# ?hpev

Computes all eigenvalues and, optionally, eigenvectors of a Hermitian matrix in packed storage.

## Syntax

FORTRAN 77:

call chpev(jobz, uplo, n, ap, w, z, ldz, work, rwork, info)

call zhpev(jobz, uplo, n, ap, w, z, ldz, work, rwork, info)

Fortran 95:

call hpev(a, w [,uplo] [,z] [,info])

## Description

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

## Input Parameters

jobz

  CHARACTER*1. Must be 'N' or 'V'.

  If `job = 'N'`, then only eigenvalues are computed.

  If `job = 'V'`, then eigenvalues and eigenvectors are computed.

uplo

  CHARACTER*1. Must be 'U' or 'L'.

  If `uplo = 'U'`, ap stores the packed upper triangular part of A.

  If `uplo = 'L'`, ap stores the packed lower triangular part of A.

n

  INTEGER. The order of the matrix A (`n ≥ 0`).

ap, work

  COMPLEX for chpev

  DOUBLE COMPLEX for zhpev.

  Arrays:

  ap(*) contains the packed upper or lower triangle of Hermitian matrix A, as specified by uplo.

  The dimension of ap must be at least max(1, n*(n+1)/2).

work

  (*) is a workspace array, DIMENSION at least max(1, 2n-1).

ldz

  INTEGER. The leading dimension of the output array z.

  Constraints:

  if `jobz = 'N'`, then `ldz ≥ 1`;

  if `jobz = 'V'`, then ldz ≥ max(1, n) .

rwork

  REAL for chpev

  DOUBLE PRECISION for zhpev.

  Workspace array, DIMENSION at least max(1, 3n-2).

## Output Parameters

w

  REAL for chpev

  DOUBLE PRECISION for zhpev.

  Array, DIMENSION at least max(1, n).

  If `info = 0`, w contains the eigenvalues of the matrix A in ascending order.

z

  COMPLEX for chpev

  DOUBLE COMPLEX for zhpev.

  Array z(ldz,*).

  The second dimension of z must be at least max(1, 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.

ap

  On exit, this array is overwritten by the values generated during the reduction to tridiagonal form. The elements of the diagonal and the off-diagonal of the tridiagonal matrix overwrite the corresponding elements of A.

info

  INTEGER.

  If `info = 0`, the execution is successful.

  If `info = -i`, the i-th parameter had an illegal value.

  If `info = i`, then the algorithm failed to converge; i indicates the number of elements of an intermediate tridiagonal form which did not converge to zero.

## Fortran 95 Interface Notes

Routines in Fortran 95 interface have fewer arguments in the calling sequence than their FORTRAN 77 counterparts. For general conventions applied to skip redundant or restorable arguments, see Fortran 95 Interface Conventions.

Specific details for the routine hpev interface are the following:

a

  Stands for argument ap in Fortan 77 interface. Holds the array A of size (n*(n+1)/2).

w

  Holds the vector of length (n).

z

  Holds the matrix Z of size (n, n).

uplo

  Must be 'U' or 'L'. The default value is 'U'.

jobz

  Restored based on the presence of the argument z as follows:

  `jobz = 'V'`, if z is present,

  `jobz = 'N'`, if z is omitted.

Parent topic: Symmetric Eigenproblems