23 February 2023 3:49:17.129 PM EISPACK_TEST FORTRAN90 version. Test the EISPACK library. BALANC_TEST BALANC balances a real general matrix. Matrix order = 5 The matrix A: Col 1 2 3 4 5 Row 1 110. 12. 13. 0. 15. 2 0. 22. 0. 0. 0. 3 310. 32. 33. 0. 35. 4 0. 0. 43. 44. 0. 5 510. 0. 53. 0. 55. LOW = 2 IGH = 4 Scaling vector SCALE: 1 4.0000000 2 1.0000000 3 1.0000000 4 0.62500000E-01 5 2.0000000 The balanced matrix A: Col 1 2 3 4 5 Row 1 44. 0. 43. 0. 0. 2 0. 55. 53. 31.8750 0. 3 0. 35. 33. 19.3750 32. 4 0. 240. 208. 110. 192. 5 0. 0. 0. 0. 22. BANDV_TEST BANDV computes the eigenvectors of a real symmetric band matrix. Matrix order = 5 Half bandwidth + 1 = 2 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 -0.512790E-15 -0.500000 0.500000 3 -0.577350 -0.133227E-14 0.577350 -0.178742E-14 -0.577350 4 -0.500000 -0.500000 -0.102558E-14 0.500000 0.500000 5 -0.288675 -0.500000 -0.577350 -0.500000 -0.288675 The residual (A-Lambda*I)*X: Col 1 2 3 4 5 Row 1 0.174860E-14 0. 0.666134E-15 0.111022E-14 0.666134E-15 2 0.555112E-15 0.111022E-14 0.122125E-14 0.333067E-14 0.888178E-15 3 -0.199840E-14 0.111022E-14 0.133227E-14 0.112129E-14 0.133227E-14 4 0.169309E-14 0.444089E-15 0.127400E-14 0.888178E-15 0.444089E-15 5 0.167921E-14 0.111022E-14 0.133227E-14 0. 0.666134E-15 BISECT_TEST BISECT computes some eigenvalues 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 BQR_TEST BQR computes some eigenvalues of a real symmetric band matrix. Matrix order = 5 Half bandwidth+1 = 2 The compressed matrix A: Col 1 2 Row 1 0. 2. 2 -1. 2. 3 -1. 2. 4 -1. 2. 5 -1. 2. Eigenvalues: 1 0.267949 2 1.00000 3 2.00000 4 3.00000 5 3.73205 CBAL_TEST CBAL balances a complex general matrix. Matrix order = 5 The matrix Ar: Col 1 2 3 4 5 Row 1 110. 12. 13. 0. 15. 2 0. 22. 0. 0. 0. 3 310. 32. 33. 0. 35. 4 0. 0. 43. 44. 0. 5 510. 0. 53. 0. 55. The matrix Ar: Col 1 2 3 4 5 Row 1 110.500 12.5000 13.5000 0. 15.5000 2 0. 22.5000 0. 0. 0. 3 310.500 32.5000 33.5000 0. 35.5000 4 0. 0. 43.5000 44.5000 0. 5 510.500 0. 53.5000 0. 55.5000 LOW = 2 IGH = 4 Scaling vector SCALE: 1 4.0000000 2 1.0000000 3 1.0000000 4 0.62500000E-01 5 2.0000000 The balanced matrix AR: Col 1 2 3 4 5 Row 1 44. 0. 43. 0. 0. 2 0. 55. 53. 31.8750 0. 3 0. 35. 33. 19.3750 32. 4 0. 240. 208. 110. 192. 5 0. 0. 0. 0. 22. The balanced matrix Ai: Col 1 2 3 4 5 Row 1 44.5000 0. 43.5000 0. 0. 2 0. 55.5000 53.5000 31.9062 0. 3 0. 35.5000 33.5000 19.4062 32.5000 4 0. 248. 216. 110.500 200. 5 0. 0. 0. 0. 22.5000 CG_LR_TEST CG_LR computes the eigenvalues and eigenvectors of a complex general matrix, using elementary transformations. Matrix order = 4 WHAT THE FUCK AR: Col 1 2 3 4 Row 1 3. 1. 0. 0. 2 1. 3. 0. 0. 3 0. 0. 1. 1. 4 0. 0. 1. 1. WHAT THE FUCK AI: Col 1 2 3 4 Row 1 0. 0. 0. 2. 2 0. 0. -2. 0. 3 0. 2. 0. 0. 4 -2. 0. 0. 0. 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 CG_LR_TEST CG_LR computes the eigenvalues and eigenvectors of a complex general matrix, using elementary transformations. Matrix order = 4 WHAT THE FUCK AR: Col 1 2 3 4 Row 1 3. 1. 0. 0. 2 1. 3. 0. 0. 3 0. 0. 1. 1. 4 0. 0. 1. 1. WHAT THE FUCK AI: Col 1 2 3 4 Row 1 0. 0. 0. 2. 2 0. 0. -2. 0. 3 0. 2. 0. 0. 4 -2. 0. 0. 0. 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 Eigenvector 1 1.00000 0.00000 -0.436130 0.00000 0.00000 -0.744309 0.00000 0.136143 Eigenvector 2 1.00000 0.00000 0.436130 0.00000 0.00000 0.744309 0.00000 0.136143 Eigenvector 3 0.00000 0.414214 0.00000 0.436130 0.744309 0.00000 0.328679 0.00000 Eigenvector 4 0.00000 -0.414214 0.00000 0.436130 0.744309 0.00000 -0.328679 0.00000 CG_QR_TEST CG_QR computes the eigenvalues and eigenvectors of a complex general matrix, using unitary transformations. 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 CG_QR_TEST CG_QR computes the eigenvalues and eigenvectors of a complex general matrix, using unitary transformations. 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 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 CH_TEST CH computes the eigenvalues and eigenvectors of a complex hermitian matrix. Matrix order = 4 The eigenvalues Lambda: 1 -0.82842712 2 0.17634623E-14 3 4.0000000 4 4.8284271 CH_TEST CH computes the eigenvalues and eigenvectors of a complex hermitian matrix. Matrix order = 4 The eigenvalues Lambda: 1 -0.82842712 2 0.13322676E-14 3 4.0000000 4 4.8284271 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 CH3_TEST CH3 computes the eigenvalues and eigenvectors of a complex hermitian matrix. Matrix order = 4 Compressed matrix A: Col 1 2 3 4 Row 1 3. 0. 0. 2. 2 1. 3. -2. 0. 3 0. 0. 1. 0. 4 0. 0. 1. 1. The eigenvalues Lambda: 1 -0.82842712 2 0.17634623E-14 3 4.0000000 4 4.8284271 CH3_TEST CH3 computes the eigenvalues and eigenvectors of a complex hermitian matrix. Matrix order = 4 Compressed matrix A: Col 1 2 3 4 Row 1 3. 0. 0. 2. 2 1. 3. -2. 0. 3 0. 0. 1. 0. 4 0. 0. 1. 1. The eigenvalues Lambda: 1 -0.82842712 2 0.13322676E-14 3 4.0000000 4 4.8284271 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 CINVIT_TEST CINVIT computes the eigenvectors of a complex Hessenberg matrix. Matrix order = 4 Matrix Real Part Ar: Col 1 2 3 4 Row 1 4. 7. 7. 7. 2 9. 8. 8. 2. 3 0. 8. 7. 7. 4 0. 0. 4. 0. Matrix Imag Part Ai: Col 1 2 3 4 Row 1 8. 6. 10. 10. 2 9. 1. 10. 5. 3 0. 3. 2. 8. 4 0. 0. 10. 1. Real and imaginary parts of eigenvalues: 1 20.260257 16.645759 2 0.568541 6.826204 3 3.324431 -2.742027 4 -5.153229 -8.729936 Eigenvector 1 0.952157 0.250710 1.00000 0.00000 -0.330070 -0.222298 0.335491 -0.680030E-01 Eigenvector 2 1.00000 0.00000 0.503206 -0.824242 1.00000 0.00000 -0.768179 0.105140E-01 Eigenvector 3 -0.501509 0.172182 0.215017 -0.275480 -0.257418 -0.309094 -1.00000 0.00000 Eigenvector 4 0.224707 0.460156E-01 -0.244894 0.613996 -0.866321 0.203311 -1.00000 -0.106965 IMTQLV_TEST IMTQLV computes the eigenvalues 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 INVIT_TEST INVIT computes the eigenvectors of a real Hessenberg matrix. Matrix order = 5 Matrix A: Col 1 2 3 4 5 Row 1 9. 4. 1. 3. 2. 2 4. 3. 1. 7. 1. 3 0. 3. 1. 2. 4. 4 0. 0. 5. 5. 1. 5 0. 0. 0. 1. 2. Real and imaginary parts of eigenvalues: 1 11.942140 0.000000 2 -0.484651 3.050400 3 -0.484651 -3.050400 4 7.232090 0.000000 5 1.795072 0.000000 Eigenvector: 1 0.576743 0.000000 2 1.000000 0.000000 3 -0.108856 0.000000 4 -0.079555 0.000000 5 0.008002 0.000000 Eigenvector: 1 -0.092926 -0.066023 2 1.000000 0.000000 3 0.023740 0.323168 4 0.118671 -0.231110 5 0.064595 -0.013712 Eigenvector: 1 -0.092926 0.066023 2 1.000000 -0.000000 3 0.023740 -0.323168 4 0.118671 0.231110 5 0.064595 0.013712 Eigenvector: 1 1.000000 0.000000 2 0.111558 0.000000 3 0.206404 0.000000 4 0.505654 0.000000 5 -0.096645 0.000000 Eigenvector: 1 -0.134922 0.000000 2 1.000000 0.000000 3 -0.018834 0.000000 4 -0.056226 0.000000 5 -0.274369 0.000000 Residuals (A*x-Lambda*x) for eigenvalue 1 1.97163 0.00000 -7.29291 0.00000 4.06401 0.00000 0.160036E-01 0.00000 -0.159110 0.00000 Residuals (A*x-Lambda*x) for eigenvalue 2 3.42618 -0.740324 4.03198 -4.62280 4.51676 -0.109692 0.129191 -0.274230E-01 0.237343 -0.462220 Residuals (A*x-Lambda*x) for eigenvalue 3 3.42618 0.740324 4.03198 4.62280 4.51676 0.109692 0.129191 0.274230E-01 0.237343 0.462220 Residuals (A*x-Lambda*x) for eigenvalue 4 3.74422 0.00000 7.17721 0.00000 -0.326924 0.00000 -0.193289 0.00000 1.01131 0.00000 Residuals (A*x-Lambda*x) for eigenvalue 5 2.29164 0.00000 -0.215472E-01 0.00000 1.80504 0.00000 -0.548739 0.00000 -0.112452 0.00000 MINFIT_TEST 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 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 RG_ELM_TEST RG_ELM computes the eigenvalues and eigenvectors of a real general matrix, using elementary transformations. 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 RG_ELM_TEST RG_ELM computes the eigenvalues and eigenvectors of a real general matrix, using elementary transformations. 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 Eigenvector: 1 1.000000 0.000000 2 -0.750000 0.000000 3 -0.250000 0.000000 Eigenvector: 1 -1.000000 0.000000 2 0.800000 0.000000 3 0.266667 0.000000 Eigenvector: 1 1.000000 0.000000 2 -0.812500 0.000000 3 -0.250000 0.000000 Residuals (A*x-Lambda*x) for eigenvalue 1 0.00000 0.00000 0.444089E-15 0.00000 0.00000 0.00000 Residuals (A*x-Lambda*x) for eigenvalue 2 0.00000 0.00000 0.666134E-15 0.00000 -0.555112E-16 0.00000 Residuals (A*x-Lambda*x) for eigenvalue 3 -0.355271E-14 0.00000 0.355271E-14 0.00000 0.999201E-15 0.00000 RG_ORT_TEST RG_ORT computes the eigenvalues and eigenvectors of a real general matrix, using orthogonal transformations. 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 3.000000 0.000000 2 1.000000 0.000000 3 2.000000 0.000000 RG_ORT_TEST RG_ORT computes the eigenvalues and eigenvectors of a real general matrix, using orthogonal transformations. 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 3.000000 0.000000 2 1.000000 0.000000 3 2.000000 0.000000 Eigenvector: 1 1.000000 0.000000 2 -0.750000 0.000000 3 -0.250000 0.000000 Eigenvector: 1 1.000000 0.000000 2 -0.800000 0.000000 3 -0.266667 0.000000 Eigenvector: 1 1.000000 0.000000 2 -0.812500 0.000000 3 -0.250000 0.000000 Residuals (A*x-Lambda*x) for eigenvalue 1 0.710543E-14 0.00000 -0.106581E-13 0.00000 -0.366374E-14 0.00000 Residuals (A*x-Lambda*x) for eigenvalue 2 0.106581E-13 0.00000 -0.138778E-13 0.00000 -0.460743E-14 0.00000 Residuals (A*x-Lambda*x) for eigenvalue 3 0.124345E-13 0.00000 -0.153211E-13 0.00000 -0.505151E-14 0.00000 RGG_TEST: 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 RGG_TEST: 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 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 RS_TEST 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 RS_TEST 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 -0.444089E-15 0. 2 0. -0.499600E-15 0.222045E-15 0. 3 0. 0.888178E-15 -0.222045E-14 -0.888178E-15 4 0. -0.888178E-15 0. 0. RSB_TEST 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 0.26794919 2 1.0000000 3 2.0000000 4 3.0000000 5 3.7320508 RSB_TEST 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 0.26794919 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 -0.414673E-16 0.500000 -0.500000 3 -0.577350 0. 0.577350 0.222045E-15 0.577350 4 -0.500000 0.500000 -0.553180E-16 -0.500000 -0.500000 5 -0.288675 0.500000 -0.577350 0.500000 0.288675 The residual (A-Lambda*I)*X: Col 1 2 3 4 5 Row 1 0.416334E-16 0. -0.222045E-15 0. -0.222045E-15 2 0.113798E-14 0. 0.111022E-15 -0.222045E-15 0.444089E-15 3 0.832667E-16 -0.111022E-15 0.222045E-15 -0.555112E-16 0. 4 0.105471E-14 0. -0.111409E-15 -0.444089E-15 0.444089E-15 5 0.277556E-15 0. -0.222045E-15 0. 0.222045E-15 RSG_TEST: 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 RSG_TEST: 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 RSGAB_TEST: 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. The eigenvalues Lambda: 1 -5.0000000 2 -2.0000000 3 -2.0000000 4 3.0000000 RSGAB_TEST: 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. 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 0.547723 -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 0.310862E-14 -0.478435E-15 0.405992E-15 0. 2 0.199840E-14 -0.444089E-15 0.222045E-15 0. 3 0.122125E-14 -0.111022E-14 0.888178E-15 0. 4 -0.444089E-15 -0.277177E-15 0.101708E-14 0.888178E-15 RSGBA_TEST: 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 RSGBA_TEST: 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 -0.291434E-15 -0.222045E-15 -0.888178E-15 2 -0.888178E-15 0.666134E-15 -0.888178E-15 0.499600E-15 3 0.127676E-14 -0.177636E-14 0.388578E-15 0.832667E-16 4 -0.266454E-14 0.666134E-15 -0.222045E-15 -0.444089E-15 RSM_TEST 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 -0.222045E-14 -0.266454E-14 2 0. -0.555112E-15 -0.155431E-14 -0.266454E-14 3 0. 0.133227E-14 -0.310862E-14 0.177636E-14 4 0. 0.666134E-15 0.133227E-14 0.177636E-14 RSP_TEST 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 RSP_TEST 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 -0.177636E-14 -0.444089E-15 4 0. -0.444089E-15 -0.888178E-15 0. RSPP_TEST 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 RSPP_TEST 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 -0.355271E-14 0.888178E-15 2 0. 0.444089E-15 -0.244249E-14 0. 3 0. 0.133227E-14 -0.310862E-14 0.444089E-15 4 0. 0. 0.222045E-14 0. RST_TEST 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 RST_TEST 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 -0.333067E-15 0. 0.222045E-15 3 -0.360822E-15 -0.601132E-16 -0.222045E-15 -0.660569E-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 RT_TEST 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 RT_TEST 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 -0.333067E-15 0. 0.222045E-15 3 -0.360822E-15 -0.601132E-16 -0.222045E-15 -0.660569E-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 STURM_SEQUENCE_TEST STURM_SEQUENCE considers a (P,Q) submatrix of a symmetric tridiagonal submatrix. It counts the number of eigenvalues less than X1. Matrix order = 5 P Q X1 Count 1 5 4.50000 5 1 5 3.50000 4 1 5 2.50000 3 1 5 1.50000 2 1 5 0.500000 1 1 5 -0.500000 0 SVD_TEST 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 TQL1_TEST TQL1 computes the eigenvalues 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 TRIDIB_TEST TRIDIB computes some eigenvalues 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 TSTURM_TEST TSTURM computes some 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 Z: Col 1 2 3 4 5 Row 1 -0.288675 -0.500000 0.577350 -0.500000 0.288675 2 -0.500000 -0.500000 0.410232E-14 0.500000 -0.500000 3 -0.577350 0.125782E-14 -0.577350 0.595808E-15 0.577350 4 -0.500000 0.500000 -0.205116E-14 -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 -0.142941E-14 -0.832667E-15 -0.444089E-14 0.222045E-15 -0.666134E-15 2 -0.638378E-15 -0.832667E-15 -0.155431E-14 -0.222045E-15 -0.111022E-14 3 0.305311E-15 -0.796095E-15 -0.155431E-14 -0.318252E-15 -0.177636E-14 4 -0.152656E-14 -0.999201E-15 -0.155982E-14 -0.444089E-15 -0.444089E-15 5 0.131839E-14 0.111022E-15 0.155431E-14 0.444089E-15 0.666134E-15 EISPACK_TEST Normal end of execution. 23 February 2023 3:49:17.133 PM