 LAPACK  3.10.0 LAPACK: Linear Algebra PACKage

## ◆ 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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