?hpev

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 3/31/2023

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?hpev

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

Syntax

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

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

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

Include Files

mkl.fi, lapack.f90

Description

The 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

COMPLEX for chpev

DOUBLE COMPLEX for zhpev.

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

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

work

COMPLEX for chpev

DOUBLE COMPLEX for zhpev.

(*) is a workspace array, size 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, size at least max(1, 3n-2).

Output Parameters

w

REAL for chpev

DOUBLE PRECISION for zhpev.

Array, size 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.

LAPACK 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 LAPACK 95 Interface Conventions.

Specific details for the routine hpev interface are the following:

ap

Holds the array A of size (n*(n+1)/2).

w

Holds the vector with the number of elements 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 Eigenvalue Problems: LAPACK Driver Routines

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

?hpev