#include "ESMF_LapackBlas.inc" !> \brief \b DLASR ! ! =========== DOCUMENTATION =========== ! ! Online html documentation available at ! http://www.netlib.org/lapack/explore-html/ ! !> \htmlonly !> Download DLASR + dependencies !> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlasr.f"> !> [TGZ]</a> !> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlasr.f"> !> [ZIP]</a> !> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlasr.f"> !> [TXT]</a> !> \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 3.4.0) -- ! -- LAPACK is a software package provided by Univ. of Tennessee, -- ! -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- ! November 2011 ! ! .. Scalar Arguments .. CHARACTER DIRECT, PIVOT, SIDE INTEGER LDA, M, N ! .. ! .. Array Arguments .. DOUBLE PRECISION A( LDA, * ), C( * ), S( * ) ! .. ! ! ===================================================================== ! ! .. Parameters .. DOUBLE PRECISION ONE, ZERO PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) ! .. ! .. Local Scalars .. INTEGER I, INFO, J DOUBLE PRECISION CTEMP, STEMP, TEMP ! .. ! .. External Functions .. LOGICAL LSAME EXTERNAL LSAME ! .. ! .. External Subroutines .. EXTERNAL XERBLA ! .. ! .. Intrinsic Functions .. INTRINSIC MAX ! .. ! .. Executable Statements .. ! ! Test the input parameters ! INFO = 0 IF( .NOT.( LSAME( SIDE, 'L' ) .OR. LSAME( SIDE, 'R' ) ) ) THEN INFO = 1 ELSE IF( .NOT.( LSAME( PIVOT, 'V' ) .OR. LSAME( PIVOT, & & 'T' ) .OR. LSAME( PIVOT, 'B' ) ) ) THEN INFO = 2 ELSE IF( .NOT.( LSAME( DIRECT, 'F' ) .OR. LSAME( DIRECT, 'B' ) ) ) & & THEN INFO = 3 ELSE IF( M.LT.0 ) THEN INFO = 4 ELSE IF( N.LT.0 ) THEN INFO = 5 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN INFO = 9 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'DLASR ', INFO ) RETURN END IF ! ! Quick return if possible ! IF( ( M.EQ.0 ) .OR. ( N.EQ.0 ) ) & & RETURN IF( LSAME( SIDE, 'L' ) ) THEN ! ! Form P * A ! IF( LSAME( PIVOT, 'V' ) ) THEN IF( LSAME( DIRECT, 'F' ) ) THEN DO 20 J = 1, M - 1 CTEMP = C( J ) STEMP = S( J ) IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN DO 10 I = 1, N TEMP = A( J+1, I ) A( J+1, I ) = CTEMP*TEMP - STEMP*A( J, I ) A( J, I ) = STEMP*TEMP + CTEMP*A( J, I ) 10 CONTINUE END IF 20 CONTINUE ELSE IF( LSAME( DIRECT, 'B' ) ) THEN DO 40 J = M - 1, 1, -1 CTEMP = C( J ) STEMP = S( J ) IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN DO 30 I = 1, N TEMP = A( J+1, I ) A( J+1, I ) = CTEMP*TEMP - STEMP*A( J, I ) A( J, I ) = STEMP*TEMP + CTEMP*A( J, I ) 30 CONTINUE END IF 40 CONTINUE END IF ELSE IF( LSAME( PIVOT, 'T' ) ) THEN IF( LSAME( DIRECT, 'F' ) ) THEN DO 60 J = 2, M CTEMP = C( J-1 ) STEMP = S( J-1 ) IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN DO 50 I = 1, N TEMP = A( J, I ) A( J, I ) = CTEMP*TEMP - STEMP*A( 1, I ) A( 1, I ) = STEMP*TEMP + CTEMP*A( 1, I ) 50 CONTINUE END IF 60 CONTINUE ELSE IF( LSAME( DIRECT, 'B' ) ) THEN DO 80 J = M, 2, -1 CTEMP = C( J-1 ) STEMP = S( J-1 ) IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN DO 70 I = 1, N TEMP = A( J, I ) A( J, I ) = CTEMP*TEMP - STEMP*A( 1, I ) A( 1, I ) = STEMP*TEMP + CTEMP*A( 1, I ) 70 CONTINUE END IF 80 CONTINUE END IF ELSE IF( LSAME( PIVOT, 'B' ) ) THEN IF( LSAME( DIRECT, 'F' ) ) THEN DO 100 J = 1, M - 1 CTEMP = C( J ) STEMP = S( J ) IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN DO 90 I = 1, N TEMP = A( J, I ) A( J, I ) = STEMP*A( M, I ) + CTEMP*TEMP A( M, I ) = CTEMP*A( M, I ) - STEMP*TEMP 90 CONTINUE END IF 100 CONTINUE ELSE IF( LSAME( DIRECT, 'B' ) ) THEN DO 120 J = M - 1, 1, -1 CTEMP = C( J ) STEMP = S( J ) IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN DO 110 I = 1, N TEMP = A( J, I ) A( J, I ) = STEMP*A( M, I ) + CTEMP*TEMP A( M, I ) = CTEMP*A( M, I ) - STEMP*TEMP 110 CONTINUE END IF 120 CONTINUE END IF END IF ELSE IF( LSAME( SIDE, 'R' ) ) THEN ! ! Form A * P**T ! IF( LSAME( PIVOT, 'V' ) ) THEN IF( LSAME( DIRECT, 'F' ) ) THEN DO 140 J = 1, N - 1 CTEMP = C( J ) STEMP = S( J ) IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN DO 130 I = 1, M TEMP = A( I, J+1 ) A( I, J+1 ) = CTEMP*TEMP - STEMP*A( I, J ) A( I, J ) = STEMP*TEMP + CTEMP*A( I, J ) 130 CONTINUE END IF 140 CONTINUE ELSE IF( LSAME( DIRECT, 'B' ) ) THEN DO 160 J = N - 1, 1, -1 CTEMP = C( J ) STEMP = S( J ) IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN DO 150 I = 1, M TEMP = A( I, J+1 ) A( I, J+1 ) = CTEMP*TEMP - STEMP*A( I, J ) A( I, J ) = STEMP*TEMP + CTEMP*A( I, J ) 150 CONTINUE END IF 160 CONTINUE END IF ELSE IF( LSAME( PIVOT, 'T' ) ) THEN IF( LSAME( DIRECT, 'F' ) ) THEN DO 180 J = 2, N CTEMP = C( J-1 ) STEMP = S( J-1 ) IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN DO 170 I = 1, M TEMP = A( I, J ) A( I, J ) = CTEMP*TEMP - STEMP*A( I, 1 ) A( I, 1 ) = STEMP*TEMP + CTEMP*A( I, 1 ) 170 CONTINUE END IF 180 CONTINUE ELSE IF( LSAME( DIRECT, 'B' ) ) THEN DO 200 J = N, 2, -1 CTEMP = C( J-1 ) STEMP = S( J-1 ) IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN DO 190 I = 1, M TEMP = A( I, J ) A( I, J ) = CTEMP*TEMP - STEMP*A( I, 1 ) A( I, 1 ) = STEMP*TEMP + CTEMP*A( I, 1 ) 190 CONTINUE END IF 200 CONTINUE END IF ELSE IF( LSAME( PIVOT, 'B' ) ) THEN IF( LSAME( DIRECT, 'F' ) ) THEN DO 220 J = 1, N - 1 CTEMP = C( J ) STEMP = S( J ) IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN DO 210 I = 1, M TEMP = A( I, J ) A( I, J ) = STEMP*A( I, N ) + CTEMP*TEMP A( I, N ) = CTEMP*A( I, N ) - STEMP*TEMP 210 CONTINUE END IF 220 CONTINUE ELSE IF( LSAME( DIRECT, 'B' ) ) THEN DO 240 J = N - 1, 1, -1 CTEMP = C( J ) STEMP = S( J ) IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN DO 230 I = 1, M TEMP = A( I, J ) A( I, J ) = STEMP*A( I, N ) + CTEMP*TEMP A( I, N ) = CTEMP*A( I, N ) - STEMP*TEMP 230 CONTINUE END IF 240 CONTINUE END IF END IF END IF ! RETURN ! ! End of DLASR ! END