1: SUBROUTINE ZHPMV(UPLO,N,ALPHA,AP,X,INCX,BETA,Y,INCY)
2: * .. Scalar Arguments ..
3: DOUBLE COMPLEX ALPHA,BETA
4: INTEGER INCX,INCY,N
5: CHARACTER UPLO
6: * ..
7: * .. Array Arguments ..
8: DOUBLE COMPLEX AP(*),X(*),Y(*)
9: * ..
10: *
11: * Purpose
12: * =======
13: *
14: * ZHPMV 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*16 .
43: * On entry, ALPHA specifies the scalar alpha.
44: * Unchanged on exit.
45: *
46: * AP - COMPLEX*16 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*16 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*16 .
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*16 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: DOUBLE COMPLEX ONE
104: PARAMETER (ONE= (1.0D+0,0.0D+0))
105: DOUBLE COMPLEX ZERO
106: PARAMETER (ZERO= (0.0D+0,0.0D+0))
107: * ..
108: * .. Local Scalars ..
109: DOUBLE 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 DBLE,DCONJG
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('ZHPMV ',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 + DCONJG(AP(K))*X(I)
202: K = K + 1
203: 50 CONTINUE
204: Y(J) = Y(J) + TEMP1*DBLE(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 + DCONJG(AP(K))*X(IX)
218: IX = IX + INCX
219: IY = IY + INCY
220: 70 CONTINUE
221: Y(JY) = Y(JY) + TEMP1*DBLE(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*DBLE(AP(KK))
236: K = KK + 1
237: DO 90 I = J + 1,N
238: Y(I) = Y(I) + TEMP1*AP(K)
239: TEMP2 = TEMP2 + DCONJG(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*DBLE(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 + DCONJG(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 ZHPMV .
271: *
272: END
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