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(*)
! ..
!
! 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.
!
! Arguments
! ==========
!
! 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
! ..
!
! 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 SUBROUTINE DGEMV