 LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ dspr()

 subroutine dspr ( character UPLO, integer N, double precision ALPHA, double precision, dimension(*) X, integer INCX, double precision, dimension(*) AP )

DSPR

Purpose:
``` DSPR    performs the symmetric rank 1 operation

A := alpha*x*x**T + A,

where alpha is a real scalar, x is an n element vector and A is an
n by n symmetric matrix, supplied in packed form.```
Parameters
 [in] UPLO ``` UPLO is CHARACTER*1 On entry, UPLO specifies whether the upper or lower triangular part of the matrix A is supplied in the packed array AP as follows: UPLO = 'U' or 'u' The upper triangular part of A is supplied in AP. UPLO = 'L' or 'l' The lower triangular part of A is supplied in AP.``` [in] N ``` N is INTEGER On entry, N specifies the order of the matrix A. N must be at least zero.``` [in] ALPHA ``` ALPHA is DOUBLE PRECISION. On entry, ALPHA specifies the scalar alpha.``` [in] X ``` X is DOUBLE PRECISION array, dimension at least ( 1 + ( n - 1 )*abs( INCX ) ). Before entry, the incremented array X must contain the n element vector x.``` [in] INCX ``` INCX is INTEGER On entry, INCX specifies the increment for the elements of X. INCX must not be zero.``` [in,out] AP ``` AP is DOUBLE PRECISION array, dimension at least ( ( n*( n + 1 ) )/2 ). Before entry with UPLO = 'U' or 'u', the array AP must contain the upper triangular part of the symmetric matrix packed sequentially, column by column, so that AP( 1 ) contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 ) respectively, and so on. On exit, the array AP is overwritten by the upper triangular part of the updated matrix. Before entry with UPLO = 'L' or 'l', the array AP must contain the lower triangular part of the symmetric matrix packed sequentially, column by column, so that AP( 1 ) contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 ) respectively, and so on. On exit, the array AP is overwritten by the lower triangular part of the updated matrix.```
Further Details:
```  Level 2 Blas routine.

-- Written on 22-October-1986.
Jack Dongarra, Argonne National Lab.
Jeremy Du Croz, Nag Central Office.
Sven Hammarling, Nag Central Office.
Richard Hanson, Sandia National Labs.```

Definition at line 126 of file dspr.f.

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*
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
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