clasr(l) [redhat man page]

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)

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)