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1.8 bertrand 1: *> \brief \b ZHPR2
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: * Definition:
9: * ===========
10: *
11: * SUBROUTINE ZHPR2(UPLO,N,ALPHA,X,INCX,Y,INCY,AP)
12: *
13: * .. Scalar Arguments ..
14: * COMPLEX*16 ALPHA
15: * INTEGER INCX,INCY,N
16: * CHARACTER UPLO
17: * ..
18: * .. Array Arguments ..
19: * COMPLEX*16 AP(*),X(*),Y(*)
20: * ..
21: *
22: *
23: *> \par Purpose:
24: * =============
25: *>
26: *> \verbatim
27: *>
28: *> ZHPR2 performs the hermitian rank 2 operation
29: *>
30: *> A := alpha*x*y**H + conjg( alpha )*y*x**H + A,
31: *>
32: *> where alpha is a scalar, x and y are n element vectors and A is an
33: *> n by n hermitian matrix, supplied in packed form.
34: *> \endverbatim
35: *
36: * Arguments:
37: * ==========
38: *
39: *> \param[in] UPLO
40: *> \verbatim
41: *> UPLO is CHARACTER*1
42: *> On entry, UPLO specifies whether the upper or lower
43: *> triangular part of the matrix A is supplied in the packed
44: *> array AP as follows:
45: *>
46: *> UPLO = 'U' or 'u' The upper triangular part of A is
47: *> supplied in AP.
48: *>
49: *> UPLO = 'L' or 'l' The lower triangular part of A is
50: *> supplied in AP.
51: *> \endverbatim
52: *>
53: *> \param[in] N
54: *> \verbatim
55: *> N is INTEGER
56: *> On entry, N specifies the order of the matrix A.
57: *> N must be at least zero.
58: *> \endverbatim
59: *>
60: *> \param[in] ALPHA
61: *> \verbatim
62: *> ALPHA is COMPLEX*16
63: *> On entry, ALPHA specifies the scalar alpha.
64: *> \endverbatim
65: *>
66: *> \param[in] X
67: *> \verbatim
68: *> X is COMPLEX*16 array of dimension at least
69: *> ( 1 + ( n - 1 )*abs( INCX ) ).
70: *> Before entry, the incremented array X must contain the n
71: *> element vector x.
72: *> \endverbatim
73: *>
74: *> \param[in] INCX
75: *> \verbatim
76: *> INCX is INTEGER
77: *> On entry, INCX specifies the increment for the elements of
78: *> X. INCX must not be zero.
79: *> \endverbatim
80: *>
81: *> \param[in] Y
82: *> \verbatim
83: *> Y is COMPLEX*16 array of dimension at least
84: *> ( 1 + ( n - 1 )*abs( INCY ) ).
85: *> Before entry, the incremented array Y must contain the n
86: *> element vector y.
87: *> \endverbatim
88: *>
89: *> \param[in] INCY
90: *> \verbatim
91: *> INCY is INTEGER
92: *> On entry, INCY specifies the increment for the elements of
93: *> Y. INCY must not be zero.
94: *> \endverbatim
95: *>
96: *> \param[in,out] AP
97: *> \verbatim
98: *> AP is COMPLEX*16 array of DIMENSION at least
99: *> ( ( n*( n + 1 ) )/2 ).
100: *> Before entry with UPLO = 'U' or 'u', the array AP must
101: *> contain the upper triangular part of the hermitian matrix
102: *> packed sequentially, column by column, so that AP( 1 )
103: *> contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 )
104: *> and a( 2, 2 ) respectively, and so on. On exit, the array
105: *> AP is overwritten by the upper triangular part of the
106: *> updated matrix.
107: *> Before entry with UPLO = 'L' or 'l', the array AP must
108: *> contain the lower triangular part of the hermitian matrix
109: *> packed sequentially, column by column, so that AP( 1 )
110: *> contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 )
111: *> and a( 3, 1 ) respectively, and so on. On exit, the array
112: *> AP is overwritten by the lower triangular part of the
113: *> updated matrix.
114: *> Note that the imaginary parts of the diagonal elements need
115: *> not be set, they are assumed to be zero, and on exit they
116: *> are set to zero.
117: *> \endverbatim
118: *
119: * Authors:
120: * ========
121: *
122: *> \author Univ. of Tennessee
123: *> \author Univ. of California Berkeley
124: *> \author Univ. of Colorado Denver
125: *> \author NAG Ltd.
126: *
127: *> \date November 2011
128: *
129: *> \ingroup complex16_blas_level2
130: *
131: *> \par Further Details:
132: * =====================
133: *>
134: *> \verbatim
135: *>
136: *> Level 2 Blas routine.
137: *>
138: *> -- Written on 22-October-1986.
139: *> Jack Dongarra, Argonne National Lab.
140: *> Jeremy Du Croz, Nag Central Office.
141: *> Sven Hammarling, Nag Central Office.
142: *> Richard Hanson, Sandia National Labs.
143: *> \endverbatim
144: *>
145: * =====================================================================
1.1 bertrand 146: SUBROUTINE ZHPR2(UPLO,N,ALPHA,X,INCX,Y,INCY,AP)
1.8 bertrand 147: *
148: * -- Reference BLAS level2 routine (version 3.4.0) --
149: * -- Reference BLAS is a software package provided by Univ. of Tennessee, --
150: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
151: * November 2011
152: *
1.1 bertrand 153: * .. Scalar Arguments ..
1.8 bertrand 154: COMPLEX*16 ALPHA
1.1 bertrand 155: INTEGER INCX,INCY,N
156: CHARACTER UPLO
157: * ..
158: * .. Array Arguments ..
1.8 bertrand 159: COMPLEX*16 AP(*),X(*),Y(*)
1.1 bertrand 160: * ..
161: *
162: * =====================================================================
163: *
164: * .. Parameters ..
1.8 bertrand 165: COMPLEX*16 ZERO
1.1 bertrand 166: PARAMETER (ZERO= (0.0D+0,0.0D+0))
167: * ..
168: * .. Local Scalars ..
1.8 bertrand 169: COMPLEX*16 TEMP1,TEMP2
1.1 bertrand 170: INTEGER I,INFO,IX,IY,J,JX,JY,K,KK,KX,KY
171: * ..
172: * .. External Functions ..
173: LOGICAL LSAME
174: EXTERNAL LSAME
175: * ..
176: * .. External Subroutines ..
177: EXTERNAL XERBLA
178: * ..
179: * .. Intrinsic Functions ..
180: INTRINSIC DBLE,DCONJG
181: * ..
182: *
183: * Test the input parameters.
184: *
185: INFO = 0
186: IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN
187: INFO = 1
188: ELSE IF (N.LT.0) THEN
189: INFO = 2
190: ELSE IF (INCX.EQ.0) THEN
191: INFO = 5
192: ELSE IF (INCY.EQ.0) THEN
193: INFO = 7
194: END IF
195: IF (INFO.NE.0) THEN
196: CALL XERBLA('ZHPR2 ',INFO)
197: RETURN
198: END IF
199: *
200: * Quick return if possible.
201: *
202: IF ((N.EQ.0) .OR. (ALPHA.EQ.ZERO)) RETURN
203: *
204: * Set up the start points in X and Y if the increments are not both
205: * unity.
206: *
207: IF ((INCX.NE.1) .OR. (INCY.NE.1)) THEN
208: IF (INCX.GT.0) THEN
209: KX = 1
210: ELSE
211: KX = 1 - (N-1)*INCX
212: END IF
213: IF (INCY.GT.0) THEN
214: KY = 1
215: ELSE
216: KY = 1 - (N-1)*INCY
217: END IF
218: JX = KX
219: JY = KY
220: END IF
221: *
222: * Start the operations. In this version the elements of the array AP
223: * are accessed sequentially with one pass through AP.
224: *
225: KK = 1
226: IF (LSAME(UPLO,'U')) THEN
227: *
228: * Form A when upper triangle is stored in AP.
229: *
230: IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN
231: DO 20 J = 1,N
232: IF ((X(J).NE.ZERO) .OR. (Y(J).NE.ZERO)) THEN
233: TEMP1 = ALPHA*DCONJG(Y(J))
234: TEMP2 = DCONJG(ALPHA*X(J))
235: K = KK
236: DO 10 I = 1,J - 1
237: AP(K) = AP(K) + X(I)*TEMP1 + Y(I)*TEMP2
238: K = K + 1
239: 10 CONTINUE
240: AP(KK+J-1) = DBLE(AP(KK+J-1)) +
241: + DBLE(X(J)*TEMP1+Y(J)*TEMP2)
242: ELSE
243: AP(KK+J-1) = DBLE(AP(KK+J-1))
244: END IF
245: KK = KK + J
246: 20 CONTINUE
247: ELSE
248: DO 40 J = 1,N
249: IF ((X(JX).NE.ZERO) .OR. (Y(JY).NE.ZERO)) THEN
250: TEMP1 = ALPHA*DCONJG(Y(JY))
251: TEMP2 = DCONJG(ALPHA*X(JX))
252: IX = KX
253: IY = KY
254: DO 30 K = KK,KK + J - 2
255: AP(K) = AP(K) + X(IX)*TEMP1 + Y(IY)*TEMP2
256: IX = IX + INCX
257: IY = IY + INCY
258: 30 CONTINUE
259: AP(KK+J-1) = DBLE(AP(KK+J-1)) +
260: + DBLE(X(JX)*TEMP1+Y(JY)*TEMP2)
261: ELSE
262: AP(KK+J-1) = DBLE(AP(KK+J-1))
263: END IF
264: JX = JX + INCX
265: JY = JY + INCY
266: KK = KK + J
267: 40 CONTINUE
268: END IF
269: ELSE
270: *
271: * Form A when lower triangle is stored in AP.
272: *
273: IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN
274: DO 60 J = 1,N
275: IF ((X(J).NE.ZERO) .OR. (Y(J).NE.ZERO)) THEN
276: TEMP1 = ALPHA*DCONJG(Y(J))
277: TEMP2 = DCONJG(ALPHA*X(J))
278: AP(KK) = DBLE(AP(KK)) +
279: + DBLE(X(J)*TEMP1+Y(J)*TEMP2)
280: K = KK + 1
281: DO 50 I = J + 1,N
282: AP(K) = AP(K) + X(I)*TEMP1 + Y(I)*TEMP2
283: K = K + 1
284: 50 CONTINUE
285: ELSE
286: AP(KK) = DBLE(AP(KK))
287: END IF
288: KK = KK + N - J + 1
289: 60 CONTINUE
290: ELSE
291: DO 80 J = 1,N
292: IF ((X(JX).NE.ZERO) .OR. (Y(JY).NE.ZERO)) THEN
293: TEMP1 = ALPHA*DCONJG(Y(JY))
294: TEMP2 = DCONJG(ALPHA*X(JX))
295: AP(KK) = DBLE(AP(KK)) +
296: + DBLE(X(JX)*TEMP1+Y(JY)*TEMP2)
297: IX = JX
298: IY = JY
299: DO 70 K = KK + 1,KK + N - J
300: IX = IX + INCX
301: IY = IY + INCY
302: AP(K) = AP(K) + X(IX)*TEMP1 + Y(IY)*TEMP2
303: 70 CONTINUE
304: ELSE
305: AP(KK) = DBLE(AP(KK))
306: END IF
307: JX = JX + INCX
308: JY = JY + INCY
309: KK = KK + N - J + 1
310: 80 CONTINUE
311: END IF
312: END IF
313: *
314: RETURN
315: *
316: * End of ZHPR2 .
317: *
318: END