dspevd(3P) Sun Performance Library dspevd(3P)NAMEdspevd - compute all the eigenvalues and, optionally, eigenvectors of a
real symmetric matrix A in packed storage
SYNOPSIS
SUBROUTINE DSPEVD(JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, LWORK, IWORK,
LIWORK, INFO)
CHARACTER * 1 JOBZ, UPLO
INTEGER N, LDZ, LWORK, LIWORK, INFO
INTEGER IWORK(*)
DOUBLE PRECISION AP(*), W(*), Z(LDZ,*), WORK(*)
SUBROUTINE DSPEVD_64(JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, LWORK,
IWORK, LIWORK, INFO)
CHARACTER * 1 JOBZ, UPLO
INTEGER*8 N, LDZ, LWORK, LIWORK, INFO
INTEGER*8 IWORK(*)
DOUBLE PRECISION AP(*), W(*), Z(LDZ,*), WORK(*)
F95 INTERFACE
SUBROUTINE SPEVD(JOBZ, UPLO, [N], AP, W, Z, [LDZ], [WORK], [LWORK],
[IWORK], [LIWORK], [INFO])
CHARACTER(LEN=1) :: JOBZ, UPLO
INTEGER :: N, LDZ, LWORK, LIWORK, INFO
INTEGER, DIMENSION(:) :: IWORK
REAL(8), DIMENSION(:) :: AP, W, WORK
REAL(8), DIMENSION(:,:) :: Z
SUBROUTINE SPEVD_64(JOBZ, UPLO, [N], AP, W, Z, [LDZ], [WORK], [LWORK],
[IWORK], [LIWORK], [INFO])
CHARACTER(LEN=1) :: JOBZ, UPLO
INTEGER(8) :: N, LDZ, LWORK, LIWORK, INFO
INTEGER(8), DIMENSION(:) :: IWORK
REAL(8), DIMENSION(:) :: AP, W, WORK
REAL(8), DIMENSION(:,:) :: Z
C INTERFACE
#include <sunperf.h>
void dspevd(char jobz, char uplo, int n, double *ap, double *w, double
*z, int ldz, int *info);
void dspevd_64(char jobz, char uplo, long n, double *ap, double *w,
double *z, long ldz, long *info);
PURPOSEdspevd computes all the eigenvalues and, optionally, eigenvectors of a
real symmetric matrix A in packed storage. 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.
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.
AP (input/output)
Double precision array, dimension (N*(N+1)/2) On entry, the
upper or lower triangle of the symmetric matrix A, packed
columnwise in a linear array. The j-th column of A is stored
in the array AP as follows: if UPLO = 'U', AP(i + (j-1)*j/2)
= A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2)
= A(i,j) for j<=i<=n.
On exit, AP is overwritten by values generated during the
reduction to tridiagonal form. If UPLO = 'U', the diagonal
and first superdiagonal of the tridiagonal matrix T overwrite
the corresponding elements of A, and if UPLO = 'L', the diag‐
onal and first subdiagonal of T overwrite the corresponding
elements of A.
W (output)
Double precision array, dimension (N) If INFO = 0, the eigen‐
values in ascending order.
Z (input) Double precision array, dimension (LDZ, N) If JOBZ = 'V',
then if INFO = 0, Z contains the orthonormal eigenvectors of
the matrix A, with the i-th column of Z holding the eigenvec‐
tor associated with W(i). If JOBZ = 'N', then Z is not ref‐
erenced.
LDZ (input)
The leading dimension of the array Z. LDZ >= 1, and if JOBZ
= 'V', LDZ >= max(1,N).
WORK (workspace)
Real array, 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. If JOBZ = 'V' and N > 1, LWORK must be
at least 1 + 6*N + 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)
The dimension of the array IWORK. If JOBZ = 'N' or 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.
6 Mar 2009 dspevd(3P)
