1       SUBROUTINE CGEMV(TRANS,M,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
  2 *     .. Scalar Arguments ..
  3       COMPLEX ALPHA,BETA
  4       INTEGER INCX,INCY,LDA,M,N
  5       CHARACTER TRANS
  6 *     ..
  7 *     .. Array Arguments ..
  8       COMPLEX A(LDA,*),X(*),Y(*)
  9 *     ..
 10 *
 11 *  Purpose
 12 *  =======
 13 *
 14 *  CGEMV performs one of the matrix-vector operations
 15 *
 16 *     y := alpha*A*x + beta*y,   or   y := alpha*A**T*x + beta*y,   or
 17 *
 18 *     y := alpha*A**H*x + beta*y,
 19 *
 20 *  where alpha and beta are scalars, x and y are vectors and A is an
 21 *  m by n matrix.
 22 *
 23 *  Arguments
 24 *  ==========
 25 *
 26 *  TRANS  - CHARACTER*1.
 27 *           On entry, TRANS specifies the operation to be performed as
 28 *           follows:
 29 *
 30 *              TRANS = 'N' or 'n'   y := alpha*A*x + beta*y.
 31 *
 32 *              TRANS = 'T' or 't'   y := alpha*A**T*x + beta*y.
 33 *
 34 *              TRANS = 'C' or 'c'   y := alpha*A**H*x + beta*y.
 35 *
 36 *           Unchanged on exit.
 37 *
 38 *  M      - INTEGER.
 39 *           On entry, M specifies the number of rows of the matrix A.
 40 *           M must be at least zero.
 41 *           Unchanged on exit.
 42 *
 43 *  N      - INTEGER.
 44 *           On entry, N specifies the number of columns of the matrix A.
 45 *           N must be at least zero.
 46 *           Unchanged on exit.
 47 *
 48 *  ALPHA  - COMPLEX         .
 49 *           On entry, ALPHA specifies the scalar alpha.
 50 *           Unchanged on exit.
 51 *
 52 *  A      - COMPLEX          array of DIMENSION ( LDA, n ).
 53 *           Before entry, the leading m by n part of the array A must
 54 *           contain the matrix of coefficients.
 55 *           Unchanged on exit.
 56 *
 57 *  LDA    - INTEGER.
 58 *           On entry, LDA specifies the first dimension of A as declared
 59 *           in the calling (sub) program. LDA must be at least
 60 *           max( 1, m ).
 61 *           Unchanged on exit.
 62 *
 63 *  X      - COMPLEX          array of DIMENSION at least
 64 *           ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n'
 65 *           and at least
 66 *           ( 1 + ( m - 1 )*abs( INCX ) ) otherwise.
 67 *           Before entry, the incremented array X must contain the
 68 *           vector x.
 69 *           Unchanged on exit.
 70 *
 71 *  INCX   - INTEGER.
 72 *           On entry, INCX specifies the increment for the elements of
 73 *           X. INCX must not be zero.
 74 *           Unchanged on exit.
 75 *
 76 *  BETA   - COMPLEX         .
 77 *           On entry, BETA specifies the scalar beta. When BETA is
 78 *           supplied as zero then Y need not be set on input.
 79 *           Unchanged on exit.
 80 *
 81 *  Y      - COMPLEX          array of DIMENSION at least
 82 *           ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n'
 83 *           and at least
 84 *           ( 1 + ( n - 1 )*abs( INCY ) ) otherwise.
 85 *           Before entry with BETA non-zero, the incremented array Y
 86 *           must contain the vector y. On exit, Y is overwritten by the
 87 *           updated vector y.
 88 *
 89 *  INCY   - INTEGER.
 90 *           On entry, INCY specifies the increment for the elements of
 91 *           Y. INCY must not be zero.
 92 *           Unchanged on exit.
 93 *
 94 *  Further Details
 95 *  ===============
 96 *
 97 *  Level 2 Blas routine.
 98 *  The vector and matrix arguments are not referenced when N = 0, or M = 0
 99 *
100 *  -- Written on 22-October-1986.
101 *     Jack Dongarra, Argonne National Lab.
102 *     Jeremy Du Croz, Nag Central Office.
103 *     Sven Hammarling, Nag Central Office.
104 *     Richard Hanson, Sandia National Labs.
105 *
106 *  =====================================================================
107 *
108 *     .. Parameters ..
109       COMPLEX ONE
110       PARAMETER (ONE= (1.0E+0,0.0E+0))
111       COMPLEX ZERO
112       PARAMETER (ZERO= (0.0E+0,0.0E+0))
113 *     ..
114 *     .. Local Scalars ..
115       COMPLEX TEMP
116       INTEGER I,INFO,IX,IY,J,JX,JY,KX,KY,LENX,LENY
117       LOGICAL NOCONJ
118 *     ..
119 *     .. External Functions ..
120       LOGICAL LSAME
121       EXTERNAL LSAME
122 *     ..
123 *     .. External Subroutines ..
124       EXTERNAL XERBLA
125 *     ..
126 *     .. Intrinsic Functions ..
127       INTRINSIC CONJG,MAX
128 *     ..
129 *
130 *     Test the input parameters.
131 *
132       INFO = 0
133       IF (.NOT.LSAME(TRANS,'N'.AND. .NOT.LSAME(TRANS,'T'.AND.
134      +    .NOT.LSAME(TRANS,'C')) THEN
135           INFO = 1
136       ELSE IF (M.LT.0THEN
137           INFO = 2
138       ELSE IF (N.LT.0THEN
139           INFO = 3
140       ELSE IF (LDA.LT.MAX(1,M)) THEN
141           INFO = 6
142       ELSE IF (INCX.EQ.0THEN
143           INFO = 8
144       ELSE IF (INCY.EQ.0THEN
145           INFO = 11
146       END IF
147       IF (INFO.NE.0THEN
148           CALL XERBLA('CGEMV ',INFO)
149           RETURN
150       END IF
151 *
152 *     Quick return if possible.
153 *
154       IF ((M.EQ.0.OR. (N.EQ.0.OR.
155      +    ((ALPHA.EQ.ZERO).AND. (BETA.EQ.ONE))) RETURN
156 *
157       NOCONJ = LSAME(TRANS,'T')
158 *
159 *     Set  LENX  and  LENY, the lengths of the vectors x and y, and set
160 *     up the start points in  X  and  Y.
161 *
162       IF (LSAME(TRANS,'N')) THEN
163           LENX = N
164           LENY = M
165       ELSE
166           LENX = M
167           LENY = N
168       END IF
169       IF (INCX.GT.0THEN
170           KX = 1
171       ELSE
172           KX = 1 - (LENX-1)*INCX
173       END IF
174       IF (INCY.GT.0THEN
175           KY = 1
176       ELSE
177           KY = 1 - (LENY-1)*INCY
178       END IF
179 *
180 *     Start the operations. In this version the elements of A are
181 *     accessed sequentially with one pass through A.
182 *
183 *     First form  y := beta*y.
184 *
185       IF (BETA.NE.ONE) THEN
186           IF (INCY.EQ.1THEN
187               IF (BETA.EQ.ZERO) THEN
188                   DO 10 I = 1,LENY
189                       Y(I) = ZERO
190    10             CONTINUE
191               ELSE
192                   DO 20 I = 1,LENY
193                       Y(I) = BETA*Y(I)
194    20             CONTINUE
195               END IF
196           ELSE
197               IY = KY
198               IF (BETA.EQ.ZERO) THEN
199                   DO 30 I = 1,LENY
200                       Y(IY) = ZERO
201                       IY = IY + INCY
202    30             CONTINUE
203               ELSE
204                   DO 40 I = 1,LENY
205                       Y(IY) = BETA*Y(IY)
206                       IY = IY + INCY
207    40             CONTINUE
208               END IF
209           END IF
210       END IF
211       IF (ALPHA.EQ.ZERO) RETURN
212       IF (LSAME(TRANS,'N')) THEN
213 *
214 *        Form  y := alpha*A*x + y.
215 *
216           JX = KX
217           IF (INCY.EQ.1THEN
218               DO 60 J = 1,N
219                   IF (X(JX).NE.ZERO) THEN
220                       TEMP = ALPHA*X(JX)
221                       DO 50 I = 1,M
222                           Y(I) = Y(I) + TEMP*A(I,J)
223    50                 CONTINUE
224                   END IF
225                   JX = JX + INCX
226    60         CONTINUE
227           ELSE
228               DO 80 J = 1,N
229                   IF (X(JX).NE.ZERO) THEN
230                       TEMP = ALPHA*X(JX)
231                       IY = KY
232                       DO 70 I = 1,M
233                           Y(IY) = Y(IY) + TEMP*A(I,J)
234                           IY = IY + INCY
235    70                 CONTINUE
236                   END IF
237                   JX = JX + INCX
238    80         CONTINUE
239           END IF
240       ELSE
241 *
242 *        Form  y := alpha*A**T*x + y  or  y := alpha*A**H*x + y.
243 *
244           JY = KY
245           IF (INCX.EQ.1THEN
246               DO 110 J = 1,N
247                   TEMP = ZERO
248                   IF (NOCONJ) THEN
249                       DO 90 I = 1,M
250                           TEMP = TEMP + A(I,J)*X(I)
251    90                 CONTINUE
252                   ELSE
253                       DO 100 I = 1,M
254                           TEMP = TEMP + CONJG(A(I,J))*X(I)
255   100                 CONTINUE
256                   END IF
257                   Y(JY) = Y(JY) + ALPHA*TEMP
258                   JY = JY + INCY
259   110         CONTINUE
260           ELSE
261               DO 140 J = 1,N
262                   TEMP = ZERO
263                   IX = KX
264                   IF (NOCONJ) THEN
265                       DO 120 I = 1,M
266                           TEMP = TEMP + A(I,J)*X(IX)
267                           IX = IX + INCX
268   120                 CONTINUE
269                   ELSE
270                       DO 130 I = 1,M
271                           TEMP = TEMP + CONJG(A(I,J))*X(IX)
272                           IX = IX + INCX
273   130                 CONTINUE
274                   END IF
275                   Y(JY) = Y(JY) + ALPHA*TEMP
276                   JY = JY + INCY
277   140         CONTINUE
278           END IF
279       END IF
280 *
281       RETURN
282 *
283 *     End of CGEMV .
284 *
285       END