zgghrd.f man page

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:ILO-1 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 N-by-N 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 N-by-N 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 i-th 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 _Matrix_Computations_,
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.

Referenced By

zgghrd(3) is an alias of zgghrd.f(3).

Sat Nov 16 2013 Version 3.4.2 LAPACK