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C DLASR     SOURCE    BP208322  18/07/10    21:15:19     9872           *> \brief \b DLASR 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 DLASR + dependencies*> &lt;a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlasr.f">*> [TGZ]&lt;/a>*> &lt;a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlasr.f">*> [ZIP]&lt;/a>*> &lt;a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlasr.f">*> [TXT]&lt;/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 ..*       REAL*8   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 &lt;= 1, an immediate*>          return is effected.*> \endverbatim*>*> \param[in] N*> \verbatim*>          N is INTEGER*>          The number of columns of the matrix A.  If n &lt;= 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 December 2016**> \ingroup OTHERauxiliary**  =====================================================================      SUBROUTINE DLASR( 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*8   A( LDA, * ), C( * ), S( * )*     ..**  =====================================================================**     .. Parameters ..      REAL*8   ONE, ZERO      PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )*     ..*     .. Local Scalars ..      INTEGER            I, INFO, J      REAL*8   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

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