sstedc(3)

NAME

SSTEDC - compute all eigenvalues and, optionally, eigen

vectors of a symmetric tridiagonal matrix using the divide and

conquer method

SYNOPSIS

SUBROUTINE SSTEDC( COMPZ, N, D, E, Z,  LDZ,  WORK,  LWORK,
IWORK, LIWORK, INFO )
    CHARACTER      COMPZ
    INTEGER        INFO, LDZ, LIWORK, LWORK, N
    INTEGER        IWORK( * )
    REAL           D( * ), E( * ), WORK( * ), Z( LDZ, * )

PURPOSE

SSTEDC 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 real symmetric

matrix can also be found if SSYTRD or SSPTRD or SSBTRD 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 SLAED3 for

details.

ARGUMENTS

COMPZ (input) CHARACTER*1

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

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

symmetric matrix also. On entry, Z contains the orthogonal ma

trix used to reduce the original matrix to tridiagonal form.

N (input) INTEGER

The dimension of the symmetric tridiagonal 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 subdiagonal elements of the tridiag

onal matrix. On exit, E has been destroyed.

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

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

thogonal matrix used in the reduction to tridiagonal form. On

exit, if INFO = 0, then if COMPZ = 'V', Z contains the orthonor

mal 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.

LDZ (input) INTEGER

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

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

WORK (workspace/output) REAL 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 N <= 1 then LWORK must be at least 1. If COMPZ = 'V' and N >

1 then LWORK 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 then LWORK must be at least ( 1 + 4*N + N**2 ).

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.

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 then LIWORK must be at least 1. If COMPZ = 'V' and N >

1 then LIWORK must be at least ( 6 + 6*N + 5*N*lg N ). If COMPZ

= 'I' and N > 1 then 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

Modified by Francoise Tisseur, University of Tennessee.

LAPACK version 3.0 15 June 2000

SSTEDC(3)