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

.in +1c
.ti -1c
.RI "subroutine \fBclarf\fP (side, m, n, v, incv, tau, c, ldc, work)"
.br
.RI "\fBCLARF\fP applies an elementary reflector to a general rectangular matrix\&. "
.ti -1c
.RI "subroutine \fBdlarf\fP (side, m, n, v, incv, tau, c, ldc, work)"
.br
.RI "\fBDLARF\fP applies an elementary reflector to a general rectangular matrix\&. "
.ti -1c
.RI "subroutine \fBslarf\fP (side, m, n, v, incv, tau, c, ldc, work)"
.br
.RI "\fBSLARF\fP applies an elementary reflector to a general rectangular matrix\&. "
.ti -1c
.RI "subroutine \fBzlarf\fP (side, m, n, v, incv, tau, c, ldc, work)"
.br
.RI "\fBZLARF\fP applies an elementary reflector to a general rectangular matrix\&. "
.in -1c
.SH "Detailed Description"
.PP 

.SH "Function Documentation"
.PP 
.SS "subroutine clarf (character side, integer m, integer n, complex, dimension( * ) v, integer incv, complex tau, complex, dimension( ldc, * ) c, integer ldc, complex, dimension( * ) work)"

.PP
\fBCLARF\fP applies an elementary reflector to a general rectangular matrix\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 CLARF applies a complex elementary reflector H to a complex M-by-N
 matrix C, from either the left or the right\&. H is represented in the
 form

       H = I - tau * v * v**H

 where tau is a complex scalar and v is a complex vector\&.

 If tau = 0, then H is taken to be the unit matrix\&.

 To apply H**H (the conjugate transpose of H), supply conjg(tau) instead
 tau\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fISIDE\fP 
.PP
.nf
          SIDE is CHARACTER*1
          = 'L': form  H * C
          = 'R': form  C * H
.fi
.PP
.br
\fIM\fP 
.PP
.nf
          M is INTEGER
          The number of rows of the matrix C\&.
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
          The number of columns of the matrix C\&.
.fi
.PP
.br
\fIV\fP 
.PP
.nf
          V is COMPLEX array, dimension
                     (1 + (M-1)*abs(INCV)) if SIDE = 'L'
                  or (1 + (N-1)*abs(INCV)) if SIDE = 'R'
          The vector v in the representation of H\&. V is not used if
          TAU = 0\&.
.fi
.PP
.br
\fIINCV\fP 
.PP
.nf
          INCV is INTEGER
          The increment between elements of v\&. INCV <> 0\&.
.fi
.PP
.br
\fITAU\fP 
.PP
.nf
          TAU is COMPLEX
          The value tau in the representation of H\&.
.fi
.PP
.br
\fIC\fP 
.PP
.nf
          C is COMPLEX array, dimension (LDC,N)
          On entry, the M-by-N matrix C\&.
          On exit, C is overwritten by the matrix H * C if SIDE = 'L',
          or C * H if SIDE = 'R'\&.
.fi
.PP
.br
\fILDC\fP 
.PP
.nf
          LDC is INTEGER
          The leading dimension of the array C\&. LDC >= max(1,M)\&.
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
          WORK is COMPLEX array, dimension
                         (N) if SIDE = 'L'
                      or (M) if SIDE = 'R'
.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 dlarf (character side, integer m, integer n, double precision, dimension( * ) v, integer incv, double precision tau, double precision, dimension( ldc, * ) c, integer ldc, double precision, dimension( * ) work)"

.PP
\fBDLARF\fP applies an elementary reflector to a general rectangular matrix\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 DLARF applies a real elementary reflector H to a real m by n matrix
 C, from either the left or the right\&. H is represented in the form

       H = I - tau * v * v**T

 where tau is a real scalar and v is a real vector\&.

 If tau = 0, then H is taken to be the unit matrix\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fISIDE\fP 
.PP
.nf
          SIDE is CHARACTER*1
          = 'L': form  H * C
          = 'R': form  C * H
.fi
.PP
.br
\fIM\fP 
.PP
.nf
          M is INTEGER
          The number of rows of the matrix C\&.
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
          The number of columns of the matrix C\&.
.fi
.PP
.br
\fIV\fP 
.PP
.nf
          V is DOUBLE PRECISION array, dimension
                     (1 + (M-1)*abs(INCV)) if SIDE = 'L'
                  or (1 + (N-1)*abs(INCV)) if SIDE = 'R'
          The vector v in the representation of H\&. V is not used if
          TAU = 0\&.
.fi
.PP
.br
\fIINCV\fP 
.PP
.nf
          INCV is INTEGER
          The increment between elements of v\&. INCV <> 0\&.
.fi
.PP
.br
\fITAU\fP 
.PP
.nf
          TAU is DOUBLE PRECISION
          The value tau in the representation of H\&.
.fi
.PP
.br
\fIC\fP 
.PP
.nf
          C is DOUBLE PRECISION array, dimension (LDC,N)
          On entry, the m by n matrix C\&.
          On exit, C is overwritten by the matrix H * C if SIDE = 'L',
          or C * H if SIDE = 'R'\&.
.fi
.PP
.br
\fILDC\fP 
.PP
.nf
          LDC is INTEGER
          The leading dimension of the array C\&. LDC >= max(1,M)\&.
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
          WORK is DOUBLE PRECISION array, dimension
                         (N) if SIDE = 'L'
                      or (M) if SIDE = 'R'
.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 slarf (character side, integer m, integer n, real, dimension( * ) v, integer incv, real tau, real, dimension( ldc, * ) c, integer ldc, real, dimension( * ) work)"

.PP
\fBSLARF\fP applies an elementary reflector to a general rectangular matrix\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 SLARF applies a real elementary reflector H to a real m by n matrix
 C, from either the left or the right\&. H is represented in the form

       H = I - tau * v * v**T

 where tau is a real scalar and v is a real vector\&.

 If tau = 0, then H is taken to be the unit matrix\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fISIDE\fP 
.PP
.nf
          SIDE is CHARACTER*1
          = 'L': form  H * C
          = 'R': form  C * H
.fi
.PP
.br
\fIM\fP 
.PP
.nf
          M is INTEGER
          The number of rows of the matrix C\&.
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
          The number of columns of the matrix C\&.
.fi
.PP
.br
\fIV\fP 
.PP
.nf
          V is REAL array, dimension
                     (1 + (M-1)*abs(INCV)) if SIDE = 'L'
                  or (1 + (N-1)*abs(INCV)) if SIDE = 'R'
          The vector v in the representation of H\&. V is not used if
          TAU = 0\&.
.fi
.PP
.br
\fIINCV\fP 
.PP
.nf
          INCV is INTEGER
          The increment between elements of v\&. INCV <> 0\&.
.fi
.PP
.br
\fITAU\fP 
.PP
.nf
          TAU is REAL
          The value tau in the representation of H\&.
.fi
.PP
.br
\fIC\fP 
.PP
.nf
          C is REAL array, dimension (LDC,N)
          On entry, the m by n matrix C\&.
          On exit, C is overwritten by the matrix H * C if SIDE = 'L',
          or C * H if SIDE = 'R'\&.
.fi
.PP
.br
\fILDC\fP 
.PP
.nf
          LDC is INTEGER
          The leading dimension of the array C\&. LDC >= max(1,M)\&.
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
          WORK is REAL array, dimension
                         (N) if SIDE = 'L'
                      or (M) if SIDE = 'R'
.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 zlarf (character side, integer m, integer n, complex*16, dimension( * ) v, integer incv, complex*16 tau, complex*16, dimension( ldc, * ) c, integer ldc, complex*16, dimension( * ) work)"

.PP
\fBZLARF\fP applies an elementary reflector to a general rectangular matrix\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 ZLARF applies a complex elementary reflector H to a complex M-by-N
 matrix C, from either the left or the right\&. H is represented in the
 form

       H = I - tau * v * v**H

 where tau is a complex scalar and v is a complex vector\&.

 If tau = 0, then H is taken to be the unit matrix\&.

 To apply H**H, supply conjg(tau) instead
 tau\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fISIDE\fP 
.PP
.nf
          SIDE is CHARACTER*1
          = 'L': form  H * C
          = 'R': form  C * H
.fi
.PP
.br
\fIM\fP 
.PP
.nf
          M is INTEGER
          The number of rows of the matrix C\&.
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
          The number of columns of the matrix C\&.
.fi
.PP
.br
\fIV\fP 
.PP
.nf
          V is COMPLEX*16 array, dimension
                     (1 + (M-1)*abs(INCV)) if SIDE = 'L'
                  or (1 + (N-1)*abs(INCV)) if SIDE = 'R'
          The vector v in the representation of H\&. V is not used if
          TAU = 0\&.
.fi
.PP
.br
\fIINCV\fP 
.PP
.nf
          INCV is INTEGER
          The increment between elements of v\&. INCV <> 0\&.
.fi
.PP
.br
\fITAU\fP 
.PP
.nf
          TAU is COMPLEX*16
          The value tau in the representation of H\&.
.fi
.PP
.br
\fIC\fP 
.PP
.nf
          C is COMPLEX*16 array, dimension (LDC,N)
          On entry, the M-by-N matrix C\&.
          On exit, C is overwritten by the matrix H * C if SIDE = 'L',
          or C * H if SIDE = 'R'\&.
.fi
.PP
.br
\fILDC\fP 
.PP
.nf
          LDC is INTEGER
          The leading dimension of the array C\&. LDC >= max(1,M)\&.
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
          WORK is COMPLEX*16 array, dimension
                         (N) if SIDE = 'L'
                      or (M) if SIDE = 'R'
.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 
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