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## man page of LAPACK-3

### LAPACK-3: computes all the eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix in packed storage

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## NAME

LAPACK-3 - computes all the eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix in packed storage## SYNOPSIS

SUBROUTINE ZHPEV( JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, RWORK, INFO ) CHARACTER JOBZ, UPLO INTEGER INFO, LDZ, N DOUBLE PRECISION RWORK( * ), W( * ) COMPLEX*16 AP( * ), WORK( * ), Z( LDZ, * )PURPOSE

ZHPEV computes all the eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix in packed storage.## 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. AP (input/output) COMPLEX*16 array, dimension (N*(N+1)/2) On entry, the upper or lower triangle of the Hermitian matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array AP as follows: if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n. On exit, AP is overwritten by values generated during the reduction to tridiagonal form. If UPLO = 'U', the diagonal and first superdiagonal of the tridiagonal matrix T overwrite the corresponding elements of A, and if UPLO = 'L', the diagonal and first subdiagonal of T overwrite the corresponding elements of A. 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 (max(1, 2*N-1)) 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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