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dlasr examples
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Man Page Details
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NAME
       DLASR - a sequence of plane rotations to a real matrix A,

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( * )

  Purpose
  =======

  DLASR   performs 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,
  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).

