Contents
zhbgv - compute all the eigenvalues, and optionally, the
eigenvectors of a complex generalized Hermitian-definite
banded eigenproblem, of the form A*x=(lambda)*B*x
SUBROUTINE ZHBGV(JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, Z,
LDZ, WORK, RWORK, INFO)
CHARACTER * 1 JOBZ, UPLO
DOUBLE COMPLEX AB(LDAB,*), BB(LDBB,*), Z(LDZ,*), WORK(*)
INTEGER N, KA, KB, LDAB, LDBB, LDZ, INFO
DOUBLE PRECISION W(*), RWORK(*)
SUBROUTINE ZHBGV_64(JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, Z,
LDZ, WORK, RWORK, INFO)
CHARACTER * 1 JOBZ, UPLO
DOUBLE COMPLEX AB(LDAB,*), BB(LDBB,*), Z(LDZ,*), WORK(*)
INTEGER*8 N, KA, KB, LDAB, LDBB, LDZ, INFO
DOUBLE PRECISION W(*), RWORK(*)
F95 INTERFACE
SUBROUTINE HBGV(JOBZ, UPLO, [N], KA, KB, AB, [LDAB], BB, [LDBB], W,
Z, [LDZ], [WORK], [RWORK], [INFO])
CHARACTER(LEN=1) :: JOBZ, UPLO
COMPLEX(8), DIMENSION(:) :: WORK
COMPLEX(8), DIMENSION(:,:) :: AB, BB, Z
INTEGER :: N, KA, KB, LDAB, LDBB, LDZ, INFO
REAL(8), DIMENSION(:) :: W, RWORK
SUBROUTINE HBGV_64(JOBZ, UPLO, [N], KA, KB, AB, [LDAB], BB, [LDBB],
W, Z, [LDZ], [WORK], [RWORK], [INFO])
CHARACTER(LEN=1) :: JOBZ, UPLO
COMPLEX(8), DIMENSION(:) :: WORK
COMPLEX(8), DIMENSION(:,:) :: AB, BB, Z
INTEGER(8) :: N, KA, KB, LDAB, LDBB, LDZ, INFO
REAL(8), DIMENSION(:) :: W, RWORK
C INTERFACE
#include <sunperf.h>
void zhbgv(char jobz, char uplo, int n, int ka, int kb,
doublecomplex *ab, int ldab, doublecomplex *bb,
int ldbb, double *w, doublecomplex *z, int ldz,
int *info);
void zhbgv_64(char jobz, char uplo, long n, long ka, long
kb, doublecomplex *ab, long ldab, doublecomplex
*bb, long ldbb, double *w, doublecomplex *z, long
ldz, long *info);
zhbgv computes all the eigenvalues, and optionally, the
eigenvectors of a complex generalized Hermitian-definite
banded eigenproblem, of the form A*x=(lambda)*B*x. Here A
and B are assumed to be Hermitian 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 Her-
mitian 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 Her-
mitian 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**H*S, as returned by CPBSTF.
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**H*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(N)
RWORK (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 CPBSTF
returned INFO = i: B is not positive definite.
The factorization of B could not be completed and
no eigenvalues or eigenvectors were computed.