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

.in +1c
.ti -1c
.RI "subroutine \fBzlarfg\fP (n, alpha, x, incx, tau)"
.br
.RI "\fBZLARFG\fP generates an elementary reflector (Householder matrix)\&. "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine zlarfg (integer n, complex*16 alpha, complex*16, dimension( * ) x, integer incx, complex*16 tau)"

.PP
\fBZLARFG\fP generates an elementary reflector (Householder matrix)\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
!>
!> ZLARFG generates a complex elementary reflector H of order n, such
!> that
!>
!>       H**H * ( alpha ) = ( beta ),   H**H * H = I\&.
!>              (   x   )   (   0  )
!>
!> where alpha and beta are scalars, with beta real, and x is an
!> (n-1)-element complex vector\&. H is represented in the form
!>
!>       H = I - tau * ( 1 ) * ( 1 v**H ) ,
!>                     ( v )
!>
!> where tau is a complex scalar and v is a complex (n-1)-element
!> vector\&. Note that H is not hermitian\&.
!>
!> If the elements of x are all zero and alpha is real, then tau = 0
!> and H is taken to be the unit matrix\&.
!>
!> Otherwise  1 <= real(tau) <= 2  and  abs(tau-1) <= 1 \&.
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIN\fP 
.PP
.nf
!>          N is INTEGER
!>          The order of the elementary reflector\&.
!> 
.fi
.PP
.br
\fIALPHA\fP 
.PP
.nf
!>          ALPHA is COMPLEX*16
!>          On entry, the value alpha\&.
!>          On exit, it is overwritten with the value beta\&.
!> 
.fi
.PP
.br
\fIX\fP 
.PP
.nf
!>          X is COMPLEX*16 array, dimension
!>                         (1+(N-2)*abs(INCX))
!>          On entry, the vector x\&.
!>          On exit, it is overwritten with the vector v\&.
!> 
.fi
.PP
.br
\fIINCX\fP 
.PP
.nf
!>          INCX is INTEGER
!>          The increment between elements of X\&. INCX > 0\&.
!> 
.fi
.PP
.br
\fITAU\fP 
.PP
.nf
!>          TAU is COMPLEX*16
!>          The value tau\&.
!> 
.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

.PP
Definition at line \fB105\fP of file \fBzlarfg\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.