LAPACK  3.10.1 LAPACK: Linear Algebra PACKage
chpr2.f
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1 *> \brief \b CHPR2
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 CHPR2(UPLO,N,ALPHA,X,INCX,Y,INCY,AP)
12 *
13 * .. Scalar Arguments ..
14 * COMPLEX ALPHA
15 * INTEGER INCX,INCY,N
16 * CHARACTER UPLO
17 * ..
18 * .. Array Arguments ..
19 * COMPLEX AP(*),X(*),Y(*)
20 * ..
21 *
22 *
23 *> \par Purpose:
24 * =============
25 *>
26 *> \verbatim
27 *>
28 *> CHPR2 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
63 *> On entry, ALPHA specifies the scalar alpha.
64 *> \endverbatim
65 *>
66 *> \param[in] X
67 *> \verbatim
68 *> X is COMPLEX 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] Y
82 *> \verbatim
83 *> Y is COMPLEX array, 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 array, 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 *> \ingroup complex_blas_level2
128 *
129 *> \par Further Details:
130 * =====================
131 *>
132 *> \verbatim
133 *>
134 *> Level 2 Blas routine.
135 *>
136 *> -- Written on 22-October-1986.
137 *> Jack Dongarra, Argonne National Lab.
138 *> Jeremy Du Croz, Nag Central Office.
139 *> Sven Hammarling, Nag Central Office.
140 *> Richard Hanson, Sandia National Labs.
141 *> \endverbatim
142 *>
143 * =====================================================================
144  SUBROUTINE chpr2(UPLO,N,ALPHA,X,INCX,Y,INCY,AP)
145 *
146 * -- Reference BLAS level2 routine --
147 * -- Reference BLAS is a software package provided by Univ. of Tennessee, --
148 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
149 *
150 * .. Scalar Arguments ..
151  COMPLEX ALPHA
152  INTEGER INCX,INCY,N
153  CHARACTER UPLO
154 * ..
155 * .. Array Arguments ..
156  COMPLEX AP(*),X(*),Y(*)
157 * ..
158 *
159 * =====================================================================
160 *
161 * .. Parameters ..
162  COMPLEX ZERO
163  parameter(zero= (0.0e+0,0.0e+0))
164 * ..
165 * .. Local Scalars ..
166  COMPLEX TEMP1,TEMP2
167  INTEGER I,INFO,IX,IY,J,JX,JY,K,KK,KX,KY
168 * ..
169 * .. External Functions ..
170  LOGICAL LSAME
171  EXTERNAL lsame
172 * ..
173 * .. External Subroutines ..
174  EXTERNAL xerbla
175 * ..
176 * .. Intrinsic Functions ..
177  INTRINSIC conjg,real
178 * ..
179 *
180 * Test the input parameters.
181 *
182  info = 0
183  IF (.NOT.lsame(uplo,'U') .AND. .NOT.lsame(uplo,'L')) THEN
184  info = 1
185  ELSE IF (n.LT.0) THEN
186  info = 2
187  ELSE IF (incx.EQ.0) THEN
188  info = 5
189  ELSE IF (incy.EQ.0) THEN
190  info = 7
191  END IF
192  IF (info.NE.0) THEN
193  CALL xerbla('CHPR2 ',info)
194  RETURN
195  END IF
196 *
197 * Quick return if possible.
198 *
199  IF ((n.EQ.0) .OR. (alpha.EQ.zero)) RETURN
200 *
201 * Set up the start points in X and Y if the increments are not both
202 * unity.
203 *
204  IF ((incx.NE.1) .OR. (incy.NE.1)) THEN
205  IF (incx.GT.0) THEN
206  kx = 1
207  ELSE
208  kx = 1 - (n-1)*incx
209  END IF
210  IF (incy.GT.0) THEN
211  ky = 1
212  ELSE
213  ky = 1 - (n-1)*incy
214  END IF
215  jx = kx
216  jy = ky
217  END IF
218 *
219 * Start the operations. In this version the elements of the array AP
220 * are accessed sequentially with one pass through AP.
221 *
222  kk = 1
223  IF (lsame(uplo,'U')) THEN
224 *
225 * Form A when upper triangle is stored in AP.
226 *
227  IF ((incx.EQ.1) .AND. (incy.EQ.1)) THEN
228  DO 20 j = 1,n
229  IF ((x(j).NE.zero) .OR. (y(j).NE.zero)) THEN
230  temp1 = alpha*conjg(y(j))
231  temp2 = conjg(alpha*x(j))
232  k = kk
233  DO 10 i = 1,j - 1
234  ap(k) = ap(k) + x(i)*temp1 + y(i)*temp2
235  k = k + 1
236  10 CONTINUE
237  ap(kk+j-1) = real(ap(kk+j-1)) +
238  + real(x(j)*temp1+y(j)*temp2)
239  ELSE
240  ap(kk+j-1) = real(ap(kk+j-1))
241  END IF
242  kk = kk + j
243  20 CONTINUE
244  ELSE
245  DO 40 j = 1,n
246  IF ((x(jx).NE.zero) .OR. (y(jy).NE.zero)) THEN
247  temp1 = alpha*conjg(y(jy))
248  temp2 = conjg(alpha*x(jx))
249  ix = kx
250  iy = ky
251  DO 30 k = kk,kk + j - 2
252  ap(k) = ap(k) + x(ix)*temp1 + y(iy)*temp2
253  ix = ix + incx
254  iy = iy + incy
255  30 CONTINUE
256  ap(kk+j-1) = real(ap(kk+j-1)) +
257  + real(x(jx)*temp1+y(jy)*temp2)
258  ELSE
259  ap(kk+j-1) = real(ap(kk+j-1))
260  END IF
261  jx = jx + incx
262  jy = jy + incy
263  kk = kk + j
264  40 CONTINUE
265  END IF
266  ELSE
267 *
268 * Form A when lower triangle is stored in AP.
269 *
270  IF ((incx.EQ.1) .AND. (incy.EQ.1)) THEN
271  DO 60 j = 1,n
272  IF ((x(j).NE.zero) .OR. (y(j).NE.zero)) THEN
273  temp1 = alpha*conjg(y(j))
274  temp2 = conjg(alpha*x(j))
275  ap(kk) = real(ap(kk)) +
276  + real(x(j)*temp1+y(j)*temp2)
277  k = kk + 1
278  DO 50 i = j + 1,n
279  ap(k) = ap(k) + x(i)*temp1 + y(i)*temp2
280  k = k + 1
281  50 CONTINUE
282  ELSE
283  ap(kk) = real(ap(kk))
284  END IF
285  kk = kk + n - j + 1
286  60 CONTINUE
287  ELSE
288  DO 80 j = 1,n
289  IF ((x(jx).NE.zero) .OR. (y(jy).NE.zero)) THEN
290  temp1 = alpha*conjg(y(jy))
291  temp2 = conjg(alpha*x(jx))
292  ap(kk) = real(ap(kk)) +
293  + real(x(jx)*temp1+y(jy)*temp2)
294  ix = jx
295  iy = jy
296  DO 70 k = kk + 1,kk + n - j
297  ix = ix + incx
298  iy = iy + incy
299  ap(k) = ap(k) + x(ix)*temp1 + y(iy)*temp2
300  70 CONTINUE
301  ELSE
302  ap(kk) = real(ap(kk))
303  END IF
304  jx = jx + incx
305  jy = jy + incy
306  kk = kk + n - j + 1
307  80 CONTINUE
308  END IF
309  END IF
310 *
311  RETURN
312 *
313 * End of CHPR2
314 *
315  END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine chpr2(UPLO, N, ALPHA, X, INCX, Y, INCY, AP)
CHPR2
Definition: chpr2.f:145