LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
dspr2.f
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1 *> \brief \b DSPR2
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 DSPR2(UPLO,N,ALPHA,X,INCX,Y,INCY,AP)
12 *
13 * .. Scalar Arguments ..
14 * DOUBLE PRECISION ALPHA
15 * INTEGER INCX,INCY,N
16 * CHARACTER UPLO
17 * ..
18 * .. Array Arguments ..
19 * DOUBLE PRECISION AP(*),X(*),Y(*)
20 * ..
21 *
22 *
23 *> \par Purpose:
24 * =============
25 *>
26 *> \verbatim
27 *>
28 *> DSPR2 performs the symmetric rank 2 operation
29 *>
30 *> A := alpha*x*y**T + alpha*y*x**T + A,
31 *>
32 *> where alpha is a scalar, x and y are n element vectors and A is an
33 *> n by n symmetric 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 symmetric 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 symmetric 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 *> \endverbatim
115 *
116 * Authors:
117 * ========
118 *
119 *> \author Univ. of Tennessee
120 *> \author Univ. of California Berkeley
121 *> \author Univ. of Colorado Denver
122 *> \author NAG Ltd.
123 *
124 *> \date November 2011
125 *
126 *> \ingroup double_blas_level2
127 *
128 *> \par Further Details:
129 * =====================
130 *>
131 *> \verbatim
132 *>
133 *> Level 2 Blas routine.
134 *>
135 *> -- Written on 22-October-1986.
136 *> Jack Dongarra, Argonne National Lab.
137 *> Jeremy Du Croz, Nag Central Office.
138 *> Sven Hammarling, Nag Central Office.
139 *> Richard Hanson, Sandia National Labs.
140 *> \endverbatim
141 *>
142 * =====================================================================
143  SUBROUTINE dspr2(UPLO,N,ALPHA,X,INCX,Y,INCY,AP)
144 *
145 * -- Reference BLAS level2 routine (version 3.4.0) --
146 * -- Reference BLAS is a software package provided by Univ. of Tennessee, --
147 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
148 * November 2011
149 *
150 * .. Scalar Arguments ..
151  DOUBLE PRECISION ALPHA
152  INTEGER INCX,INCY,N
153  CHARACTER UPLO
154 * ..
155 * .. Array Arguments ..
156  DOUBLE PRECISION AP(*),X(*),Y(*)
157 * ..
158 *
159 * =====================================================================
160 *
161 * .. Parameters ..
162  DOUBLE PRECISION ZERO
163  parameter(zero=0.0d+0)
164 * ..
165 * .. Local Scalars ..
166  DOUBLE PRECISION 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 *
177 * Test the input parameters.
178 *
179  info = 0
180  IF (.NOT.lsame(uplo,'U') .AND. .NOT.lsame(uplo,'L')) THEN
181  info = 1
182  ELSE IF (n.LT.0) THEN
183  info = 2
184  ELSE IF (incx.EQ.0) THEN
185  info = 5
186  ELSE IF (incy.EQ.0) THEN
187  info = 7
188  END IF
189  IF (info.NE.0) THEN
190  CALL xerbla('DSPR2 ',info)
191  RETURN
192  END IF
193 *
194 * Quick return if possible.
195 *
196  IF ((n.EQ.0) .OR. (alpha.EQ.zero)) RETURN
197 *
198 * Set up the start points in X and Y if the increments are not both
199 * unity.
200 *
201  IF ((incx.NE.1) .OR. (incy.NE.1)) THEN
202  IF (incx.GT.0) THEN
203  kx = 1
204  ELSE
205  kx = 1 - (n-1)*incx
206  END IF
207  IF (incy.GT.0) THEN
208  ky = 1
209  ELSE
210  ky = 1 - (n-1)*incy
211  END IF
212  jx = kx
213  jy = ky
214  END IF
215 *
216 * Start the operations. In this version the elements of the array AP
217 * are accessed sequentially with one pass through AP.
218 *
219  kk = 1
220  IF (lsame(uplo,'U')) THEN
221 *
222 * Form A when upper triangle is stored in AP.
223 *
224  IF ((incx.EQ.1) .AND. (incy.EQ.1)) THEN
225  DO 20 j = 1,n
226  IF ((x(j).NE.zero) .OR. (y(j).NE.zero)) THEN
227  temp1 = alpha*y(j)
228  temp2 = alpha*x(j)
229  k = kk
230  DO 10 i = 1,j
231  ap(k) = ap(k) + x(i)*temp1 + y(i)*temp2
232  k = k + 1
233  10 CONTINUE
234  END IF
235  kk = kk + j
236  20 CONTINUE
237  ELSE
238  DO 40 j = 1,n
239  IF ((x(jx).NE.zero) .OR. (y(jy).NE.zero)) THEN
240  temp1 = alpha*y(jy)
241  temp2 = alpha*x(jx)
242  ix = kx
243  iy = ky
244  DO 30 k = kk,kk + j - 1
245  ap(k) = ap(k) + x(ix)*temp1 + y(iy)*temp2
246  ix = ix + incx
247  iy = iy + incy
248  30 CONTINUE
249  END IF
250  jx = jx + incx
251  jy = jy + incy
252  kk = kk + j
253  40 CONTINUE
254  END IF
255  ELSE
256 *
257 * Form A when lower triangle is stored in AP.
258 *
259  IF ((incx.EQ.1) .AND. (incy.EQ.1)) THEN
260  DO 60 j = 1,n
261  IF ((x(j).NE.zero) .OR. (y(j).NE.zero)) THEN
262  temp1 = alpha*y(j)
263  temp2 = alpha*x(j)
264  k = kk
265  DO 50 i = j,n
266  ap(k) = ap(k) + x(i)*temp1 + y(i)*temp2
267  k = k + 1
268  50 CONTINUE
269  END IF
270  kk = kk + n - j + 1
271  60 CONTINUE
272  ELSE
273  DO 80 j = 1,n
274  IF ((x(jx).NE.zero) .OR. (y(jy).NE.zero)) THEN
275  temp1 = alpha*y(jy)
276  temp2 = alpha*x(jx)
277  ix = jx
278  iy = jy
279  DO 70 k = kk,kk + n - j
280  ap(k) = ap(k) + x(ix)*temp1 + y(iy)*temp2
281  ix = ix + incx
282  iy = iy + incy
283  70 CONTINUE
284  END IF
285  jx = jx + incx
286  jy = jy + incy
287  kk = kk + n - j + 1
288  80 CONTINUE
289  END IF
290  END IF
291 *
292  RETURN
293 *
294 * End of DSPR2 .
295 *
296  END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
subroutine dspr2(UPLO, N, ALPHA, X, INCX, Y, INCY, AP)
DSPR2
Definition: dspr2.f:144