1: SUBROUTINE ZHPR2(UPLO,N,ALPHA,X,INCX,Y,INCY,AP)
2: * .. Scalar Arguments ..
3: DOUBLE COMPLEX ALPHA
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: * ZHPR2 performs the hermitian rank 2 operation
15: *
16: * A := alpha*x*conjg( y' ) + conjg( alpha )*y*conjg( x' ) + A,
17: *
18: * where alpha is a scalar, x and y are n element vectors and A is an
19: * 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: * X - COMPLEX*16 array of dimension at least
47: * ( 1 + ( n - 1 )*abs( INCX ) ).
48: * Before entry, the incremented array X must contain the n
49: * element vector x.
50: * Unchanged on exit.
51: *
52: * INCX - INTEGER.
53: * On entry, INCX specifies the increment for the elements of
54: * X. INCX must not be zero.
55: * Unchanged on exit.
56: *
57: * Y - COMPLEX*16 array of dimension at least
58: * ( 1 + ( n - 1 )*abs( INCY ) ).
59: * Before entry, the incremented array Y must contain the n
60: * element vector y.
61: * Unchanged on exit.
62: *
63: * INCY - INTEGER.
64: * On entry, INCY specifies the increment for the elements of
65: * Y. INCY must not be zero.
66: * Unchanged on exit.
67: *
68: * AP - COMPLEX*16 array of DIMENSION at least
69: * ( ( n*( n + 1 ) )/2 ).
70: * Before entry with UPLO = 'U' or 'u', the array AP must
71: * contain the upper triangular part of the hermitian matrix
72: * packed sequentially, column by column, so that AP( 1 )
73: * contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 )
74: * and a( 2, 2 ) respectively, and so on. On exit, the array
75: * AP is overwritten by the upper triangular part of the
76: * updated matrix.
77: * Before entry with UPLO = 'L' or 'l', the array AP must
78: * contain the lower triangular part of the hermitian matrix
79: * packed sequentially, column by column, so that AP( 1 )
80: * contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 )
81: * and a( 3, 1 ) respectively, and so on. On exit, the array
82: * AP is overwritten by the lower triangular part of the
83: * updated matrix.
84: * Note that the imaginary parts of the diagonal elements need
85: * not be set, they are assumed to be zero, and on exit they
86: * are set to zero.
87: *
88: * Further Details
89: * ===============
90: *
91: * Level 2 Blas routine.
92: *
93: * -- Written on 22-October-1986.
94: * Jack Dongarra, Argonne National Lab.
95: * Jeremy Du Croz, Nag Central Office.
96: * Sven Hammarling, Nag Central Office.
97: * Richard Hanson, Sandia National Labs.
98: *
99: * =====================================================================
100: *
101: * .. Parameters ..
102: DOUBLE COMPLEX ZERO
103: PARAMETER (ZERO= (0.0D+0,0.0D+0))
104: * ..
105: * .. Local Scalars ..
106: DOUBLE COMPLEX TEMP1,TEMP2
107: INTEGER I,INFO,IX,IY,J,JX,JY,K,KK,KX,KY
108: * ..
109: * .. External Functions ..
110: LOGICAL LSAME
111: EXTERNAL LSAME
112: * ..
113: * .. External Subroutines ..
114: EXTERNAL XERBLA
115: * ..
116: * .. Intrinsic Functions ..
117: INTRINSIC DBLE,DCONJG
118: * ..
119: *
120: * Test the input parameters.
121: *
122: INFO = 0
123: IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN
124: INFO = 1
125: ELSE IF (N.LT.0) THEN
126: INFO = 2
127: ELSE IF (INCX.EQ.0) THEN
128: INFO = 5
129: ELSE IF (INCY.EQ.0) THEN
130: INFO = 7
131: END IF
132: IF (INFO.NE.0) THEN
133: CALL XERBLA('ZHPR2 ',INFO)
134: RETURN
135: END IF
136: *
137: * Quick return if possible.
138: *
139: IF ((N.EQ.0) .OR. (ALPHA.EQ.ZERO)) RETURN
140: *
141: * Set up the start points in X and Y if the increments are not both
142: * unity.
143: *
144: IF ((INCX.NE.1) .OR. (INCY.NE.1)) THEN
145: IF (INCX.GT.0) THEN
146: KX = 1
147: ELSE
148: KX = 1 - (N-1)*INCX
149: END IF
150: IF (INCY.GT.0) THEN
151: KY = 1
152: ELSE
153: KY = 1 - (N-1)*INCY
154: END IF
155: JX = KX
156: JY = KY
157: END IF
158: *
159: * Start the operations. In this version the elements of the array AP
160: * are accessed sequentially with one pass through AP.
161: *
162: KK = 1
163: IF (LSAME(UPLO,'U')) THEN
164: *
165: * Form A when upper triangle is stored in AP.
166: *
167: IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN
168: DO 20 J = 1,N
169: IF ((X(J).NE.ZERO) .OR. (Y(J).NE.ZERO)) THEN
170: TEMP1 = ALPHA*DCONJG(Y(J))
171: TEMP2 = DCONJG(ALPHA*X(J))
172: K = KK
173: DO 10 I = 1,J - 1
174: AP(K) = AP(K) + X(I)*TEMP1 + Y(I)*TEMP2
175: K = K + 1
176: 10 CONTINUE
177: AP(KK+J-1) = DBLE(AP(KK+J-1)) +
178: + DBLE(X(J)*TEMP1+Y(J)*TEMP2)
179: ELSE
180: AP(KK+J-1) = DBLE(AP(KK+J-1))
181: END IF
182: KK = KK + J
183: 20 CONTINUE
184: ELSE
185: DO 40 J = 1,N
186: IF ((X(JX).NE.ZERO) .OR. (Y(JY).NE.ZERO)) THEN
187: TEMP1 = ALPHA*DCONJG(Y(JY))
188: TEMP2 = DCONJG(ALPHA*X(JX))
189: IX = KX
190: IY = KY
191: DO 30 K = KK,KK + J - 2
192: AP(K) = AP(K) + X(IX)*TEMP1 + Y(IY)*TEMP2
193: IX = IX + INCX
194: IY = IY + INCY
195: 30 CONTINUE
196: AP(KK+J-1) = DBLE(AP(KK+J-1)) +
197: + DBLE(X(JX)*TEMP1+Y(JY)*TEMP2)
198: ELSE
199: AP(KK+J-1) = DBLE(AP(KK+J-1))
200: END IF
201: JX = JX + INCX
202: JY = JY + INCY
203: KK = KK + J
204: 40 CONTINUE
205: END IF
206: ELSE
207: *
208: * Form A when lower triangle is stored in AP.
209: *
210: IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN
211: DO 60 J = 1,N
212: IF ((X(J).NE.ZERO) .OR. (Y(J).NE.ZERO)) THEN
213: TEMP1 = ALPHA*DCONJG(Y(J))
214: TEMP2 = DCONJG(ALPHA*X(J))
215: AP(KK) = DBLE(AP(KK)) +
216: + DBLE(X(J)*TEMP1+Y(J)*TEMP2)
217: K = KK + 1
218: DO 50 I = J + 1,N
219: AP(K) = AP(K) + X(I)*TEMP1 + Y(I)*TEMP2
220: K = K + 1
221: 50 CONTINUE
222: ELSE
223: AP(KK) = DBLE(AP(KK))
224: END IF
225: KK = KK + N - J + 1
226: 60 CONTINUE
227: ELSE
228: DO 80 J = 1,N
229: IF ((X(JX).NE.ZERO) .OR. (Y(JY).NE.ZERO)) THEN
230: TEMP1 = ALPHA*DCONJG(Y(JY))
231: TEMP2 = DCONJG(ALPHA*X(JX))
232: AP(KK) = DBLE(AP(KK)) +
233: + DBLE(X(JX)*TEMP1+Y(JY)*TEMP2)
234: IX = JX
235: IY = JY
236: DO 70 K = KK + 1,KK + N - J
237: IX = IX + INCX
238: IY = IY + INCY
239: AP(K) = AP(K) + X(IX)*TEMP1 + Y(IY)*TEMP2
240: 70 CONTINUE
241: ELSE
242: AP(KK) = DBLE(AP(KK))
243: END IF
244: JX = JX + INCX
245: JY = JY + INCY
246: KK = KK + N - J + 1
247: 80 CONTINUE
248: END IF
249: END IF
250: *
251: RETURN
252: *
253: * End of ZHPR2 .
254: *
255: END
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