Contents
ssbgv - compute all the eigenvalues, and optionally, the
eigenvectors of a real generalized symmetric-definite banded
eigenproblem, of the form A*x=(lambda)*B*x
SUBROUTINE SSBGV(JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, Z,
LDZ, WORK, INFO)
CHARACTER * 1 JOBZ, UPLO
INTEGER N, KA, KB, LDAB, LDBB, LDZ, INFO
REAL AB(LDAB,*), BB(LDBB,*), W(*), Z(LDZ,*), WORK(*)
SUBROUTINE SSBGV_64(JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, Z,
LDZ, WORK, INFO)
CHARACTER * 1 JOBZ, UPLO
INTEGER*8 N, KA, KB, LDAB, LDBB, LDZ, INFO
REAL AB(LDAB,*), BB(LDBB,*), W(*), Z(LDZ,*), WORK(*)
F95 INTERFACE
SUBROUTINE SBGV(JOBZ, UPLO, [N], KA, KB, AB, [LDAB], BB, [LDBB], W,
Z, [LDZ], [WORK], [INFO])
CHARACTER(LEN=1) :: JOBZ, UPLO
INTEGER :: N, KA, KB, LDAB, LDBB, LDZ, INFO
REAL, DIMENSION(:) :: W, WORK
REAL, DIMENSION(:,:) :: AB, BB, Z
SUBROUTINE SBGV_64(JOBZ, UPLO, [N], KA, KB, AB, [LDAB], BB, [LDBB],
W, Z, [LDZ], [WORK], [INFO])
CHARACTER(LEN=1) :: JOBZ, UPLO
INTEGER(8) :: N, KA, KB, LDAB, LDBB, LDZ, INFO
REAL, DIMENSION(:) :: W, WORK
REAL, DIMENSION(:,:) :: AB, BB, Z
C INTERFACE
#include <sunperf.h>
void ssbgv(char jobz, char uplo, int n, int ka, int kb,
float *ab, int ldab, float *bb, int ldbb, float
*w, float *z, int ldz, int *info);
void ssbgv_64(char jobz, char uplo, long n, long ka, long
kb, float *ab, long ldab, float *bb, long ldbb,
float *w, float *z, long ldz, long *info);
ssbgv computes all the eigenvalues, and optionally, the
eigenvectors of a real generalized symmetric-definite banded
eigenproblem, of the form A*x=(lambda)*B*x. Here A and B are
assumed to be symmetric and banded, and B is also positive
definite.
JOBZ (input)
= 'N': Compute eigenvalues only;
= 'V': Compute eigenvalues and eigenvectors.
UPLO (input)
= 'U': Upper triangles of A and B are stored;
= 'L': Lower triangles of A and B are stored.
N (input) The order of the matrices A and B. N >= 0.
KA (input)
The number of superdiagonals of the matrix A if
UPLO = 'U', or the number of subdiagonals if UPLO
= 'L'. KA >= 0.
KB (input)
The number of superdiagonals of the matrix B if
UPLO = 'U', or the number of subdiagonals if UPLO
= 'L'. KB >= 0.
AB (input/output)
On entry, the upper or lower triangle of the sym-
metric band matrix A, stored in the first ka+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(ka+1+i-j,j) = A(i,j) for max(1,j-
ka)<=i<=j; if UPLO = 'L', AB(1+i-j,j) = A(i,j)
for j<=i<=min(n,j+ka).
On exit, the contents of AB are destroyed.
LDAB (input)
The leading dimension of the array AB. LDAB >=
KA+1.
BB (input/output)
On entry, the upper or lower triangle of the sym-
metric band matrix B, stored in the first kb+1
rows of the array. The j-th column of B is stored
in the j-th column of the array BB as follows: if
UPLO = 'U', BB(kb+1+i-j,j) = B(i,j) for max(1,j-
kb)<=i<=j; if UPLO = 'L', BB(1+i-j,j) = B(i,j)
for j<=i<=min(n,j+kb).
On exit, the factor S from the split Cholesky fac-
torization B = S**T*S, as returned by SPBSTF.
LDBB (input)
The leading dimension of the array BB. LDBB >=
KB+1.
W (output)
If INFO = 0, the eigenvalues in ascending order.
Z (input) If JOBZ = 'V', then if INFO = 0, Z contains the
matrix Z of eigenvectors, with the i-th column of
Z holding the eigenvector associated with W(i).
The eigenvectors are normalized so that Z**T*B*Z =
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 >= N.
WORK (workspace)
dimension(3*N)
INFO (output)
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an ille-
gal value
> 0: if INFO = i, and i is:
<= N: the algorithm failed to converge: i off-
diagonal elements of an intermediate tridiagonal
form did not converge to zero; > N: if INFO = N
+ i, for 1 <= i <= N, then SPBSTF
returned INFO = i: B is not positive definite.
The factorization of B could not be completed and
no eigenvalues or eigenvectors were computed.