 LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
 subroutine dspr2 ( character UPLO, integer N, double precision ALPHA, double precision, dimension(*) X, integer INCX, double precision, dimension(*) Y, integer INCY, double precision, dimension(*) AP )

DSPR2

Purpose:
``` DSPR2  performs the symmetric rank 2 operation

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

where alpha is a scalar, x and y are n element vectors 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 of 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] Y ``` Y is DOUBLE PRECISION array of dimension at least ( 1 + ( n - 1 )*abs( INCY ) ). Before entry, the incremented array Y must contain the n element vector y.``` [in] INCY ``` INCY is INTEGER On entry, INCY specifies the increment for the elements of Y. INCY must not be zero.``` [in,out] AP ``` AP is DOUBLE PRECISION array of 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.```
Date
November 2011
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 144 of file dspr2.f.

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 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55

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