
zgghrd.f(3) LAPACK zgghrd.f(3)
NAME
zgghrd.f 
SYNOPSIS
Functions/Subroutines
subroutine zgghrd (COMPQ, COMPZ, N, ILO, IHI, A, LDA, B, LDB, Q, LDQ, Z, LDZ, INFO)
ZGGHRD
Function/Subroutine Documentation
subroutine zgghrd (characterCOMPQ, characterCOMPZ, integerN, integerILO, integerIHI,
complex*16, dimension( lda, * )A, integerLDA, complex*16, dimension( ldb, * )B,
integerLDB, complex*16, dimension( ldq, * )Q, integerLDQ, complex*16, dimension( ldz, *
)Z, integerLDZ, integerINFO)
ZGGHRD
Purpose:
ZGGHRD reduces a pair of complex matrices (A,B) to generalized upper
Hessenberg form using unitary transformations, where A is a
general matrix and B is upper triangular. The form of the
generalized eigenvalue problem is
A*x = lambda*B*x,
and B is typically made upper triangular by computing its QR
factorization and moving the unitary matrix Q to the left side
of the equation.
This subroutine simultaneously reduces A to a Hessenberg matrix H:
Q**H*A*Z = H
and transforms B to another upper triangular matrix T:
Q**H*B*Z = T
in order to reduce the problem to its standard form
H*y = lambda*T*y
where y = Z**H*x.
The unitary matrices Q and Z are determined as products of Givens
rotations. They may either be formed explicitly, or they may be
postmultiplied into input matrices Q1 and Z1, so that
Q1 * A * Z1**H = (Q1*Q) * H * (Z1*Z)**H
Q1 * B * Z1**H = (Q1*Q) * T * (Z1*Z)**H
If Q1 is the unitary matrix from the QR factorization of B in the
original equation A*x = lambda*B*x, then ZGGHRD reduces the original
problem to generalized Hessenberg form.
Parameters:
COMPQ
COMPQ is CHARACTER*1
= 'N': do not compute Q;
= 'I': Q is initialized to the unit matrix, and the
unitary matrix Q is returned;
= 'V': Q must contain a unitary matrix Q1 on entry,
and the product Q1*Q is returned.
COMPZ
COMPZ is CHARACTER*1
= 'N': do not compute Q;
= 'I': Q is initialized to the unit matrix, and the
unitary matrix Q is returned;
= 'V': Q must contain a unitary matrix Q1 on entry,
and the product Q1*Q is returned.
N
N is INTEGER
The order of the matrices A and B. N >= 0.
ILO
ILO is INTEGER
IHI
IHI is INTEGER
ILO and IHI mark the rows and columns of A which are to be
reduced. It is assumed that A is already upper triangular
in rows and columns 1:ILO1 and IHI+1:N. ILO and IHI are
normally set by a previous call to ZGGBAL; otherwise they
should be set to 1 and N respectively.
1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.
A
A is COMPLEX*16 array, dimension (LDA, N)
On entry, the NbyN general matrix to be reduced.
On exit, the upper triangle and the first subdiagonal of A
are overwritten with the upper Hessenberg matrix H, and the
rest is set to zero.
LDA
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,N).
B
B is COMPLEX*16 array, dimension (LDB, N)
On entry, the NbyN upper triangular matrix B.
On exit, the upper triangular matrix T = Q**H B Z. The
elements below the diagonal are set to zero.
LDB
LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,N).
Q
Q is COMPLEX*16 array, dimension (LDQ, N)
On entry, if COMPQ = 'V', the unitary matrix Q1, typically
from the QR factorization of B.
On exit, if COMPQ='I', the unitary matrix Q, and if
COMPQ = 'V', the product Q1*Q.
Not referenced if COMPQ='N'.
LDQ
LDQ is INTEGER
The leading dimension of the array Q.
LDQ >= N if COMPQ='V' or 'I'; LDQ >= 1 otherwise.
Z
Z is COMPLEX*16 array, dimension (LDZ, N)
On entry, if COMPZ = 'V', the unitary matrix Z1.
On exit, if COMPZ='I', the unitary matrix Z, and if
COMPZ = 'V', the product Z1*Z.
Not referenced if COMPZ='N'.
LDZ
LDZ is INTEGER
The leading dimension of the array Z.
LDZ >= N if COMPZ='V' or 'I'; LDZ >= 1 otherwise.
INFO
INFO is INTEGER
= 0: successful exit.
< 0: if INFO = i, the ith argument had an illegal value.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
Further Details:
This routine reduces A to Hessenberg and B to triangular form by
an unblocked reduction, as described in <em>Matrix_Computations</em>,
by Golub and van Loan (Johns Hopkins Press).
Definition at line 204 of file zgghrd.f.
Author
Generated automatically by Doxygen for LAPACK from the source code.
Version 3.4.2 Tue Sep 25 2012 zgghrd.f(3) 
