001:       SUBROUTINE CHEMV(UPLO,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
002: *     .. Scalar Arguments ..
003:       COMPLEX ALPHA,BETA
004:       INTEGER INCX,INCY,LDA,N
005:       CHARACTER UPLO
006: *     ..
007: *     .. Array Arguments ..
008:       COMPLEX A(LDA,*),X(*),Y(*)
009: *     ..
010: *
011: *  Purpose
012: *  =======
013: *
014: *  CHEMV  performs the matrix-vector  operation
015: *
016: *     y := alpha*A*x + beta*y,
017: *
018: *  where alpha and beta are scalars, x and y are n element vectors and
019: *  A is an n by n hermitian matrix.
020: *
021: *  Arguments
022: *  ==========
023: *
024: *  UPLO   - CHARACTER*1.
025: *           On entry, UPLO specifies whether the upper or lower
026: *           triangular part of the array A is to be referenced as
027: *           follows:
028: *
029: *              UPLO = 'U' or 'u'   Only the upper triangular part of A
030: *                                  is to be referenced.
031: *
032: *              UPLO = 'L' or 'l'   Only the lower triangular part of A
033: *                                  is to be referenced.
034: *
035: *           Unchanged on exit.
036: *
037: *  N      - INTEGER.
038: *           On entry, N specifies the order of the matrix A.
039: *           N must be at least zero.
040: *           Unchanged on exit.
041: *
042: *  ALPHA  - COMPLEX         .
043: *           On entry, ALPHA specifies the scalar alpha.
044: *           Unchanged on exit.
045: *
046: *  A      - COMPLEX          array of DIMENSION ( LDA, n ).
047: *           Before entry with  UPLO = 'U' or 'u', the leading n by n
048: *           upper triangular part of the array A must contain the upper
049: *           triangular part of the hermitian matrix and the strictly
050: *           lower triangular part of A is not referenced.
051: *           Before entry with UPLO = 'L' or 'l', the leading n by n
052: *           lower triangular part of the array A must contain the lower
053: *           triangular part of the hermitian matrix and the strictly
054: *           upper triangular part of A is not referenced.
055: *           Note that the imaginary parts of the diagonal elements need
056: *           not be set and are assumed to be zero.
057: *           Unchanged on exit.
058: *
059: *  LDA    - INTEGER.
060: *           On entry, LDA specifies the first dimension of A as declared
061: *           in the calling (sub) program. LDA must be at least
062: *           max( 1, n ).
063: *           Unchanged on exit.
064: *
065: *  X      - COMPLEX          array of dimension at least
066: *           ( 1 + ( n - 1 )*abs( INCX ) ).
067: *           Before entry, the incremented array X must contain the n
068: *           element vector x.
069: *           Unchanged on exit.
070: *
071: *  INCX   - INTEGER.
072: *           On entry, INCX specifies the increment for the elements of
073: *           X. INCX must not be zero.
074: *           Unchanged on exit.
075: *
076: *  BETA   - COMPLEX         .
077: *           On entry, BETA specifies the scalar beta. When BETA is
078: *           supplied as zero then Y need not be set on input.
079: *           Unchanged on exit.
080: *
081: *  Y      - COMPLEX          array of dimension at least
082: *           ( 1 + ( n - 1 )*abs( INCY ) ).
083: *           Before entry, the incremented array Y must contain the n
084: *           element vector y. On exit, Y is overwritten by the updated
085: *           vector y.
086: *
087: *  INCY   - INTEGER.
088: *           On entry, INCY specifies the increment for the elements of
089: *           Y. INCY must not be zero.
090: *           Unchanged on exit.
091: *
092: *
093: *  Level 2 Blas routine.
094: *
095: *  -- Written on 22-October-1986.
096: *     Jack Dongarra, Argonne National Lab.
097: *     Jeremy Du Croz, Nag Central Office.
098: *     Sven Hammarling, Nag Central Office.
099: *     Richard Hanson, Sandia National Labs.
100: *
101: *
102: *     .. Parameters ..
103:       COMPLEX ONE
104:       PARAMETER (ONE= (1.0E+0,0.0E+0))
105:       COMPLEX ZERO
106:       PARAMETER (ZERO= (0.0E+0,0.0E+0))
107: *     ..
108: *     .. Local Scalars ..
109:       COMPLEX TEMP1,TEMP2
110:       INTEGER I,INFO,IX,IY,J,JX,JY,KX,KY
111: *     ..
112: *     .. External Functions ..
113:       LOGICAL LSAME
114:       EXTERNAL LSAME
115: *     ..
116: *     .. External Subroutines ..
117:       EXTERNAL XERBLA
118: *     ..
119: *     .. Intrinsic Functions ..
120:       INTRINSIC CONJG,MAX,REAL
121: *     ..
122: *
123: *     Test the input parameters.
124: *
125:       INFO = 0
126:       IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN
127:           INFO = 1
128:       ELSE IF (N.LT.0) THEN
129:           INFO = 2
130:       ELSE IF (LDA.LT.MAX(1,N)) THEN
131:           INFO = 5
132:       ELSE IF (INCX.EQ.0) THEN
133:           INFO = 7
134:       ELSE IF (INCY.EQ.0) THEN
135:           INFO = 10
136:       END IF
137:       IF (INFO.NE.0) THEN
138:           CALL XERBLA('CHEMV ',INFO)
139:           RETURN
140:       END IF
141: *
142: *     Quick return if possible.
143: *
144:       IF ((N.EQ.0) .OR. ((ALPHA.EQ.ZERO).AND. (BETA.EQ.ONE))) RETURN
145: *
146: *     Set up the start points in  X  and  Y.
147: *
148:       IF (INCX.GT.0) THEN
149:           KX = 1
150:       ELSE
151:           KX = 1 - (N-1)*INCX
152:       END IF
153:       IF (INCY.GT.0) THEN
154:           KY = 1
155:       ELSE
156:           KY = 1 - (N-1)*INCY
157:       END IF
158: *
159: *     Start the operations. In this version the elements of A are
160: *     accessed sequentially with one pass through the triangular part
161: *     of A.
162: *
163: *     First form  y := beta*y.
164: *
165:       IF (BETA.NE.ONE) THEN
166:           IF (INCY.EQ.1) THEN
167:               IF (BETA.EQ.ZERO) THEN
168:                   DO 10 I = 1,N
169:                       Y(I) = ZERO
170:    10             CONTINUE
171:               ELSE
172:                   DO 20 I = 1,N
173:                       Y(I) = BETA*Y(I)
174:    20             CONTINUE
175:               END IF
176:           ELSE
177:               IY = KY
178:               IF (BETA.EQ.ZERO) THEN
179:                   DO 30 I = 1,N
180:                       Y(IY) = ZERO
181:                       IY = IY + INCY
182:    30             CONTINUE
183:               ELSE
184:                   DO 40 I = 1,N
185:                       Y(IY) = BETA*Y(IY)
186:                       IY = IY + INCY
187:    40             CONTINUE
188:               END IF
189:           END IF
190:       END IF
191:       IF (ALPHA.EQ.ZERO) RETURN
192:       IF (LSAME(UPLO,'U')) THEN
193: *
194: *        Form  y  when A is stored in upper triangle.
195: *
196:           IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN
197:               DO 60 J = 1,N
198:                   TEMP1 = ALPHA*X(J)
199:                   TEMP2 = ZERO
200:                   DO 50 I = 1,J - 1
201:                       Y(I) = Y(I) + TEMP1*A(I,J)
202:                       TEMP2 = TEMP2 + CONJG(A(I,J))*X(I)
203:    50             CONTINUE
204:                   Y(J) = Y(J) + TEMP1*REAL(A(J,J)) + ALPHA*TEMP2
205:    60         CONTINUE
206:           ELSE
207:               JX = KX
208:               JY = KY
209:               DO 80 J = 1,N
210:                   TEMP1 = ALPHA*X(JX)
211:                   TEMP2 = ZERO
212:                   IX = KX
213:                   IY = KY
214:                   DO 70 I = 1,J - 1
215:                       Y(IY) = Y(IY) + TEMP1*A(I,J)
216:                       TEMP2 = TEMP2 + CONJG(A(I,J))*X(IX)
217:                       IX = IX + INCX
218:                       IY = IY + INCY
219:    70             CONTINUE
220:                   Y(JY) = Y(JY) + TEMP1*REAL(A(J,J)) + ALPHA*TEMP2
221:                   JX = JX + INCX
222:                   JY = JY + INCY
223:    80         CONTINUE
224:           END IF
225:       ELSE
226: *
227: *        Form  y  when A is stored in lower triangle.
228: *
229:           IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN
230:               DO 100 J = 1,N
231:                   TEMP1 = ALPHA*X(J)
232:                   TEMP2 = ZERO
233:                   Y(J) = Y(J) + TEMP1*REAL(A(J,J))
234:                   DO 90 I = J + 1,N
235:                       Y(I) = Y(I) + TEMP1*A(I,J)
236:                       TEMP2 = TEMP2 + CONJG(A(I,J))*X(I)
237:    90             CONTINUE
238:                   Y(J) = Y(J) + ALPHA*TEMP2
239:   100         CONTINUE
240:           ELSE
241:               JX = KX
242:               JY = KY
243:               DO 120 J = 1,N
244:                   TEMP1 = ALPHA*X(JX)
245:                   TEMP2 = ZERO
246:                   Y(JY) = Y(JY) + TEMP1*REAL(A(J,J))
247:                   IX = JX
248:                   IY = JY
249:                   DO 110 I = J + 1,N
250:                       IX = IX + INCX
251:                       IY = IY + INCY
252:                       Y(IY) = Y(IY) + TEMP1*A(I,J)
253:                       TEMP2 = TEMP2 + CONJG(A(I,J))*X(IX)
254:   110             CONTINUE
255:                   Y(JY) = Y(JY) + ALPHA*TEMP2
256:                   JX = JX + INCX
257:                   JY = JY + INCY
258:   120         CONTINUE
259:           END IF
260:       END IF
261: *
262:       RETURN
263: *
264: *     End of CHEMV .
265: *
266:       END
267: