.TH CHBEV 1 "November 2006" " LAPACK driver routine (version 3.1) " " LAPACK driver routine (version 3.1) " .SH NAME CHBEV - all the eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A .SH SYNOPSIS .TP 18 SUBROUTINE CHBEV( JOBZ, UPLO, N, KD, AB, LDAB, W, Z, LDZ, WORK, RWORK, INFO ) .TP 18 .ti +4 CHARACTER JOBZ, UPLO .TP 18 .ti +4 INTEGER INFO, KD, LDAB, LDZ, N .TP 18 .ti +4 REAL RWORK( * ), W( * ) .TP 18 .ti +4 COMPLEX AB( LDAB, * ), WORK( * ), Z( LDZ, * ) .SH PURPOSE CHBEV computes all the eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A. .SH ARGUMENTS .TP 8 JOBZ (input) CHARACTER*1 = \(aqN\(aq: Compute eigenvalues only; .br = \(aqV\(aq: Compute eigenvalues and eigenvectors. .TP 8 UPLO (input) CHARACTER*1 .br = \(aqU\(aq: Upper triangle of A is stored; .br = \(aqL\(aq: Lower triangle of A is stored. .TP 8 N (input) INTEGER The order of the matrix A. N >= 0. .TP 8 KD (input) INTEGER The number of superdiagonals of the matrix A if UPLO = \(aqU\(aq, or the number of subdiagonals if UPLO = \(aqL\(aq. KD >= 0. .TP 8 AB (input/output) COMPLEX array, dimension (LDAB, N) On entry, the upper or lower triangle of the Hermitian band matrix A, stored in the first KD+1 rows of the array. The j-th column of A is stored in the j-th column of the array AB as follows: if UPLO = \(aqU\(aq, AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; if UPLO = \(aqL\(aq, AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). On exit, AB is overwritten by values generated during the reduction to tridiagonal form. If UPLO = \(aqU\(aq, the first superdiagonal and the diagonal of the tridiagonal matrix T are returned in rows KD and KD+1 of AB, and if UPLO = \(aqL\(aq, the diagonal and first subdiagonal of T are returned in the first two rows of AB. .TP 8 LDAB (input) INTEGER The leading dimension of the array AB. LDAB >= KD + 1. .TP 8 W (output) REAL array, dimension (N) If INFO = 0, the eigenvalues in ascending order. .TP 8 Z (output) COMPLEX array, dimension (LDZ, N) If JOBZ = \(aqV\(aq, then if INFO = 0, Z contains the orthonormal eigenvectors of the matrix A, with the i-th column of Z holding the eigenvector associated with W(i). If JOBZ = \(aqN\(aq, then Z is not referenced. .TP 8 LDZ (input) INTEGER The leading dimension of the array Z. LDZ >= 1, and if JOBZ = \(aqV\(aq, LDZ >= max(1,N). .TP 8 WORK (workspace) COMPLEX array, dimension (N) .TP 8 RWORK (workspace) REAL array, dimension (max(1,3*N-2)) .TP 8 INFO (output) INTEGER = 0: successful exit. .br < 0: if INFO = -i, the i-th argument had an illegal value. .br > 0: if INFO = i, the algorithm failed to converge; i off-diagonal elements of an intermediate tridiagonal form did not converge to zero.