LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ sspmv()

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

SSPMV

Purpose:
``` SSPMV  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, 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] 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. 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.``` [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 146 of file sspmv.f.

147*
148* -- Reference BLAS level2 routine --
149* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
150* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
151*
152* .. Scalar Arguments ..
153 REAL ALPHA,BETA
154 INTEGER INCX,INCY,N
155 CHARACTER UPLO
156* ..
157* .. Array Arguments ..
158 REAL AP(*),X(*),Y(*)
159* ..
160*
161* =====================================================================
162*
163* .. Parameters ..
164 REAL ONE,ZERO
165 parameter(one=1.0e+0,zero=0.0e+0)
166* ..
167* .. Local Scalars ..
168 REAL TEMP1,TEMP2
169 INTEGER I,INFO,IX,IY,J,JX,JY,K,KK,KX,KY
170* ..
171* .. External Functions ..
172 LOGICAL LSAME
173 EXTERNAL lsame
174* ..
175* .. External Subroutines ..
176 EXTERNAL xerbla
177* ..
178*
179* Test the input parameters.
180*
181 info = 0
182 IF (.NOT.lsame(uplo,'U') .AND. .NOT.lsame(uplo,'L')) THEN
183 info = 1
184 ELSE IF (n.LT.0) THEN
185 info = 2
186 ELSE IF (incx.EQ.0) THEN
187 info = 6
188 ELSE IF (incy.EQ.0) THEN
189 info = 9
190 END IF
191 IF (info.NE.0) THEN
192 CALL xerbla('SSPMV ',info)
193 RETURN
194 END IF
195*
196* Quick return if possible.
197*
198 IF ((n.EQ.0) .OR. ((alpha.EQ.zero).AND. (beta.EQ.one))) RETURN
199*
200* Set up the start points in X and Y.
201*
202 IF (incx.GT.0) THEN
203 kx = 1
204 ELSE
205 kx = 1 - (n-1)*incx
206 END IF
207 IF (incy.GT.0) THEN
208 ky = 1
209 ELSE
210 ky = 1 - (n-1)*incy
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* First form y := beta*y.
217*
218 IF (beta.NE.one) THEN
219 IF (incy.EQ.1) THEN
220 IF (beta.EQ.zero) THEN
221 DO 10 i = 1,n
222 y(i) = zero
223 10 CONTINUE
224 ELSE
225 DO 20 i = 1,n
226 y(i) = beta*y(i)
227 20 CONTINUE
228 END IF
229 ELSE
230 iy = ky
231 IF (beta.EQ.zero) THEN
232 DO 30 i = 1,n
233 y(iy) = zero
234 iy = iy + incy
235 30 CONTINUE
236 ELSE
237 DO 40 i = 1,n
238 y(iy) = beta*y(iy)
239 iy = iy + incy
240 40 CONTINUE
241 END IF
242 END IF
243 END IF
244 IF (alpha.EQ.zero) RETURN
245 kk = 1
246 IF (lsame(uplo,'U')) THEN
247*
248* Form y when AP contains the upper triangle.
249*
250 IF ((incx.EQ.1) .AND. (incy.EQ.1)) THEN
251 DO 60 j = 1,n
252 temp1 = alpha*x(j)
253 temp2 = zero
254 k = kk
255 DO 50 i = 1,j - 1
256 y(i) = y(i) + temp1*ap(k)
257 temp2 = temp2 + ap(k)*x(i)
258 k = k + 1
259 50 CONTINUE
260 y(j) = y(j) + temp1*ap(kk+j-1) + alpha*temp2
261 kk = kk + j
262 60 CONTINUE
263 ELSE
264 jx = kx
265 jy = ky
266 DO 80 j = 1,n
267 temp1 = alpha*x(jx)
268 temp2 = zero
269 ix = kx
270 iy = ky
271 DO 70 k = kk,kk + j - 2
272 y(iy) = y(iy) + temp1*ap(k)
273 temp2 = temp2 + ap(k)*x(ix)
274 ix = ix + incx
275 iy = iy + incy
276 70 CONTINUE
277 y(jy) = y(jy) + temp1*ap(kk+j-1) + alpha*temp2
278 jx = jx + incx
279 jy = jy + incy
280 kk = kk + j
281 80 CONTINUE
282 END IF
283 ELSE
284*
285* Form y when AP contains the lower triangle.
286*
287 IF ((incx.EQ.1) .AND. (incy.EQ.1)) THEN
288 DO 100 j = 1,n
289 temp1 = alpha*x(j)
290 temp2 = zero
291 y(j) = y(j) + temp1*ap(kk)
292 k = kk + 1
293 DO 90 i = j + 1,n
294 y(i) = y(i) + temp1*ap(k)
295 temp2 = temp2 + ap(k)*x(i)
296 k = k + 1
297 90 CONTINUE
298 y(j) = y(j) + alpha*temp2
299 kk = kk + (n-j+1)
300 100 CONTINUE
301 ELSE
302 jx = kx
303 jy = ky
304 DO 120 j = 1,n
305 temp1 = alpha*x(jx)
306 temp2 = zero
307 y(jy) = y(jy) + temp1*ap(kk)
308 ix = jx
309 iy = jy
310 DO 110 k = kk + 1,kk + n - j
311 ix = ix + incx
312 iy = iy + incy
313 y(iy) = y(iy) + temp1*ap(k)
314 temp2 = temp2 + ap(k)*x(ix)
315 110 CONTINUE
316 y(jy) = y(jy) + alpha*temp2
317 jx = jx + incx
318 jy = jy + incy
319 kk = kk + (n-j+1)
320 120 CONTINUE
321 END IF
322 END IF
323*
324 RETURN
325*
326* End of SSPMV
327*
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
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