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

.in +1c
.ti -1c
.RI "subroutine \fBslasr\fP (side, pivot, direct, m, n, c, s, a, lda)"
.br
.RI "\fBSLASR\fP applies a sequence of plane rotations to a general rectangular matrix\&. "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine slasr (character side, character pivot, character direct, integer m, integer n, real, dimension( * ) c, real, dimension( * ) s, real, dimension( lda, * ) a, integer lda)"

.PP
\fBSLASR\fP applies a sequence of plane rotations to a general rectangular matrix\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
!>
!> SLASR applies a sequence of plane rotations to a real matrix A,
!> from either the left or the right\&.
!>
!> When SIDE = 'L', the transformation takes the form
!>
!>    A := P*A
!>
!> and when SIDE = 'R', the transformation takes the form
!>
!>    A := A*P**T
!>
!> where P is an orthogonal matrix consisting of a sequence of z plane
!> rotations, with z = M when SIDE = 'L' and z = N when SIDE = 'R',
!> and P**T is the transpose of P\&.
!>
!> When DIRECT = 'F' (Forward sequence), then
!>
!>    P = P(z-1) * \&.\&.\&. * P(2) * P(1)
!>
!> and when DIRECT = 'B' (Backward sequence), then
!>
!>    P = P(1) * P(2) * \&.\&.\&. * P(z-1)
!>
!> where P(k) is a plane rotation matrix defined by the 2-by-2 rotation
!>
!>    R(k) = (  c(k)  s(k) )
!>         = ( -s(k)  c(k) )\&.
!>
!> When PIVOT = 'V' (Variable pivot), the rotation is performed
!> for the plane (k,k+1), i\&.e\&., P(k) has the form
!>
!>    P(k) = (  1                                            )
!>           (       \&.\&.\&.                                     )
!>           (              1                                )
!>           (                   c(k)  s(k)                  )
!>           (                  -s(k)  c(k)                  )
!>           (                                1              )
!>           (                                     \&.\&.\&.       )
!>           (                                            1  )
!>
!> where R(k) appears as a rank-2 modification to the identity matrix in
!> rows and columns k and k+1\&.
!>
!> When PIVOT = 'T' (Top pivot), the rotation is performed for the
!> plane (1,k+1), so P(k) has the form
!>
!>    P(k) = (  c(k)                    s(k)                 )
!>           (         1                                     )
!>           (              \&.\&.\&.                              )
!>           (                     1                         )
!>           ( -s(k)                    c(k)                 )
!>           (                                 1             )
!>           (                                      \&.\&.\&.      )
!>           (                                             1 )
!>
!> where R(k) appears in rows and columns 1 and k+1\&.
!>
!> Similarly, when PIVOT = 'B' (Bottom pivot), the rotation is
!> performed for the plane (k,z), giving P(k) the form
!>
!>    P(k) = ( 1                                             )
!>           (      \&.\&.\&.                                      )
!>           (             1                                 )
!>           (                  c(k)                    s(k) )
!>           (                         1                     )
!>           (                              \&.\&.\&.              )
!>           (                                     1         )
!>           (                 -s(k)                    c(k) )
!>
!> where R(k) appears in rows and columns k and z\&.  The rotations are
!> performed without ever forming P(k) explicitly\&.
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fISIDE\fP 
.PP
.nf
!>          SIDE is CHARACTER*1
!>          Specifies whether the plane rotation matrix P is applied to
!>          A on the left or the right\&.
!>          = 'L':  Left, compute A := P*A
!>          = 'R':  Right, compute A:= A*P**T
!> 
.fi
.PP
.br
\fIPIVOT\fP 
.PP
.nf
!>          PIVOT is CHARACTER*1
!>          Specifies the plane for which P(k) is a plane rotation
!>          matrix\&.
!>          = 'V':  Variable pivot, the plane (k,k+1)
!>          = 'T':  Top pivot, the plane (1,k+1)
!>          = 'B':  Bottom pivot, the plane (k,z)
!> 
.fi
.PP
.br
\fIDIRECT\fP 
.PP
.nf
!>          DIRECT is CHARACTER*1
!>          Specifies whether P is a forward or backward sequence of
!>          plane rotations\&.
!>          = 'F':  Forward, P = P(z-1)*\&.\&.\&.*P(2)*P(1)
!>          = 'B':  Backward, P = P(1)*P(2)*\&.\&.\&.*P(z-1)
!> 
.fi
.PP
.br
\fIM\fP 
.PP
.nf
!>          M is INTEGER
!>          The number of rows of the matrix A\&.  If m <= 1, an immediate
!>          return is effected\&.
!> 
.fi
.PP
.br
\fIN\fP 
.PP
.nf
!>          N is INTEGER
!>          The number of columns of the matrix A\&.  If n <= 1, an
!>          immediate return is effected\&.
!> 
.fi
.PP
.br
\fIC\fP 
.PP
.nf
!>          C is REAL array, dimension
!>                  (M-1) if SIDE = 'L'
!>                  (N-1) if SIDE = 'R'
!>          The cosines c(k) of the plane rotations\&.
!> 
.fi
.PP
.br
\fIS\fP 
.PP
.nf
!>          S is REAL array, dimension
!>                  (M-1) if SIDE = 'L'
!>                  (N-1) if SIDE = 'R'
!>          The sines s(k) of the plane rotations\&.  The 2-by-2 plane
!>          rotation part of the matrix P(k), R(k), has the form
!>          R(k) = (  c(k)  s(k) )
!>                 ( -s(k)  c(k) )\&.
!> 
.fi
.PP
.br
\fIA\fP 
.PP
.nf
!>          A is REAL array, dimension (LDA,N)
!>          The M-by-N matrix A\&.  On exit, A is overwritten by P*A if
!>          SIDE = 'R' or by A*P**T if SIDE = 'L'\&.
!> 
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
!>          LDA is INTEGER
!>          The leading dimension of the array A\&.  LDA >= max(1,M)\&.
!> 
.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 \fB198\fP of file \fBslasr\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.