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zhbgst.f(3) LAPACK zhbgst.f(3)

NAME

zhbgst.f -

SYNOPSIS

Functions/Subroutines


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

Function/Subroutine Documentation

subroutine zhbgst (characterVECT, characterUPLO, integerN, integerKA, integerKB, complex*16, dimension( ldab, * )AB, integerLDAB, complex*16, dimension( ldbb, * )BB, integerLDBB, complex*16, dimension( ldx, * )X, integerLDX, complex*16, dimension( * )WORK, double precision, dimension( * )RWORK, integerINFO)

ZHBGST

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:

VECT


VECT is CHARACTER*1
= 'N': do not form the transformation matrix X;
= 'V': form X.

UPLO


UPLO is CHARACTER*1
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.

N


N is INTEGER
The order of the matrices A and B. N >= 0.

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.

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.

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.

LDAB


LDAB is INTEGER
The leading dimension of the array AB. LDAB >= KA+1.

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.

LDBB


LDBB is INTEGER
The leading dimension of the array BB. LDBB >= KB+1.

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.

LDX


LDX is INTEGER
The leading dimension of the array X.
LDX >= max(1,N) if VECT = 'V'; LDX >= 1 otherwise.

WORK


WORK is COMPLEX*16 array, dimension (N)

RWORK


RWORK is DOUBLE PRECISION array, dimension (N)

INFO


INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

November 2011

Definition at line 165 of file zhbgst.f.

Author

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Tue Sep 25 2012 Version 3.4.2