14 July 2013 11:52:41.189 PM JACOBI_EIGENVALUE_TEST FORTRAN90 version Test the JACOBI_EIGENVALUE library. TEST01 For a symmetric matrix A, JACOBI_EIGENVALUE computes the eigenvalues D and eigenvectors V so that A * V = D * V. Input matrix A: Col 1 2 3 4 Row 1: 4. -30. 60. -35. 2: -30. 300. -675. 420. 3: 60. -675. 1620. -1050. 4: -35. 420. -1050. 700. Number of iterations = 11 Number of rotations = 21 Eigenvalues D: 1: 2585.2538 2: 37.101491 3: 1.4780548 4: 0.16664286 Eigenvector matrix V: Col 1 2 3 4 Row 1: 0.291933E-01 0.179186 0.582076 0.792608 2: -0.328712 -0.741918 -0.370502 0.451923 3: 0.791411 0.100228 -0.509579 0.322416 4: -0.514553 0.638283 -0.514048 0.252161 Frobenius norm error in eigensystem A*V-D*V = 0.120349E-11 TEST02 For a symmetric matrix A, JACOBI_EIGENVALUE computes the eigenvalues D and eigenvectors V so that A * V = D * V. As a sanity check, input a diagonal matrix. Input matrix A: Col 1 2 3 4 Row 1: 4. 0. 0. 0. 2: 0. 1. 0. 0. 3: 0. 0. 3. 0. 4: 0. 0. 0. 2. Number of iterations = 1 Number of rotations = 0 Eigenvalues D: 1: 4.0000000 2: 3.0000000 3: 2.0000000 4: 1.0000000 Eigenvector matrix V: Col 1 2 3 4 Row 1: 1. 0. 0. 0. 2: 0. 0. 0. 1. 3: 0. 1. 0. 0. 4: 0. 0. 1. 0. Frobenius norm error in eigensystem A*V-D*V = 0.00000 TEST03 For a symmetric matrix A, JACOBI_EIGENVALUE computes the eigenvalues D and eigenvectors V so that A * V = D * V. Use the discretized second derivative matrix. Input 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. Number of iterations = 10 Number of rotations = 43 Eigenvalues D: 1: -0.26794919 2: -1.0000000 3: -2.0000000 4: -3.0000000 5: -3.7320508 Eigenvector matrix V: Col 1 2 3 4 5 Row 1: 0.288675 -0.500000 0.577350 0.500000 0.288675 2: 0.500000 -0.500000 -0.444985E-16 -0.500000 -0.500000 3: 0.577350 -0.705760E-16 -0.577350 0.505017E-16 0.577350 4: 0.500000 0.500000 0.186451E-15 0.500000 -0.500000 5: 0.288675 0.500000 0.577350 -0.500000 0.288675 Frobenius norm error in eigensystem A*V-D*V = 0.940195E-15 JACOBI_EIGENVALUE_TEST Normal end of execution. 14 July 2013 11:52:41.191 PM