06 October 2025 6:21:16.670 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. Infinity norm = 15.0000 Matrix reciprocal condition number = 0.193548E-01 dgeev_test(): dgeev() computes eigenvalues and eigenvectors: (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 0.601911 0.318243E-01 0.406125 0.234022 0.288103 2 0.770604 0.370396E-01 0.124471 0.918273 0.124753E-01 3 0.880850 0.919800 0.791849 0.937458 0.702392 4 0.386057 0.397585 0.525973 0.919025 0.260723 5 0.535963 0.590473 0.534815 0.574703 0.134030 6 0.400324 0.339147 0.319402 0.798643 0.308543 7 0.981185 0.694154 0.138952 0.832450 0.725264 8 0.934791 0.691854 0.815009 0.107680 0.368337 Col 6 Row 1 0.439641 2 0.862394 3 0.727902 4 0.239321 5 0.520349E-01 6 0.461664 7 0.744340 8 0.323781 The Q factor: Col 1 2 3 4 5 Row 1 -0.294929 -0.496607 0.403918 0.135334 0.506582 2 -0.377587 -0.640737 -0.106382 -0.332881 -0.453442 3 -0.431606 0.440315 0.931905E-01 -0.102839 0.260771 4 -0.189163 0.185573 0.329636 -0.543413 0.849917E-01 5 -0.262615 0.309093 0.112115 -0.653039E-01 -0.575268 6 -0.196154 0.946916E-01 0.514506E-01 -0.408122 0.170443 7 -0.480769 0.488700E-01 -0.767330 0.955592E-01 0.232410 8 -0.458036 0.873519E-01 0.322764 0.620518 -0.220319 Col 6 Row 1 0.299010 2 -0.314320 3 -0.578628 4 0.404106 5 0.425728 6 -0.146039 7 0.324311 8 -0.770284E-01 The R factor: Col 1 2 3 4 5 Row 1 -2.04087 -1.36778 -1.25125 -1.75133 -1.05527 2 0. 0.748229 0.438366 0.182083 0.344852 3 0. 0. 0.630800 -0.111341 -0.140286 4 0. 0. 0. -1.08693 -0.158871E-01 5 0. 0. 0. 0. 0.408508 6 0. 0. 0. 0. 0. Col 6 Row 1 -1.42511 2 -0.281521 3 -0.204505 4 -0.352255 5 0.192235 6 -0.292895 The product Q * R: Col 1 2 3 4 5 Row 1 0.601911 0.318243E-01 0.406125 0.234022 0.288103 2 0.770604 0.370396E-01 0.124471 0.918273 0.124753E-01 3 0.880850 0.919800 0.791849 0.937458 0.702392 4 0.386057 0.397585 0.525973 0.919025 0.260723 5 0.535963 0.590473 0.534815 0.574703 0.134030 6 0.400324 0.339147 0.319402 0.798643 0.308543 7 0.981185 0.694154 0.138952 0.832450 0.725264 8 0.934791 0.691854 0.815009 0.107680 0.368337 Col 6 Row 1 0.439641 2 0.862394 3 0.727902 4 0.239321 5 0.520349E-01 6 0.461664 7 0.744340 8 0.323781 dgesvd_test(): dgesvd() computes the singular value decomposition: A = U * S * V' for a double precision real matrix (D) in general storage mode (GE): The matrix A: Col 1 2 3 4 Row 1 0.119130 0.291289 0.526716 0.790215 2 0.677590 0.702541 0.961717E-03 0.495100 3 0.572165 0.373037 0.293314E-01 0.643078 4 0.728585 0.434859 0.538641 0.304723 5 0.337747 0.949288 0.455943 0.219354 6 0.457878 0.890153 0.140366 0.983158 Singular values 1 2.4961982 2 0.71475922 3 0.64299015 4 0.53555456 Left singular vectors U: Col 1 2 3 4 5 Row 1 -0.330480 0.504176 0.675023 0.861662E-01 0.405710 2 -0.415935 -0.144662 -0.512777 0.391940E-01 0.720583 3 -0.351262 0.250124 -0.342298 0.332580 -0.265173 4 -0.370906 -0.417571 0.232326 0.684347 -0.238313 5 -0.396458 -0.597984 0.288411 -0.510561 -0.382715E-01 6 -0.547400 0.361063 -0.164555 -0.389137 -0.433111 Col 6 Row 1 -0.943811E-01 2 0.149515 3 -0.718303 4 0.330097 5 -0.374057 6 0.451549 Right singular vectors V': Col 1 2 3 4 Row 1 -0.471503 -0.618710 -0.257253 -0.573327 2 -0.329800 -0.404761 -0.243623 0.817342 3 -0.422332 -0.979419E-01 0.899786 0.492828E-01 4 0.700395 -0.666163 0.254664 0.286239E-01 The product U * S * V': Col 1 2 3 4 Row 1 0.119130 0.291289 0.526716 0.790215 2 0.677590 0.702541 0.961717E-03 0.495100 3 0.572165 0.373037 0.293314E-01 0.643078 4 0.728585 0.434859 0.538641 0.304723 5 0.337747 0.949288 0.455943 0.219354 6 0.457878 0.890153 0.140366 0.983158 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() computes 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 0.257292 0.431165 0.637392 0.286101 0.119606 2 0.819927 0.617530 0.367484E-01 0.434438 0.690141 3 0.379169 0.938103 0.865984 0.481015 0.353766 4 0.881869 0.422638 0.534573 0.798713 0.765369 5 0.712435 0.492944E-01 0.672699 0.604299 0.884940E-01 6 0.303021 0.251906 0.935082 0.211762 0.134035 7 0.957690 0.918828 0.230100 0.343950 0.198190E-01 8 0.408654 0.892949 0.432293 0.605704E-01 0.322867 Col 6 Row 1 0.453592E-01 2 0.733886 3 0.375112 4 0.799536 5 0.523886 6 0.688235 7 0.776068 8 0.631820 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. 06 October 2025 6:21:16.672 PM