DSYEVD(1) LAPACK driver routine (version 3.2) DSYEVD(1)NAME
DSYEVD - computes all eigenvalues and, optionally, eigenvectors 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, 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 dig‐
its, 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 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 tri‐
angle (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 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 (workspace/output) INTEGER array, dimension (MAX(1,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 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 (output) 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 tridiago‐
nal form did not converge to zero; if INFO = i and JOBZ = 'V',
then the algorithm failed to compute an eigenvalue while work‐
ing on the submatrix lying in rows and columns INFO/(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.
Modified description of INFO. Sven, 16 Feb 05.
LAPACK driver routine (version 3November 2008 DSYEVD(1)
