p?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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p?heev

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

Syntax

call pcheev(jobz, uplo, n, a, ia, ja, desca, w, z, iz, jz, descz, work, lwork, rwork, lrwork, info)

call pzheev(jobz, uplo, n, a, ia, ja, desca, w, z, iz, jz, descz, work, lwork, rwork, lrwork, info)

Include Files

Description

The p?heev routine computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A by calling the recommended sequence of ScaLAPACK routines. The routine assumes a homogeneous system and makes spot checks of the consistency of the eigenvalues across the different processes. A heterogeneous system may return incorrect results without any error messages.

Input Parameters

np = the number of rows local to a given process.

nq = the number of columns local to a given process.

jobz

(global) CHARACTER*1. Must be 'N' or 'V'.

Specifies if it is necessary to compute the eigenvectors:

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

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

uplo

(global) CHARACTER*1. Must be 'U' or 'L'.

Specifies whether the upper or lower triangular part of the Hermitian matrix A is stored:

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

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

n

(global) INTEGER. The number of rows and columns of the matrix A(n≥ 0).

a

(local).

COMPLEX for pcheev

DOUBLE COMPLEX for pzheev.

Block cyclic array of global size (n, n) and local size (lld_a, LOCc(ja+n-1)). On entry, the Hermitian matrix A.

If uplo = 'U', only the upper triangular part of A is used to define the elements of the Hermitian matrix.

If uplo = 'L', only the lower triangular part of A is used to define the elements of the Hermitian matrix.

ia, ja

(global) INTEGER. The row and column indices in the global matrix A indicating the first row and the first column of the submatrix A, respectively.

desca

(global and local) INTEGER array of size dlen_. The array descriptor for the distributed matrix A. If desca(ctxt_) is incorrect, p?heev cannot guarantee correct error reporting.

iz, jz

(global) INTEGER. The row and column indices in the global matrix Z indicating the first row and the first column of the submatrix Z, respectively.

descz

(global and local) INTEGER array of size dlen_. The array descriptor for the distributed matrix Z. descz(ctxt_) must equal desca(ctxt_).

work

(local).

COMPLEX for pcheev

DOUBLE COMPLEX for pzheev.

Array of size lwork.

lwork

(local) INTEGER. The size of the array work.

If only eigenvalues are requested (jobz = 'N'):

lwork≥max(nb*(np0 + 1), 3) + 3*n

If eigenvectors are requested (jobz = 'V'), then the amount of workspace required:

lwork≥ (np0+nq0+nb)*nb + 3*n + n²

with nb = desca( mb_ ) = desca( nb_ ) = nb = descz( mb_ ) = descz( nb_ )

np0 = numroc(nn, nb, 0, 0, NPROW).

nq0 = numroc( max( n, nb, 2 ), nb, 0, 0, NPCOL).

If lwork = -1, then lwork is global input and a workspace query is assumed; the routine only calculates the size required for optimal performance for all work arrays. The required workspace is returned as the first element of the corresponding work arrays, and no error message is issued by pxerbla.

rwork

(local).

REAL for pcheev

DOUBLE PRECISION for pzheev.

Workspace array of size lrwork.

lrwork

(local) INTEGER. The size of the array rwork.

See below for definitions of variables used to define lrwork.

If no eigenvectors are requested (jobz = 'N'), then lrwork≥ 2*n.

If eigenvectors are requested (jobz = 'V'), then lrwork≥ 2*n + 2*n-2.

If lrwork = -1, then lrwork is global input and a workspace query is assumed; the routine only calculates the minimum size required for the rwork array. The required workspace is returned as the first element of rwork, and no error message is issued by pxerbla.

Output Parameters

a

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

w

(global).

REAL for pcheev

DOUBLE PRECISION for pzheev.

Array of size n. The first m elements contain the selected eigenvalues in ascending order.

z

(local).

COMPLEX for pcheev

DOUBLE COMPLEX for pzheev.

Array, global size (n, n), local size (lld_z, LOCc(jz+n-1)).

If jobz ='V', then on normal exit the first m columns of z contain the orthonormal eigenvectors of the matrix corresponding to the selected eigenvalues. If an eigenvector fails to converge, then that column of z contains the latest approximation to the eigenvector, and the index of the eigenvector is returned in ifail.

If jobz = 'N', then z is not referenced.

work(1)

On exit, returns adequate workspace to allow optimal performance.

If jobz ='N', then work(1) = minimal workspace only for eigenvalues.

If jobz ='V', then work(1) = minimal workspace required to generate all the eigenvectors.

rwork(1)

(local)

COMPLEX for pcheev

DOUBLE COMPLEX for pzheev.

On output, rwork(1) returns workspace required to guarantee completion.

info

(global) INTEGER.

If info = 0, the execution is successful.

If info < 0:

If the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j). If the i-th argument is a scalar and had an illegal value, then info = -i.

If info> 0:

If info = 1 through n, the i-th eigenvalue did not converge in ?steqr2 after a total of 30*n iterations.

If info = n+1, then p?heev detected heterogeneity, and the accuracy of the results cannot be guaranteed.

Parent topic: ScaLAPACK Driver Routines

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