.TH "SRC/zgghrd.f" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
SRC/zgghrd.f
.SH SYNOPSIS
.br
.PP
.SS "Functions/Subroutines"

.in +1c
.ti -1c
.RI "subroutine \fBzgghrd\fP (compq, compz, n, ilo, ihi, a, lda, b, ldb, q, ldq, z, ldz, info)"
.br
.RI "\fBZGGHRD\fP "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine zgghrd (character compq, character compz, integer n, integer ilo, integer ihi, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( ldb, * ) b, integer ldb, complex*16, dimension( ldq, * ) q, integer ldq, complex*16, dimension( ldz, * ) z, integer ldz, integer info)"

.PP
\fBZGGHRD\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
!>
!> 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\&.
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fICOMPQ\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fICOMPZ\fP 
.PP
.nf
!>          COMPZ is CHARACTER*1
!>          = 'N': do not compute Z;
!>          = 'I': Z is initialized to the unit matrix, and the
!>                 unitary matrix Z is returned;
!>          = 'V': Z must contain a unitary matrix Z1 on entry,
!>                 and the product Z1*Z is returned\&.
!> 
.fi
.PP
.br
\fIN\fP 
.PP
.nf
!>          N is INTEGER
!>          The order of the matrices A and B\&.  N >= 0\&.
!> 
.fi
.PP
.br
\fIILO\fP 
.PP
.nf
!>          ILO is INTEGER
!> 
.fi
.PP
.br
\fIIHI\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fIA\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
!>          LDA is INTEGER
!>          The leading dimension of the array A\&.  LDA >= max(1,N)\&.
!> 
.fi
.PP
.br
\fIB\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fILDB\fP 
.PP
.nf
!>          LDB is INTEGER
!>          The leading dimension of the array B\&.  LDB >= max(1,N)\&.
!> 
.fi
.PP
.br
\fIQ\fP 
.PP
.nf
!>          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'\&.
!> 
.fi
.PP
.br
\fILDQ\fP 
.PP
.nf
!>          LDQ is INTEGER
!>          The leading dimension of the array Q\&.
!>          LDQ >= N if COMPQ='V' or 'I'; LDQ >= 1 otherwise\&.
!> 
.fi
.PP
.br
\fIZ\fP 
.PP
.nf
!>          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'\&.
!> 
.fi
.PP
.br
\fILDZ\fP 
.PP
.nf
!>          LDZ is INTEGER
!>          The leading dimension of the array Z\&.
!>          LDZ >= N if COMPZ='V' or 'I'; LDZ >= 1 otherwise\&.
!> 
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
!>          INFO is INTEGER
!>          = 0:  successful exit\&.
!>          < 0:  if INFO = -i, the i-th argument had an illegal value\&.
!> 
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 

.PP
Univ\&. of California Berkeley 

.PP
Univ\&. of Colorado Denver 

.PP
NAG Ltd\&. 
.RE
.PP
\fBFurther Details:\fP
.RS 4

.PP
.nf
!>
!>  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)\&.
!> 
.fi
.PP
 
.RE
.PP

.PP
Definition at line \fB202\fP of file \fBzgghrd\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.