DSYEVD - compute all eigenvalues and, optionally, eigen
vectors of a real symmetric matrix A
SYNOPSIS
SUBROUTINE DSYEVD( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK,
IWORK, LIWORK, INFO )
CHARACTER JOBZ, UPLO
INTEGER INFO, LDA, LIWORK, LWORK, N
INTEGER IWORK( * )
DOUBLE PRECISION A( LDA, * ), W( * ), WORK( *
)
PURPOSE
DSYEVD 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 hexadecimal or decimal machines with
out guard digits, but we know of none.
Because of large use of BLAS of level 3, DSYEVD needs N**2
more workspace than DSYEVX.
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) DOUBLE PRECISION array, dimension
(LDA, N)
On entry, the symmetric matrix A. If UPLO = 'U',
the leading N-by-N upper triangular part of A con
tains 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
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 (input) INTEGER
The leading dimension of the array A. LDA >=
max(1,N).
W (output) DOUBLE PRECISION array, dimension (N)
If INFO = 0, the eigenvalues in ascending order.
WORK (workspace/output) DOUBLE PRECISION 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
(LIWORK)
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.
Based on contributions by
Jeff Rutter, Computer Science Division, University of
California
at Berkeley, USA
Modified by Francoise Tisseur, University of Tennessee.
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