October 18 2009 11:03:02.473 AM EISPACK_PRB1 FORTRAN90 version. Sample problems for EISPACK TEST01 CG computes the eigenvalues and eigenvectors of a complex general matrix. Matrix order = 4 Real and imaginary parts of eigenvalues: 1 4.828427 0.000000 2 4.000000 0.000000 3 -0.000000 0.000000 4 -0.828427 0.000000 The eigenvectors are: Eigenvector 1 0.653281 0.00000 0.500000 0.00000 -0.500000 0.00000 0.270598 0.00000 Eigenvector 2 0.653281 0.00000 -0.500000 0.00000 0.500000 0.00000 0.270598 0.00000 Eigenvector 3 0.00000 0.270598 0.00000 -0.500000 0.00000 -0.500000 0.00000 -0.653281 Eigenvector 4 0.00000 -0.270598 0.00000 -0.500000 0.00000 -0.500000 0.00000 0.653281 TEST02 CH computes the eigenvalues and eigenvectors of a complex hermitian matrix. Matrix order = 4 Error flag = 0 The eigenvalues Lambda: 1 -0.82842712 2 0.13322676E-14 3 4.0000000 4 4.8284271 Eigenvectors are: Eigenvector 1 0.00000 0.270598 0.00000 0.500000 0.00000 0.500000 0.00000 0.653281 Eigenvector 2 0.00000 0.270598 0.00000 -0.500000 0.00000 -0.500000 0.00000 0.653281 Eigenvector 3 0.653281 0.00000 -0.500000 0.00000 0.500000 0.00000 -0.270598 0.00000 Eigenvector 4 -0.653281 0.00000 -0.500000 0.00000 0.500000 -0.00000 0.270598 -0.00000 TEST03 MINFIT solves an overdetermined linear system using least squares methods. Matrix rows = 5 Matrix columns = 2 The matrix A: Col 1 2 Row 1 1. 1. 2 2.05000 -1. 3 3.06000 1. 4 -1.02000 2. 5 4.08000 -1. The right hand side B: Col 1 Row 1 1.98000 2 0.950000 3 3.98000 4 0.920000 5 2.90000 MINFIT error code IERR = 0 The singular values: 1 5.7385075 2 2.7059992 The least squares solution X: 1 0.96310140 2 0.98854334 The residual A * X - B: 1 -0.28355256E-01 2 0.35814526E-01 3 -0.44366372E-01 4 0.74723261E-01 5 0.40910368E-01 TEST04 RG computes the eigenvalues and eigenvectors of a real general matrix. Matrix order = 3 The matrix A: Col 1 2 3 Row 1 33. 16. 72. 2 -24. -10. -57. 3 -8. -4. -17. Real and imaginary parts of eigenvalues: 1 3 0 2 1 0 3 2 0 The eigenvectors may be complex: Eigenvector 1 0.800000 -0.600000 -0.200000 Eigenvector 2 -25.0000 20.0000 6.66667 Eigenvector 3 48.0000 -39.0000 -12.0000 Residuals (A*x-Lambda*x) for eigenvalue 1 0.00000 -0.222045E-14 0.444089E-15 Residuals (A*x-Lambda*x) for eigenvalue 2 0.639488E-13 0.497380E-13 -0.115463E-13 Residuals (A*x-Lambda*x) for eigenvalue 3 -0.142109E-13 0.852651E-13 0.355271E-13 TEST05: RGG for real generalized problem. Find scalars LAMBDA and vectors X so that A*X = LAMBDA * B * X Matrix order = 4 The matrix A: Col 1 2 3 4 Row 1 -7. 7. 6. 6. 2 -10. 8. 10. 8. 3 -8. 3. 10. 11. 4 -4. 0. 4. 12. The matrix B: Col 1 2 3 4 Row 1 2. 1. 0. 0. 2 1. 2. 1. 0. 3 0. 1. 2. 1. 4 0. 0. 1. 2. Real and imaginary parts of eigenvalues: 1 2.000000 0.000000 2 1.000000 0.000000 3 4.000000 0.000000 4 3.000000 0.000000 The eigenvectors are: Eigenvector 1 1.00000 1.00000 -1.00000 1.00000 Eigenvector 2 1.00000 0.750000 -1.00000 1.00000 Eigenvector 3 0.666667 0.500000 -1.00000 1.00000 Eigenvector 4 0.333333 0.250000 -1.00000 0.500000 Residuals (A*x-(Alfr+Alfi*I)*B*x) for eigenvalue 1 0.199840E-14 0.222045E-15 -0.888178E-15 0.666134E-15 Residuals (A*x-(Alfr+Alfi*I)*B*x) for eigenvalue 2 0.277556E-14 0.210942E-14 0.333067E-15 0.122125E-14 Residuals (A*x-(Alfr+Alfi*I)*B*x) for eigenvalue 3 -0.488498E-14 -0.133227E-14 0.00000 -0.355271E-14 Residuals (A*x-(Alfr+Alfi*I)*B*x) for eigenvalue 4 0.577316E-14 0.133227E-14 0.888178E-15 0.222045E-14 TEST06 RS computes the eigenvalues and eigenvectors of a real symmetric matrix. Matrix order = 4 The matrix A: Col 1 2 3 4 Row 1 5. 4. 1. 1. 2 4. 5. 1. 1. 3 1. 1. 4. 2. 4 1. 1. 2. 4. The eigenvalues Lambda: 1 1.0000000 2 2.0000000 3 5.0000000 4 10.000000 The eigenvector matrix: Col 1 2 3 4 Row 1 0.707107 -0.971445E-16 0.316228 0.632456 2 -0.707107 -0.277556E-16 0.316228 0.632456 3 0. 0.707107 -0.632456 0.316228 4 0. -0.707107 -0.632456 0.316228 The residual (A-Lambda*I)*X: Col 1 2 3 4 Row 1 0. -0.360822E-15 -0.888178E-15 0. 2 0. -0.499600E-15 0. 0.888178E-15 3 0. 0.888178E-15 -0.266454E-14 -0.133227E-14 4 0. -0.111022E-14 0. 0. TEST07 RSB computes the eigenvalues and eigenvectors of a real symmetric band matrix. Matrix order = 5 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 eigenvalues Lambda: 1 0.0000000 2 0.0000000 3 0.0000000 4 0.0000000 5 0.0000000 The eigenvector matrix X: Col 1 2 3 4 5 Row 1 1. -0.266454E-14 0. -0.971445E-16 0.316228 2 0.888178E-15 1. 0.707107 -0.277556E-16 -0.632456 3 -0.111022E-14 0. 1. 0.707107 -0.632456 4 -0.888178E-15 0.888178E-15 0. 1. 0.632456 5 0. -0.133227E-14 0. 0.316228 1. The residual (A-Lambda*I)*X: Col 1 2 3 4 5 Row 1 0. 0. 0. 0. 0. 2 0. 0. 0. 0. 0. 3 0.888178E-15 -0.888178E-15 0. -1. -0.632456 4 -0.177636E-14 0.310862E-14 0. 1.68377 0.264911 5 0.888178E-15 -0.355271E-14 0. -0.367544 1.36754 TEST08: RSG for real symmetric generalized problem. Find scalars LAMBDA and vectors X so that A*X = LAMBDA * B * X Matrix order = 4 The matrix A: Col 1 2 3 4 Row 1 0. 1. 2. 3. 2 1. 0. 1. 2. 3 2. 1. 0. 1. 4 3. 2. 1. 0. The matrix B: Col 1 2 3 4 Row 1 2. -1. 0. 0. 2 -1. 2. -1. 0. 3 0. -1. 2. -1. 4 0. 0. -1. 2. The eigenvalues Lambda: 1 -2.4357817 2 -0.52079729 3 -0.16421833 4 11.520797 The eigenvector matrix X: Col 1 2 3 4 Row 1 0.526940 0.251292 -0.149448 0.660948 2 0.287038 -0.409656 0.342942 0.912240 3 -0.287038 -0.409656 -0.342942 0.912240 4 -0.526940 0.251292 0.149448 0.660948 Residuals (A*x-(w*I)*B*x) for eigenvalue 1 -0.222045E-15 0.111022E-15 0.133227E-14 -0.133227E-14 Residuals (A*x-(w*I)*B*x) for eigenvalue 2 0.222045E-15 -0.721645E-15 -0.693889E-15 0.183187E-14 Residuals (A*x-(w*I)*B*x) for eigenvalue 3 0.929812E-15 -0.256739E-15 0.534295E-15 0.107553E-14 Residuals (A*x-(w*I)*B*x) for eigenvalue 4 0.355271E-14 -0.177636E-14 -0.177636E-14 0.355271E-14 TEST09: RSGAB for real symmetric generalized problem. Find scalars LAMBDA and vectors X so that A*B*X = LAMBDA * X Matrix order = 4 The matrix A: Col 1 2 3 4 Row 1 0. 1. 2. 3. 2 1. 0. 1. 2. 3 2. 1. 0. 1. 4 3. 2. 1. 0. The matrix B: Col 1 2 3 4 Row 1 2. -1. 0. 0. 2 -1. 2. -1. 0. 3 0. -1. 2. -1. 4 0. 0. -1. 2. EThe eigenvalues Lambda: 1 -5.0000000 2 -2.0000000 3 -2.0000000 4 3.0000000 The eigenvector matrix X: Col 1 2 3 4 Row 1 0.547723 -0.171729E-16 0.314018E-15 0.707107 2 0.182574 0.325082E-01 0.815849 0.707107 3 -0.182574 -0.690292 0.436078 0.707107 4 -0.547723 -0.138588E-15 0.644493E-16 0.707107 The residual matrix (A*B-Lambda*I)*X: Col 1 2 3 4 Row 1 0.355271E-14 0.766765E-16 0.461504E-15 -0.444089E-15 2 0.199840E-14 -0.222045E-15 0.222045E-15 -0.444089E-15 3 0.122125E-14 -0.111022E-14 0.888178E-15 0. 4 -0.444089E-15 -0.551323E-16 0.128769E-14 0.444089E-15 TEST10: RSGBA for real symmetric generalized problem. Find scalars LAMBDA and vectors X so that B*A*X = LAMBDA * X Matrix order = 4 The matrix A: Col 1 2 3 4 Row 1 0. 1. 2. 3. 2 1. 0. 1. 2. 3 2. 1. 0. 1. 4 3. 2. 1. 0. The matrix B: Col 1 2 3 4 Row 1 2. -1. 0. 0. 2 -1. 2. -1. 0. 3 0. -1. 2. -1. 4 0. 0. -1. 2. The eigenvalues Lambda: 1 -5.0000000 2 -2.0000000 3 -2.0000000 4 3.0000000 The eigenvector matrix X: Col 1 2 3 4 Row 1 0.912871 -0.325082E-01 -0.815849 0.707107 2 -0.222045E-15 0.755308 1.19562 -0.166533E-15 3 0.388578E-15 -1.41309 0.563058E-01 -0.277556E-16 4 -0.912871 0.690292 -0.436078 0.707107 The residual matrix (B*A-Lambda*I)*X: Col 1 2 3 4 Row 1 0.532907E-14 -0.735523E-15 -0.222045E-15 -0.888178E-15 2 -0.888178E-15 0.666134E-15 -0.888178E-15 0.138778E-14 3 0.105471E-14 -0.133227E-14 0.166533E-15 -0.360822E-15 4 -0.266454E-14 0.444089E-15 0.222045E-15 0. TEST11 RSM computes some eigenvalues and eigenvectors of a real symmetric matrix. Matrix order = 4 Number of eigenvectors desired = 4 The matrix A: Col 1 2 3 4 Row 1 5. 4. 1. 1. 2 4. 5. 1. 1. 3 1. 1. 4. 2. 4 1. 1. 2. 4. The eigenvalues Lambda: 1 1.0000000 2 2.0000000 3 5.0000000 4 10.000000 The eigenvector matrix X: Col 1 2 3 4 Row 1 0.707107 -0.222045E-15 0.316228 0.632456 2 -0.707107 -0.555112E-16 0.316228 0.632456 3 0. 0.707107 -0.632456 0.316228 4 0. -0.707107 -0.632456 0.316228 The residual (A-Lambda*I)*X: Col 1 2 3 4 Row 1 0. -0.333067E-15 -0.266454E-14 -0.266454E-14 2 0. -0.444089E-15 -0.155431E-14 -0.266454E-14 3 0. 0.888178E-15 -0.310862E-14 0.222045E-14 4 0. 0.666134E-15 0.888178E-15 0.177636E-14 TEST12 RSP computes the eigenvalues and eigenvectors of a real symmetric packed matrix. Matrix order = 4 The matrix A: Col 1 2 3 4 Row 1 5. 4. 1. 1. 2 4. 5. 1. 1. 3 1. 1. 4. 2. 4 1. 1. 2. 4. The eigenvalues Lambda: 1 1.0000000 2 2.0000000 3 5.0000000 4 10.000000 The eigenvector matrix X: Col 1 2 3 4 Row 1 0.707107 0.555112E-16 0.316228 0.632456 2 -0.707107 0.111022E-15 0.316228 0.632456 3 0. 0.707107 -0.632456 0.316228 4 0. -0.707107 -0.632456 0.316228 The residual matrix (A-Lambda*I)*X: Col 1 2 3 4 Row 1 0. 0.777156E-15 -0.177636E-14 -0.888178E-15 2 0. 0.777156E-15 -0.666134E-15 0. 3 0. 0.133227E-14 -0.222045E-14 -0.888178E-15 4 0. -0.222045E-15 -0.888178E-15 0. TEST13 RSPP finds some eigenvalues and eigenvectors of a real symmetric packed matrix. Matrix order = 4 The matrix A: Col 1 2 3 4 Row 1 5. 4. 1. 1. 2 4. 5. 1. 1. 3 1. 1. 4. 2. 4 1. 1. 2. 4. The eigenvalues Lambda: 1 1.0000000 2 2.0000000 3 5.0000000 4 10.000000 The eigenvector matrix X: Col 1 2 3 4 Row 1 0.707107 -0.555112E-16 0.316228 -0.632456 2 -0.707107 0.111022E-15 0.316228 -0.632456 3 0. 0.707107 -0.632456 -0.316228 4 0. -0.707107 -0.632456 -0.316228 The residual matrix (A-Lambda*I)*X: Col 1 2 3 4 Row 1 0. 0.555112E-15 -0.333067E-14 0.888178E-15 2 0. 0.444089E-15 -0.222045E-14 0. 3 0. 0.133227E-14 -0.310862E-14 0.888178E-15 4 0. 0. 0.222045E-14 0. TEST14 RST computes the eigenvalues and eigenvectors of a real symmetric tridiagonal matrix. Matrix order = 5 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 eigenvalues Lambda: 1 0.26794919 2 1.0000000 3 2.0000000 4 3.0000000 5 3.7320508 The eigenvector matrix X: Col 1 2 3 4 5 Row 1 -0.288675 0.500000 -0.577350 -0.500000 -0.288675 2 -0.500000 0.500000 0.346252E-15 0.500000 0.500000 3 -0.577350 -0.226647E-15 0.577350 -0.489055E-15 -0.577350 4 -0.500000 -0.500000 -0.150268E-15 -0.500000 0.500000 5 -0.288675 -0.500000 -0.577350 0.500000 -0.288675 The residual matrix (A-Lambda*I)*X: Col 1 2 3 4 5 Row 1 -0.555112E-15 0. -0.444089E-15 -0.222045E-15 0. 2 0. -0.222045E-15 -0.359436E-15 0. 0. 3 -0.249800E-15 -0.509091E-16 -0.222045E-15 -0.871483E-16 0. 4 -0.832667E-16 0.166533E-15 -0.325319E-16 0. 0. 5 -0.180411E-15 0.444089E-15 0.222045E-15 -0.222045E-15 0.444089E-15 TEST15 RT computes the eigenvalues and eigenvectors of a real sign-symmetric tridiagonal matrix. Matrix order = 5 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 eigenvalues Lambda: 1 0.26794919 2 1.0000000 3 2.0000000 4 3.0000000 5 3.7320508 The eigenvector matrix X: Col 1 2 3 4 5 Row 1 -0.288675 0.500000 -0.577350 -0.500000 -0.288675 2 -0.500000 0.500000 0.346252E-15 0.500000 0.500000 3 -0.577350 -0.226647E-15 0.577350 -0.489055E-15 -0.577350 4 -0.500000 -0.500000 -0.150268E-15 -0.500000 0.500000 5 -0.288675 -0.500000 -0.577350 0.500000 -0.288675 The residual matrix (A-Lambda*I)*X: Col 1 2 3 4 5 Row 1 -0.555112E-15 0. -0.444089E-15 -0.222045E-15 0. 2 0. -0.222045E-15 -0.359436E-15 0. 0. 3 -0.249800E-15 -0.509091E-16 -0.222045E-15 -0.871483E-16 0. 4 -0.832667E-16 0.166533E-15 -0.325319E-16 0. 0. 5 -0.180411E-15 0.444089E-15 0.222045E-15 -0.222045E-15 0.444089E-15 TEST16 SVD computes the singular value decomposition of a real general matrix. Matrix order = 4 The matrix A: Col 1 2 3 4 Row 1 0.990000 0.200000E-02 0.600000E-02 0.200000E-02 2 0.200000E-02 0.990000 0.200000E-02 0.600000E-02 3 0.600000E-02 0.200000E-02 0.990000 0.200000E-02 4 0.200000E-02 0.600000E-02 0.200000E-02 0.990000 The singular values S 1 1.0000000 2 0.98400000 3 0.99200000 4 0.98400000 The U matrix: Col 1 2 3 4 Row 1 -0.500000 -0.707107 0.500000 -0.219026E-18 2 -0.500000 0.104916E-13 -0.500000 0.707107 3 -0.500000 0.707107 0.500000 0.194289E-14 4 -0.500000 0.124623E-13 -0.500000 -0.707107 The V matrix: Col 1 2 3 4 Row 1 -0.500000 -0.707107 0.500000 -0. 2 -0.500000 0.104916E-13 -0.500000 0.707107 3 -0.500000 0.707107 0.500000 0.194289E-14 4 -0.500000 0.125178E-13 -0.500000 -0.707107 The product U * S * Transpose(V): Col 1 2 3 4 Row 1 0.990000 0.200000E-02 0.600000E-02 0.200000E-02 2 0.200000E-02 0.990000 0.200000E-02 0.600000E-02 3 0.600000E-02 0.200000E-02 0.990000 0.200000E-02 4 0.200000E-02 0.600000E-02 0.200000E-02 0.990000 EISPACK_PRB1 Normal end of execution. October 18 2009 11:03:02.494 AM