zgemv.f

Go to the documentation of this file.

*> \brief \b ZGEMV
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at
*            http://www.netlib.org/lapack/explore-html/
*
*  Definition:
*  ===========
*
*       SUBROUTINE ZGEMV(TRANS,M,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
*
*       .. Scalar Arguments ..
*       COMPLEX*16 ALPHA,BETA
*       INTEGER INCX,INCY,LDA,M,N
*       CHARACTER TRANS
*       ..
*       .. Array Arguments ..
*       COMPLEX*16 A(LDA,*),X(*),Y(*)
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> ZGEMV  performs one of the matrix-vector operations
*>
*>    y := alpha*A*x + beta*y,   or   y := alpha*A**T*x + beta*y,   or
*>
*>    y := alpha*A**H*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**H*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 COMPLEX*16
*>           On entry, ALPHA specifies the scalar alpha.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*>          A is COMPLEX*16 array, 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 COMPLEX*16 array, 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 COMPLEX*16
*>           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 COMPLEX*16 array, 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.
*>           If either m or n is zero, then Y not referenced and the function
*>           performs a quick return.
*> \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.
*
*> \ingroup gemv
*
*> \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 zgemv(TRANS,M,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
*
*  -- Reference BLAS level2 routine --
*  -- Reference BLAS is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
*     .. Scalar Arguments ..
      COMPLEX*16 ALPHA,BETA
      INTEGER INCX,INCY,LDA,M,N
      CHARACTER TRANS
*     ..
*     .. Array Arguments ..
      COMPLEX*16 A(LDA,*),X(*),Y(*)
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      COMPLEX*16 ONE
      parameter(one= (1.0d+0,0.0d+0))
      COMPLEX*16 ZERO
      parameter(zero= (0.0d+0,0.0d+0))
*     ..
*     .. Local Scalars ..
      COMPLEX*16 TEMP
      INTEGER I,INFO,IX,IY,J,JX,JY,KX,KY,LENX,LENY
      LOGICAL NOCONJ
*     ..
*     .. External Functions ..
      LOGICAL LSAME
      EXTERNAL lsame
*     ..
*     .. External Subroutines ..
      EXTERNAL xerbla
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC dconjg,max
*     ..
*
*     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('ZGEMV ',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
*
      noconj = lsame(trans,'T')
*
*     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
                  temp = alpha*x(jx)
                  DO 50 i = 1,m
                      y(i) = y(i) + temp*a(i,j)
   50             CONTINUE
                  jx = jx + incx
   60         CONTINUE
          ELSE
              DO 80 j = 1,n
                  temp = alpha*x(jx)
                  iy = ky
                  DO 70 i = 1,m
                      y(iy) = y(iy) + temp*a(i,j)
                      iy = iy + incy
   70             CONTINUE
                  jx = jx + incx
   80         CONTINUE
          END IF
      ELSE
*
*        Form  y := alpha*A**T*x + y  or  y := alpha*A**H*x + y.
*
          jy = ky
          IF (incx.EQ.1) THEN
              DO 110 j = 1,n
                  temp = zero
                  IF (noconj) THEN
                      DO 90 i = 1,m
                          temp = temp + a(i,j)*x(i)
   90                 CONTINUE
                  ELSE
                      DO 100 i = 1,m
                          temp = temp + dconjg(a(i,j))*x(i)
  100                 CONTINUE
                  END IF
                  y(jy) = y(jy) + alpha*temp
                  jy = jy + incy
  110         CONTINUE
          ELSE
              DO 140 j = 1,n
                  temp = zero
                  ix = kx
                  IF (noconj) THEN
                      DO 120 i = 1,m
                          temp = temp + a(i,j)*x(ix)
                          ix = ix + incx
  120                 CONTINUE
                  ELSE
                      DO 130 i = 1,m
                          temp = temp + dconjg(a(i,j))*x(ix)
                          ix = ix + incx
  130                 CONTINUE
                  END IF
                  y(jy) = y(jy) + alpha*temp
                  jy = jy + incy
  140         CONTINUE
          END IF
      END IF
*
      RETURN
*
*     End of ZGEMV
*
      END