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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  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 per-
       formed without ever forming P(k) explicitly.


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**T

       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)

       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)

       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       (input) DOUBLE PRECISION array, dimension
               (M-1) if SIDE = 'L' (N-1) if SIDE = 'R' The cosines c(k) of the
               plane rotations.

       S       (input) DOUBLE PRECISION 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)
               ).

       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**T if SIDE = 'L'.

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

