# p?heevd

Computes all eigenvalues and eigenvectors of a complex Hermitian matrix by using a divide and conquer algorithm.

## Syntax

void pcheevd (char *jobz , char *uplo , MKL_INT *n , MKL_Complex8 *a , MKL_INT *ia , MKL_INT *ja , MKL_INT *desca , float *w , MKL_Complex8 *z , MKL_INT *iz , MKL_INT *jz , MKL_INT *descz , MKL_Complex8 *work , MKL_INT *lwork , float *rwork , MKL_INT *lrwork , MKL_INT *iwork , MKL_INT *liwork , MKL_INT *info );

void pzheevd (char *jobz , char *uplo , MKL_INT *n , MKL_Complex16 *a , MKL_INT *ia , MKL_INT *ja , MKL_INT *desca , double *w , MKL_Complex16 *z , MKL_INT *iz , MKL_INT *jz , MKL_INT *descz , MKL_Complex16 *work , MKL_INT *lwork , double *rwork , MKL_INT *lrwork , MKL_INT *iwork , MKL_INT *liwork , MKL_INT *info );

## Include Files

• mkl_scalapack.h

## Description

The p?heevd function computes all eigenvalues and eigenvectors of a complex Hermitian matrix A by using a divide and conquer algorithm.

## Input Parameters

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

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

jobz

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

a

(local).

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) 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) array of size dlen_. The array descriptor for the distributed matrix A. If desca[ctxt_ - 1] is incorrect, p?heevd cannot guarantee correct error reporting.

iz, jz

(global) 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) array of size dlen_. The array descriptor for the distributed matrix Z. descz[ctxt_ - 1] must equal desca[ctxt_ - 1].

work

(local).

Array of size lwork.

lwork

(local) The size of the array work.

If eigenvalues are requested:

lwork = n + (nb0 + mq0 + nb)*nb

with np0 = numroc( max( n, nb, 2 ), nb, 0, 0, NPROW)

mq0 = numroc( max( n, nb, 2 ), nb, 0, 0, NPCOL)

If lwork = -1, then lwork is global input and a workspace query is assumed; the function 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).

Workspace array of size lrwork.

lrwork

(local) The size of the array rwork.

lrwork 1 + 9*n + 3*np*nq,

with np = numroc( n, nb, myrow, iarow, NPROW)

nq = numroc( n, nb, mycol, iacol, NPCOL)

iwork

(local) Workspace array of size liwork.

liwork

(local) , size of iwork.

liwork = 7*n + 8*npcol + 2.

## 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).

Array of size n. If info = 0, w contains the eigenvalues in the ascending order.

z

(local).

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

The z parameter contains the orthonormal eigenvectors of the matrix A.

work

On exit, returns adequate workspace to allow optimal performance.

rwork

(local)

On output, rwork returns workspace required to guarantee completion.

iwork

(local).

On return, iwork contains the amount of integer workspace required.

info

(global)

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.