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.