.TH "larfg" 3 "Wed Feb 7 2024 11:30:40" "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
larfg \- larfg: generate Householder reflector
.SH SYNOPSIS
.br
.PP
.SS "Functions"

.in +1c
.ti -1c
.RI "subroutine \fBclarfg\fP (n, alpha, x, incx, tau)"
.br
.RI "\fBCLARFG\fP generates an elementary reflector (Householder matrix)\&. "
.ti -1c
.RI "subroutine \fBdlarfg\fP (n, alpha, x, incx, tau)"
.br
.RI "\fBDLARFG\fP generates an elementary reflector (Householder matrix)\&. "
.ti -1c
.RI "subroutine \fBslarfg\fP (n, alpha, x, incx, tau)"
.br
.RI "\fBSLARFG\fP generates an elementary reflector (Householder matrix)\&. "
.ti -1c
.RI "subroutine \fBzlarfg\fP (n, alpha, x, incx, tau)"
.br
.RI "\fBZLARFG\fP generates an elementary reflector (Householder matrix)\&. "
.in -1c
.SH "Detailed Description"
.PP 

.SH "Function Documentation"
.PP 
.SS "subroutine clarfg (integer n, complex alpha, complex, dimension( * ) x, integer incx, complex tau)"

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

.PP
.nf
 CLARFG 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
          On entry, the value alpha\&.
          On exit, it is overwritten with the value beta\&.
.fi
.PP
.br
\fIX\fP 
.PP
.nf
          X is COMPLEX 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
          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

.SS "subroutine dlarfg (integer n, double precision alpha, double precision, dimension( * ) x, integer incx, double precision tau)"

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

.PP
.nf
 DLARFG 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, 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\&.

 Otherwise  1 <= tau <= 2\&.
.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 DOUBLE PRECISION
          On entry, the value alpha\&.
          On exit, it is overwritten with the value beta\&.
.fi
.PP
.br
\fIX\fP 
.PP
.nf
          X is DOUBLE PRECISION 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 DOUBLE PRECISION
          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

.SS "subroutine slarfg (integer n, real alpha, real, dimension( * ) x, integer incx, real tau)"

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

.PP
.nf
 SLARFG 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, 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\&.

 Otherwise  1 <= tau <= 2\&.
.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

.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

.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.