1      SUBROUTINE CHPMV(UPLO,N,ALPHA,AP,X,INCX,BETA,Y,INCY)
2*     .. Scalar Arguments ..
3      COMPLEX ALPHA,BETA
4      INTEGER INCX,INCY,N
5      CHARACTER UPLO
6*     ..
7*     .. Array Arguments ..
8      COMPLEX AP(*),X(*),Y(*)
9*     ..
10*
11*  Purpose
12*  =======
13*
14*  CHPMV  performs the matrix-vector operation
15*
16*     y := alpha*A*x + beta*y,
17*
18*  where alpha and beta are scalars, x and y are n element vectors and
19*  A is an n by n hermitian matrix, supplied in packed form.
20*
21*  Arguments
22*  ==========
23*
24*  UPLO   - CHARACTER*1.
25*           On entry, UPLO specifies whether the upper or lower
26*           triangular part of the matrix A is supplied in the packed
27*           array AP as follows:
28*
29*              UPLO = 'U' or 'u'   The upper triangular part of A is
30*                                  supplied in AP.
31*
32*              UPLO = 'L' or 'l'   The lower triangular part of A is
33*                                  supplied in AP.
34*
35*           Unchanged on exit.
36*
37*  N      - INTEGER.
38*           On entry, N specifies the order of the matrix A.
39*           N must be at least zero.
40*           Unchanged on exit.
41*
42*  ALPHA  - COMPLEX         .
43*           On entry, ALPHA specifies the scalar alpha.
44*           Unchanged on exit.
45*
46*  AP     - COMPLEX          array of DIMENSION at least
47*           ( ( n*( n + 1 ) )/2 ).
48*           Before entry with UPLO = 'U' or 'u', the array AP must
49*           contain the upper triangular part of the hermitian matrix
50*           packed sequentially, column by column, so that AP( 1 )
51*           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 )
52*           and a( 2, 2 ) respectively, and so on.
53*           Before entry with UPLO = 'L' or 'l', the array AP must
54*           contain the lower triangular part of the hermitian matrix
55*           packed sequentially, column by column, so that AP( 1 )
56*           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 )
57*           and a( 3, 1 ) respectively, and so on.
58*           Note that the imaginary parts of the diagonal elements need
59*           not be set and are assumed to be zero.
60*           Unchanged on exit.
61*
62*  X      - COMPLEX          array of dimension at least
63*           ( 1 + ( n - 1 )*abs( INCX ) ).
64*           Before entry, the incremented array X must contain the n
65*           element vector x.
66*           Unchanged on exit.
67*
68*  INCX   - INTEGER.
69*           On entry, INCX specifies the increment for the elements of
70*           X. INCX must not be zero.
71*           Unchanged on exit.
72*
73*  BETA   - COMPLEX         .
74*           On entry, BETA specifies the scalar beta. When BETA is
75*           supplied as zero then Y need not be set on input.
76*           Unchanged on exit.
77*
78*  Y      - COMPLEX          array of dimension at least
79*           ( 1 + ( n - 1 )*abs( INCY ) ).
80*           Before entry, the incremented array Y must contain the n
81*           element vector y. On exit, Y is overwritten by the updated
82*           vector y.
83*
84*  INCY   - INTEGER.
85*           On entry, INCY specifies the increment for the elements of
86*           Y. INCY must not be zero.
87*           Unchanged on exit.
88*
89*  Further Details
90*  ===============
91*
92*  Level 2 Blas routine.
93*
94*  -- Written on 22-October-1986.
95*     Jack Dongarra, Argonne National Lab.
96*     Jeremy Du Croz, Nag Central Office.
97*     Sven Hammarling, Nag Central Office.
98*     Richard Hanson, Sandia National Labs.
99*
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,K,KK,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,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 (INCX.EQ.0) THEN
131          INFO = 6
132      ELSE IF (INCY.EQ.0) THEN
133          INFO = 9
134      END IF
135      IF (INFO.NE.0) THEN
136          CALL XERBLA('CHPMV ',INFO)
137          RETURN
138      END IF
139*
140*     Quick return if possible.
141*
142      IF ((N.EQ.0) .OR. ((ALPHA.EQ.ZERO).AND. (BETA.EQ.ONE))) RETURN
143*
144*     Set up the start points in  X  and  Y.
145*
146      IF (INCX.GT.0) THEN
147          KX = 1
148      ELSE
149          KX = 1 - (N-1)*INCX
150      END IF
151      IF (INCY.GT.0) THEN
152          KY = 1
153      ELSE
154          KY = 1 - (N-1)*INCY
155      END IF
156*
157*     Start the operations. In this version the elements of the array AP
158*     are accessed sequentially with one pass through AP.
159*
160*     First form  y := beta*y.
161*
162      IF (BETA.NE.ONE) THEN
163          IF (INCY.EQ.1) THEN
164              IF (BETA.EQ.ZERO) THEN
165                  DO 10 I = 1,N
166                      Y(I) = ZERO
167   10             CONTINUE
168              ELSE
169                  DO 20 I = 1,N
170                      Y(I) = BETA*Y(I)
171   20             CONTINUE
172              END IF
173          ELSE
174              IY = KY
175              IF (BETA.EQ.ZERO) THEN
176                  DO 30 I = 1,N
177                      Y(IY) = ZERO
178                      IY = IY + INCY
179   30             CONTINUE
180              ELSE
181                  DO 40 I = 1,N
182                      Y(IY) = BETA*Y(IY)
183                      IY = IY + INCY
184   40             CONTINUE
185              END IF
186          END IF
187      END IF
188      IF (ALPHA.EQ.ZERO) RETURN
189      KK = 1
190      IF (LSAME(UPLO,'U')) THEN
191*
192*        Form  y  when AP contains the upper triangle.
193*
194          IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN
195              DO 60 J = 1,N
196                  TEMP1 = ALPHA*X(J)
197                  TEMP2 = ZERO
198                  K = KK
199                  DO 50 I = 1,J - 1
200                      Y(I) = Y(I) + TEMP1*AP(K)
201                      TEMP2 = TEMP2 + CONJG(AP(K))*X(I)
202                      K = K + 1
203   50             CONTINUE
204                  Y(J) = Y(J) + TEMP1*REAL(AP(KK+J-1)) + ALPHA*TEMP2
205                  KK = KK + J
206   60         CONTINUE
207          ELSE
208              JX = KX
209              JY = KY
210              DO 80 J = 1,N
211                  TEMP1 = ALPHA*X(JX)
212                  TEMP2 = ZERO
213                  IX = KX
214                  IY = KY
215                  DO 70 K = KK,KK + J - 2
216                      Y(IY) = Y(IY) + TEMP1*AP(K)
217                      TEMP2 = TEMP2 + CONJG(AP(K))*X(IX)
218                      IX = IX + INCX
219                      IY = IY + INCY
220   70             CONTINUE
221                  Y(JY) = Y(JY) + TEMP1*REAL(AP(KK+J-1)) + ALPHA*TEMP2
222                  JX = JX + INCX
223                  JY = JY + INCY
224                  KK = KK + J
225   80         CONTINUE
226          END IF
227      ELSE
228*
229*        Form  y  when AP contains the lower triangle.
230*
231          IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN
232              DO 100 J = 1,N
233                  TEMP1 = ALPHA*X(J)
234                  TEMP2 = ZERO
235                  Y(J) = Y(J) + TEMP1*REAL(AP(KK))
236                  K = KK + 1
237                  DO 90 I = J + 1,N
238                      Y(I) = Y(I) + TEMP1*AP(K)
239                      TEMP2 = TEMP2 + CONJG(AP(K))*X(I)
240                      K = K + 1
241   90             CONTINUE
242                  Y(J) = Y(J) + ALPHA*TEMP2
243                  KK = KK + (N-J+1)
244  100         CONTINUE
245          ELSE
246              JX = KX
247              JY = KY
248              DO 120 J = 1,N
249                  TEMP1 = ALPHA*X(JX)
250                  TEMP2 = ZERO
251                  Y(JY) = Y(JY) + TEMP1*REAL(AP(KK))
252                  IX = JX
253                  IY = JY
254                  DO 110 K = KK + 1,KK + N - J
255                      IX = IX + INCX
256                      IY = IY + INCY
257                      Y(IY) = Y(IY) + TEMP1*AP(K)
258                      TEMP2 = TEMP2 + CONJG(AP(K))*X(IX)
259  110             CONTINUE
260                  Y(JY) = Y(JY) + ALPHA*TEMP2
261                  JX = JX + INCX
262                  JY = JY + INCY
263                  KK = KK + (N-J+1)
264  120         CONTINUE
265          END IF
266      END IF
267*
268      RETURN
269*
270*     End of CHPMV .
271*
272      END
273