cgghrd.f(3)							      LAPACK							       cgghrd.f(3)

NAME

       cgghrd.f -

SYNOPSIS

   Functions/Subroutines
       subroutine cgghrd (COMPQ, COMPZ, N, ILO, IHI, A, LDA, B, LDB, Q, LDQ, Z, LDZ, INFO)
	   CGGHRD

Function/Subroutine Documentation
   subroutine cgghrd (characterCOMPQ, characterCOMPZ, integerN, integerILO, integerIHI, complex, dimension( lda, * )A, integerLDA, complex,
       dimension( ldb, * )B, integerLDB, complex, dimension( ldq, * )Q, integerLDQ, complex, dimension( ldz, * )Z, integerLDZ, integerINFO)
       CGGHRD

       Purpose:

	    CGGHRD 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 CGGHRD 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 CGGBAL; 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 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 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 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 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 cgghrd.f.

Author
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Version 3.4.1							  Sun May 26 2013						       cgghrd.f(3)