LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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## ◆ ssymv()

 subroutine ssymv ( character uplo, integer n, real alpha, real, dimension(lda,*) a, integer lda, real, dimension(*) x, integer incx, real beta, real, dimension(*) y, integer incy )

SSYMV

Purpose:
``` SSYMV  performs the matrix-vector  operation

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

where alpha and beta are scalars, x and y are n element vectors 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 REAL On entry, ALPHA specifies the scalar alpha.``` [in] A ``` A is REAL 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. 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.``` [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 ).``` [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] BETA ``` BETA is REAL On entry, BETA specifies the scalar beta. When BETA is supplied as zero then Y need not be set on input.``` [in,out] 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. On exit, Y is overwritten by the updated vector y.``` [in] INCY ``` INCY is INTEGER On entry, INCY specifies the increment for the elements of Y. INCY must not be zero.```
Further Details:
```  Level 2 Blas routine.
The vector and matrix arguments are not referenced when N = 0, or M = 0

-- 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 151 of file ssymv.f.

152*
153* -- Reference BLAS level2 routine --
154* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
155* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
156*
157* .. Scalar Arguments ..
158 REAL ALPHA,BETA
159 INTEGER INCX,INCY,LDA,N
160 CHARACTER UPLO
161* ..
162* .. Array Arguments ..
163 REAL A(LDA,*),X(*),Y(*)
164* ..
165*
166* =====================================================================
167*
168* .. Parameters ..
169 REAL ONE,ZERO
170 parameter(one=1.0e+0,zero=0.0e+0)
171* ..
172* .. Local Scalars ..
173 REAL TEMP1,TEMP2
174 INTEGER I,INFO,IX,IY,J,JX,JY,KX,KY
175* ..
176* .. External Functions ..
177 LOGICAL LSAME
178 EXTERNAL lsame
179* ..
180* .. External Subroutines ..
181 EXTERNAL xerbla
182* ..
183* .. Intrinsic Functions ..
184 INTRINSIC max
185* ..
186*
187* Test the input parameters.
188*
189 info = 0
190 IF (.NOT.lsame(uplo,'U') .AND. .NOT.lsame(uplo,'L')) THEN
191 info = 1
192 ELSE IF (n.LT.0) THEN
193 info = 2
194 ELSE IF (lda.LT.max(1,n)) THEN
195 info = 5
196 ELSE IF (incx.EQ.0) THEN
197 info = 7
198 ELSE IF (incy.EQ.0) THEN
199 info = 10
200 END IF
201 IF (info.NE.0) THEN
202 CALL xerbla('SSYMV ',info)
203 RETURN
204 END IF
205*
206* Quick return if possible.
207*
208 IF ((n.EQ.0) .OR. ((alpha.EQ.zero).AND. (beta.EQ.one))) RETURN
209*
210* Set up the start points in X and Y.
211*
212 IF (incx.GT.0) THEN
213 kx = 1
214 ELSE
215 kx = 1 - (n-1)*incx
216 END IF
217 IF (incy.GT.0) THEN
218 ky = 1
219 ELSE
220 ky = 1 - (n-1)*incy
221 END IF
222*
223* Start the operations. In this version the elements of A are
224* accessed sequentially with one pass through the triangular part
225* of A.
226*
227* First form y := beta*y.
228*
229 IF (beta.NE.one) THEN
230 IF (incy.EQ.1) THEN
231 IF (beta.EQ.zero) THEN
232 DO 10 i = 1,n
233 y(i) = zero
234 10 CONTINUE
235 ELSE
236 DO 20 i = 1,n
237 y(i) = beta*y(i)
238 20 CONTINUE
239 END IF
240 ELSE
241 iy = ky
242 IF (beta.EQ.zero) THEN
243 DO 30 i = 1,n
244 y(iy) = zero
245 iy = iy + incy
246 30 CONTINUE
247 ELSE
248 DO 40 i = 1,n
249 y(iy) = beta*y(iy)
250 iy = iy + incy
251 40 CONTINUE
252 END IF
253 END IF
254 END IF
255 IF (alpha.EQ.zero) RETURN
256 IF (lsame(uplo,'U')) THEN
257*
258* Form y when A is stored in upper triangle.
259*
260 IF ((incx.EQ.1) .AND. (incy.EQ.1)) THEN
261 DO 60 j = 1,n
262 temp1 = alpha*x(j)
263 temp2 = zero
264 DO 50 i = 1,j - 1
265 y(i) = y(i) + temp1*a(i,j)
266 temp2 = temp2 + a(i,j)*x(i)
267 50 CONTINUE
268 y(j) = y(j) + temp1*a(j,j) + alpha*temp2
269 60 CONTINUE
270 ELSE
271 jx = kx
272 jy = ky
273 DO 80 j = 1,n
274 temp1 = alpha*x(jx)
275 temp2 = zero
276 ix = kx
277 iy = ky
278 DO 70 i = 1,j - 1
279 y(iy) = y(iy) + temp1*a(i,j)
280 temp2 = temp2 + a(i,j)*x(ix)
281 ix = ix + incx
282 iy = iy + incy
283 70 CONTINUE
284 y(jy) = y(jy) + temp1*a(j,j) + alpha*temp2
285 jx = jx + incx
286 jy = jy + incy
287 80 CONTINUE
288 END IF
289 ELSE
290*
291* Form y when A is stored in lower triangle.
292*
293 IF ((incx.EQ.1) .AND. (incy.EQ.1)) THEN
294 DO 100 j = 1,n
295 temp1 = alpha*x(j)
296 temp2 = zero
297 y(j) = y(j) + temp1*a(j,j)
298 DO 90 i = j + 1,n
299 y(i) = y(i) + temp1*a(i,j)
300 temp2 = temp2 + a(i,j)*x(i)
301 90 CONTINUE
302 y(j) = y(j) + alpha*temp2
303 100 CONTINUE
304 ELSE
305 jx = kx
306 jy = ky
307 DO 120 j = 1,n
308 temp1 = alpha*x(jx)
309 temp2 = zero
310 y(jy) = y(jy) + temp1*a(j,j)
311 ix = jx
312 iy = jy
313 DO 110 i = j + 1,n
314 ix = ix + incx
315 iy = iy + incy
316 y(iy) = y(iy) + temp1*a(i,j)
317 temp2 = temp2 + a(i,j)*x(ix)
318 110 CONTINUE
319 y(jy) = y(jy) + alpha*temp2
320 jx = jx + incx
321 jy = jy + incy
322 120 CONTINUE
323 END IF
324 END IF
325*
326 RETURN
327*
328* End of SSYMV
329*
subroutine xerbla(srname, info)
Definition cblat2.f:3285
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
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