LAPACK: BLAS/SRC/dgemv.f Source File

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00001       SUBROUTINE DGEMV(TRANS,M,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
00002 *     .. Scalar Arguments ..
00003       DOUBLE PRECISION ALPHA,BETA
00004       INTEGER INCX,INCY,LDA,M,N
00005       CHARACTER TRANS
00006 *     ..
00007 *     .. Array Arguments ..
00008       DOUBLE PRECISION A(LDA,*),X(*),Y(*)
00009 *     ..
00010 *
00011 *  Purpose
00012 *  =======
00013 *
00014 *  DGEMV  performs one of the matrix-vector operations
00015 *
00016 *     y := alpha*A*x + beta*y,   or   y := alpha*A'*x + beta*y,
00017 *
00018 *  where alpha and beta are scalars, x and y are vectors and A is an
00019 *  m by n matrix.
00020 *
00021 *  Arguments
00022 *  ==========
00023 *
00024 *  TRANS  - CHARACTER*1.
00025 *           On entry, TRANS specifies the operation to be performed as
00026 *           follows:
00027 *
00028 *              TRANS = 'N' or 'n'   y := alpha*A*x + beta*y.
00029 *
00030 *              TRANS = 'T' or 't'   y := alpha*A'*x + beta*y.
00031 *
00032 *              TRANS = 'C' or 'c'   y := alpha*A'*x + beta*y.
00033 *
00034 *           Unchanged on exit.
00035 *
00036 *  M      - INTEGER.
00037 *           On entry, M specifies the number of rows of the matrix A.
00038 *           M must be at least zero.
00039 *           Unchanged on exit.
00040 *
00041 *  N      - INTEGER.
00042 *           On entry, N specifies the number of columns of the matrix A.
00043 *           N must be at least zero.
00044 *           Unchanged on exit.
00045 *
00046 *  ALPHA  - DOUBLE PRECISION.
00047 *           On entry, ALPHA specifies the scalar alpha.
00048 *           Unchanged on exit.
00049 *
00050 *  A      - DOUBLE PRECISION array of DIMENSION ( LDA, n ).
00051 *           Before entry, the leading m by n part of the array A must
00052 *           contain the matrix of coefficients.
00053 *           Unchanged on exit.
00054 *
00055 *  LDA    - INTEGER.
00056 *           On entry, LDA specifies the first dimension of A as declared
00057 *           in the calling (sub) program. LDA must be at least
00058 *           max( 1, m ).
00059 *           Unchanged on exit.
00060 *
00061 *  X      - DOUBLE PRECISION array of DIMENSION at least
00062 *           ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n'
00063 *           and at least
00064 *           ( 1 + ( m - 1 )*abs( INCX ) ) otherwise.
00065 *           Before entry, the incremented array X must contain the
00066 *           vector x.
00067 *           Unchanged on exit.
00068 *
00069 *  INCX   - INTEGER.
00070 *           On entry, INCX specifies the increment for the elements of
00071 *           X. INCX must not be zero.
00072 *           Unchanged on exit.
00073 *
00074 *  BETA   - DOUBLE PRECISION.
00075 *           On entry, BETA specifies the scalar beta. When BETA is
00076 *           supplied as zero then Y need not be set on input.
00077 *           Unchanged on exit.
00078 *
00079 *  Y      - DOUBLE PRECISION array of DIMENSION at least
00080 *           ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n'
00081 *           and at least
00082 *           ( 1 + ( n - 1 )*abs( INCY ) ) otherwise.
00083 *           Before entry with BETA non-zero, the incremented array Y
00084 *           must contain the vector y. On exit, Y is overwritten by the
00085 *           updated vector y.
00086 *
00087 *  INCY   - INTEGER.
00088 *           On entry, INCY specifies the increment for the elements of
00089 *           Y. INCY must not be zero.
00090 *           Unchanged on exit.
00091 *
00092 *  Further Details
00093 *  ===============
00094 *
00095 *  Level 2 Blas routine.
00096 *
00097 *  -- Written on 22-October-1986.
00098 *     Jack Dongarra, Argonne National Lab.
00099 *     Jeremy Du Croz, Nag Central Office.
00100 *     Sven Hammarling, Nag Central Office.
00101 *     Richard Hanson, Sandia National Labs.
00102 *
00103 *  =====================================================================
00104 *
00105 *     .. Parameters ..
00106       DOUBLE PRECISION ONE,ZERO
00107       PARAMETER (ONE=1.0D+0,ZERO=0.0D+0)
00108 *     ..
00109 *     .. Local Scalars ..
00110       DOUBLE PRECISION TEMP
00111       INTEGER I,INFO,IX,IY,J,JX,JY,KX,KY,LENX,LENY
00112 *     ..
00113 *     .. External Functions ..
00114       LOGICAL LSAME
00115       EXTERNAL LSAME
00116 *     ..
00117 *     .. External Subroutines ..
00118       EXTERNAL XERBLA
00119 *     ..
00120 *     .. Intrinsic Functions ..
00121       INTRINSIC MAX
00122 *     ..
00123 *
00124 *     Test the input parameters.
00125 *
00126       INFO = 0
00127       IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND.
00128      +    .NOT.LSAME(TRANS,'C')) THEN
00129           INFO = 1
00130       ELSE IF (M.LT.0) THEN
00131           INFO = 2
00132       ELSE IF (N.LT.0) THEN
00133           INFO = 3
00134       ELSE IF (LDA.LT.MAX(1,M)) THEN
00135           INFO = 6
00136       ELSE IF (INCX.EQ.0) THEN
00137           INFO = 8
00138       ELSE IF (INCY.EQ.0) THEN
00139           INFO = 11
00140       END IF
00141       IF (INFO.NE.0) THEN
00142           CALL XERBLA('DGEMV ',INFO)
00143           RETURN
00144       END IF
00145 *
00146 *     Quick return if possible.
00147 *
00148       IF ((M.EQ.0) .OR. (N.EQ.0) .OR.
00149      +    ((ALPHA.EQ.ZERO).AND. (BETA.EQ.ONE))) RETURN
00150 *
00151 *     Set  LENX  and  LENY, the lengths of the vectors x and y, and set
00152 *     up the start points in  X  and  Y.
00153 *
00154       IF (LSAME(TRANS,'N')) THEN
00155           LENX = N
00156           LENY = M
00157       ELSE
00158           LENX = M
00159           LENY = N
00160       END IF
00161       IF (INCX.GT.0) THEN
00162           KX = 1
00163       ELSE
00164           KX = 1 - (LENX-1)*INCX
00165       END IF
00166       IF (INCY.GT.0) THEN
00167           KY = 1
00168       ELSE
00169           KY = 1 - (LENY-1)*INCY
00170       END IF
00171 *
00172 *     Start the operations. In this version the elements of A are
00173 *     accessed sequentially with one pass through A.
00174 *
00175 *     First form  y := beta*y.
00176 *
00177       IF (BETA.NE.ONE) THEN
00178           IF (INCY.EQ.1) THEN
00179               IF (BETA.EQ.ZERO) THEN
00180                   DO 10 I = 1,LENY
00181                       Y(I) = ZERO
00182    10             CONTINUE
00183               ELSE
00184                   DO 20 I = 1,LENY
00185                       Y(I) = BETA*Y(I)
00186    20             CONTINUE
00187               END IF
00188           ELSE
00189               IY = KY
00190               IF (BETA.EQ.ZERO) THEN
00191                   DO 30 I = 1,LENY
00192                       Y(IY) = ZERO
00193                       IY = IY + INCY
00194    30             CONTINUE
00195               ELSE
00196                   DO 40 I = 1,LENY
00197                       Y(IY) = BETA*Y(IY)
00198                       IY = IY + INCY
00199    40             CONTINUE
00200               END IF
00201           END IF
00202       END IF
00203       IF (ALPHA.EQ.ZERO) RETURN
00204       IF (LSAME(TRANS,'N')) THEN
00205 *
00206 *        Form  y := alpha*A*x + y.
00207 *
00208           JX = KX
00209           IF (INCY.EQ.1) THEN
00210               DO 60 J = 1,N
00211                   IF (X(JX).NE.ZERO) THEN
00212                       TEMP = ALPHA*X(JX)
00213                       DO 50 I = 1,M
00214                           Y(I) = Y(I) + TEMP*A(I,J)
00215    50                 CONTINUE
00216                   END IF
00217                   JX = JX + INCX
00218    60         CONTINUE
00219           ELSE
00220               DO 80 J = 1,N
00221                   IF (X(JX).NE.ZERO) THEN
00222                       TEMP = ALPHA*X(JX)
00223                       IY = KY
00224                       DO 70 I = 1,M
00225                           Y(IY) = Y(IY) + TEMP*A(I,J)
00226                           IY = IY + INCY
00227    70                 CONTINUE
00228                   END IF
00229                   JX = JX + INCX
00230    80         CONTINUE
00231           END IF
00232       ELSE
00233 *
00234 *        Form  y := alpha*A'*x + y.
00235 *
00236           JY = KY
00237           IF (INCX.EQ.1) THEN
00238               DO 100 J = 1,N
00239                   TEMP = ZERO
00240                   DO 90 I = 1,M
00241                       TEMP = TEMP + A(I,J)*X(I)
00242    90             CONTINUE
00243                   Y(JY) = Y(JY) + ALPHA*TEMP
00244                   JY = JY + INCY
00245   100         CONTINUE
00246           ELSE
00247               DO 120 J = 1,N
00248                   TEMP = ZERO
00249                   IX = KX
00250                   DO 110 I = 1,M
00251                       TEMP = TEMP + A(I,J)*X(IX)
00252                       IX = IX + INCX
00253   110             CONTINUE
00254                   Y(JY) = Y(JY) + ALPHA*TEMP
00255                   JY = JY + INCY
00256   120         CONTINUE
00257           END IF
00258       END IF
00259 *
00260       RETURN
00261 *
00262 *     End of DGEMV .
00263 *
00264       END