9 March 2018 2:16:30.836 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: 0.555112E-16 -0.111022E-15 -0.104083E-15 -0.111022E-14 2: 0.00000 -0.277556E-16 -0.166533E-15 -0.111022E-15 3: 0.222045E-15 -0.166533E-15 -0.138778E-15 -0.666134E-15 4: -0.124900E-15 0.555112E-16 0.222045E-15 -0.222045E-15 Setup time = 0.00000 Solve time = 0.00000 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 = 0.00000 Solve time = 0.00000 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 = 0.400000E-02 Solve time = 0.400000E-02 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 = 0.416000 Solve time = 0.208000 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: 0.124900E-15 -0.555112E-16 -0.589806E-16 -0.444089E-15 2: 0.00000 -0.555112E-16 -0.166533E-15 -0.222045E-15 3: 0.222045E-15 -0.194289E-15 -0.138778E-15 -0.888178E-15 4: -0.693889E-16 -0.555112E-16 0.222045E-15 -0.222045E-15 Setup time = 0.00000 Solve time = 0.00000 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 = 0.00000 Solve time = 0.00000 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 = 0.800000E-02 Solve time = 0.400000E-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 = 0.404000 Solve time = 0.136000 LAPACK_EIGEN_TEST Normal end of execution. 9 March 2018 2:16:32.026 PM