -4.00000 0.00000 3 6.00000 0.00000 4 -2.00000 0.00000 5 0.501558E-15 0.00000 6 4.00000 0.00000 7 2.00000 0.00000 DGEQRF_TEST DGEQRF computes the QR factorization: A = Q * R DORGQR computes the explicit form of the Q factor. For a double precision real matrix (D) in general storage mode (GE): In this case, our M x N matrix A has more rows than columns: M = 8 N = 6 The matrix A: Col 1 2 3 4 5 Row 1 0.391828 0.340558 0.475848 0.972474 0.144144 2 0.443793 0.604494 0.689401 0.170271 0.142146 3 0.761145 0.608842 0.490633 0.413926 0.562266 4 0.226983 0.885325 0.848926 0.521575 0.534588 5 0.523376E-01 0.714437 0.470004 0.540682 0.663186 6 0.478858 0.522160 0.144355 0.654488 0.167217 7 0.148963 0.616216 0.165155 0.784319 0.203608 8 0.981706 0.244430 0.321000 0.239347 0.794047 Col 6 Row 1 0.919394 2 0.329841 3 0.787452 4 0.223923 5 0.459557 6 0.749200 7 0.380256E-01 8 0.831432E-01 The Q factor: Col 1 2 3 4 5 Row 1 -0.264211 -0.322043E-01 0.343026 0.885661 0.775359E-01 2 -0.299251 -0.211237 0.388628 -0.316890 0.559538 3 -0.513243 -0.204533E-01 -0.814967E-01 -0.206980 0.401638E-01 4 -0.153055 -0.568288 0.387415 -0.120395 -0.101797 5 -0.352914E-01 -0.538680 -0.546525E-01 -0.332544E-01 -0.591917 6 -0.322896 -0.124001 -0.540339 0.807346E-01 0.342944 7 -0.100446 -0.401071 -0.528731 0.204964 0.850742E-01 8 -0.661968 0.405662 0.772608E-02 -0.906336E-01 -0.440131 Col 6 Row 1 -0.122779 2 0.919690E-01 3 -0.448872 4 0.252270 5 -0.367957 6 -0.298115 7 0.590115 8 0.372613 The R factor: Col 1 2 3 4 5 Row 1 -1.48301 -1.13638 -1.00605 -1.06780 -1.07451 2 0. -1.25182 -0.860525 -0.962042 -0.487496 3 0. 0. 0.531520 -0.227952 0.378538E-01 4 0. 0. 0. 0.832780 -0.136910 5 0. 0. 0. 0. -0.608492 6 0. 0. 0. 0. 0. Col 6 Row 1 -1.09703 2 -0.564621 3 0.167368E-01 4 0.565264 5 0.216232 6 -0.718549 The product Q * R: Col 1 2 3 4 5 Row 1 0.391828 0.340558 0.475848 0.972474 0.144144 2 0.443793 0.604494 0.689401 0.170271 0.142146 3 0.761145 0.608842 0.490633 0.413926 0.562266 4 0.226983 0.885325 0.848926 0.521575 0.534588 5 0.523376E-01 0.714437 0.470004 0.540682 0.663186 6 0.478858 0.522160 0.144355 0.654488 0.167217 7 0.148963 0.616216 0.165155 0.784319 0.203608 8 0.981706 0.244430 0.321000 0.239347 0.794047 Col 6 Row 1 0.919394 2 0.329841 3 0.787452 4 0.223923 5 0.459557 6 0.749200 7 0.380256E-01 8 0.831432E-01 DGESVD_TEST For a double precision real matrix (D) in general storage mode (GE): DGESVD computes the singular value decomposition: A = U * S * V' The matrix A: Col 1 2 3 4 Row 1 0.599326 0.379090 0.379716E-01 0.633839 2 0.131470E-02 0.139011 0.910218 0.754150 3 0.653481 0.341367 0.624103 0.687155 4 0.555371 0.107817 0.267413 0.268591E-01 5 0.136071 0.318970 0.635173 0.844164 6 0.153154 0.223947 0.172557E-01 0.151707 Singular values 1 2.1137771 2 0.86489025 3 0.47247009 4 0.11884566 Left singular vectors U: Col 1 2 3 4 5 Row 1 -0.369855 -0.556961 -0.521993 0.378800 -0.281881 2 -0.505597 0.596940 0.184384 0.136032 -0.564628 3 -0.547736 -0.255029 0.268598 0.365047E-01 0.149149 4 -0.190631 -0.402551 0.697286 -0.109917 0.714264E-01 5 -0.508951 0.275016 -0.311812 -0.217233 0.659500 6 -0.110421 -0.175318 -0.194795 -0.881704 -0.373431 Col 6 Row 1 -0.239955 2 -0.129336 3 0.734318 4 -0.546096 5 -0.293218 6 0.476798E-01 Right singular vectors V': Col 1 2 3 4 Row 1 -0.365364 -0.286261 -0.564036 -0.682955 2 -0.823997 -0.242987 0.493753 0.134888 3 0.376558 -0.314229 0.636420 -0.595344 4 0.213874 -0.871936 -0.181774 0.401178 The product U * S * V': Col 1 2 3 4 Row 1 0.599326 0.379090 0.379716E-01 0.633839 2 0.131470E-02 0.139011 0.910218 0.754150 3 0.653481 0.341367 0.624103 0.687155 4 0.555371 0.107817 0.267413 0.268591E-01 5 0.136071 0.318970 0.635173 0.844164 6 0.153154 0.223947 0.172557E-01 0.151707 DGETRF_TEST DGETRF factors a general matrix; DGETRS solves a linear system; For a double precision real matrix (D) in general storage mode (GE): Partial solution (all should be 1) 1 1.0000000 2 1.0000000 3 1.0000000 4 1.0000000 5 1.0000000 DGETRI_TEST DGETRI computes the inverse of a double precision real matrix (D) in general storage mode (GE): The matrix A: Col 1 2 3 Row 1 1. 2. 3. 2 4. 5. 6. 3 7. 8. 0. The inverse matrix: Col 1 2 3 Row 1 -1.77778 0.888889 -0.111111 2 1.55556 -0.777778 0.222222 3 -0.111111 0.222222 -0.111111 DGTSV_TEST DGTSV factors and solves a linear system with a general tridiagonal matrix for a double precision real matrix (D) in general tridiagonal storage mode (GT). The system is of order N = 100 Partial solution (Should be 1,2,3...) 1 1.0000000 2 2.0000000 3 3.0000000 4 4.0000000 5 5.0000000 DORMGQR_TEST DORMQR can compute Q' * b. after DGEQRF computes the QR factorization: A = Q * R storing a double precision real matrix (D) in general storage mode (GE). We use these routines to carry out a QR solve of an M by N linear system A * x = b. In this case, our M x N matrix A has more rows than columns: M = 8 N = 6 The matrix A: Col 1 2 3 4 5 Row 1 0.367182 0.120200 0.977304 0.171287 0.298418 2 0.271710 0.159432 0.652859 0.678429 0.598389 3 0.732196 0.998275 0.763428 0.231808 0.713332E-01 4 0.471319 0.108050 0.931650 0.703068 0.643022 5 0.632423 0.517553 0.497101 0.310382 0.947618 6 0.520375 0.296702 0.992978 0.644721 0.176780 7 0.615981 0.995747 0.725140 0.580584 0.970351 8 0.148918 0.363825 0.401269 0.959101 0.414081 Col 6 Row 1 0.281489 2 0.218770E-01 3 0.511087 4 0.961081 5 0.472838 6 0.413199 7 0.605409 8 0.690960 The solution X: 1 1.0000000 2 2.0000000 3 3.0000000 4 4.0000000 5 5.0000000 6 6.0000000 DPBTRF_TEST DPBTRF computes the lower Cholesky factor A = L*L' or the upper Cholesky factor A = U'*U; For a double precision real matrix (D) in positive definite band storage mode (PB): The lower Cholesky factor L: 1.414214 0.000000 0.000000 0.000000 0.000000 -0.707107 1.224745 0.000000 0.000000 0.000000 0.000000 -0.816497 1.154701 0.000000 0.000000 0.000000 0.000000 -0.866025 1.118034 0.000000 0.000000 0.000000 0.000000 -0.894427 1.095445 DPBTRS_TEST DPBTRS solves linear systems for a positive definite symmetric band matrix, stored as a double precision real matrix (D) in positive definite band storage mode (PB): Partial solution (all should be 1) 1 1.0000000 2 1.0000000 3 1.0000000 4 1.0000000 5 1.0000000 DPOTRF_TEST DPOTRF computes the Cholesky factorization R'*R for a double precision real matrix (D) in positive definite storage mode (PO). The matrix A: Col 1 2 3 4 5 Row 1 2. -1. 0. 0. 0. 2 -1. 2. -1. 0. 0. 3 0. -1. 2. -1. 0. 4 0. 0. -1. 2. -1. 5 0. 0. 0. -1. 2. The Cholesky factor R: Col 1 2 3 4 5 Row 1 1.41421 -0.707107 0. 0. 0. 2 0. 1.22474 -0.816497 0. 0. 3 0. 0. 1.15470 -0.866025 0. 4 0. 0. 0. 1.11803 -0.894427 5 0. 0. 0. 0. 1.09545 The product R' * R Col 1 2 3 4 5 Row 1 2.00000 -1. 0. 0. 0. 2 -1. 2.00000 -1. 0. 0. 3 0. -1. 2. -1. 0. 4 0. 0. -1. 2.00000 -1. 5 0. 0. 0. -1. 2.00000 DPOTRI_TEST DPOTRI computes the inverse for a double precision real matrix (D) in positive definite storage mode (PO). The matrix A: Col 1 2 3 4 5 Row 1 2. -1. 0. 0. 0. 2 -1. 2. -1. 0. 0. 3 0. -1. 2. -1. 0. 4 0. 0. -1. 2. -1. 5 0. 0. 0. -1. 2. The Cholesky factor R: Col 1 2 3 4 5 Row 1 1.41421 -0.707107 0. 0. 0. 2 0. 1.22474 -0.816497 0. 0. 3 0. 0. 1.15470 -0.866025 0. 4 0. 0. 0. 1.11803 -0.894427 5 0. 0. 0. 0. 1.09545 The product R' * R Col 1 2 3 4 5 Row 1 2.00000 -1. 0. 0. 0. 2 -1. 2.00000 -1. 0. 0. 3 0. -1. 2. -1. 0. 4 0. 0. -1. 2.00000 -1. 5 0. 0. 0. -1. 2.00000 The inverse matrix B: Col 1 2 3 4 5 Row 1 0.833333 0.666667 0.500000 0.333333 0.166667 2 0.666667 1.33333 1.00000 0.666667 0.333333 3 0.500000 1.00000 1.50000 1. 0.500000 4 0.333333 0.666667 1. 1.33333 0.666667 5 0.166667 0.333333 0.500000 0.666667 0.833333 The product B * A Col 1 2 3 4 5 Row 1 1.00000 0.444089E-15 0. -0.111022E-15 0. 2 -0.444089E-15 1.00000 0. 0.555112E-16 -0.111022E-15 3 -0.444089E-15 0.444089E-15 1.00000 -0.444089E-15 0. 4 -0.444089E-15 0.666134E-15 0. 1.00000 0. 5 -0.166533E-15 0.222045E-15 0. -0.222045E-15 1. DSBGVX_TEST DSBGVX solves the generalized eigenvalue problem A * X = LAMBDA * B * X for a symmetric banded NxN matrix A, and a symmetric banded positive definite NxN matrix B, Computed eigenvalues 1 1.0581164 Computed eigenvalues 1 4.7709121 dsyev_test() dsyev() computes eigenvalues and eigenvectors For a double precision real matrix (D) in symmetric storage mode (SY). The matrix A: Col 1 2 3 4 5 Row 1 0. 2.44949 0. 0. 0. 2 2.44949 0. 3.16228 0. 0. 3 0. 3.16228 0. 3.46410 0. 4 0. 0. 3.46410 0. 3.46410 5 0. 0. 0. 3.46410 0. 6 0. 0. 0. 0. 3.16228 7 0. 0. 0. 0. 0. Col 6 7 Row 1 0. 0. 2 0. 0. 3 0. 0. 4 0. 0. 5 3.16228 0. 6 0. 2.44949 7 2.44949 0. The eigenvalues: 1 -6.0000000 2 -4.0000000 3 -2.0000000 4 -0.19194523E-15 5 2.0000000 6 4.0000000 7 6.0000000 The eigenvector matrix: Col 1 2 3 4 5 Row 1 0.125000 0.306186 0.484123 -0.559017 0.484123 2 -0.306186 -0.500000 -0.395285 0.132008E-15 0.395285 3 0.484123 0.395285 -0.125000 0.433013 -0.125000 4 -0.559017 0.117123E-15 0.433013 -0.350963E-16 -0.433013 5 0.484123 -0.395285 -0.125000 -0.433013 -0.125000 6 -0.306186 0.500000 -0.395285 0.252279E-15 0.395285 7 0.125000 -0.306186 0.484123 0.559017 0.484123 Col 6 7 Row 1 -0.306186 0.125000 2 -0.500000 0.306186 3 -0.395285 0.484123 4 -0.225514E-15 0.559017 5 0.395285 0.484123 6 0.500000 0.306186 7 0.306186 0.125000 lapack_test(): Normal end of execution. 01 April 2024 3:32:19.654 PM