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## man page of LAPACK-3

### LAPACK-3: computes all the eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A

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NAME

LAPACK-3 - computes all the eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A## SYNOPSIS

SUBROUTINE ZHBEV( JOBZ, UPLO, N, KD, AB, LDAB, W, Z, LDZ, WORK, RWORK, INFO ) CHARACTER JOBZ, UPLO INTEGER INFO, KD, LDAB, LDZ, N DOUBLE PRECISION RWORK( * ), W( * ) COMPLEX*16 AB( LDAB, * ), WORK( * ), Z( LDZ, * )## PURPOSE

ZHBEV computes all the eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A.## ARGUMENTS

JOBZ (input) CHARACTER*1 = 'N': Compute eigenvalues only; = 'V': Compute eigenvalues and eigenvectors. UPLO (input) CHARACTER*1 = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored. N (input) INTEGER The order of the matrix A. N >= 0. KD (input) INTEGER The number of superdiagonals of the matrix A if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. KD >= 0. AB (input/output) COMPLEX*16 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 = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; if UPLO = 'L', 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 = 'U', the first superdiagonal and the diagonal of the tridiagonal matrix T are returned in rows KD and KD+1 of AB, and if UPLO = 'L', the diagonal and first subdiagonal of T are returned in the first two rows of AB. LDAB (input) INTEGER The leading dimension of the array AB. LDAB >= KD + 1. W (output) DOUBLE PRECISION array, dimension (N) If INFO = 0, the eigenvalues in ascending order. Z (output) COMPLEX*16 array, dimension (LDZ, N) If JOBZ = 'V', 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 = 'N', then Z is not referenced. LDZ (input) INTEGER The leading dimension of the array Z. LDZ >= 1, and if JOBZ = 'V', LDZ >= max(1,N). WORK (workspace) COMPLEX*16 array, dimension (N) RWORK (workspace) DOUBLE PRECISION array, dimension (max(1,3*N-2)) INFO (output) INTEGER = 0: successful exit. < 0: if INFO = -i, the i-th argument had an illegal value. > 0: if INFO = i, the algorithm failed to converge; i off-diagonal elements of an intermediate tridiagonal form did not converge to zero. LAPACK driver routine (version 3.March 2011 LAPACK-3(3)

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