zgemv()

subroutine zgemv	(	character	trans,
		integer	m,
		integer	n,
		complex*16	alpha,
		complex*16, dimension(lda,*)	a,
		integer	lda,
		complex*16, dimension(*)	x,
		integer	incx,
		complex*16	beta,
		complex*16, dimension(*)	y,
		integer	incy
	)

ZGEMV

Purpose:

 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.

Parameters

[in]	TRANS	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.
[in]	M	M is INTEGER On entry, M specifies the number of rows of the matrix A. M must be at least zero.
[in]	N	N is INTEGER On entry, N specifies the number of columns of the matrix A. N must be at least zero.
[in]	ALPHA	ALPHA is COMPLEX*16 On entry, ALPHA specifies the scalar alpha.
[in]	A	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.
[in]	LDA	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 ).
[in]	X	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.
[in]	INCX	INCX is INTEGER On entry, INCX specifies the increment for the elements of X. INCX must not be zero.
[in]	BETA	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.
[in,out]	Y	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.
[in]	INCY	INCY is INTEGER On entry, INCY specifies the increment for the elements of Y. INCY must not be zero.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

  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.

Definition at line 159 of file zgemv.f.

*
*  -- 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
*

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