*> \brief \b DGEMV
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 
*
*  Definition:
*  ===========
*
*       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 TRANS
*       ..
*       .. Array Arguments ..
*       DOUBLE PRECISION A(LDA,*),X(*),Y(*)
*       ..
*  
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> DGEMV  performs one of the matrix-vector operations
*>
*>    y := alpha*A*x + beta*y,   or   y := alpha*A**T*x + beta*y,
*>
*> where alpha and beta are scalars, x and y are vectors and A is an
*> m by n matrix.
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] TRANS
*> \verbatim
*>          TRANS is 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**T*x + beta*y.
*>
*>              TRANS = 'C' or 'c'   y := alpha*A**T*x + beta*y.
*> \endverbatim
*>
*> \param[in] M
*> \verbatim
*>          M is INTEGER
*>           On entry, M specifies the number of rows of the matrix A.
*>           M must be at least zero.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*>          N is INTEGER
*>           On entry, N specifies the number of columns of the matrix A.
*>           N must be at least zero.
*> \endverbatim
*>
*> \param[in] ALPHA
*> \verbatim
*>          ALPHA is DOUBLE PRECISION.
*>           On entry, ALPHA specifies the scalar alpha.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*>          A is 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.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*>          LDA is 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 ).
*> \endverbatim
*>
*> \param[in] X
*> \verbatim
*>          X is 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.
*> \endverbatim
*>
*> \param[in] INCX
*> \verbatim
*>          INCX is INTEGER
*>           On entry, INCX specifies the increment for the elements of
*>           X. INCX must not be zero.
*> \endverbatim
*>
*> \param[in] BETA
*> \verbatim
*>          BETA is DOUBLE PRECISION.
*>           On entry, BETA specifies the scalar beta. When BETA is
*>           supplied as zero then Y need not be set on input.
*> \endverbatim
*>
*> \param[in,out] Y
*> \verbatim
*>          Y is 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.
*> \endverbatim
*>
*> \param[in] INCY
*> \verbatim
*>          INCY is INTEGER
*>           On entry, INCY specifies the increment for the elements of
*>           Y. INCY must not be zero.
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date November 2011
*
*> \ingroup double_blas_level2
*
*> \par Further Details:
*  =====================
*>
*> \verbatim
*>
*>  Level 2 Blas routine.
*>  The vector and matrix arguments are not referenced when N = 0, or M = 0
*>
*>  -- 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.
*> \endverbatim
*>
*  =====================================================================
      SUBROUTINE GAL_DGEMV(TRANS,M,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
*
*  -- Reference BLAS level2 routine (version 3.4.0) --
*  -- Reference BLAS is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     November 2011
*
*     .. Scalar Arguments ..
      DOUBLE PRECISION ALPHA,BETA
      INTEGER INCX,INCY,LDA,M,N
      CHARACTERTRANS
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION A(LDA,*),X(*),Y(*)
*     ..
*
*  =====================================================================
*
*     .. 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 GAL_LSAME
      EXTERNAL GAL_LSAME
*     ..
*     .. External Subroutines ..
      EXTERNAL GAL_XERBLA
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC MAX
*     ..
*
*     Test the input parameters.
*
      INFO=0
      IF(.NOT.GAL_LSAME(TRANS,'N').AND..NOT.GAL_LSAME(TRANS,'T').AND.
     +.NOT.GAL_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 GAL_XERBLA('GAL_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(GAL_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 10I=1,LENY
      Y(I)=ZERO
   10 CONTINUE
      ELSE 
      DO 20I=1,LENY
      Y(I)=BETA*Y(I)
   20 CONTINUE
      END IF
      ELSE 
      IY=KY
      IF(BETA.EQ.ZERO)THEN
      DO 30I=1,LENY
      Y(IY)=ZERO
      IY=IY+INCY
   30 CONTINUE
      ELSE 
      DO 40I=1,LENY
      Y(IY)=BETA*Y(IY)
      IY=IY+INCY
   40 CONTINUE
      END IF
      END IF
      END IF
      IF(ALPHA.EQ.ZERO)RETURN
      IF(GAL_LSAME(TRANS,'N'))THEN
*
*        Form  y := alpha*A*x + y.
*
      JX=KX
      IF(INCY.EQ.1)THEN
      DO 60J=1,N
      IF(X(JX).NE.ZERO)THEN
      TEMP=ALPHA*X(JX)
      DO 50I=1,M
      Y(I)=Y(I)+TEMP*A(I,J)
   50 CONTINUE
      END IF
      JX=JX+INCX
   60 CONTINUE
      ELSE 
      DO 80J=1,N
      IF(X(JX).NE.ZERO)THEN
      TEMP=ALPHA*X(JX)
      IY=KY
      DO 70I=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**T*x + y.
*
      JY=KY
      IF(INCX.EQ.1)THEN
      DO 100J=1,N
      TEMP=ZERO
      DO 90I=1,M
      TEMP=TEMP+A(I,J)*X(I)
   90 CONTINUE
      Y(JY)=Y(JY)+ALPHA*TEMP
      JY=JY+INCY
  100 CONTINUE
      ELSE 
      DO 120J=1,N
      TEMP=ZERO
      IX=KX
      DO 110I=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 
