.TH "slarfgp.f" 3 "Tue Nov 14 2017" "Version 3.8.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
slarfgp.f
.SH SYNOPSIS
.br
.PP
.SS "Functions/Subroutines"

.in +1c
.ti -1c
.RI "subroutine \fBslarfgp\fP (\fBN\fP, ALPHA, X, INCX, TAU)"
.br
.RI "\fBSLARFGP\fP generates an elementary reflector (Householder matrix) with non-negative beta\&. "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine slarfgp (integer N, real ALPHA, real, dimension( * ) X, integer INCX, real TAU)"

.PP
\fBSLARFGP\fP generates an elementary reflector (Householder matrix) with non-negative beta\&.  
.PP
\fBPurpose: \fP
.RS 4

.PP
.nf
 SLARFGP generates a real elementary reflector H of order n, such
 that

       H * ( alpha ) = ( beta ),   H**T * H = I.
           (   x   )   (   0  )

 where alpha and beta are scalars, beta is non-negative, and x is
 an (n-1)-element real vector.  H is represented in the form

       H = I - tau * ( 1 ) * ( 1 v**T ) ,
                     ( v )

 where tau is a real scalar and v is a real (n-1)-element
 vector.

 If the elements of x are all zero, then tau = 0 and H is taken to be
 the unit matrix.
.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 REAL
          On entry, the value alpha.
          On exit, it is overwritten with the value beta.
.fi
.PP
.br
\fIX\fP 
.PP
.nf
          X is REAL 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 REAL
          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
\fBDate:\fP
.RS 4
November 2017 
.RE
.PP

.PP
Definition at line 106 of file slarfgp\&.f\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.
