zlasr.f

          SUBROUTINE ZLASR( SIDE, PIVOT, DIRECT, M, N, C, S, A, LDA )
    *
    *  -- LAPACK auxiliary routine (version 3.1) --
    *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
    *     November 2006
    *
    *     .. Scalar Arguments ..
          CHARACTER          DIRECT, PIVOT, SIDE
          INTEGER            LDA, M, N
    *     ..
    *     .. Array Arguments ..
          DOUBLE PRECISION   C( * ), S( * )
          COMPLEX*16         A( LDA, * )
    *     ..
    *
    *  Purpose
    *  =======
    *
    *  ZLASR applies a sequence of real plane rotations to a complex 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) COMPLEX*16 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 ..
          DOUBLE PRECISION   ONE, ZERO
          PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
    *     ..
    *     .. Local Scalars ..
          INTEGER            I, INFO, J
          DOUBLE PRECISION   CTEMP, STEMP
          COMPLEX*16         TEMP
    *     ..
    *     .. Intrinsic Functions ..
          INTRINSIC          MAX
    *     ..
    *     .. External Functions ..
          LOGICAL            LSAME
          EXTERNAL           LSAME
    *     ..
    *     .. External Subroutines ..
          EXTERNAL           XERBLA
    *     ..
    *     .. 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( 'ZLASR ', 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'
    *
             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 ZLASR
    *
          END