dgemv.f

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      SUBROUTINE dgemv ( TRANS, M, N, ALPHA, A, LDA, X, INCX,
     $                   BETA, Y, INCY )
*     .. Scalar Arguments ..
      DOUBLE PRECISION   ALPHA, BETA
      INTEGER            INCX, INCY, LDA, M, N
      CHARACTER*1        TRANS
*     .. Array Arguments ..
      DOUBLE PRECISION   A( LDA, * ), X( * ), Y( * )
*     ..
*
*  Purpose
*  =======
*
*  DGEMV  performs one of the matrix-vector operations
*
*     y := alpha*A*x + beta*y,   or   y := alpha*A'*x + beta*y,
*
*  where alpha and beta are scalars, x and y are vectors and A is an
*  m by n matrix.
*
*  Parameters
*  ==========
*
*  TRANS  - CHARACTER*1.
*           On entry, TRANS specifies the operation to be performed as
*           follows:
*
*              TRANS = 'N' or 'n'   y := alpha*A*x + beta*y.
*
*              TRANS = 'T' or 't'   y := alpha*A'*x + beta*y.
*
*              TRANS = 'C' or 'c'   y := alpha*A'*x + beta*y.
*
*           Unchanged on exit.
*
*  M      - INTEGER.
*           On entry, M specifies the number of rows of the matrix A.
*           M must be at least zero.
*           Unchanged on exit.
*
*  N      - INTEGER.
*           On entry, N specifies the number of columns of the matrix A.
*           N must be at least zero.
*           Unchanged on exit.
*
*  ALPHA  - DOUBLE PRECISION.
*           On entry, ALPHA specifies the scalar alpha.
*           Unchanged on exit.
*
*  A      - DOUBLE PRECISION array of DIMENSION ( LDA, n ).
*           Before entry, the leading m by n part of the array A must
*           contain the matrix of coefficients.
*           Unchanged on exit.
*
*  LDA    - INTEGER.
*           On entry, LDA specifies the first dimension of A as declared
*           in the calling (sub) program. LDA must be at least
*           max( 1, m ).
*           Unchanged on exit.
*
*  X      - DOUBLE PRECISION array of DIMENSION at least
*           ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n'
*           and at least
*           ( 1 + ( m - 1 )*abs( INCX ) ) otherwise.
*           Before entry, the incremented array X must contain the
*           vector x.
*           Unchanged on exit.
*
*  INCX   - INTEGER.
*           On entry, INCX specifies the increment for the elements of
*           X. INCX must not be zero.
*           Unchanged on exit.
*
*  BETA   - DOUBLE PRECISION.
*           On entry, BETA specifies the scalar beta. When BETA is
*           supplied as zero then Y need not be set on input.
*           Unchanged on exit.
*
*  Y      - DOUBLE PRECISION array of DIMENSION at least
*           ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n'
*           and at least
*           ( 1 + ( n - 1 )*abs( INCY ) ) otherwise.
*           Before entry with BETA non-zero, the incremented array Y
*           must contain the vector y. On exit, Y is overwritten by the
*           updated vector y.
*
*  INCY   - INTEGER.
*           On entry, INCY specifies the increment for the elements of
*           Y. INCY must not be zero.
*           Unchanged on exit.
*
*
*  Level 2 Blas routine.
*
*  -- Written on 22-October-1986.
*     Jack Dongarra, Argonne National Lab.
*     Jeremy Du Croz, Nag Central Office.
*     Sven Hammarling, Nag Central Office.
*     Richard Hanson, Sandia National Labs.
*
*
*     .. Parameters ..
      DOUBLE PRECISION   ONE         , ZERO
      parameter( one = 1.0d+0, zero = 0.0d+0 )
*     .. Local Scalars ..
      DOUBLE PRECISION   TEMP
      INTEGER            I, INFO, IX, IY, J, JX, JY, KX, KY, LENX, LENY
*     .. 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( trans, 'N' ).AND.
     $         .NOT.lsame( trans, 'T' ).AND.
     $         .NOT.lsame( trans, 'C' )      )THEN
         info = 1
      ELSE IF( m.LT.0 )THEN
         info = 2
      ELSE IF( n.LT.0 )THEN
         info = 3
      ELSE IF( lda.LT.max( 1, m ) )THEN
         info = 6
      ELSE IF( incx.EQ.0 )THEN
         info = 8
      ELSE IF( incy.EQ.0 )THEN
         info = 11
      END IF
      IF( info.NE.0 )THEN
         CALL xerbla( 'DGEMV ', info )
         RETURN
      END IF
*
*     Quick return if possible.
*
      IF( ( m.EQ.0 ).OR.( n.EQ.0 ).OR.
     $    ( ( alpha.EQ.zero ).AND.( beta.EQ.one ) ) )
     $   RETURN
*
*     Set  LENX  and  LENY, the lengths of the vectors x and y, and set
*     up the start points in  X  and  Y.
*
      IF( lsame( trans, 'N' ) )THEN
         lenx = n
         leny = m
      ELSE
         lenx = m
         leny = n
      END IF
      IF( incx.GT.0 )THEN
         kx = 1
      ELSE
         kx = 1 - ( lenx - 1 )*incx
      END IF
      IF( incy.GT.0 )THEN
         ky = 1
      ELSE
         ky = 1 - ( leny - 1 )*incy
      END IF
*
*     Start the operations. In this version the elements of A are
*     accessed sequentially with one pass through A.
*
*     First form  y := beta*y.
*
      IF( beta.NE.one )THEN
         IF( incy.EQ.1 )THEN
            IF( beta.EQ.zero )THEN
               DO 10, i = 1, leny
                  y( i ) = zero
   10          CONTINUE
            ELSE
               DO 20, i = 1, leny
                  y( i ) = beta*y( i )
   20          CONTINUE
            END IF
         ELSE
            iy = ky
            IF( beta.EQ.zero )THEN
               DO 30, i = 1, leny
                  y( iy ) = zero
                  iy      = iy   + incy
   30          CONTINUE
            ELSE
               DO 40, i = 1, leny
                  y( iy ) = beta*y( iy )
                  iy      = iy           + incy
   40          CONTINUE
            END IF
         END IF
      END IF
      IF( alpha.EQ.zero )
     $   RETURN
      IF( lsame( trans, 'N' ) )THEN
*
*        Form  y := alpha*A*x + y.
*
         jx = kx
         IF( incy.EQ.1 )THEN
            DO 60, j = 1, n
               IF( x( jx ).NE.zero )THEN
                  temp = alpha*x( jx )
                  DO 50, i = 1, m
                     y( i ) = y( i ) + temp*a( i, j )
   50             CONTINUE
               END IF
               jx = jx + incx
   60       CONTINUE
         ELSE
            DO 80, j = 1, n
               IF( x( jx ).NE.zero )THEN
                  temp = alpha*x( jx )
                  iy   = ky
                  DO 70, i = 1, m
                     y( iy ) = y( iy ) + temp*a( i, j )
                     iy      = iy      + incy
   70             CONTINUE
               END IF
               jx = jx + incx
   80       CONTINUE
         END IF
      ELSE
*
*        Form  y := alpha*A'*x + y.
*
         jy = ky
         IF( incx.EQ.1 )THEN
            DO 100, j = 1, n
               temp = zero
               DO 90, i = 1, m
                  temp = temp + a( i, j )*x( i )
   90          CONTINUE
               y( jy ) = y( jy ) + alpha*temp
               jy      = jy      + incy
  100       CONTINUE
         ELSE
            DO 120, j = 1, n
               temp = zero
               ix   = kx
               DO 110, i = 1, m
                  temp = temp + a( i, j )*x( ix )
                  ix   = ix   + incx
  110          CONTINUE
               y( jy ) = y( jy ) + alpha*temp
               jy      = jy      + incy
  120       CONTINUE
         END IF
      END IF
*
      RETURN
*
*     End of DGEMV .
*
      END