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

.in +1c
.ti -1c
.RI "subroutine \fBslasr\fP (SIDE, PIVOT, DIRECT, M, \fBN\fP, C, S, A, \fBLDA\fP)"
.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
\fBDate:\fP
.RS 4
December 2016 
.RE
.PP

.PP
Definition at line 201 of file slasr\&.f\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.
