LAPACK  3.10.0
LAPACK: Linear Algebra PACKage
cher2.f
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1 *> \brief \b CHER2
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 CHER2(UPLO,N,ALPHA,X,INCX,Y,INCY,A,LDA)
12 *
13 * .. Scalar Arguments ..
14 * COMPLEX ALPHA
15 * INTEGER INCX,INCY,LDA,N
16 * CHARACTER UPLO
17 * ..
18 * .. Array Arguments ..
19 * COMPLEX A(LDA,*),X(*),Y(*)
20 * ..
21 *
22 *
23 *> \par Purpose:
24 * =============
25 *>
26 *> \verbatim
27 *>
28 *> CHER2 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 n
33 *> by n hermitian matrix.
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 array A is to be referenced as
44 *> follows:
45 *>
46 *> UPLO = 'U' or 'u' Only the upper triangular part of A
47 *> is to be referenced.
48 *>
49 *> UPLO = 'L' or 'l' Only the lower triangular part of A
50 *> is to be referenced.
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] A
97 *> \verbatim
98 *> A is COMPLEX array, dimension ( LDA, N )
99 *> Before entry with UPLO = 'U' or 'u', the leading n by n
100 *> upper triangular part of the array A must contain the upper
101 *> triangular part of the hermitian matrix and the strictly
102 *> lower triangular part of A is not referenced. On exit, the
103 *> upper triangular part of the array A is overwritten by the
104 *> upper triangular part of the updated matrix.
105 *> Before entry with UPLO = 'L' or 'l', the leading n by n
106 *> lower triangular part of the array A must contain the lower
107 *> triangular part of the hermitian matrix and the strictly
108 *> upper triangular part of A is not referenced. On exit, the
109 *> lower triangular part of the array A is overwritten by the
110 *> lower triangular part of the updated matrix.
111 *> Note that the imaginary parts of the diagonal elements need
112 *> not be set, they are assumed to be zero, and on exit they
113 *> are set to zero.
114 *> \endverbatim
115 *>
116 *> \param[in] LDA
117 *> \verbatim
118 *> LDA is INTEGER
119 *> On entry, LDA specifies the first dimension of A as declared
120 *> in the calling (sub) program. LDA must be at least
121 *> max( 1, n ).
122 *> \endverbatim
123 *
124 * Authors:
125 * ========
126 *
127 *> \author Univ. of Tennessee
128 *> \author Univ. of California Berkeley
129 *> \author Univ. of Colorado Denver
130 *> \author NAG Ltd.
131 *
132 *> \ingroup complex_blas_level2
133 *
134 *> \par Further Details:
135 * =====================
136 *>
137 *> \verbatim
138 *>
139 *> Level 2 Blas routine.
140 *>
141 *> -- Written on 22-October-1986.
142 *> Jack Dongarra, Argonne National Lab.
143 *> Jeremy Du Croz, Nag Central Office.
144 *> Sven Hammarling, Nag Central Office.
145 *> Richard Hanson, Sandia National Labs.
146 *> \endverbatim
147 *>
148 * =====================================================================
149  SUBROUTINE cher2(UPLO,N,ALPHA,X,INCX,Y,INCY,A,LDA)
150 *
151 * -- Reference BLAS level2 routine --
152 * -- Reference BLAS is a software package provided by Univ. of Tennessee, --
153 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
154 *
155 * .. Scalar Arguments ..
156  COMPLEX ALPHA
157  INTEGER INCX,INCY,LDA,N
158  CHARACTER UPLO
159 * ..
160 * .. Array Arguments ..
161  COMPLEX A(LDA,*),X(*),Y(*)
162 * ..
163 *
164 * =====================================================================
165 *
166 * .. Parameters ..
167  COMPLEX ZERO
168  parameter(zero= (0.0e+0,0.0e+0))
169 * ..
170 * .. Local Scalars ..
171  COMPLEX TEMP1,TEMP2
172  INTEGER I,INFO,IX,IY,J,JX,JY,KX,KY
173 * ..
174 * .. External Functions ..
175  LOGICAL LSAME
176  EXTERNAL lsame
177 * ..
178 * .. External Subroutines ..
179  EXTERNAL xerbla
180 * ..
181 * .. Intrinsic Functions ..
182  INTRINSIC conjg,max,real
183 * ..
184 *
185 * Test the input parameters.
186 *
187  info = 0
188  IF (.NOT.lsame(uplo,'U') .AND. .NOT.lsame(uplo,'L')) THEN
189  info = 1
190  ELSE IF (n.LT.0) THEN
191  info = 2
192  ELSE IF (incx.EQ.0) THEN
193  info = 5
194  ELSE IF (incy.EQ.0) THEN
195  info = 7
196  ELSE IF (lda.LT.max(1,n)) THEN
197  info = 9
198  END IF
199  IF (info.NE.0) THEN
200  CALL xerbla('CHER2 ',info)
201  RETURN
202  END IF
203 *
204 * Quick return if possible.
205 *
206  IF ((n.EQ.0) .OR. (alpha.EQ.zero)) RETURN
207 *
208 * Set up the start points in X and Y if the increments are not both
209 * unity.
210 *
211  IF ((incx.NE.1) .OR. (incy.NE.1)) THEN
212  IF (incx.GT.0) THEN
213  kx = 1
214  ELSE
215  kx = 1 - (n-1)*incx
216  END IF
217  IF (incy.GT.0) THEN
218  ky = 1
219  ELSE
220  ky = 1 - (n-1)*incy
221  END IF
222  jx = kx
223  jy = ky
224  END IF
225 *
226 * Start the operations. In this version the elements of A are
227 * accessed sequentially with one pass through the triangular part
228 * of A.
229 *
230  IF (lsame(uplo,'U')) THEN
231 *
232 * Form A when A is stored in the upper triangle.
233 *
234  IF ((incx.EQ.1) .AND. (incy.EQ.1)) THEN
235  DO 20 j = 1,n
236  IF ((x(j).NE.zero) .OR. (y(j).NE.zero)) THEN
237  temp1 = alpha*conjg(y(j))
238  temp2 = conjg(alpha*x(j))
239  DO 10 i = 1,j - 1
240  a(i,j) = a(i,j) + x(i)*temp1 + y(i)*temp2
241  10 CONTINUE
242  a(j,j) = real(a(j,j)) +
243  + real(x(j)*temp1+y(j)*temp2)
244  ELSE
245  a(j,j) = real(a(j,j))
246  END IF
247  20 CONTINUE
248  ELSE
249  DO 40 j = 1,n
250  IF ((x(jx).NE.zero) .OR. (y(jy).NE.zero)) THEN
251  temp1 = alpha*conjg(y(jy))
252  temp2 = conjg(alpha*x(jx))
253  ix = kx
254  iy = ky
255  DO 30 i = 1,j - 1
256  a(i,j) = a(i,j) + x(ix)*temp1 + y(iy)*temp2
257  ix = ix + incx
258  iy = iy + incy
259  30 CONTINUE
260  a(j,j) = real(a(j,j)) +
261  + real(x(jx)*temp1+y(jy)*temp2)
262  ELSE
263  a(j,j) = real(a(j,j))
264  END IF
265  jx = jx + incx
266  jy = jy + incy
267  40 CONTINUE
268  END IF
269  ELSE
270 *
271 * Form A when A is stored in the lower triangle.
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*conjg(y(j))
277  temp2 = conjg(alpha*x(j))
278  a(j,j) = real(a(j,j)) +
279  + real(x(j)*temp1+y(j)*temp2)
280  DO 50 i = j + 1,n
281  a(i,j) = a(i,j) + x(i)*temp1 + y(i)*temp2
282  50 CONTINUE
283  ELSE
284  a(j,j) = real(a(j,j))
285  END IF
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  a(j,j) = real(a(j,j)) +
293  + real(x(jx)*temp1+y(jy)*temp2)
294  ix = jx
295  iy = jy
296  DO 70 i = j + 1,n
297  ix = ix + incx
298  iy = iy + incy
299  a(i,j) = a(i,j) + x(ix)*temp1 + y(iy)*temp2
300  70 CONTINUE
301  ELSE
302  a(j,j) = real(a(j,j))
303  END IF
304  jx = jx + incx
305  jy = jy + incy
306  80 CONTINUE
307  END IF
308  END IF
309 *
310  RETURN
311 *
312 * End of CHER2
313 *
314  END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine cher2(UPLO, N, ALPHA, X, INCX, Y, INCY, A, LDA)
CHER2
Definition: cher2.f:150