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