csteqr(3)

NAME

CSTEQR - compute all eigenvalues and, optionally, eigen

vectors of a symmetric tridiagonal matrix using the implicit QL

or QR method

SYNOPSIS

SUBROUTINE CSTEQR( COMPZ, N, D, E, Z, LDZ, WORK, INFO )
    CHARACTER      COMPZ
    INTEGER        INFO, LDZ, N
    REAL           D( * ), E( * ), WORK( * )
    COMPLEX        Z( LDZ, * )

PURPOSE

CSTEQR computes all eigenvalues and, optionally, eigenvec

tors of a symmetric tridiagonal matrix using the implicit QL or

QR method. The eigenvectors of a full or band complex Hermitian

matrix can also be found if CHETRD or CHPTRD or CHBTRD has been

used to reduce this matrix to tridiagonal form.

ARGUMENTS

COMPZ (input) CHARACTER*1

= 'N': Compute eigenvalues only.
= 'V': Compute eigenvalues and eigenvectors of

the original Hermitian matrix. On entry, Z must contain the uni

tary matrix used to reduce the original matrix to tridiagonal

form. = 'I': Compute eigenvalues and eigenvectors of the tridi

agonal matrix. Z is initialized to the identity matrix.

N (input) INTEGER

The order of the matrix. N >= 0.

D (input/output) REAL array, dimension (N)

On entry, the diagonal elements of the tridiagonal

matrix. On exit, if INFO = 0, the eigenvalues in ascending or

der.

E (input/output) REAL array, dimension (N-1)

On entry, the (n-1) subdiagonal elements of the

tridiagonal matrix. On exit, E has been destroyed.

Z (input/output) COMPLEX array, dimension (LDZ, N)

On entry, if COMPZ = 'V', then Z contains the

unitary matrix used in the reduction to tridiagonal form. On ex

it, if INFO = 0, then if COMPZ = 'V', Z contains the orthonormal

eigenvectors of the original Hermitian matrix, and if COMPZ =

'I', Z contains the orthonormal eigenvectors of the symmetric

tridiagonal matrix. If COMPZ = 'N', then Z is not referenced.

LDZ (input) INTEGER

The leading dimension of the array Z. LDZ >= 1,

and if eigenvectors are desired, then LDZ >= max(1,N).

WORK (workspace) REAL array, dimension (max(1,2*N-2))

If COMPZ = 'N', then WORK is not referenced.

INFO (output) INTEGER

= 0: successful exit
< 0: if INFO = -i, the i-th argument had an ille

gal value
> 0: the algorithm has failed to find all the

eigenvalues in a total of 30*N iterations; if INFO = i, then i

elements of E have not converged to zero; on exit, D and E con

tain the elements of a symmetric tridiagonal matrix which is uni

tarily similar to the original matrix.

LAPACK version 3.0 15 June 2000

CSTEQR(3)