dsbgv(3P) Sun Performance Library dsbgv(3P)NAMEdsbgv - compute all the eigenvalues, and optionally, the eigenvectors
of a real generalized symmetric-definite banded eigenproblem, of the
form A*x=(lambda)*B*x
SYNOPSIS
SUBROUTINE DSBGV(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
DOUBLE PRECISION AB(LDAB,*), BB(LDBB,*), W(*), Z(LDZ,*), WORK(*)
SUBROUTINE DSBGV_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
DOUBLE PRECISION 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(8), DIMENSION(:) :: W, WORK
REAL(8), 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(8), DIMENSION(:) :: W, WORK
REAL(8), DIMENSION(:,:) :: AB, BB, Z
C INTERFACE
#include <sunperf.h>
void dsbgv(char jobz, char uplo, int n, int ka, int kb, double *ab, int
ldab, double *bb, int ldbb, double *w, double *z, int ldz,
int *info);
void dsbgv_64(char jobz, char uplo, long n, long ka, long kb, double
*ab, long ldab, double *bb, long ldbb, double *w, double *z,
long ldz, long *info);
PURPOSEdsbgv 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.
ARGUMENTS
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 symmetric 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 symmetric 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 factorization 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 (output)
If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of
eigenvectors, with the i-th column of Z holding the eigenvec‐
tor 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 illegal value
> 0: if INFO = i, and i is:
<= N: the algorithm failed to converge: i off-diagonal ele‐
ments 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 factor‐
ization of B could not be completed and no eigenvalues or
eigenvectors were computed.
6 Mar 2009 dsbgv(3P)
