1: *> \brief \b ZHPR
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 ZHPR(UPLO,N,ALPHA,X,INCX,AP)
12: *
13: * .. Scalar Arguments ..
14: * DOUBLE PRECISION ALPHA
15: * INTEGER INCX,N
16: * CHARACTER UPLO
17: * ..
18: * .. Array Arguments ..
19: * COMPLEX*16 AP(*),X(*)
20: * ..
21: *
22: *
23: *> \par Purpose:
24: * =============
25: *>
26: *> \verbatim
27: *>
28: *> ZHPR performs the hermitian rank 1 operation
29: *>
30: *> A := alpha*x*x**H + A,
31: *>
32: *> where alpha is a real scalar, x is an n element vector 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 DOUBLE PRECISION.
63: *> On entry, ALPHA specifies the scalar alpha.
64: *> \endverbatim
65: *>
66: *> \param[in] X
67: *> \verbatim
68: *> X is COMPLEX*16 array, 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,out] AP
82: *> \verbatim
83: *> AP is COMPLEX*16 array, dimension at least
84: *> ( ( n*( n + 1 ) )/2 ).
85: *> Before entry with UPLO = 'U' or 'u', the array AP must
86: *> contain the upper triangular part of the hermitian matrix
87: *> packed sequentially, column by column, so that AP( 1 )
88: *> contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 )
89: *> and a( 2, 2 ) respectively, and so on. On exit, the array
90: *> AP is overwritten by the upper triangular part of the
91: *> updated matrix.
92: *> Before entry with UPLO = 'L' or 'l', the array AP must
93: *> contain the lower triangular part of the hermitian matrix
94: *> packed sequentially, column by column, so that AP( 1 )
95: *> contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 )
96: *> and a( 3, 1 ) respectively, and so on. On exit, the array
97: *> AP is overwritten by the lower triangular part of the
98: *> updated matrix.
99: *> Note that the imaginary parts of the diagonal elements need
100: *> not be set, they are assumed to be zero, and on exit they
101: *> are set to zero.
102: *> \endverbatim
103: *
104: * Authors:
105: * ========
106: *
107: *> \author Univ. of Tennessee
108: *> \author Univ. of California Berkeley
109: *> \author Univ. of Colorado Denver
110: *> \author NAG Ltd.
111: *
112: *> \ingroup complex16_blas_level2
113: *
114: *> \par Further Details:
115: * =====================
116: *>
117: *> \verbatim
118: *>
119: *> Level 2 Blas routine.
120: *>
121: *> -- Written on 22-October-1986.
122: *> Jack Dongarra, Argonne National Lab.
123: *> Jeremy Du Croz, Nag Central Office.
124: *> Sven Hammarling, Nag Central Office.
125: *> Richard Hanson, Sandia National Labs.
126: *> \endverbatim
127: *>
128: * =====================================================================
129: SUBROUTINE ZHPR(UPLO,N,ALPHA,X,INCX,AP)
130: *
131: * -- Reference BLAS level2 routine --
132: * -- Reference BLAS is a software package provided by Univ. of Tennessee, --
133: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
134: *
135: * .. Scalar Arguments ..
136: DOUBLE PRECISION ALPHA
137: INTEGER INCX,N
138: CHARACTER UPLO
139: * ..
140: * .. Array Arguments ..
141: COMPLEX*16 AP(*),X(*)
142: * ..
143: *
144: * =====================================================================
145: *
146: * .. Parameters ..
147: COMPLEX*16 ZERO
148: PARAMETER (ZERO= (0.0D+0,0.0D+0))
149: * ..
150: * .. Local Scalars ..
151: COMPLEX*16 TEMP
152: INTEGER I,INFO,IX,J,JX,K,KK,KX
153: * ..
154: * .. External Functions ..
155: LOGICAL LSAME
156: EXTERNAL LSAME
157: * ..
158: * .. External Subroutines ..
159: EXTERNAL XERBLA
160: * ..
161: * .. Intrinsic Functions ..
162: INTRINSIC DBLE,DCONJG
163: * ..
164: *
165: * Test the input parameters.
166: *
167: INFO = 0
168: IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN
169: INFO = 1
170: ELSE IF (N.LT.0) THEN
171: INFO = 2
172: ELSE IF (INCX.EQ.0) THEN
173: INFO = 5
174: END IF
175: IF (INFO.NE.0) THEN
176: CALL XERBLA('ZHPR ',INFO)
177: RETURN
178: END IF
179: *
180: * Quick return if possible.
181: *
182: IF ((N.EQ.0) .OR. (ALPHA.EQ.DBLE(ZERO))) RETURN
183: *
184: * Set the start point in X if the increment is not unity.
185: *
186: IF (INCX.LE.0) THEN
187: KX = 1 - (N-1)*INCX
188: ELSE IF (INCX.NE.1) THEN
189: KX = 1
190: END IF
191: *
192: * Start the operations. In this version the elements of the array AP
193: * are accessed sequentially with one pass through AP.
194: *
195: KK = 1
196: IF (LSAME(UPLO,'U')) THEN
197: *
198: * Form A when upper triangle is stored in AP.
199: *
200: IF (INCX.EQ.1) THEN
201: DO 20 J = 1,N
202: IF (X(J).NE.ZERO) THEN
203: TEMP = ALPHA*DCONJG(X(J))
204: K = KK
205: DO 10 I = 1,J - 1
206: AP(K) = AP(K) + X(I)*TEMP
207: K = K + 1
208: 10 CONTINUE
209: AP(KK+J-1) = DBLE(AP(KK+J-1)) + DBLE(X(J)*TEMP)
210: ELSE
211: AP(KK+J-1) = DBLE(AP(KK+J-1))
212: END IF
213: KK = KK + J
214: 20 CONTINUE
215: ELSE
216: JX = KX
217: DO 40 J = 1,N
218: IF (X(JX).NE.ZERO) THEN
219: TEMP = ALPHA*DCONJG(X(JX))
220: IX = KX
221: DO 30 K = KK,KK + J - 2
222: AP(K) = AP(K) + X(IX)*TEMP
223: IX = IX + INCX
224: 30 CONTINUE
225: AP(KK+J-1) = DBLE(AP(KK+J-1)) + DBLE(X(JX)*TEMP)
226: ELSE
227: AP(KK+J-1) = DBLE(AP(KK+J-1))
228: END IF
229: JX = JX + INCX
230: KK = KK + J
231: 40 CONTINUE
232: END IF
233: ELSE
234: *
235: * Form A when lower triangle is stored in AP.
236: *
237: IF (INCX.EQ.1) THEN
238: DO 60 J = 1,N
239: IF (X(J).NE.ZERO) THEN
240: TEMP = ALPHA*DCONJG(X(J))
241: AP(KK) = DBLE(AP(KK)) + DBLE(TEMP*X(J))
242: K = KK + 1
243: DO 50 I = J + 1,N
244: AP(K) = AP(K) + X(I)*TEMP
245: K = K + 1
246: 50 CONTINUE
247: ELSE
248: AP(KK) = DBLE(AP(KK))
249: END IF
250: KK = KK + N - J + 1
251: 60 CONTINUE
252: ELSE
253: JX = KX
254: DO 80 J = 1,N
255: IF (X(JX).NE.ZERO) THEN
256: TEMP = ALPHA*DCONJG(X(JX))
257: AP(KK) = DBLE(AP(KK)) + DBLE(TEMP*X(JX))
258: IX = JX
259: DO 70 K = KK + 1,KK + N - J
260: IX = IX + INCX
261: AP(K) = AP(K) + X(IX)*TEMP
262: 70 CONTINUE
263: ELSE
264: AP(KK) = DBLE(AP(KK))
265: END IF
266: JX = JX + INCX
267: KK = KK + N - J + 1
268: 80 CONTINUE
269: END IF
270: END IF
271: *
272: RETURN
273: *
274: * End of ZHPR
275: *
276: END
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