ssyevd(3)

NAME

SSYEVD - compute all eigenvalues and, optionally, eigen

vectors of a real symmetric matrix A

SYNOPSIS

SUBROUTINE  SSYEVD( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK,
IWORK, LIWORK, INFO )
    CHARACTER      JOBZ, UPLO
    INTEGER        INFO, LDA, LIWORK, LWORK, N
    INTEGER        IWORK( * )
    REAL           A( LDA, * ), W( * ), WORK( * )

PURPOSE

SSYEVD computes all eigenvalues and, optionally, eigenvec

tors of a real symmetric matrix A. If eigenvectors are desired,

it uses a divide and conquer algorithm.

The divide and conquer algorithm makes very mild assump

tions 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 hexadeci

mal or decimal machines without guard digits, but we know of

none.

Because of large use of BLAS of level 3, SSYEVD needs N**2

more workspace than SSYEVX.

ARGUMENTS

JOBZ (input) CHARACTER*1

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

UPLO (input) CHARACTER*1

= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.

N (input) INTEGER

The order of the matrix A. N >= 0.

A (input/output) REAL array, dimension (LDA, N)

On entry, the symmetric matrix A. If UPLO = 'U',

the leading N-by-N upper triangular part of A contains the upper

triangular part of the matrix A. If UPLO = 'L', the leading N

by-N lower triangular part of A contains the lower triangular

part of the matrix A. On exit, if JOBZ = 'V', then if INFO = 0,

A contains the orthonormal eigenvectors of the matrix A. If JOBZ

= 'N', then on exit the lower triangle (if UPLO='L') or the upper

triangle (if UPLO='U') of A, including the diagonal, is de

stroyed.

LDA (input) INTEGER

The leading dimension of the array A. LDA >=

max(1,N).

W (output) REAL array, dimension (N)

If INFO = 0, the eigenvalues in ascending order.

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 N <= 1,

LWORK must be at least 1. If JOBZ = 'N' and N > 1, LWORK must be

at least 2*N+1. If JOBZ = 'V' and N > 1, LWORK must be at least

1 + 6*N + 2*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 N <= 1,

LIWORK must be at least 1. If JOBZ = 'N' and N > 1, LIWORK must

be at least 1. If JOBZ = 'V' and 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: if INFO = i, the algorithm failed to con

verge; i off-diagonal elements of an intermediate tridiagonal

form did not converge to zero.

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

SSYEVD(3)