?steqr2

Syntax

Include Files

The C interfaces are specified in the mkl_scalapack.h include file.

Description

The ?steqr2 routine is a modified version of LAPACK routine ?steqr. The ?steqr2 routine computes all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the implicit QL or QR method. ?steqr2 is modified from ?steqr to allow each ScaLAPACK process running ?steqr2 to perform updates on a distributed matrix Q. Proper usage of ?steqr2 can be gleaned from examination of ScaLAPACK routine p?syev.

Input Parameters

compz

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

If compz = 'N', the routine computes eigenvalues only. If compz = 'I', the routine computes the eigenvalues and eigenvectors of the tridiagonal matrix T.

z must be initialized to the identity matrix by p?laset or ?laset prior to entering this subroutine.

n

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

d, e, work

REAL for single-precision flavors

DOUBLE PRECISION for double-precision flavors.

Arrays: d contains the diagonal elements of T. The dimension of d must be at least max(1, n).

e contains the (n-1) subdiagonal elements of T. The dimension of e must be at least max(1, n-1).

work is a workspace array. The dimension of work is max(1, 2*n-2). If compz = 'N', then work is not referenced.

z

(local)

REAL for ssteqr2

DOUBLE PRECISION for dsteqr2

Array, global DIMENSION (n, n), local DIMENSION (ldz, nr).

If compz = 'V', then z contains the orthogonal matrix used in the reduction to tridiagonal form.

ldz

INTEGER. The leading dimension of the array z. Constraints:

ldz ≥ 1,

ldz ≥ max(1, n), if eigenvectors are desired.

nr

INTEGER. nr = max(1, numroc(n, nb, myprow, 0, nprocs)).

If compz = 'N', then nr is not referenced.

Output Parameters

d

REAL array, DIMENSION (n), for ssteqr2.

DOUBLE PRECISION array, DIMENSION (n), for dsteqr2.

On exit, the eigenvalues in ascending order, if info = 0.

See also info.

e

REAL array, DIMENSION (n-1), for ssteqr2.

DOUBLE PRECISION array, DIMENSION (n-1), for dsteqr2.

On exit, e has been destroyed.

z

(local)

REAL for ssteqr2

DOUBLE PRECISION for dsteqr2

Array, global DIMENSION (n, n), local DIMENSION (ldz, nr).

On exit, if info = 0, then,

if compz = 'V', z contains the orthonormal eigenvectors of the original symmetric matrix, and if compz = 'I', z contains the orthonormal eigenvectors of the symmetric tridiagonal matrix. If compz = 'N', then z is not referenced.

info

INTEGER.

info = 0, the exit is successful.

info < 0: if info = -i, the i-th had an illegal value.

info > 0: the algorithm has failed to find all the eigenvalues in a total of 30n iterations;

if info = i, then i elements of e have not converged to zero; on exit, d and e contain the elements of a symmetric tridiagonal matrix, which is orthogonally similar to the original matrix.