LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
 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 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,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 129 of file dspr.f.

129 *
130 * -- Reference BLAS level2 routine (version 3.4.0) --
131 * -- Reference BLAS is a software package provided by Univ. of Tennessee, --
132 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
133 * November 2011
134 *
135 * .. Scalar Arguments ..
136  DOUBLE PRECISION alpha
137  INTEGER incx,n
138  CHARACTER uplo
139 * ..
140 * .. Array Arguments ..
141  DOUBLE PRECISION ap(*),x(*)
142 * ..
143 *
144 * =====================================================================
145 *
146 * .. Parameters ..
147  DOUBLE PRECISION zero
148  parameter(zero=0.0d+0)
149 * ..
150 * .. Local Scalars ..
151  DOUBLE PRECISION temp
152  INTEGER i,info,ix,j,jx,k,kk,kx
153 * ..
154 * .. External Functions ..
155  LOGICAL lsame
156  EXTERNAL lsame
157 * ..
158 * .. External Subroutines ..
159  EXTERNAL xerbla
160 * ..
161 *
162 * Test the input parameters.
163 *
164  info = 0
165  IF (.NOT.lsame(uplo,'U') .AND. .NOT.lsame(uplo,'L')) THEN
166  info = 1
167  ELSE IF (n.LT.0) THEN
168  info = 2
169  ELSE IF (incx.EQ.0) THEN
170  info = 5
171  END IF
172  IF (info.NE.0) THEN
173  CALL xerbla('DSPR ',info)
174  RETURN
175  END IF
176 *
177 * Quick return if possible.
178 *
179  IF ((n.EQ.0) .OR. (alpha.EQ.zero)) RETURN
180 *
181 * Set the start point in X if the increment is not unity.
182 *
183  IF (incx.LE.0) THEN
184  kx = 1 - (n-1)*incx
185  ELSE IF (incx.NE.1) THEN
186  kx = 1
187  END IF
188 *
189 * Start the operations. In this version the elements of the array AP
190 * are accessed sequentially with one pass through AP.
191 *
192  kk = 1
193  IF (lsame(uplo,'U')) THEN
194 *
195 * Form A when upper triangle is stored in AP.
196 *
197  IF (incx.EQ.1) THEN
198  DO 20 j = 1,n
199  IF (x(j).NE.zero) THEN
200  temp = alpha*x(j)
201  k = kk
202  DO 10 i = 1,j
203  ap(k) = ap(k) + x(i)*temp
204  k = k + 1
205  10 CONTINUE
206  END IF
207  kk = kk + j
208  20 CONTINUE
209  ELSE
210  jx = kx
211  DO 40 j = 1,n
212  IF (x(jx).NE.zero) THEN
213  temp = alpha*x(jx)
214  ix = kx
215  DO 30 k = kk,kk + j - 1
216  ap(k) = ap(k) + x(ix)*temp
217  ix = ix + incx
218  30 CONTINUE
219  END IF
220  jx = jx + incx
221  kk = kk + j
222  40 CONTINUE
223  END IF
224  ELSE
225 *
226 * Form A when lower triangle is stored in AP.
227 *
228  IF (incx.EQ.1) THEN
229  DO 60 j = 1,n
230  IF (x(j).NE.zero) THEN
231  temp = alpha*x(j)
232  k = kk
233  DO 50 i = j,n
234  ap(k) = ap(k) + x(i)*temp
235  k = k + 1
236  50 CONTINUE
237  END IF
238  kk = kk + n - j + 1
239  60 CONTINUE
240  ELSE
241  jx = kx
242  DO 80 j = 1,n
243  IF (x(jx).NE.zero) THEN
244  temp = alpha*x(jx)
245  ix = jx
246  DO 70 k = kk,kk + n - j
247  ap(k) = ap(k) + x(ix)*temp
248  ix = ix + incx
249  70 CONTINUE
250  END IF
251  jx = jx + incx
252  kk = kk + n - j + 1
253  80 CONTINUE
254  END IF
255  END IF
256 *
257  RETURN
258 *
259 * End of DSPR .
260 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55

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