 LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ dsyr()

 subroutine dsyr ( character UPLO, integer N, double precision ALPHA, double precision, dimension(*) X, integer INCX, double precision, dimension(lda,*) A, integer LDA )

DSYR

Purpose:
``` DSYR   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.```
Parameters
 [in] UPLO ``` UPLO is CHARACTER*1 On entry, UPLO specifies whether the upper or lower triangular part of the array A is to be referenced as follows: UPLO = 'U' or 'u' Only the upper triangular part of A is to be referenced. UPLO = 'L' or 'l' Only the lower triangular part of A is to be referenced.``` [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] A ``` A is DOUBLE PRECISION array, dimension ( LDA, N ) Before entry with UPLO = 'U' or 'u', the leading n by n upper triangular part of the array A must contain the upper triangular part of the symmetric matrix and the strictly lower triangular part of A is not referenced. On exit, the upper triangular part of the array A is overwritten by the upper triangular part of the updated matrix. Before entry with UPLO = 'L' or 'l', the leading n by n lower triangular part of the array A must contain the lower triangular part of the symmetric matrix and the strictly upper triangular part of A is not referenced. On exit, the lower triangular part of the array A is overwritten by the lower triangular part of the updated matrix.``` [in] LDA ``` LDA is INTEGER On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. LDA must be at least max( 1, n ).```
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 131 of file dsyr.f.

132 *
133 * -- Reference BLAS level2 routine --
134 * -- Reference BLAS is a software package provided by Univ. of Tennessee, --
135 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
136 *
137 * .. Scalar Arguments ..
138  DOUBLE PRECISION ALPHA
139  INTEGER INCX,LDA,N
140  CHARACTER UPLO
141 * ..
142 * .. Array Arguments ..
143  DOUBLE PRECISION A(LDA,*),X(*)
144 * ..
145 *
146 * =====================================================================
147 *
148 * .. Parameters ..
149  DOUBLE PRECISION ZERO
150  parameter(zero=0.0d+0)
151 * ..
152 * .. Local Scalars ..
153  DOUBLE PRECISION TEMP
154  INTEGER I,INFO,IX,J,JX,KX
155 * ..
156 * .. External Functions ..
157  LOGICAL LSAME
158  EXTERNAL lsame
159 * ..
160 * .. External Subroutines ..
161  EXTERNAL xerbla
162 * ..
163 * .. Intrinsic Functions ..
164  INTRINSIC max
165 * ..
166 *
167 * Test the input parameters.
168 *
169  info = 0
170  IF (.NOT.lsame(uplo,'U') .AND. .NOT.lsame(uplo,'L')) THEN
171  info = 1
172  ELSE IF (n.LT.0) THEN
173  info = 2
174  ELSE IF (incx.EQ.0) THEN
175  info = 5
176  ELSE IF (lda.LT.max(1,n)) THEN
177  info = 7
178  END IF
179  IF (info.NE.0) THEN
180  CALL xerbla('DSYR ',info)
181  RETURN
182  END IF
183 *
184 * Quick return if possible.
185 *
186  IF ((n.EQ.0) .OR. (alpha.EQ.zero)) RETURN
187 *
188 * Set the start point in X if the increment is not unity.
189 *
190  IF (incx.LE.0) THEN
191  kx = 1 - (n-1)*incx
192  ELSE IF (incx.NE.1) THEN
193  kx = 1
194  END IF
195 *
196 * Start the operations. In this version the elements of A are
197 * accessed sequentially with one pass through the triangular part
198 * of A.
199 *
200  IF (lsame(uplo,'U')) THEN
201 *
202 * Form A when A is stored in upper triangle.
203 *
204  IF (incx.EQ.1) THEN
205  DO 20 j = 1,n
206  IF (x(j).NE.zero) THEN
207  temp = alpha*x(j)
208  DO 10 i = 1,j
209  a(i,j) = a(i,j) + x(i)*temp
210  10 CONTINUE
211  END IF
212  20 CONTINUE
213  ELSE
214  jx = kx
215  DO 40 j = 1,n
216  IF (x(jx).NE.zero) THEN
217  temp = alpha*x(jx)
218  ix = kx
219  DO 30 i = 1,j
220  a(i,j) = a(i,j) + x(ix)*temp
221  ix = ix + incx
222  30 CONTINUE
223  END IF
224  jx = jx + incx
225  40 CONTINUE
226  END IF
227  ELSE
228 *
229 * Form A when A is stored in lower triangle.
230 *
231  IF (incx.EQ.1) THEN
232  DO 60 j = 1,n
233  IF (x(j).NE.zero) THEN
234  temp = alpha*x(j)
235  DO 50 i = j,n
236  a(i,j) = a(i,j) + x(i)*temp
237  50 CONTINUE
238  END IF
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 i = j,n
247  a(i,j) = a(i,j) + x(ix)*temp
248  ix = ix + incx
249  70 CONTINUE
250  END IF
251  jx = jx + incx
252  80 CONTINUE
253  END IF
254  END IF
255 *
256  RETURN
257 *
258 * End of DSYR
259 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
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