09 May 2025 9:17:00.960 PM lapack_d_test(): Fortran90 version Test lapack_d(). 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. The factored matrix A: Col 1 2 3 Row 1 7. 8. 0. 2 0.142857 0.857143 3. 3 0.571429 0.500000 4.50000 The pivot vector 1: 3 2: 3 3: 3 Matrix reciprocal condition number = 0.240000E-01 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 0.234165 0.437382 0.633663 0.416315 0.317987 2 0.348238 0.815769 0.983816 0.802386 0.964128 3 0.750363 0.640072 0.701822 0.384009 0.849880 4 0.386224 0.764573 0.872810 0.283005 0.584730E-02 5 0.529820 0.918620 0.732184 0.564769 0.832738 6 0.906885 0.423042 0.680494 0.268742 0.886057 7 0.582017 0.474352 0.193239 0.368315 0.284494 8 0.763431 0.954763E-01 0.793862E-01 0.388505 0.340715 Col 6 Row 1 0.304052 2 0.515431 3 0.753062 4 0.357630 5 0.291778 6 0.109219 7 0.105746 8 0.936056 The Q factor: Col 1 2 3 4 5 Row 1 -0.137198 -0.228243 0.354971 0.261640 0.272721 2 -0.204034 -0.492845 0.275433 0.604604 -0.178592 3 -0.439641 -0.247307E-01 0.440071E-01 -0.224362 -0.297137 4 -0.226290 -0.416518 0.156298 -0.467557 0.662135 5 -0.310424 -0.450536 -0.444430 -0.530054E-01 -0.326438 6 -0.531348 0.295415 0.430249 -0.297018 -0.288379 7 -0.341007 0.134354E-02 -0.617458 0.521317E-01 0.204661 8 -0.447298 0.490566 -0.887736E-01 0.450891 0.367974 Col 6 Row 1 -0.161870 2 -0.551023E-01 3 0.630906 4 0.102208 5 0.350075E-01 6 -0.494892 7 -0.462756 8 0.319353 The R factor: Col 1 2 3 4 5 Row 1 -1.70676 -1.39528 -1.48400 -1.07119 -1.59403 2 0. -1.07759 -1.10004 -0.601822 -0.517096 3 0. 0. 0.504224 0.326335E-01 0.221966 4 0. 0. 0. 0.460190 0.333842 5 0. 0. 0. 0. -0.677881 6 0. 0. 0. 0. 0. Col 6 Row 1 -1.16225 2 -0.130860 3 0.107859 4 0.434680 5 0.243249 6 0.640205 The product Q * R: Col 1 2 3 4 5 Row 1 0.234165 0.437382 0.633663 0.416315 0.317987 2 0.348238 0.815769 0.983816 0.802386 0.964128 3 0.750363 0.640072 0.701822 0.384009 0.849880 4 0.386224 0.764573 0.872810 0.283005 0.584730E-02 5 0.529820 0.918620 0.732184 0.564769 0.832738 6 0.906885 0.423042 0.680494 0.268742 0.886057 7 0.582017 0.474352 0.193239 0.368315 0.284494 8 0.763431 0.954763E-01 0.793862E-01 0.388505 0.340715 Col 6 Row 1 0.304052 2 0.515431 3 0.753062 4 0.357630 5 0.291778 6 0.109219 7 0.105746 8 0.936056 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 0.310804 0.243509E-01 0.710870 0.486942 2 0.281703 0.211168 0.661361 0.637780E-01 3 0.959350 0.950706 0.662798 0.140260 4 0.604468 0.426741 0.619402 0.684954 5 0.867101 0.768645 0.271511 0.473136 6 0.197193 0.788911 0.903488 0.619166 Singular values 1 2.7010968 2 0.88767851 3 0.53270867 4 0.47120637 Left singular vectors U: Col 1 2 3 4 5 Row 1 -0.278131 -0.517320 -0.232880 0.469693 0.128672 2 -0.240763 -0.222500 0.465287 0.435173 0.426338 3 -0.526688 0.494482 0.443797 0.219693 -0.401777 4 -0.422025 -0.178350 -0.510837 0.888595E-01 -0.517116 5 -0.438372 0.477290 -0.442060 -0.120761 0.608295 6 -0.465834 -0.422784 0.275586 -0.720603 0.531362E-01 Col 6 Row 1 -0.603011 2 0.552173 3 -0.267288 4 0.503813 5 -0.813365E-03 6 -0.788141E-01 Right singular vectors V': Col 1 2 3 4 Row 1 -0.513354 -0.534186 -0.558046 -0.373762 2 0.533525 0.414275 -0.619617 -0.399752 3 -0.287779 0.326884 0.467185 -0.769460 4 0.607456 -0.660430 0.293935 -0.329289 The product U * S * V': Col 1 2 3 4 Row 1 0.310804 0.243509E-01 0.710870 0.486942 2 0.281703 0.211168 0.661361 0.637780E-01 3 0.959350 0.950706 0.662798 0.140260 4 0.604468 0.426741 0.619402 0.684954 5 0.867101 0.768645 0.271511 0.473136 6 0.197193 0.788911 0.903488 0.619166 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 0.863663 0.400139 0.569609 0.160763 0.329429 2 0.645898 0.924684 0.319729 0.346074 0.389950 3 0.419163 0.156046 0.919541 0.412040 0.499052 4 0.888841 0.542821 0.971095 0.856553 0.527547 5 0.905065 0.192278 0.228189 0.840879 0.856329 6 0.512059 0.531356 0.233077 0.704756 0.607115 7 0.309664 0.663700 0.955326 0.245685E-02 0.931394 8 0.711735 0.957701 0.589343 0.312633 0.633833 Col 6 Row 1 0.864611E-01 2 0.154806 3 0.215145 4 0.611681 5 0.443484 6 0.771815E-01 7 0.402807 8 0.714037 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 0.222045E-15 0. -0.111022E-15 0. 2 -0.666134E-15 1.00000 0.444089E-15 -0.166533E-15 -0.111022E-15 3 -0.666134E-15 0.133227E-14 1.00000 -0.222045E-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 -0.67072288E-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 -0.315775E-15 -0.395285 3 -0.484123 0.395285 -0.125000 0.433013 0.125000 4 0.559017 0.336779E-15 0.433013 -0.862557E-16 0.433013 5 -0.484123 -0.395285 -0.125000 -0.433013 0.125000 6 0.306186 0.500000 -0.395285 0.157289E-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 0.104083E-16 0.559017 5 0.395285 0.484123 6 0.500000 0.306186 7 0.306186 0.125000 lapack_d_test(): Normal end of execution. 09 May 2025 9:17:00.962 PM