--- rpl/lapack/lapack/dlasr.f 2011/07/22 07:38:08 1.8
+++ rpl/lapack/lapack/dlasr.f 2011/11/21 20:42:59 1.9
@@ -1,9 +1,208 @@
+*> \brief \b DLASR
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download DLASR + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
+*> [TXT]
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE DLASR( SIDE, PIVOT, DIRECT, M, N, C, S, A, LDA )
+*
+* .. Scalar Arguments ..
+* CHARACTER DIRECT, PIVOT, SIDE
+* INTEGER LDA, M, N
+* ..
+* .. Array Arguments ..
+* DOUBLE PRECISION A( LDA, * ), C( * ), S( * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> 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.
+*> \endverbatim
+*
+* Arguments:
+* ==========
+*
+*> \param[in] SIDE
+*> \verbatim
+*> 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
+*> \endverbatim
+*>
+*> \param[in] PIVOT
+*> \verbatim
+*> 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)
+*> \endverbatim
+*>
+*> \param[in] DIRECT
+*> \verbatim
+*> 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)
+*> \endverbatim
+*>
+*> \param[in] M
+*> \verbatim
+*> M is INTEGER
+*> The number of rows of the matrix A. If m <= 1, an immediate
+*> return is effected.
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*> N is INTEGER
+*> The number of columns of the matrix A. If n <= 1, an
+*> immediate return is effected.
+*> \endverbatim
+*>
+*> \param[in] C
+*> \verbatim
+*> C is DOUBLE PRECISION array, dimension
+*> (M-1) if SIDE = 'L'
+*> (N-1) if SIDE = 'R'
+*> The cosines c(k) of the plane rotations.
+*> \endverbatim
+*>
+*> \param[in] S
+*> \verbatim
+*> 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) ).
+*> \endverbatim
+*>
+*> \param[in,out] A
+*> \verbatim
+*> 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'.
+*> \endverbatim
+*>
+*> \param[in] LDA
+*> \verbatim
+*> LDA is INTEGER
+*> The leading dimension of the array A. LDA >= max(1,M).
+*> \endverbatim
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date November 2011
+*
+*> \ingroup auxOTHERauxiliary
+*
+* =====================================================================
SUBROUTINE DLASR( SIDE, PIVOT, DIRECT, M, N, C, S, A, LDA )
*
-* -- LAPACK auxiliary routine (version 3.2) --
+* -- LAPACK auxiliary routine (version 3.4.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-* November 2006
+* November 2011
*
* .. Scalar Arguments ..
CHARACTER DIRECT, PIVOT, SIDE
@@ -13,131 +212,6 @@
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
-* performed 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).
-*
* =====================================================================
*
* .. Parameters ..