dlasr man page on Scientific

```DLASR(1)	    LAPACK auxiliary routine (version 3.2)	      DLASR(1)

NAME
DLASR - applies a sequence of plane rotations to a real matrix A,

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  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 per‐
formed without ever forming P(k) explicitly.

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**T

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)

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)

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

S       (input) 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       (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**T if SIDE = 'L'.

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

LAPACK auxiliary routine (versioNovember 2008			      DLASR(1)
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