 LAPACK  3.4.2 LAPACK: Linear Algebra PACKage
zhbgst.f File Reference

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## Functions/Subroutines

subroutine zhbgst (VECT, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, X, LDX, WORK, RWORK, INFO)
ZHBGST

## Function/Subroutine Documentation

 subroutine zhbgst ( character VECT, character UPLO, integer N, integer KA, integer KB, complex*16, dimension( ldab, * ) AB, integer LDAB, complex*16, dimension( ldbb, * ) BB, integer LDBB, complex*16, dimension( ldx, * ) X, integer LDX, complex*16, dimension( * ) WORK, double precision, dimension( * ) RWORK, integer INFO )

ZHBGST

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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.```
Parameters:
 [in] VECT ``` VECT is CHARACTER*1 = 'N': do not form the transformation matrix X; = 'V': form X.``` [in] UPLO ``` UPLO is CHARACTER*1 = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored.``` [in] N ``` N is INTEGER The order of the matrices A and B. N >= 0.``` [in] KA ``` KA is INTEGER The number of superdiagonals of the matrix A if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. KA >= 0.``` [in] KB ``` KB is INTEGER The number of superdiagonals of the matrix B if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. KA >= KB >= 0.``` [in,out] AB ``` AB is 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.``` [in] LDAB ``` LDAB is INTEGER The leading dimension of the array AB. LDAB >= KA+1.``` [in] BB ``` BB is 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.``` [in] LDBB ``` LDBB is INTEGER The leading dimension of the array BB. LDBB >= KB+1.``` [out] X ``` X is COMPLEX*16 array, dimension (LDX,N) If VECT = 'V', the n-by-n matrix X. If VECT = 'N', the array X is not referenced.``` [in] LDX ``` LDX is INTEGER The leading dimension of the array X. LDX >= max(1,N) if VECT = 'V'; LDX >= 1 otherwise.``` [out] WORK ` WORK is COMPLEX*16 array, dimension (N)` [out] RWORK ` RWORK is DOUBLE PRECISION array, dimension (N)` [out] INFO ``` INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value.```
Date:
November 2011

Definition at line 165 of file zhbgst.f.

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