 LAPACK  3.10.0 LAPACK: Linear Algebra PACKage

## ◆ sspr2()

 subroutine sspr2 ( character UPLO, integer N, real ALPHA, real, dimension(*) X, integer INCX, real, dimension(*) Y, integer INCY, real, dimension(*) AP )

SSPR2

Purpose:
``` SSPR2  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 REAL On entry, ALPHA specifies the scalar alpha.``` [in] X ``` X is REAL 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] Y ``` Y is REAL array, 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 REAL 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 141 of file sspr2.f.

142 *
143 * -- Reference BLAS level2 routine --
144 * -- Reference BLAS is a software package provided by Univ. of Tennessee, --
145 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
146 *
147 * .. Scalar Arguments ..
148  REAL ALPHA
149  INTEGER INCX,INCY,N
150  CHARACTER UPLO
151 * ..
152 * .. Array Arguments ..
153  REAL AP(*),X(*),Y(*)
154 * ..
155 *
156 * =====================================================================
157 *
158 * .. Parameters ..
159  REAL ZERO
160  parameter(zero=0.0e+0)
161 * ..
162 * .. Local Scalars ..
163  REAL TEMP1,TEMP2
164  INTEGER I,INFO,IX,IY,J,JX,JY,K,KK,KX,KY
165 * ..
166 * .. External Functions ..
167  LOGICAL LSAME
168  EXTERNAL lsame
169 * ..
170 * .. External Subroutines ..
171  EXTERNAL xerbla
172 * ..
173 *
174 * Test the input parameters.
175 *
176  info = 0
177  IF (.NOT.lsame(uplo,'U') .AND. .NOT.lsame(uplo,'L')) THEN
178  info = 1
179  ELSE IF (n.LT.0) THEN
180  info = 2
181  ELSE IF (incx.EQ.0) THEN
182  info = 5
183  ELSE IF (incy.EQ.0) THEN
184  info = 7
185  END IF
186  IF (info.NE.0) THEN
187  CALL xerbla('SSPR2 ',info)
188  RETURN
189  END IF
190 *
191 * Quick return if possible.
192 *
193  IF ((n.EQ.0) .OR. (alpha.EQ.zero)) RETURN
194 *
195 * Set up the start points in X and Y if the increments are not both
196 * unity.
197 *
198  IF ((incx.NE.1) .OR. (incy.NE.1)) THEN
199  IF (incx.GT.0) THEN
200  kx = 1
201  ELSE
202  kx = 1 - (n-1)*incx
203  END IF
204  IF (incy.GT.0) THEN
205  ky = 1
206  ELSE
207  ky = 1 - (n-1)*incy
208  END IF
209  jx = kx
210  jy = ky
211  END IF
212 *
213 * Start the operations. In this version the elements of the array AP
214 * are accessed sequentially with one pass through AP.
215 *
216  kk = 1
217  IF (lsame(uplo,'U')) THEN
218 *
219 * Form A when upper triangle is stored in AP.
220 *
221  IF ((incx.EQ.1) .AND. (incy.EQ.1)) THEN
222  DO 20 j = 1,n
223  IF ((x(j).NE.zero) .OR. (y(j).NE.zero)) THEN
224  temp1 = alpha*y(j)
225  temp2 = alpha*x(j)
226  k = kk
227  DO 10 i = 1,j
228  ap(k) = ap(k) + x(i)*temp1 + y(i)*temp2
229  k = k + 1
230  10 CONTINUE
231  END IF
232  kk = kk + j
233  20 CONTINUE
234  ELSE
235  DO 40 j = 1,n
236  IF ((x(jx).NE.zero) .OR. (y(jy).NE.zero)) THEN
237  temp1 = alpha*y(jy)
238  temp2 = alpha*x(jx)
239  ix = kx
240  iy = ky
241  DO 30 k = kk,kk + j - 1
242  ap(k) = ap(k) + x(ix)*temp1 + y(iy)*temp2
243  ix = ix + incx
244  iy = iy + incy
245  30 CONTINUE
246  END IF
247  jx = jx + incx
248  jy = jy + incy
249  kk = kk + j
250  40 CONTINUE
251  END IF
252  ELSE
253 *
254 * Form A when lower triangle is stored in AP.
255 *
256  IF ((incx.EQ.1) .AND. (incy.EQ.1)) THEN
257  DO 60 j = 1,n
258  IF ((x(j).NE.zero) .OR. (y(j).NE.zero)) THEN
259  temp1 = alpha*y(j)
260  temp2 = alpha*x(j)
261  k = kk
262  DO 50 i = j,n
263  ap(k) = ap(k) + x(i)*temp1 + y(i)*temp2
264  k = k + 1
265  50 CONTINUE
266  END IF
267  kk = kk + n - j + 1
268  60 CONTINUE
269  ELSE
270  DO 80 j = 1,n
271  IF ((x(jx).NE.zero) .OR. (y(jy).NE.zero)) THEN
272  temp1 = alpha*y(jy)
273  temp2 = alpha*x(jx)
274  ix = jx
275  iy = jy
276  DO 70 k = kk,kk + n - j
277  ap(k) = ap(k) + x(ix)*temp1 + y(iy)*temp2
278  ix = ix + incx
279  iy = iy + incy
280  70 CONTINUE
281  END IF
282  jx = jx + incx
283  jy = jy + incy
284  kk = kk + n - j + 1
285  80 CONTINUE
286  END IF
287  END IF
288 *
289  RETURN
290 *
291 * End of SSPR2
292 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
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