LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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dspr.f
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1*> \brief \b DSPR
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 DSPR(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* DOUBLE PRECISION AP(*),X(*)
20* ..
21*
22*
23*> \par Purpose:
24* =============
25*>
26*> \verbatim
27*>
28*> DSPR performs the symmetric rank 1 operation
29*>
30*> A := alpha*x*x**T + A,
31*>
32*> where alpha is a real scalar, x is an n element vector 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, 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 DOUBLE PRECISION 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 symmetric 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 symmetric 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*> \endverbatim
100*
101* Authors:
102* ========
103*
104*> \author Univ. of Tennessee
105*> \author Univ. of California Berkeley
106*> \author Univ. of Colorado Denver
107*> \author NAG Ltd.
108*
109*> \ingroup hpr
110*
111*> \par Further Details:
112* =====================
113*>
114*> \verbatim
115*>
116*> Level 2 Blas routine.
117*>
118*> -- Written on 22-October-1986.
119*> Jack Dongarra, Argonne National Lab.
120*> Jeremy Du Croz, Nag Central Office.
121*> Sven Hammarling, Nag Central Office.
122*> Richard Hanson, Sandia National Labs.
123*> \endverbatim
124*>
125* =====================================================================
126 SUBROUTINE dspr(UPLO,N,ALPHA,X,INCX,AP)
127*
128* -- Reference BLAS level2 routine --
129* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
130* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
131*
132* .. Scalar Arguments ..
133 DOUBLE PRECISION ALPHA
134 INTEGER INCX,N
135 CHARACTER UPLO
136* ..
137* .. Array Arguments ..
138 DOUBLE PRECISION AP(*),X(*)
139* ..
140*
141* =====================================================================
142*
143* .. Parameters ..
144 DOUBLE PRECISION ZERO
145 parameter(zero=0.0d+0)
146* ..
147* .. Local Scalars ..
148 DOUBLE PRECISION TEMP
149 INTEGER I,INFO,IX,J,JX,K,KK,KX
150* ..
151* .. External Functions ..
152 LOGICAL LSAME
153 EXTERNAL lsame
154* ..
155* .. External Subroutines ..
156 EXTERNAL xerbla
157* ..
158*
159* Test the input parameters.
160*
161 info = 0
162 IF (.NOT.lsame(uplo,'U') .AND. .NOT.lsame(uplo,'L')) THEN
163 info = 1
164 ELSE IF (n.LT.0) THEN
165 info = 2
166 ELSE IF (incx.EQ.0) THEN
167 info = 5
168 END IF
169 IF (info.NE.0) THEN
170 CALL xerbla('DSPR ',info)
171 RETURN
172 END IF
173*
174* Quick return if possible.
175*
176 IF ((n.EQ.0) .OR. (alpha.EQ.zero)) RETURN
177*
178* Set the start point in X if the increment is not unity.
179*
180 IF (incx.LE.0) THEN
181 kx = 1 - (n-1)*incx
182 ELSE IF (incx.NE.1) THEN
183 kx = 1
184 END IF
185*
186* Start the operations. In this version the elements of the array AP
187* are accessed sequentially with one pass through AP.
188*
189 kk = 1
190 IF (lsame(uplo,'U')) THEN
191*
192* Form A when upper triangle is stored in AP.
193*
194 IF (incx.EQ.1) THEN
195 DO 20 j = 1,n
196 IF (x(j).NE.zero) THEN
197 temp = alpha*x(j)
198 k = kk
199 DO 10 i = 1,j
200 ap(k) = ap(k) + x(i)*temp
201 k = k + 1
202 10 CONTINUE
203 END IF
204 kk = kk + j
205 20 CONTINUE
206 ELSE
207 jx = kx
208 DO 40 j = 1,n
209 IF (x(jx).NE.zero) THEN
210 temp = alpha*x(jx)
211 ix = kx
212 DO 30 k = kk,kk + j - 1
213 ap(k) = ap(k) + x(ix)*temp
214 ix = ix + incx
215 30 CONTINUE
216 END IF
217 jx = jx + incx
218 kk = kk + j
219 40 CONTINUE
220 END IF
221 ELSE
222*
223* Form A when lower triangle is stored in AP.
224*
225 IF (incx.EQ.1) THEN
226 DO 60 j = 1,n
227 IF (x(j).NE.zero) THEN
228 temp = alpha*x(j)
229 k = kk
230 DO 50 i = j,n
231 ap(k) = ap(k) + x(i)*temp
232 k = k + 1
233 50 CONTINUE
234 END IF
235 kk = kk + n - j + 1
236 60 CONTINUE
237 ELSE
238 jx = kx
239 DO 80 j = 1,n
240 IF (x(jx).NE.zero) THEN
241 temp = alpha*x(jx)
242 ix = jx
243 DO 70 k = kk,kk + n - j
244 ap(k) = ap(k) + x(ix)*temp
245 ix = ix + incx
246 70 CONTINUE
247 END IF
248 jx = jx + incx
249 kk = kk + n - j + 1
250 80 CONTINUE
251 END IF
252 END IF
253*
254 RETURN
255*
256* End of DSPR
257*
258 END
subroutine xerbla(srname, info)
Definition cblat2.f:3285
subroutine dspr(uplo, n, alpha, x, incx, ap)
DSPR
Definition dspr.f:127