7 October 2025 1:11:44.620 PM LAPACK_EIGEN_TEST Fortran77 version Test some of the LAPACK routines for real symmetric eigenproblems. DSYEV_TEST DSYEV computes eigenvalues and eigenvectors for a double precision real matrix (D) in symmetric storage mode (SY) Matrix order = 4 Random number SEED = 123456789 R8SYMM_GEN will give us a symmetric matrix with known eigenstructure. The matrix A: Col 1 2 3 4 Row 1 1.23120 0.302862 0.756471 0.603923 2 0.302862 0.727516 0.413587 0.144622 3 0.756471 0.413587 1.27884 0.608408 4 0.603923 0.144622 0.608408 1.17153 The eigenvector matrix Q: Col 1 2 3 4 Row 1 -0.573676 0.790270 0.214467 -0.193004E-01 2 -0.253054 -0.368913 0.624901 -0.639817 3 -0.600374 -0.253780 -0.697581 -0.297538 4 -0.496398 -0.418297 0.277278 0.708332 LAMBDA_MIN = 0.433940 LAMBDA_MAX = 2.67904 The eigenvalues LAMBDA: 1 2.6790403 2 0.52723120 3 0.43394019 4 0.76887587 The column norms of A*Q: 1 2.6790403 2 0.52723120 3 0.43394019 4 0.76887587 Now call DSYEV and see if it can recover Q and LAMBDA. LAMBDA_MIN = 0.433940 LAMBDA_MAX = 2.67904 Computed eigenvalues: 1 0.43394019 2 0.52723120 3 0.76887587 4 2.6790403 The eigenvector matrix: Col 1 2 3 4 Row 1 0.214467 0.790270 0.193004E-01 0.573676 2 0.624901 -0.368913 0.639817 0.253054 3 -0.697581 -0.253780 0.297538 0.600374 4 0.277278 -0.418297 -0.708332 0.496398 The residual (A-Lambda*I)*X: Col 1 2 3 4 Row 1 0.249800E-15 0.111022E-15 -0.114492E-15 -0.888178E-15 2 0.555112E-16 0.111022E-15 -0.111022E-15 0.00000 3 0.444089E-15 -0.277556E-16 -0.194289E-15 -0.133227E-14 4 0.111022E-15 0.00000 0.00000 0.00000 Setup time = 0.212000E-03 Solve time = 0.625200E-02 DSYEV_TEST DSYEV computes eigenvalues and eigenvectors for a double precision real matrix (D) in symmetric storage mode (SY) Matrix order = 16 Random number SEED = 123456789 R8SYMM_GEN will give us a symmetric matrix with known eigenstructure. LAMBDA_MIN = -1.24246 LAMBDA_MAX = 2.67904 Now call DSYEV and see if it can recover Q and LAMBDA. LAMBDA_MIN = -1.24246 LAMBDA_MAX = 2.67904 Setup time = 0.106900E-02 Solve time = 0.382400E-02 DSYEV_TEST DSYEV computes eigenvalues and eigenvectors for a double precision real matrix (D) in symmetric storage mode (SY) Matrix order = 64 Random number SEED = 123456789 R8SYMM_GEN will give us a symmetric matrix with known eigenstructure. LAMBDA_MIN = -1.83804 LAMBDA_MAX = 3.16400 Now call DSYEV and see if it can recover Q and LAMBDA. LAMBDA_MIN = -1.83804 LAMBDA_MAX = 3.16400 Setup time = 0.507920E-01 Solve time = 0.613020E-01 DSYEV_TEST DSYEV computes eigenvalues and eigenvectors for a double precision real matrix (D) in symmetric storage mode (SY) Matrix order = 256 Random number SEED = 123456789 R8SYMM_GEN will give us a symmetric matrix with known eigenstructure. LAMBDA_MIN = -1.83804 LAMBDA_MAX = 4.32858 Now call DSYEV and see if it can recover Q and LAMBDA. LAMBDA_MIN = -1.83804 LAMBDA_MAX = 4.32858 Setup time = 1.41917 Solve time = 0.285182 DSYEVD_TEST DSYEVD gets eigenvalues and eigenvectors for a double precision real matrix (D) in symmetric storage mode (SY) Matrix order = 4 Random number SEED = 123456789 R8SYMM_GEN will give us a symmetric matrix with known eigenstructure. The matrix A: Col 1 2 3 4 Row 1 1.23120 0.302862 0.756471 0.603923 2 0.302862 0.727516 0.413587 0.144622 3 0.756471 0.413587 1.27884 0.608408 4 0.603923 0.144622 0.608408 1.17153 The eigenvector matrix Q: Col 1 2 3 4 Row 1 -0.573676 0.790270 0.214467 -0.193004E-01 2 -0.253054 -0.368913 0.624901 -0.639817 3 -0.600374 -0.253780 -0.697581 -0.297538 4 -0.496398 -0.418297 0.277278 0.708332 LAMBDA_MIN = 0.433940 LAMBDA_MAX = 2.67904 The eigenvalues: 1 2.6790403 2 0.52723120 3 0.43394019 4 0.76887587 The column norms of A*Q: 1 2.6790403 2 0.52723120 3 0.43394019 4 0.76887587 Now call DSYEVD and see if it can recover Q and LAMBDA. LAMBDA_MIN = 0.433940 LAMBDA_MAX = 2.67904 The computed eigenvalues: 1 0.43394019 2 0.52723120 3 0.76887587 4 2.6790403 The eigenvector matrix: Col 1 2 3 4 Row 1 0.214467 0.790270 0.193004E-01 0.573676 2 0.624901 -0.368913 0.639817 0.253054 3 -0.697581 -0.253780 0.297538 0.600374 4 0.277278 -0.418297 -0.708332 0.496398 The residual (A-Lambda*I)*X: Col 1 2 3 4 Row 1 0.111022E-15 -0.111022E-15 -0.416334E-16 -0.888178E-15 2 -0.111022E-15 0.00000 -0.166533E-15 -0.111022E-15 3 0.277556E-15 -0.249800E-15 -0.277556E-16 -0.133227E-14 4 -0.555112E-16 -0.111022E-15 0.00000 0.00000 Setup time = 0.550000E-04 Solve time = 0.163000E-03 DSYEVD_TEST DSYEVD gets eigenvalues and eigenvectors for a double precision real matrix (D) in symmetric storage mode (SY) Matrix order = 16 Random number SEED = 123456789 R8SYMM_GEN will give us a symmetric matrix with known eigenstructure. LAMBDA_MIN = -1.24246 LAMBDA_MAX = 2.67904 Now call DSYEVD and see if it can recover Q and LAMBDA. LAMBDA_MIN = -1.24246 LAMBDA_MAX = 2.67904 Setup time = 0.998000E-03 Solve time = 0.445000E-03 DSYEVD_TEST DSYEVD gets eigenvalues and eigenvectors for a double precision real matrix (D) in symmetric storage mode (SY) Matrix order = 64 Random number SEED = 123456789 R8SYMM_GEN will give us a symmetric matrix with known eigenstructure. LAMBDA_MIN = -1.83804 LAMBDA_MAX = 3.16400 Now call DSYEVD and see if it can recover Q and LAMBDA. LAMBDA_MIN = -1.83804 LAMBDA_MAX = 3.16400 Setup time = 0.573730E-01 Solve time = 0.626500E-02 DSYEVD_TEST DSYEVD gets eigenvalues and eigenvectors for a double precision real matrix (D) in symmetric storage mode (SY) Matrix order = 256 Random number SEED = 123456789 R8SYMM_GEN will give us a symmetric matrix with known eigenstructure. LAMBDA_MIN = -1.83804 LAMBDA_MAX = 4.32858 Now call DSYEVD and see if it can recover Q and LAMBDA. LAMBDA_MIN = -1.83804 LAMBDA_MAX = 4.32858 Setup time = 1.43168 Solve time = 0.697260E-01 LAPACK_EIGEN_TEST Normal end of execution. 7 October 2025 1:11:45.513 PM