?heev

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 3/31/2023

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?heev

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

Syntax

call cheev(jobz, uplo, n, a, lda, w, work, lwork, rwork, info)

call zheev(jobz, uplo, n, a, lda, w, work, lwork, rwork, info)

call heev(a, w [,jobz] [,uplo] [,info])

Include Files

mkl.fi, lapack.f90

Description

The routine computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A.

Note that for most cases of complex Hermitian eigenvalue problems the default choice should be heevr function as its underlying algorithm is faster and uses less workspace.

Input Parameters

jobz

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

If jobz = 'N', then only eigenvalues are computed.

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

uplo

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

If uplo = 'U', a stores the upper triangular part of A.

If uplo = 'L', a stores the lower triangular part of A.

n

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

a, work

COMPLEX for cheev

DOUBLE COMPLEX for zheev

Arrays:

a(lda,*) is an array containing either upper or lower triangular part of the Hermitian matrix A, as specified by uplo.

The second dimension of a must be at least max(1, n).

work is a workspace array, its dimension max(1, lwork).

lda

INTEGER. The leading dimension of the array a. Must be at least max(1, n).

lwork

INTEGER.

The dimension of the array work. C

onstraint: lwork≥ max(1, 2n-1).

If lwork = -1, then a workspace query is assumed; the routine only calculates the optimal size of the work array, returns this value as the first entry of the work array, and no error message related to lwork is issued by xerbla.

See Application Notes for the suggested value of lwork.

rwork

REAL for cheev

DOUBLE PRECISION for zheev.

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

Output Parameters

a

On exit, if jobz = 'V', then if info = 0, array a contains the orthonormal eigenvectors of the matrix A.

If jobz = 'N', then on exit the lower triangle

(if uplo = 'L') or the upper triangle (if uplo = 'U') of A, including the diagonal, is overwritten.

w

REAL for cheev

DOUBLE PRECISION for zheev

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

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

work(1)

On exit, if lwork > 0, then work(1) returns the required minimal size of lwork.

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 heev interface are the following:

a: Holds the matrix A of size (n, n).
w: Holds the vector of length n.
job: Must be 'N' or 'V'. The default value is 'N'.
uplo: Must be 'U' or 'L'. The default value is 'U'.

Application Notes

For optimum performance use

lwork≥ (nb+1)*n,

where nb is the blocksize for ?hetrd returned by ilaenv.

If you are in doubt how much workspace to supply, use a generous value of lwork for the first run or set lwork = -1.

If you choose the first option and set any of admissible lwork sizes, which is no less than the minimal value described, the routine completes the task, though probably not so fast as with a recommended workspace, and provides the recommended workspace in the first element of the corresponding array work on exit. Use this value (work(1)) for subsequent runs.

If you set lwork = -1, the routine returns immediately and provides the recommended workspace in the first element of the corresponding array (work). This operation is called a workspace query.

Note that if you set lwork to less than the minimal required value and not -1, the routine returns immediately with an error exit and does not provide any information on the recommended workspace.

Parent topic: Symmetric Eigenvalue Problems: LAPACK Driver Routines

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

?heev