dlasr(l) [redhat man page]

DLASR(l)								 )								  DLASR(l)

NAME

       DLASR  -  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 real matrix and P is an orthogonal matrix,

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 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 real 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 ) )

       This version vectorises across rows of the array A when SIDE = 'L'.

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)  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) 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' if SIDE = 'L'.

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

LAPACK version 3.0						   15 June 2000 							  DLASR(l)

dlasr.f(3)							      LAPACK								dlasr.f(3)

NAME

       dlasr.f -

SYNOPSIS

   Functions/Subroutines
       subroutine dlasr (SIDE, PIVOT, DIRECT, M, N, C, S, A, LDA)
	   DLASR

Function/Subroutine Documentation
   subroutine dlasr (characterSIDE, characterPIVOT, characterDIRECT, integerM, integerN, double precision, dimension( * )C, double precision,
       dimension( * )S, double precision, dimension( lda, * )A, integerLDA)
       DLASR

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

	   S

		     S is 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

		     A is 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

		     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:
	   November 2011

       Definition at line 200 of file dlasr.f.

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

Version 3.4.1							  Sun May 26 2013							dlasr.f(3)