CHBGV - compute all the eigenvalues, and optionally, the
eigenvectors of a complex generalized Hermitian-definite
banded eigenproblem, of the form A*x=(lambda)*B*x
SYNOPSIS
SUBROUTINE CHBGV( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB,
LDBB, W, Z, LDZ, WORK, RWORK, INFO )
CHARACTER JOBZ, UPLO
INTEGER INFO, KA, KB, LDAB, LDBB, LDZ, N
REAL RWORK( * ), W( * )
COMPLEX AB( LDAB, * ), BB( LDBB, * ), WORK( * ),
Z( LDZ, * )
PURPOSE
CHBGV 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.
ARGUMENTS
JOBZ (input) CHARACTER*1
= 'N': Compute eigenvalues only;
= 'V': Compute eigenvalues and eigenvectors.
UPLO (input) CHARACTER*1
= 'U': Upper triangles of A and B are stored;
= 'L': Lower triangles of A and B are stored.
N (input) INTEGER
The order of the matrices A and B. N >= 0.
KA (input) INTEGER
The number of superdiagonals of the matrix A if
UPLO = 'U', or the number of subdiagonals if UPLO
= 'L'. KA >= 0.
KB (input) INTEGER
The number of superdiagonals of the matrix B if
UPLO = 'U', or the number of subdiagonals if UPLO
= 'L'. KB >= 0.
AB (input/output) COMPLEX array, dimension (LDAB, N)
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-
for j<=i<=min(n,j+ka).
On exit, the contents of AB are destroyed.
LDAB (input) INTEGER
The leading dimension of the array AB. LDAB >=
KA+1.
BB (input/output) COMPLEX array, dimension (LDBB, N)
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) INTEGER
The leading dimension of the array BB. LDBB >=
KB+1.
W (output) REAL array, dimension (N)
If INFO = 0, the eigenvalues in ascending order.
Z (output) COMPLEX array, dimension (LDZ, N)
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) INTEGER
The leading dimension of the array Z. LDZ >= 1,
and if JOBZ = 'V', LDZ >= N.
WORK (workspace) COMPLEX array, dimension (N)
RWORK (workspace) REAL array, dimension (3*N)
INFO (output) INTEGER
= 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
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