---
name: "zhpev"
section: "3lapack"
platform: "linux"
package: "liblapack-doc"
version: "3.2.1-8"
release: "Debian 6.0 (Squeeze)"
platforms: ["linux"]
url: "https://new.carta.tech/zhpev/3lapack"
---

# zhpev(3lapack)

computes all the eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix in packed storage

## NAME

ZHPEV - 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.