Contents
ssbevd - compute all the eigenvalues and, optionally, eigen-
vectors of a real symmetric band matrix A
SUBROUTINE SSBEVD(JOBZ, UPLO, N, KD, AB, LDAB, W, Z, LDZ, WORK,
LWORK, IWORK, LIWORK, INFO)
CHARACTER * 1 JOBZ, UPLO
INTEGER N, KD, LDAB, LDZ, LWORK, LIWORK, INFO
INTEGER IWORK(*)
REAL AB(LDAB,*), W(*), Z(LDZ,*), WORK(*)
SUBROUTINE SSBEVD_64(JOBZ, UPLO, N, KD, AB, LDAB, W, Z, LDZ, WORK,
LWORK, IWORK, LIWORK, INFO)
CHARACTER * 1 JOBZ, UPLO
INTEGER*8 N, KD, LDAB, LDZ, LWORK, LIWORK, INFO
INTEGER*8 IWORK(*)
REAL AB(LDAB,*), W(*), Z(LDZ,*), WORK(*)
F95 INTERFACE
SUBROUTINE SBEVD(JOBZ, UPLO, [N], KD, AB, [LDAB], W, Z, [LDZ], [WORK],
[LWORK], [IWORK], [LIWORK], [INFO])
CHARACTER(LEN=1) :: JOBZ, UPLO
INTEGER :: N, KD, LDAB, LDZ, LWORK, LIWORK, INFO
INTEGER, DIMENSION(:) :: IWORK
REAL, DIMENSION(:) :: W, WORK
REAL, DIMENSION(:,:) :: AB, Z
SUBROUTINE SBEVD_64(JOBZ, UPLO, [N], KD, AB, [LDAB], W, Z, [LDZ],
[WORK], [LWORK], [IWORK], [LIWORK], [INFO])
CHARACTER(LEN=1) :: JOBZ, UPLO
INTEGER(8) :: N, KD, LDAB, LDZ, LWORK, LIWORK, INFO
INTEGER(8), DIMENSION(:) :: IWORK
REAL, DIMENSION(:) :: W, WORK
REAL, DIMENSION(:,:) :: AB, Z
C INTERFACE
#include <sunperf.h>
void ssbevd(char jobz, char uplo, int n, int kd, float *ab,
int ldab, float *w, float *z, int ldz, int *info);
void ssbevd_64(char jobz, char uplo, long n, long kd, float
*ab, long ldab, float *w, float *z, long ldz, long
*info);
ssbevd computes all the eigenvalues and, optionally, eigen-
vectors of a real symmetric band 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
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.
KD (input)
The number of superdiagonals of the matrix A if
UPLO = 'U', or the number of subdiagonals if UPLO
= 'L'. KD >= 0.
AB (input/output)
On entry, the upper or lower triangle of the sym-
metric band matrix A, stored in the first KD+1
rows of the array. The j-th column of A is stored
in the j-th column of the array AB as follows: if
UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-
kd)<=i<=j; if UPLO = 'L', AB(1+i-j,j) = A(i,j)
for j<=i<=min(n,j+kd).
On exit, AB is overwritten by values generated
during the reduction to tridiagonal form. If UPLO
= 'U', the first superdiagonal and the diagonal of
the tridiagonal matrix T are returned in rows KD
and KD+1 of AB, and if UPLO = 'L', the diagonal
and first subdiagonal of T are returned in the
first two rows of AB.
LDAB (input)
The leading dimension of the array AB. LDAB >= KD
+ 1.
W (output)
If INFO = 0, the eigenvalues in ascending order.
Z (output)
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 eigenvector associ-
ated 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)
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 >
2, LWORK must be at least 2*N. If JOBZ = 'V' and
N > 2, LWORK must be at least ( 1 + 5*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 LIWORK. If JOBZ = 'N'
or N <= 1, LIWORK must be at least 1. If JOBZ =
'V' and N > 2, 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.