.TH SSTEQR 1 "November 2006" " LAPACK routine (version 3.1) " " LAPACK routine (version 3.1) " .SH NAME SSTEQR - all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the implicit QL or QR method .SH SYNOPSIS .TP 19 SUBROUTINE SSTEQR( COMPZ, N, D, E, Z, LDZ, WORK, INFO ) .TP 19 .ti +4 CHARACTER COMPZ .TP 19 .ti +4 INTEGER INFO, LDZ, N .TP 19 .ti +4 REAL D( * ), E( * ), WORK( * ), Z( LDZ, * ) .SH PURPOSE SSTEQR computes all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the implicit QL or QR method. The eigenvectors of a full or band symmetric matrix can also be found if SSYTRD or SSPTRD or SSBTRD has been used to reduce this matrix to tridiagonal form. .br .SH ARGUMENTS .TP 8 COMPZ (input) CHARACTER*1 = \(aqN\(aq: Compute eigenvalues only. .br = \(aqV\(aq: 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. = \(aqI\(aq: Compute eigenvalues and eigenvectors of the tridiagonal matrix. Z is initialized to the identity matrix. .TP 8 N (input) INTEGER The order of the matrix. N >= 0. .TP 8 D (input/output) REAL array, dimension (N) On entry, the diagonal elements of the tridiagonal matrix. On exit, if INFO = 0, the eigenvalues in ascending order. .TP 8 E (input/output) REAL array, dimension (N-1) On entry, the (n-1) subdiagonal elements of the tridiagonal matrix. On exit, E has been destroyed. .TP 8 Z (input/output) REAL array, dimension (LDZ, N) On entry, if COMPZ = \(aqV\(aq, then Z contains the orthogonal matrix used in the reduction to tridiagonal form. On exit, if INFO = 0, then if COMPZ = \(aqV\(aq, Z contains the orthonormal eigenvectors of the original symmetric matrix, and if COMPZ = \(aqI\(aq, Z contains the orthonormal eigenvectors of the symmetric tridiagonal matrix. If COMPZ = \(aqN\(aq, then Z is not referenced. .TP 8 LDZ (input) INTEGER The leading dimension of the array Z. LDZ >= 1, and if eigenvectors are desired, then LDZ >= max(1,N). .TP 8 WORK (workspace) REAL array, dimension (max(1,2*N-2)) If COMPZ = \(aqN\(aq, then WORK is not referenced. .TP 8 INFO (output) INTEGER = 0: successful exit .br < 0: if INFO = -i, the i-th argument had an illegal value .br > 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.