CXML
        	    
LAPACK version 3.0
cgghrd(3)

PURPOSE
  CGGHRD - reduce 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

SYNTAX
  SUBROUTINE CGGHRD( COMPQ, COMPZ, N, ILO, IHI, A, LDA, B, LDB, Q, LDQ, Z,
		     LDZ, INFO )

      CHARACTER	     COMPQ, COMPZ

      INTEGER	     IHI, ILO, INFO, LDA, LDB, LDQ, LDZ, N

      COMPLEX	     A( LDA, * ), B( LDB, * ), Q( LDQ, * ), Z( LDZ, * )

DESCRIPTION
  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: Q' * A * Z = H and Q' * B * Z = T, where H is
  upper Hessenberg, T is upper triangular, and Q and Z are unitary, and '
  means conjugate transpose.

  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' = (Q1*Q) * H * (Z1*Z)'
       Q1 * B * Z1' = (Q1*Q) * T * (Z1*Z)'

ARGUMENTS
  COMPQ	  (input) 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	  (input) 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	  (input) INTEGER
	  The order of the matrices A and B.  N >= 0.

  ILO	  (input) INTEGER
	  IHI	  (input) INTEGER 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	  (input/output) 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	  (input) INTEGER
	  The leading dimension of the array A.	 LDA >= max(1,N).

  B	  (input/output) COMPLEX array, dimension (LDB, N)
	  On entry, the N-by-N upper triangular matrix B.  On exit, the upper
	  triangular matrix T = Q' B Z.	 The elements below the diagonal are
	  set to zero.

  LDB	  (input) INTEGER
	  The leading dimension of the array B.	 LDB >= max(1,N).

  Q	  (input/output) COMPLEX array, dimension (LDQ, N)
	  If COMPQ='N':	 Q is not referenced.
	  If COMPQ='I':	 on entry, Q need not be set, and on exit it contains
	  the unitary matrix Q, where Q' is the product of the Givens
	  transformations which are applied to A and B on the left.  If
	  COMPQ='V':  on entry, Q must contain a unitary matrix Q1, and on
	  exit this is overwritten by Q1*Q.

  LDQ	  (input) INTEGER
	  The leading dimension of the array Q.	 LDQ >= N if COMPQ='V' or
	  'I'; LDQ >= 1 otherwise.

  Z	  (input/output) COMPLEX array, dimension (LDZ, N)
	  If COMPZ='N':	 Z is not referenced.
	  If COMPZ='I':	 on entry, Z need not be set, and on exit it contains
	  the unitary matrix Z, which is the product of the Givens
	  transformations which are applied to A and B on the right.  If
	  COMPZ='V':  on entry, Z must contain a unitary matrix Z1, and on
	  exit this is overwritten by Z1*Z.

  LDZ	  (input) INTEGER
	  The leading dimension of the array Z.	 LDZ >= N if COMPZ='V' or
	  'I'; LDZ >= 1 otherwise.

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

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).