dsyevd(3P) Sun Performance Library dsyevd(3P)NAMEdsyevd - compute 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 * 1 JOBZ, UPLO
INTEGER N, LDA, LWORK, LIWORK, INFO
INTEGER IWORK(*)
DOUBLE PRECISION A(LDA,*), W(*), WORK(*)
SUBROUTINE DSYEVD_64(JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, IWORK,
LIWORK, INFO)
CHARACTER * 1 JOBZ, UPLO
INTEGER*8 N, LDA, LWORK, LIWORK, INFO
INTEGER*8 IWORK(*)
DOUBLE PRECISION A(LDA,*), W(*), WORK(*)
F95 INTERFACE
SUBROUTINE SYEVD(JOBZ, UPLO, N, A, [LDA], W, [WORK], [LWORK], [IWORK],
[LIWORK], [INFO])
CHARACTER(LEN=1) :: JOBZ, UPLO
INTEGER :: N, LDA, LWORK, LIWORK, INFO
INTEGER, DIMENSION(:) :: IWORK
REAL(8), DIMENSION(:) :: W, WORK
REAL(8), DIMENSION(:,:) :: A
SUBROUTINE SYEVD_64(JOBZ, UPLO, N, A, [LDA], W, [WORK], [LWORK],
[IWORK], [LIWORK], [INFO])
CHARACTER(LEN=1) :: JOBZ, UPLO
INTEGER(8) :: N, LDA, LWORK, LIWORK, INFO
INTEGER(8), DIMENSION(:) :: IWORK
REAL(8), DIMENSION(:) :: W, WORK
REAL(8), DIMENSION(:,:) :: A
C INTERFACE
#include <sunperf.h>
void dsyevd(char jobz, char uplo, int n, double *a, int lda, double *w,
int *info);
void dsyevd_64(char jobz, char uplo, long n, double *a, long lda, dou‐
ble *w, long *info);
PURPOSEdsyevd 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)
= 'N': Compute eigenvalues only;
= 'V': Compute eigenvalues and eigenvectors.
UPLO (input)
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
N (input) The order of the matrix A. N >= 0.
A (input/output)
On entry, the symmetric matrix A. If UPLO = 'U', the leading
N-by-N upper triangular part of A contains the upper triangu‐
lar 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 diago‐
nal, is destroyed.
LDA (input)
The leading dimension of the array A. LDA >= max(1,N).
W (output)
If INFO = 0, the eigenvalues in ascending order.
WORK (workspace)
dimension (LWORK) On exit, if INFO = 0, WORK(1) returns the
optimal LWORK.
LWORK (input)
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)
On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
LIWORK (input)
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 rou‐
tine 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)
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, the algorithm failed to converge; 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.
6 Mar 2009 dsyevd(3P)
