*> \brief \b SLASR applies a sequence of plane rotations to a general rectangular matrix. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download SLASR + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE SLASR( SIDE, PIVOT, DIRECT, M, N, C, S, A, LDA ) * * .. Scalar Arguments .. * CHARACTER DIRECT, PIVOT, SIDE * INTEGER LDA, M, N * .. * .. Array Arguments .. * REAL A( LDA, * ), C( * ), S( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> SLASR 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 REAL 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 REAL 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 REAL 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 December 2016 * *> \ingroup OTHERauxiliary * * ===================================================================== SUBROUTINE SLASR( SIDE, PIVOT, DIRECT, M, N, C, S, A, LDA ) * * -- LAPACK auxiliary routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. CHARACTER DIRECT, PIVOT, SIDE INTEGER LDA, M, N * .. * .. Array Arguments .. REAL A( LDA, * ), C( * ), S( * ) * .. * * ===================================================================== * * .. Parameters .. REAL ONE, ZERO PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 ) * .. * .. Local Scalars .. INTEGER I, INFO, J REAL 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( 'SLASR ', 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 SLASR * END