.TH "larfy" 3 "Wed Feb 7 2024 11:30:40" "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
larfy \- larfy: apply Householder reflector symmetrically (2-sided)
.SH SYNOPSIS
.br
.PP
.SS "Functions"

.in +1c
.ti -1c
.RI "subroutine \fBclarfy\fP (uplo, n, v, incv, tau, c, ldc, work)"
.br
.RI "\fBCLARFY\fP "
.ti -1c
.RI "subroutine \fBdlarfy\fP (uplo, n, v, incv, tau, c, ldc, work)"
.br
.RI "\fBDLARFY\fP "
.ti -1c
.RI "subroutine \fBslarfy\fP (uplo, n, v, incv, tau, c, ldc, work)"
.br
.RI "\fBSLARFY\fP "
.ti -1c
.RI "subroutine \fBzlarfy\fP (uplo, n, v, incv, tau, c, ldc, work)"
.br
.RI "\fBZLARFY\fP "
.in -1c
.SH "Detailed Description"
.PP 

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

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

.PP
.nf
 CLARFY applies an elementary reflector, or Householder matrix, H,
 to an n x n Hermitian matrix C, from both the left and the right\&.

 H is represented in the form

    H = I - tau * v * v'

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

 If  tau  is  zero, then  H  is taken to be the unit matrix\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIUPLO\fP 
.PP
.nf
          UPLO is CHARACTER*1
          Specifies whether the upper or lower triangular part of the
          Hermitian matrix C is stored\&.
          = 'U':  Upper triangle
          = 'L':  Lower triangle
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
          The number of rows and columns of the matrix C\&.  N >= 0\&.
.fi
.PP
.br
\fIV\fP 
.PP
.nf
          V is COMPLEX array, dimension
                  (1 + (N-1)*abs(INCV))
          The vector v as described above\&.
.fi
.PP
.br
\fIINCV\fP 
.PP
.nf
          INCV is INTEGER
          The increment between successive elements of v\&.  INCV must
          not be zero\&.
.fi
.PP
.br
\fITAU\fP 
.PP
.nf
          TAU is COMPLEX
          The value tau as described above\&.
.fi
.PP
.br
\fIC\fP 
.PP
.nf
          C is COMPLEX array, dimension (LDC, N)
          On entry, the matrix C\&.
          On exit, C is overwritten by H * C * H'\&.
.fi
.PP
.br
\fILDC\fP 
.PP
.nf
          LDC is INTEGER
          The leading dimension of the array C\&.  LDC >= max( 1, N )\&.
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
          WORK is COMPLEX array, dimension (N)
.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 dlarfy (character uplo, integer n, double precision, dimension( * ) v, integer incv, double precision tau, double precision, dimension( ldc, * ) c, integer ldc, double precision, dimension( * ) work)"

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

.PP
.nf
 DLARFY applies an elementary reflector, or Householder matrix, H,
 to an n x n symmetric matrix C, from both the left and the right\&.

 H is represented in the form

    H = I - tau * v * v'

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

 If  tau  is  zero, then  H  is taken to be the unit matrix\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIUPLO\fP 
.PP
.nf
          UPLO is CHARACTER*1
          Specifies whether the upper or lower triangular part of the
          symmetric matrix C is stored\&.
          = 'U':  Upper triangle
          = 'L':  Lower triangle
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
          The number of rows and columns of the matrix C\&.  N >= 0\&.
.fi
.PP
.br
\fIV\fP 
.PP
.nf
          V is DOUBLE PRECISION array, dimension
                  (1 + (N-1)*abs(INCV))
          The vector v as described above\&.
.fi
.PP
.br
\fIINCV\fP 
.PP
.nf
          INCV is INTEGER
          The increment between successive elements of v\&.  INCV must
          not be zero\&.
.fi
.PP
.br
\fITAU\fP 
.PP
.nf
          TAU is DOUBLE PRECISION
          The value tau as described above\&.
.fi
.PP
.br
\fIC\fP 
.PP
.nf
          C is DOUBLE PRECISION array, dimension (LDC, N)
          On entry, the matrix C\&.
          On exit, C is overwritten by H * C * H'\&.
.fi
.PP
.br
\fILDC\fP 
.PP
.nf
          LDC is INTEGER
          The leading dimension of the array C\&.  LDC >= max( 1, N )\&.
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
          WORK is DOUBLE PRECISION array, dimension (N)
.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 slarfy (character uplo, integer n, real, dimension( * ) v, integer incv, real tau, real, dimension( ldc, * ) c, integer ldc, real, dimension( * ) work)"

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

.PP
.nf
 SLARFY applies an elementary reflector, or Householder matrix, H,
 to an n x n symmetric matrix C, from both the left and the right\&.

 H is represented in the form

    H = I - tau * v * v'

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

 If  tau  is  zero, then  H  is taken to be the unit matrix\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIUPLO\fP 
.PP
.nf
          UPLO is CHARACTER*1
          Specifies whether the upper or lower triangular part of the
          symmetric matrix C is stored\&.
          = 'U':  Upper triangle
          = 'L':  Lower triangle
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
          The number of rows and columns of the matrix C\&.  N >= 0\&.
.fi
.PP
.br
\fIV\fP 
.PP
.nf
          V is REAL array, dimension
                  (1 + (N-1)*abs(INCV))
          The vector v as described above\&.
.fi
.PP
.br
\fIINCV\fP 
.PP
.nf
          INCV is INTEGER
          The increment between successive elements of v\&.  INCV must
          not be zero\&.
.fi
.PP
.br
\fITAU\fP 
.PP
.nf
          TAU is REAL
          The value tau as described above\&.
.fi
.PP
.br
\fIC\fP 
.PP
.nf
          C is REAL array, dimension (LDC, N)
          On entry, the matrix C\&.
          On exit, C is overwritten by H * C * H'\&.
.fi
.PP
.br
\fILDC\fP 
.PP
.nf
          LDC is INTEGER
          The leading dimension of the array C\&.  LDC >= max( 1, N )\&.
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
          WORK is REAL array, dimension (N)
.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 zlarfy (character uplo, integer n, complex*16, dimension( * ) v, integer incv, complex*16 tau, complex*16, dimension( ldc, * ) c, integer ldc, complex*16, dimension( * ) work)"

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

.PP
.nf
 ZLARFY applies an elementary reflector, or Householder matrix, H,
 to an n x n Hermitian matrix C, from both the left and the right\&.

 H is represented in the form

    H = I - tau * v * v'

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

 If  tau  is  zero, then  H  is taken to be the unit matrix\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIUPLO\fP 
.PP
.nf
          UPLO is CHARACTER*1
          Specifies whether the upper or lower triangular part of the
          Hermitian matrix C is stored\&.
          = 'U':  Upper triangle
          = 'L':  Lower triangle
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
          The number of rows and columns of the matrix C\&.  N >= 0\&.
.fi
.PP
.br
\fIV\fP 
.PP
.nf
          V is COMPLEX*16 array, dimension
                  (1 + (N-1)*abs(INCV))
          The vector v as described above\&.
.fi
.PP
.br
\fIINCV\fP 
.PP
.nf
          INCV is INTEGER
          The increment between successive elements of v\&.  INCV must
          not be zero\&.
.fi
.PP
.br
\fITAU\fP 
.PP
.nf
          TAU is COMPLEX*16
          The value tau as described above\&.
.fi
.PP
.br
\fIC\fP 
.PP
.nf
          C is COMPLEX*16 array, dimension (LDC, N)
          On entry, the matrix C\&.
          On exit, C is overwritten by H * C * H'\&.
.fi
.PP
.br
\fILDC\fP 
.PP
.nf
          LDC is INTEGER
          The leading dimension of the array C\&.  LDC >= max( 1, N )\&.
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
          WORK is COMPLEX*16 array, dimension (N)
.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\&.