LAPACK 3.3.1 Linear Algebra PACKage

# cgemv.f

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```00001       SUBROUTINE CGEMV(TRANS,M,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
00002 *     .. Scalar Arguments ..
00003       COMPLEX ALPHA,BETA
00004       INTEGER INCX,INCY,LDA,M,N
00005       CHARACTER TRANS
00006 *     ..
00007 *     .. Array Arguments ..
00008       COMPLEX A(LDA,*),X(*),Y(*)
00009 *     ..
00010 *
00011 *  Purpose
00012 *  =======
00013 *
00014 *  CGEMV performs one of the matrix-vector operations
00015 *
00016 *     y := alpha*A*x + beta*y,   or   y := alpha*A**T*x + beta*y,   or
00017 *
00018 *     y := alpha*A**H*x + beta*y,
00019 *
00020 *  where alpha and beta are scalars, x and y are vectors and A is an
00021 *  m by n matrix.
00022 *
00023 *  Arguments
00024 *  ==========
00025 *
00026 *  TRANS  - CHARACTER*1.
00027 *           On entry, TRANS specifies the operation to be performed as
00028 *           follows:
00029 *
00030 *              TRANS = 'N' or 'n'   y := alpha*A*x + beta*y.
00031 *
00032 *              TRANS = 'T' or 't'   y := alpha*A**T*x + beta*y.
00033 *
00034 *              TRANS = 'C' or 'c'   y := alpha*A**H*x + beta*y.
00035 *
00036 *           Unchanged on exit.
00037 *
00038 *  M      - INTEGER.
00039 *           On entry, M specifies the number of rows of the matrix A.
00040 *           M must be at least zero.
00041 *           Unchanged on exit.
00042 *
00043 *  N      - INTEGER.
00044 *           On entry, N specifies the number of columns of the matrix A.
00045 *           N must be at least zero.
00046 *           Unchanged on exit.
00047 *
00048 *  ALPHA  - COMPLEX         .
00049 *           On entry, ALPHA specifies the scalar alpha.
00050 *           Unchanged on exit.
00051 *
00052 *  A      - COMPLEX          array of DIMENSION ( LDA, n ).
00053 *           Before entry, the leading m by n part of the array A must
00054 *           contain the matrix of coefficients.
00055 *           Unchanged on exit.
00056 *
00057 *  LDA    - INTEGER.
00058 *           On entry, LDA specifies the first dimension of A as declared
00059 *           in the calling (sub) program. LDA must be at least
00060 *           max( 1, m ).
00061 *           Unchanged on exit.
00062 *
00063 *  X      - COMPLEX          array of DIMENSION at least
00064 *           ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n'
00065 *           and at least
00066 *           ( 1 + ( m - 1 )*abs( INCX ) ) otherwise.
00067 *           Before entry, the incremented array X must contain the
00068 *           vector x.
00069 *           Unchanged on exit.
00070 *
00071 *  INCX   - INTEGER.
00072 *           On entry, INCX specifies the increment for the elements of
00073 *           X. INCX must not be zero.
00074 *           Unchanged on exit.
00075 *
00076 *  BETA   - COMPLEX         .
00077 *           On entry, BETA specifies the scalar beta. When BETA is
00078 *           supplied as zero then Y need not be set on input.
00079 *           Unchanged on exit.
00080 *
00081 *  Y      - COMPLEX          array of DIMENSION at least
00082 *           ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n'
00083 *           and at least
00084 *           ( 1 + ( n - 1 )*abs( INCY ) ) otherwise.
00085 *           Before entry with BETA non-zero, the incremented array Y
00086 *           must contain the vector y. On exit, Y is overwritten by the
00087 *           updated vector y.
00088 *
00089 *  INCY   - INTEGER.
00090 *           On entry, INCY specifies the increment for the elements of
00091 *           Y. INCY must not be zero.
00092 *           Unchanged on exit.
00093 *
00094 *  Further Details
00095 *  ===============
00096 *
00097 *  Level 2 Blas routine.
00098 *  The vector and matrix arguments are not referenced when N = 0, or M = 0
00099 *
00100 *  -- Written on 22-October-1986.
00101 *     Jack Dongarra, Argonne National Lab.
00102 *     Jeremy Du Croz, Nag Central Office.
00103 *     Sven Hammarling, Nag Central Office.
00104 *     Richard Hanson, Sandia National Labs.
00105 *
00106 *  =====================================================================
00107 *
00108 *     .. Parameters ..
00109       COMPLEX ONE
00110       PARAMETER (ONE= (1.0E+0,0.0E+0))
00111       COMPLEX ZERO
00112       PARAMETER (ZERO= (0.0E+0,0.0E+0))
00113 *     ..
00114 *     .. Local Scalars ..
00115       COMPLEX TEMP
00116       INTEGER I,INFO,IX,IY,J,JX,JY,KX,KY,LENX,LENY
00117       LOGICAL NOCONJ
00118 *     ..
00119 *     .. External Functions ..
00120       LOGICAL LSAME
00121       EXTERNAL LSAME
00122 *     ..
00123 *     .. External Subroutines ..
00124       EXTERNAL XERBLA
00125 *     ..
00126 *     .. Intrinsic Functions ..
00127       INTRINSIC CONJG,MAX
00128 *     ..
00129 *
00130 *     Test the input parameters.
00131 *
00132       INFO = 0
00133       IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND.
00134      +    .NOT.LSAME(TRANS,'C')) THEN
00135           INFO = 1
00136       ELSE IF (M.LT.0) THEN
00137           INFO = 2
00138       ELSE IF (N.LT.0) THEN
00139           INFO = 3
00140       ELSE IF (LDA.LT.MAX(1,M)) THEN
00141           INFO = 6
00142       ELSE IF (INCX.EQ.0) THEN
00143           INFO = 8
00144       ELSE IF (INCY.EQ.0) THEN
00145           INFO = 11
00146       END IF
00147       IF (INFO.NE.0) THEN
00148           CALL XERBLA('CGEMV ',INFO)
00149           RETURN
00150       END IF
00151 *
00152 *     Quick return if possible.
00153 *
00154       IF ((M.EQ.0) .OR. (N.EQ.0) .OR.
00155      +    ((ALPHA.EQ.ZERO).AND. (BETA.EQ.ONE))) RETURN
00156 *
00157       NOCONJ = LSAME(TRANS,'T')
00158 *
00159 *     Set  LENX  and  LENY, the lengths of the vectors x and y, and set
00160 *     up the start points in  X  and  Y.
00161 *
00162       IF (LSAME(TRANS,'N')) THEN
00163           LENX = N
00164           LENY = M
00165       ELSE
00166           LENX = M
00167           LENY = N
00168       END IF
00169       IF (INCX.GT.0) THEN
00170           KX = 1
00171       ELSE
00172           KX = 1 - (LENX-1)*INCX
00173       END IF
00174       IF (INCY.GT.0) THEN
00175           KY = 1
00176       ELSE
00177           KY = 1 - (LENY-1)*INCY
00178       END IF
00179 *
00180 *     Start the operations. In this version the elements of A are
00181 *     accessed sequentially with one pass through A.
00182 *
00183 *     First form  y := beta*y.
00184 *
00185       IF (BETA.NE.ONE) THEN
00186           IF (INCY.EQ.1) THEN
00187               IF (BETA.EQ.ZERO) THEN
00188                   DO 10 I = 1,LENY
00189                       Y(I) = ZERO
00190    10             CONTINUE
00191               ELSE
00192                   DO 20 I = 1,LENY
00193                       Y(I) = BETA*Y(I)
00194    20             CONTINUE
00195               END IF
00196           ELSE
00197               IY = KY
00198               IF (BETA.EQ.ZERO) THEN
00199                   DO 30 I = 1,LENY
00200                       Y(IY) = ZERO
00201                       IY = IY + INCY
00202    30             CONTINUE
00203               ELSE
00204                   DO 40 I = 1,LENY
00205                       Y(IY) = BETA*Y(IY)
00206                       IY = IY + INCY
00207    40             CONTINUE
00208               END IF
00209           END IF
00210       END IF
00211       IF (ALPHA.EQ.ZERO) RETURN
00212       IF (LSAME(TRANS,'N')) THEN
00213 *
00214 *        Form  y := alpha*A*x + y.
00215 *
00216           JX = KX
00217           IF (INCY.EQ.1) THEN
00218               DO 60 J = 1,N
00219                   IF (X(JX).NE.ZERO) THEN
00220                       TEMP = ALPHA*X(JX)
00221                       DO 50 I = 1,M
00222                           Y(I) = Y(I) + TEMP*A(I,J)
00223    50                 CONTINUE
00224                   END IF
00225                   JX = JX + INCX
00226    60         CONTINUE
00227           ELSE
00228               DO 80 J = 1,N
00229                   IF (X(JX).NE.ZERO) THEN
00230                       TEMP = ALPHA*X(JX)
00231                       IY = KY
00232                       DO 70 I = 1,M
00233                           Y(IY) = Y(IY) + TEMP*A(I,J)
00234                           IY = IY + INCY
00235    70                 CONTINUE
00236                   END IF
00237                   JX = JX + INCX
00238    80         CONTINUE
00239           END IF
00240       ELSE
00241 *
00242 *        Form  y := alpha*A**T*x + y  or  y := alpha*A**H*x + y.
00243 *
00244           JY = KY
00245           IF (INCX.EQ.1) THEN
00246               DO 110 J = 1,N
00247                   TEMP = ZERO
00248                   IF (NOCONJ) THEN
00249                       DO 90 I = 1,M
00250                           TEMP = TEMP + A(I,J)*X(I)
00251    90                 CONTINUE
00252                   ELSE
00253                       DO 100 I = 1,M
00254                           TEMP = TEMP + CONJG(A(I,J))*X(I)
00255   100                 CONTINUE
00256                   END IF
00257                   Y(JY) = Y(JY) + ALPHA*TEMP
00258                   JY = JY + INCY
00259   110         CONTINUE
00260           ELSE
00261               DO 140 J = 1,N
00262                   TEMP = ZERO
00263                   IX = KX
00264                   IF (NOCONJ) THEN
00265                       DO 120 I = 1,M
00266                           TEMP = TEMP + A(I,J)*X(IX)
00267                           IX = IX + INCX
00268   120                 CONTINUE
00269                   ELSE
00270                       DO 130 I = 1,M
00271                           TEMP = TEMP + CONJG(A(I,J))*X(IX)
00272                           IX = IX + INCX
00273   130                 CONTINUE
00274                   END IF
00275                   Y(JY) = Y(JY) + ALPHA*TEMP
00276                   JY = JY + INCY
00277   140         CONTINUE
00278           END IF
00279       END IF
00280 *
00281       RETURN
00282 *
00283 *     End of CGEMV .
00284 *
00285       END
```