ZLASR  - 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 complex
       matrix and P is an orthogonal matrix,


SYNOPSIS

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

           CHARACTER     DIRECT, PIVOT, SIDE

           INTEGER       LDA, M, N

           DOUBLE        PRECISION C( * ), S( * )

           COMPLEX*16    A( LDA, * )


PURPOSE

       ZLASR  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 complex
       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 ) )

       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) COMPLEX*16 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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