Contents
sspevd - compute all the eigenvalues and, optionally, eigen-
vectors of a real symmetric matrix A in packed storage
SUBROUTINE SSPEVD(JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, LWORK, IWORK,
LIWORK, INFO)
CHARACTER * 1 JOBZ, UPLO
INTEGER N, LDZ, LWORK, LIWORK, INFO
INTEGER IWORK(*)
REAL AP(*), W(*), Z(LDZ,*), WORK(*)
SUBROUTINE SSPEVD_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(*)
REAL 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, DIMENSION(:) :: AP, W, WORK
REAL, 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, DIMENSION(:) :: AP, W, WORK
REAL, DIMENSION(:,:) :: Z
C INTERFACE
#include <sunperf.h>
void sspevd(char jobz, char uplo, int n, float *ap, float
*w, float *z, int ldz, int *info);
void sspevd_64(char jobz, char uplo, long n, float *ap,
float *w, float *z, long ldz, long *info);
sspevd computes all the eigenvalues and, optionally, eigen-
vectors of a real symmetric matrix A in packed storage. If
eigenvectors are desired, it uses a divide and conquer algo-
rithm.
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.
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)
Real 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 diagonal and
first subdiagonal of T overwrite the corresponding
elements of A.
W (output)
Real array, dimension (N) If INFO = 0, the eigen-
values in ascending order.
Z (input) Real array, dimension (LDZ, N) If JOBZ = 'V', then
if INFO = 0, Z contains the orthonormal eigenvec-
tors of the matrix A, with the i-th column of Z
holding the eigenvector associated with W(i). If
JOBZ = 'N', then Z is not referenced.
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 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)
= 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.