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. 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 0.849444 0.560008 0.984340 0.687494 0.285526 2 0.227941 0.330455 0.345217 0.118450E-01 0.125814 3 0.256459 0.933233 0.729582 0.651431E-01 0.232360 4 0.279038 0.254974 0.127873 0.525390 0.159834 5 0.844975 0.122357 0.470057 0.913857 0.290661 6 0.324313 0.817839 0.546847 0.108359 0.391838 7 0.686374 0.977716 0.736035 0.372547E-02 0.958835E-01 8 0.514615 0.472315 0.764206 0.593991 0.542949 Col 6 Row 1 0.250423 2 0.233465 3 0.694768 4 0.491774 5 0.968067E-01 6 0.745875 7 0.661223 8 0.774185 The Q factor: Col 1 2 3 4 5 Row 1 -0.540243 0.151458 -0.437194 0.148855 0.410628 2 -0.144970 -0.113761 -0.890528E-01 0.213873 -0.182240 3 -0.163107 -0.609103 -0.229382 -0.232233 0.416325 4 -0.177467 -0.111008E-01 0.425566 -0.679920 0.292153 5 -0.537400 0.523173 0.266132 -0.117081 -0.132319 6 -0.206261 -0.459786 0.175081 -0.186720 -0.543294 7 -0.436531 -0.327690 0.454600 0.542648 0.525051E-01 8 -0.327293 -0.222557E-01 -0.508987 -0.269884 -0.473349 Col 6 Row 1 -0.194267 2 0.124564E-01 3 -0.203989 4 0.326453 5 -0.327656 6 -0.491730 7 0.403511 8 0.549494 The R factor: Col 1 2 3 4 5 Row 1 -1.57234 -1.36374 -1.66035 -1.18649 -0.695339 2 0. -1.16696 -0.599706 0.471111 -0.185972 3 0. 0. -0.407554 -0.131439 -0.208121 4 0. 0. 0. -0.552997 -0.294923 5 0. 0. 0. 0. -0.265563 6 0. 0. 0. 0. 0. Col 6 Row 1 -1.11763 2 -0.943478 3 -0.174647E-01 4 -0.409239 5 -0.256575 6 0.266808 The product Q * R: Col 1 2 3 4 5 Row 1 0.849444 0.560008 0.984340 0.687494 0.285526 2 0.227941 0.330455 0.345217 0.118450E-01 0.125814 3 0.256459 0.933233 0.729582 0.651431E-01 0.232360 4 0.279038 0.254974 0.127873 0.525390 0.159834 5 0.844975 0.122357 0.470057 0.913857 0.290661 6 0.324313 0.817839 0.546847 0.108359 0.391838 7 0.686374 0.977716 0.736035 0.372547E-02 0.958835E-01 8 0.514615 0.472315 0.764206 0.593991 0.542949 Col 6 Row 1 0.250423 2 0.233465 3 0.694768 4 0.491774 5 0.968067E-01 6 0.745875 7 0.661223 8 0.774185 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 0.150938 0.963743 0.531193E-01 0.301695 2 0.545909 0.714594 0.911562 0.472171 3 0.241587 0.161481 0.425474 0.128526 4 0.292039 0.745178 0.761537 0.915584 5 0.220947 0.715835 0.626284 0.592427 6 0.399337 0.319660 0.293729 0.260498 Singular values 1 2.5036042 2 0.69684404 3 0.42064730 4 0.19603617 Left singular vectors U: Col 1 2 3 4 5 Row 1 -0.325155 -0.870961 -0.284537 0.361169E-01 -0.230913 2 -0.530342 0.339246 -0.480116 0.275495 0.768361E-01 3 -0.185796 0.327735 -0.261095 0.190419 -0.593585 4 -0.561287 0.734715E-01 0.667026 -0.268163 -0.359163 5 -0.453474 -0.525003E-01 0.231842 0.347478 0.627216 6 -0.240439 0.103801 -0.348831 -0.832998 0.256971 Col 6 Row 1 0.107301E-01 2 -0.539757 3 0.633479 4 -0.183648 5 0.472983 6 0.223185 Right singular vectors V': Col 1 2 3 4 Row 1 -0.297016 -0.615942 -0.543948 -0.486330 2 0.264365 -0.708461 0.654353 0.394126E-02 3 -0.621429 -0.256663 -0.312778E-01 0.739575 4 -0.675069 0.229829 0.524370 -0.465292 The product U * S * V': Col 1 2 3 4 Row 1 0.150938 0.963743 0.531193E-01 0.301695 2 0.545909 0.714594 0.911562 0.472171 3 0.241587 0.161481 0.425474 0.128526 4 0.292039 0.745178 0.761537 0.915584 5 0.220947 0.715835 0.626284 0.592427 6 0.399337 0.319660 0.293729 0.260498 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 0.588764 0.949712 0.185963 0.460961E-02 0.197628 2 0.960742E-01 0.149768 0.892087 0.151581 0.421809 3 0.679010 0.180575 0.589991 0.906154 0.405813 4 0.954731E-01 0.544650 0.544419 0.787819 0.201156 5 0.288324 0.284398 0.790882 0.565856 0.941715 6 0.829485 0.204302 0.528183 0.954581 0.191298 7 0.866120 0.375458E-01 0.339411 0.631126 0.746687 8 0.379717 0.568125 0.181257 0.110730 0.304972 Col 6 Row 1 0.515221 2 0.644937 3 0.245398 4 0.866118 5 0.221916 6 0.633411 7 0.460543 8 0.243969 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.