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clasr.f(3)				      LAPACK				       clasr.f(3)

NAME
       clasr.f -

SYNOPSIS
   Functions/Subroutines
       subroutine clasr (SIDE, PIVOT, DIRECT, M, N, C, S, A, LDA)
	   CLASR applies a sequence of plane rotations to a general rectangular matrix.

Function/Subroutine Documentation
   subroutine clasr (characterSIDE, characterPIVOT, characterDIRECT, integerM, integerN, real,
       dimension( * )C, real, dimension( * )S, complex, dimension( lda, * )A, integerLDA)
       CLASR applies a sequence of plane rotations to a general rectangular matrix.

       Purpose:

	    CLASR applies a sequence of real plane rotations to a complex 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
	    performed without ever forming P(k) explicitly.

       Parameters:
	   SIDE

		     SIDE is 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

		     PIVOT is 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

		     DIRECT is 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

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

	   N

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

	   C

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

	   S

		     S is REAL 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

		     A is 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**T if SIDE = 'L'.

	   LDA

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

       Author:
	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

       Date:
	   September 2012

       Definition at line 201 of file clasr.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2				 Tue Sep 25 2012			       clasr.f(3)
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