\brief \b ESMF_DLASR \htmlonly Download ESMF_DLASR + dependencies [TGZ] [ZIP] [TXT] \endhtmlonly \par Purpose:
\verbatim
ESMF_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 := AP*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 \param[in] SIDE \verbatim SIDE is CHARACTER1 Specifies whether the plane rotation matrix P is applied to A on the left or the right. = ‘L’: Left, compute A := PA = ‘R’: Right, compute A:= AP*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 CHARACTER1 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 PA if SIDE = ‘R’ or by AP**T if SIDE = ‘L’. \endverbatim
\param[in] LDA \verbatim LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M). \endverbatim \author Univ. of Tennessee \author Univ. of California Berkeley \author Univ. of Colorado Denver \author NAG Ltd. \date November 2011 \ingroup auxOTHERauxiliary
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| character(len=1) | :: | SIDE | ||||
| character(len=1) | :: | PIVOT | ||||
| character(len=1) | :: | DIRECT | ||||
| integer | :: | M | ||||
| integer | :: | N | ||||
| double precision | :: | C(*) | ||||
| double precision | :: | S(*) | ||||
| double precision | :: | A(LDA,*) | ||||
| integer | :: | LDA |