zstedc(3)

NAME

ZSTEDC - compute all eigenvalues and, optionally, eigen

vectors of a symmetric tridiagonal matrix using the divide and

conquer method

SYNOPSIS

SUBROUTINE ZSTEDC( COMPZ, N, D, E, Z,  LDZ,  WORK,  LWORK,
RWORK, LRWORK, IWORK, LIWORK, INFO )
    CHARACTER      COMPZ
    INTEGER        INFO, LDZ, LIWORK, LRWORK, LWORK, N
    INTEGER        IWORK( * )
    DOUBLE         PRECISION D( * ), E( * ), RWORK( * )
    COMPLEX*16     WORK( * ), Z( LDZ, * )

PURPOSE

ZSTEDC computes all eigenvalues and, optionally, eigenvec

tors of a symmetric tridiagonal matrix using the divide and con

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

matrix can also be found if ZHETRD or ZHPTRD or ZHBTRD has been

used to reduce this matrix to tridiagonal form.

This code makes very mild assumptions about floating point

arithmetic. It will work on machines with a guard digit in

add/subtract, or on those binary machines without guard digits

which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or

Cray-2. It could conceivably fail on hexadecimal or decimal ma

chines without guard digits, but we know of none. See DLAED3 for

details.

ARGUMENTS

COMPZ (input) CHARACTER*1

= 'N': Compute eigenvalues only.
= 'I': Compute eigenvectors of tridiagonal matrix

also.
= 'V': Compute eigenvectors of original Hermitian

matrix also. On entry, Z contains the unitary matrix used to re

duce the original matrix to tridiagonal form.

N (input) INTEGER

The dimension of the symmetric tridiagonal matrix.

N >= 0.

D (input/output) DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension

(N-1)

On entry, the subdiagonal elements of the tridiag

onal matrix. On exit, E has been destroyed.

Z (input/output) COMPLEX*16 array, dimension (LDZ,N)

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

tary matrix used in the reduction to tridiagonal form. On exit,

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.

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

WORK (workspace/output) COMPLEX*16 array, dimension

(LWORK)

On exit, if INFO = 0, WORK(1) returns the optimal

LWORK.

LWORK (input) INTEGER

The dimension of the array WORK. If COMPZ = 'N'

or 'I', or N <= 1, LWORK must be at least 1. If COMPZ = 'V' and

N > 1, LWORK must be at least N*N.

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.

RWORK (workspace/output) DOUBLE PRECISION array,

dimension (LRWORK) On exit, if INFO = 0, RWORK(1)

returns the optimal LRWORK.

LRWORK (input) INTEGER

The dimension of the array RWORK. If COMPZ = 'N'

or N <= 1, LRWORK must be at least 1. If COMPZ = 'V' and N > 1,

LRWORK must be at least 1 + 3*N + 2*N*lg N + 3*N**2 , where lg( N

) = smallest integer k such that 2**k >= N. If COMPZ = 'I' and N

> 1, LRWORK must be at least 1 + 4*N + 2*N**2 .

If LRWORK = -1, then a workspace query is assumed;

the routine only calculates the optimal size of the RWORK array,

returns this value as the first entry of the RWORK array, and no

error message related to LRWORK is issued by XERBLA.

IWORK (workspace/output) INTEGER array, dimension (LI

WORK)

On exit, if INFO = 0, IWORK(1) returns the optimal

LIWORK.

LIWORK (input) INTEGER

The dimension of the array IWORK. If COMPZ = 'N'

or N <= 1, LIWORK must be at least 1. If COMPZ = 'V' or N > 1,

LIWORK must be at least 6 + 6*N + 5*N*lg N. If COMPZ = 'I' or N

> 1, LIWORK must be at least 3 + 5*N .

If LIWORK = -1, then a workspace query is assumed;

the routine only calculates the optimal size of the IWORK array,

returns this value as the first entry of the IWORK array, and no

error message related to LIWORK is issued by XERBLA.

INFO (output) INTEGER

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

gal value.
> 0: The algorithm failed to compute an eigenval

ue while working on the submatrix lying in rows and columns IN

FO/(N+1) through mod(INFO,N+1).

FURTHER DETAILS

Based on contributions by

Jeff Rutter, Computer Science Division, University of

California
at Berkeley, USA

LAPACK version 3.0 15 June 2000

ZSTEDC(3)