 CHBGST(3) reduces a complex Hermitian-definite banded generalized eigenproblem A*x = lambda*B*x to standard form C*y = lambda*y,

## SYNOPSIS

SUBROUTINE CHBGST(
VECT, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, X, LDX, WORK, RWORK, INFO )

CHARACTER UPLO, VECT

INTEGER INFO, KA, KB, LDAB, LDBB, LDX, N

REAL RWORK( * )

COMPLEX AB( LDAB, * ), BB( LDBB, * ), WORK( * ), X( LDX, * )

## PURPOSE

CHBGST reduces a complex Hermitian-definite banded generalized eigenproblem A*x = lambda*B*x to standard form C*y = lambda*y, such that C has the same bandwidth as A.
B must have been previously factorized as S**H*S by CPBSTF, using a split Cholesky factorization. A is overwritten by C = X**H*A*X, where X = S**(-1)*Q and Q is a unitary matrix chosen to preserve the bandwidth of A.

## ARGUMENTS

VECT (input) CHARACTER*1
= 'N': do not form the transformation matrix X;
= 'V': form X.
UPLO (input) CHARACTER*1

= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is 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'. KA >= KB >= 0.
AB (input/output) COMPLEX array, dimension (LDAB,N)
On entry, the upper or lower triangle of the Hermitian 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 transformed matrix X**H*A*X, stored in the same format as A.
LDAB (input) INTEGER
The leading dimension of the array AB. LDAB >= KA+1.
BB (input) COMPLEX array, dimension (LDBB,N)
The banded factor S from the split Cholesky factorization of B, as returned by CPBSTF, stored in the first kb+1 rows of the array.
LDBB (input) INTEGER
The leading dimension of the array BB. LDBB >= KB+1.
X (output) COMPLEX array, dimension (LDX,N)
If VECT = 'V', the n-by-n matrix X. If VECT = 'N', the array X is not referenced.
LDX (input) INTEGER
The leading dimension of the array X. LDX >= max(1,N) if VECT = 'V'; LDX >= 1 otherwise.
WORK (workspace) COMPLEX array, dimension (N)
RWORK (workspace) REAL array, dimension (N)
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value.