Previous: zstein Up: ../lapack-z.html Next: zsycon
NAME ZSTEQR - compute all eigenvalues and, optionally, eigenvec- tors of a symmetric tridiagonal matrix using the implicit QL or QR method SYNOPSIS SUBROUTINE ZSTEQR( COMPZ, N, D, E, Z, LDZ, WORK, INFO ) CHARACTER COMPZ INTEGER INFO, LDZ, N DOUBLE PRECISION D( * ), E( * ), WORK( * ) COMPLEX*16 Z( LDZ, * ) PURPOSE ZSTEQR computes all eigenvalues and, optionally, eigenvec- tors of a symmetric tridiagonal matrix using the implicit QL or QR method. The eigenvectors of a full or band complex Hermitian matrix can also be found if ZSYTRD or ZSPTRD or ZSBTRD has been used to reduce this matrix to tridiagonal form. ARGUMENTS COMPZ (input) CHARACTER*1 = 'N': Compute eigenvalues only. = 'V': Compute eigenvalues and eigenvectors of the original symmetric matrix. On entry, Z must contain the orthogonal matrix used to reduce the original matrix to tridiagonal form. = 'I': Compute eigen- values and eigenvectors of the tridiagonal matrix. Z is initialized to the identity matrix. N (input) INTEGER The order of the matrix. N >= 0. D (input/output) DOUBLE PRECISION array, dimension (N) On entry, the diagonal elements of the tridiagonal matrix. On exit, if INFO = 0, the eigenvalues in ascending order. E (input/output) DOUBLE PRECISION array, dimension (N- 1) On entry, the (n-1) subdiagonal elements of the tri- diagonal matrix. On exit, E has been destroyed. Z (input/output) COMPLEX*16 array, dimension (LDZ, N) On entry, if COMPZ = 'V', then Z contains the uni- tary matrix used in the reduction to tridiagonal form. On exit, if COMPZ = 'V', Z contains the orthonormal eigenvectors of the original Hermitian matrix, and if COMPZ = 'I', Z contains the orthonor- mal eigenvectors of the symmetric tridiagonal matrix. If an error exit is made, Z contains the eigenvectors associated with the stored eigenvalues. If COMPZ = 'N', then Z is not referenced. LDZ (input) INTEGER The leading dimension of the array Z. LDZ >= 1, and if eigenvectors are desired, then LDZ >= max(1,N). (max(1,2*N-2)) WORK (workspace) DOUBLE PRECISION array, dimension If COMPZ = 'N', then WORK is not referenced. INFO (output) INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: the algorithm has failed to find all the eigenvalues in a total of 30*N iterations; if INFO = i, then i elements of E have not converged to zero; on exit, D and E contain the elements of a symmetric tridiagonal matrix which is orthogonally similar to the original matrix.