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

.in +1c
.ti -1c
.RI "subroutine \fBzgehrd\fP (n, ilo, ihi, a, lda, tau, work, lwork, info)"
.br
.RI "\fBZGEHRD\fP "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine zgehrd (integer n, integer ilo, integer ihi, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) tau, complex*16, dimension( * ) work, integer lwork, integer info)"

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

.PP
.nf
!>
!> ZGEHRD reduces a complex general matrix A to upper Hessenberg form H by
!> an unitary similarity transformation:  Q**H * A * Q = H \&.
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIN\fP 
.PP
.nf
!>          N is INTEGER
!>          The order of the matrix A\&.  N >= 0\&.
!> 
.fi
.PP
.br
\fIILO\fP 
.PP
.nf
!>          ILO is INTEGER
!> 
.fi
.PP
.br
\fIIHI\fP 
.PP
.nf
!>          IHI is 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 ZGEBAL; otherwise they should be
!>          set to 1 and N respectively\&. See Further Details\&.
!>          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
!>          elements below the first subdiagonal, with the array TAU,
!>          represent the unitary matrix Q as a product of elementary
!>          reflectors\&. See Further Details\&.
!> 
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
!>          LDA is INTEGER
!>          The leading dimension of the array A\&.  LDA >= max(1,N)\&.
!> 
.fi
.PP
.br
\fITAU\fP 
.PP
.nf
!>          TAU is COMPLEX*16 array, dimension (N-1)
!>          The scalar factors of the elementary reflectors (see Further
!>          Details)\&. Elements 1:ILO-1 and IHI:N-1 of TAU are set to
!>          zero\&.
!> 
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
!>          WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
!>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK\&.
!> 
.fi
.PP
.br
\fILWORK\fP 
.PP
.nf
!>          LWORK is INTEGER
!>          The length of the array WORK\&.  LWORK >= max(1,N)\&.
!>          For good performance, LWORK should generally be larger\&.
!>
!>          If LWORK = -1, then a workspace query is assumed; the routine
!>          only calculates the optimal size of the WORK array, returns
!>          this value as the first entry of the WORK array, and no error
!>          message related to LWORK is issued by XERBLA\&.
!> 
.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
!>
!>  The matrix Q is represented as a product of (ihi-ilo) elementary
!>  reflectors
!>
!>     Q = H(ilo) H(ilo+1) \&. \&. \&. H(ihi-1)\&.
!>
!>  Each H(i) has the form
!>
!>     H(i) = I - tau * v * v**H
!>
!>  where tau is a complex scalar, and v is a complex vector with
!>  v(1:i) = 0, v(i+1) = 1 and v(ihi+1:n) = 0; v(i+2:ihi) is stored on
!>  exit in A(i+2:ihi,i), and tau in TAU(i)\&.
!>
!>  The contents of A are illustrated by the following example, with
!>  n = 7, ilo = 2 and ihi = 6:
!>
!>  on entry,                        on exit,
!>
!>  ( a   a   a   a   a   a   a )    (  a   a   h   h   h   h   a )
!>  (     a   a   a   a   a   a )    (      a   h   h   h   h   a )
!>  (     a   a   a   a   a   a )    (      h   h   h   h   h   h )
!>  (     a   a   a   a   a   a )    (      v2  h   h   h   h   h )
!>  (     a   a   a   a   a   a )    (      v2  v3  h   h   h   h )
!>  (     a   a   a   a   a   a )    (      v2  v3  v4  h   h   h )
!>  (                         a )    (                          a )
!>
!>  where a denotes an element of the original matrix A, h denotes a
!>  modified element of the upper Hessenberg matrix H, and vi denotes an
!>  element of the vector defining H(i)\&.
!>
!>  This file is a slight modification of LAPACK-3\&.0's ZGEHRD
!>  subroutine incorporating improvements proposed by Quintana-Orti and
!>  Van de Geijn (2006)\&. (See ZLAHR2\&.)
!> 
.fi
.PP
 
.RE
.PP

.PP
Definition at line \fB166\fP of file \fBzgehrd\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.