slaed0(3)

NAME

SLAED0 - compute all eigenvalues and corresponding eigen

vectors of a symmetric tridiagonal matrix using the divide and

conquer method

SYNOPSIS

SUBROUTINE SLAED0( ICOMPQ, QSIZ, N, D, E, Q, LDQ,  QSTORE,
LDQS, WORK, IWORK, INFO )
    INTEGER        ICOMPQ, INFO, LDQ, LDQS, N, QSIZ
    INTEGER        IWORK( * )
    REAL            D(  *  ), E( * ), Q( LDQ, * ), QSTORE(
LDQS, * ), WORK( * )

PURPOSE

SLAED0 computes all eigenvalues and corresponding eigen

vectors of a symmetric tridiagonal matrix using the divide and

conquer method.

ARGUMENTS

ICOMPQ (input) INTEGER

= 0: Compute eigenvalues only.
= 1: Compute eigenvectors of original dense sym

metric matrix also. On entry, Q contains the orthogonal matrix

used to reduce the original matrix to tridiagonal form. = 2:

Compute eigenvalues and eigenvectors of tridiagonal matrix.

QSIZ (input) INTEGER

The dimension of the orthogonal matrix used to re

duce the full matrix to tridiagonal form. QSIZ >= N if ICOMPQ =

1.

N (input) INTEGER

The dimension of the symmetric tridiagonal matrix.

N >= 0.

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

On entry, the main diagonal of the tridiagonal ma

trix. On exit, its eigenvalues.

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

The off-diagonal elements of the tridiagonal ma

trix. On exit, E has been destroyed.

Q (input/output) REAL array, dimension (LDQ, N)

On entry, Q must contain an N-by-N orthogonal ma

trix. If ICOMPQ = 0 Q is not referenced. If ICOMPQ = 1 On

entry, Q is a subset of the columns of the orthogonal matrix used

to reduce the full matrix to tridiagonal form corresponding to

the subset of the full matrix which is being decomposed at this

time. If ICOMPQ = 2 On entry, Q will be the identity matrix.

On exit, Q contains the eigenvectors of the tridiagonal matrix.

LDQ (input) INTEGER

The leading dimension of the array Q. If eigenvec

tors are desired, then LDQ >= max(1,N). In any case, LDQ >= 1.

QSTORE (workspace) REAL array, dimension (LDQS, N)

Referenced only when ICOMPQ = 1. Used to store parts of the

eigenvector matrix when the updating matrix multiplies take

place.

LDQS (input) INTEGER

The leading dimension of the array QSTORE. If

ICOMPQ = 1, then LDQS >= max(1,N). In any case, LDQS >= 1.

WORK (workspace) REAL array,

If ICOMPQ = 0 or 1, the dimension of WORK must be

at least 1 + 3*N + 2*N*lg N + 2*N**2 ( lg( N ) = smallest integer

k such that 2^k >= N ) If ICOMPQ = 2, the dimension of WORK must

be at least 4*N + N**2.

IWORK (workspace) INTEGER array,

If ICOMPQ = 0 or 1, the dimension of IWORK must be

at least 6 + 6*N + 5*N*lg N. ( lg( N ) = smallest integer k such

that 2^k >= N ) If ICOMPQ = 2, the dimension of IWORK must be at

least 3 + 5*N.

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 eigenvalue

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

SLAED0(3)