# SSYEVD (3) - Linux Manuals

ssyevd.f -

## SYNOPSIS

### Functions/Subroutines

subroutine ssyevd (JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, IWORK, LIWORK, INFO)
SSYEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for SY matrices

## Function/Subroutine Documentation

### subroutine ssyevd (characterJOBZ, characterUPLO, integerN, real, dimension( lda, * )A, integerLDA, real, dimension( * )W, real, dimension( * )WORK, integerLWORK, integer, dimension( * )IWORK, integerLIWORK, integerINFO)

SSYEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for SY matrices

Purpose:

SSYEVD computes all eigenvalues and, optionally, eigenvectors 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 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 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.

Parameters:

JOBZ

JOBZ is CHARACTER*1
= 'N':  Compute eigenvalues only;
= 'V':  Compute eigenvalues and eigenvectors.

UPLO

UPLO is CHARACTER*1
= 'U':  Upper triangle of A is stored;
= 'L':  Lower triangle of A is stored.

N

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

A

A is 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 destroyed.

LDA

LDA is INTEGER
The leading dimension of the array A.  LDA >= max(1,N).

W

W is REAL array, dimension (N)
If INFO = 0, the eigenvalues in ascending order.

WORK

WORK is REAL array,
dimension (LWORK)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK

LWORK is 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 sizes of the WORK and IWORK
arrays, returns these values as the first entries of the WORK
and IWORK arrays, and no error message related to LWORK or
LIWORK is issued by XERBLA.

IWORK

IWORK is INTEGER array, dimension (MAX(1,LIWORK))
On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.

LIWORK

LIWORK is 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 sizes of the WORK and
IWORK arrays, returns these values as the first entries of
the WORK and IWORK arrays, and no error message related to
LWORK or LIWORK is issued by XERBLA.

INFO

INFO is INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value
> 0:  if INFO = i and JOBZ = 'N', then the algorithm failed
to converge; i off-diagonal elements of an intermediate
tridiagonal form did not converge to zero;
if INFO = i and JOBZ = 'V', then the algorithm failed
to compute an eigenvalue while working on the submatrix
lying in rows and columns INFO/(N+1) through
mod(INFO,N+1).

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

November 2011

Contributors:

Jeff Rutter, Computer Science Division, University of California at Berkeley, USA

Modified by Francoise Tisseur, University of Tennessee

Modified description of INFO. Sven, 16 Feb 05.

Definition at line 183 of file ssyevd.f.

## Author

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