LAPACK  3.10.1 LAPACK: Linear Algebra PACKage
chpr.f
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1 *> \brief \b CHPR
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 CHPR(UPLO,N,ALPHA,X,INCX,AP)
12 *
13 * .. Scalar Arguments ..
14 * REAL ALPHA
15 * INTEGER INCX,N
16 * CHARACTER UPLO
17 * ..
18 * .. Array Arguments ..
19 * COMPLEX AP(*),X(*)
20 * ..
21 *
22 *
23 *> \par Purpose:
24 * =============
25 *>
26 *> \verbatim
27 *>
28 *> CHPR 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 REAL
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,out] AP
82 *> \verbatim
83 *> AP is COMPLEX 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 complex_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 chpr(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  REAL ALPHA
137  INTEGER INCX,N
138  CHARACTER UPLO
139 * ..
140 * .. Array Arguments ..
141  COMPLEX AP(*),X(*)
142 * ..
143 *
144 * =====================================================================
145 *
146 * .. Parameters ..
147  COMPLEX ZERO
148  parameter(zero= (0.0e+0,0.0e+0))
149 * ..
150 * .. Local Scalars ..
151  COMPLEX 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 conjg,real
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('CHPR ',info)
177  RETURN
178  END IF
179 *
180 * Quick return if possible.
181 *
182  IF ((n.EQ.0) .OR. (alpha.EQ.real(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*conjg(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) = real(ap(kk+j-1)) + real(x(j)*temp)
210  ELSE
211  ap(kk+j-1) = real(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*conjg(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) = real(ap(kk+j-1)) + real(x(jx)*temp)
226  ELSE
227  ap(kk+j-1) = real(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*conjg(x(j))
241  ap(kk) = real(ap(kk)) + real(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) = real(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*conjg(x(jx))
257  ap(kk) = real(ap(kk)) + real(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) = real(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 CHPR
275 *
276  END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine chpr(UPLO, N, ALPHA, X, INCX, AP)
CHPR
Definition: chpr.f:130