ZHBGST
June 2010
Purpose
ZHBGST 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 ZPBSTF, 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.
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 ZPBSTF, 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*16 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*16 array, dimension (LDBB,N)
The banded factor S from the split Cholesky factorization of
B, as returned by ZPBSTF, 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*16 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*16 array, dimension (N)
|
| RWORK |
(workspace) DOUBLE PRECISION array, dimension (N)
|
| INFO |
(output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value. |