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NAME
     dlasr - perform the transformation   A := P*A, when  SIDE  =
     'L'  or  'l' ( Left-hand side )   A := A*P', when SIDE = 'R'
     or 'r' ( Right-hand side )  where A is an m by n real matrix
     and P is an orthogonal matrix,

SYNOPSIS
     SUBROUTINE DLASR( SIDE, PIVOT, DIRECT, M, N, C, S, A, LDA )

     CHARACTER DIRECT, PIVOT, SIDE

     INTEGER LDA, M, N

     DOUBLE PRECISION A( LDA, * ), C( * ), S( * )



     #include <sunperf.h>

     void dlasr(char side, char pivot, char direct, int m, int n,
               double *dc, double *s, double *da, intlda);

PURPOSE
     DLASR   performs the transformation consisting of a sequence
     of  plane  rotations  determined by the parameters PIVOT and
     DIRECT as follows ( z = m when SIDE = 'L' or 'l' and z  =  n
     when SIDE = 'R' or 'r' ):

     When  DIRECT = 'F' or 'f'  ( Forward sequence ) then

        P = P( z - 1 )*...*P( 2 )*P( 1 ),

     and when DIRECT = 'B' or 'b'  ( Backward sequence ) then

        P = P( 1 )*P( 2 )*...*P( z - 1 ),

     where  P( k ) is a plane rotation matrix for  the  following
     planes:

        when  PIVOT = 'V' or 'v'  ( Variable pivot ),
           the plane ( k, k + 1 )

        when  PIVOT = 'T' or 't'  ( Top pivot ),
           the plane ( 1, k + 1 )

        when  PIVOT = 'B' or 'b'  ( Bottom pivot ),
           the plane ( k, z )

     c( k ) and s( k )  must contain the  cosine  and  sine  that
     define  the  matrix   P( k ).  The two by two plane rotation
     part of the matrix P( k ), R( k ), is assumed to be  of  the
     form
        R( k ) = (  c( k )  s( k ) ).
                 ( -s( k )  c( k ) )

     This version vectorises across rows of the array A when SIDE
     = 'L'.


ARGUMENTS
     SIDE      (input) 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'

     DIRECT    (input) 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 )

     PIVOT     (input) 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)

     M         (input) INTEGER
               The number of rows of the matrix A.  If m <= 1, an
               immediate return is effected.

     N         (input) INTEGER
               The number of columns of the matrix A.  If n <= 1,
               an immediate return is effected.

               C, S    (input) DOUBLE PRECISION arrays, dimension
               (M-1)  if  SIDE = 'L' (N-1) if SIDE = 'R' c(k) and
               s(k) contain the cosine and sine that  define  the
               matrix  P(k).   The two by two plane rotation part
               of the matrix P(k), R(k), is assumed to be of  the
               form  R( k ) = (  c( k )  s( k ) ).  ( -s( k )  c(
               k ) )

     A         (input/output) DOUBLE PRECISION  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' if SIDE = 'L'.

     LDA       (input) INTEGER
               The leading dimension of  the  array  A.   LDA  >=
               max(1,M).

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