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RedHat 9 (Linux i386) - man page for clasr (redhat section l)

CLASR(l)					)					 CLASR(l)

NAME
       CLASR - 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 CLASR( SIDE, PIVOT, DIRECT, M, N, C, S, A, LDA )

	   CHARACTER	 DIRECT, PIVOT, SIDE

	   INTEGER	 LDA, M, N

	   REAL 	 C( * ), S( * )

	   COMPLEX	 A( LDA, * )

PURPOSE
       CLASR 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 ) )

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) REAL 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 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).

LAPACK version 3.0			   15 June 2000 				 CLASR(l)


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