LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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◆ sgemv()

subroutine sgemv ( character  trans,
integer  m,
integer  n,
real  alpha,
real, dimension(lda,*)  a,
integer  lda,
real, dimension(*)  x,
integer  incx,
real  beta,
real, dimension(*)  y,
integer  incy 
)

SGEMV

Purpose:
 SGEMV  performs one of the matrix-vector operations

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

 where alpha and beta are scalars, x and y are vectors and A is an
 m by n matrix.
Parameters
[in]TRANS
          TRANS is CHARACTER*1
           On entry, TRANS specifies the operation to be performed as
           follows:

              TRANS = 'N' or 'n'   y := alpha*A*x + beta*y.

              TRANS = 'T' or 't'   y := alpha*A**T*x + beta*y.

              TRANS = 'C' or 'c'   y := alpha*A**T*x + beta*y.
[in]M
          M is INTEGER
           On entry, M specifies the number of rows of the matrix A.
           M must be at least zero.
[in]N
          N is INTEGER
           On entry, N specifies the number of columns 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, the leading m by n part of the array A must
           contain the matrix of coefficients.
[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, m ).
[in]X
          X is REAL array, dimension at least
           ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n'
           and at least
           ( 1 + ( m - 1 )*abs( INCX ) ) otherwise.
           Before entry, the incremented array X must contain the
           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 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n'
           and at least
           ( 1 + ( n - 1 )*abs( INCY ) ) otherwise.
           Before entry with BETA non-zero, the incremented array Y
           must contain the vector y. On exit, Y is overwritten by the
           updated vector y.
           If either m or n is zero, then Y not referenced and the function
           performs a quick return.
[in]INCY
          INCY is INTEGER
           On entry, INCY specifies the increment for the elements of
           Y. INCY must not be zero.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
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 157 of file sgemv.f.

158*
159* -- Reference BLAS level2 routine --
160* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
161* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
162*
163* .. Scalar Arguments ..
164 REAL ALPHA,BETA
165 INTEGER INCX,INCY,LDA,M,N
166 CHARACTER TRANS
167* ..
168* .. Array Arguments ..
169 REAL A(LDA,*),X(*),Y(*)
170* ..
171*
172* =====================================================================
173*
174* .. Parameters ..
175 REAL ONE,ZERO
176 parameter(one=1.0e+0,zero=0.0e+0)
177* ..
178* .. Local Scalars ..
179 REAL TEMP
180 INTEGER I,INFO,IX,IY,J,JX,JY,KX,KY,LENX,LENY
181* ..
182* .. External Functions ..
183 LOGICAL LSAME
184 EXTERNAL lsame
185* ..
186* .. External Subroutines ..
187 EXTERNAL xerbla
188* ..
189* .. Intrinsic Functions ..
190 INTRINSIC max
191* ..
192*
193* Test the input parameters.
194*
195 info = 0
196 IF (.NOT.lsame(trans,'N') .AND. .NOT.lsame(trans,'T') .AND.
197 + .NOT.lsame(trans,'C')) THEN
198 info = 1
199 ELSE IF (m.LT.0) THEN
200 info = 2
201 ELSE IF (n.LT.0) THEN
202 info = 3
203 ELSE IF (lda.LT.max(1,m)) THEN
204 info = 6
205 ELSE IF (incx.EQ.0) THEN
206 info = 8
207 ELSE IF (incy.EQ.0) THEN
208 info = 11
209 END IF
210 IF (info.NE.0) THEN
211 CALL xerbla('SGEMV ',info)
212 RETURN
213 END IF
214*
215* Quick return if possible.
216*
217 IF ((m.EQ.0) .OR. (n.EQ.0) .OR.
218 + ((alpha.EQ.zero).AND. (beta.EQ.one))) RETURN
219*
220* Set LENX and LENY, the lengths of the vectors x and y, and set
221* up the start points in X and Y.
222*
223 IF (lsame(trans,'N')) THEN
224 lenx = n
225 leny = m
226 ELSE
227 lenx = m
228 leny = n
229 END IF
230 IF (incx.GT.0) THEN
231 kx = 1
232 ELSE
233 kx = 1 - (lenx-1)*incx
234 END IF
235 IF (incy.GT.0) THEN
236 ky = 1
237 ELSE
238 ky = 1 - (leny-1)*incy
239 END IF
240*
241* Start the operations. In this version the elements of A are
242* accessed sequentially with one pass through A.
243*
244* First form y := beta*y.
245*
246 IF (beta.NE.one) THEN
247 IF (incy.EQ.1) THEN
248 IF (beta.EQ.zero) THEN
249 DO 10 i = 1,leny
250 y(i) = zero
251 10 CONTINUE
252 ELSE
253 DO 20 i = 1,leny
254 y(i) = beta*y(i)
255 20 CONTINUE
256 END IF
257 ELSE
258 iy = ky
259 IF (beta.EQ.zero) THEN
260 DO 30 i = 1,leny
261 y(iy) = zero
262 iy = iy + incy
263 30 CONTINUE
264 ELSE
265 DO 40 i = 1,leny
266 y(iy) = beta*y(iy)
267 iy = iy + incy
268 40 CONTINUE
269 END IF
270 END IF
271 END IF
272 IF (alpha.EQ.zero) RETURN
273 IF (lsame(trans,'N')) THEN
274*
275* Form y := alpha*A*x + y.
276*
277 jx = kx
278 IF (incy.EQ.1) THEN
279 DO 60 j = 1,n
280 temp = alpha*x(jx)
281 DO 50 i = 1,m
282 y(i) = y(i) + temp*a(i,j)
283 50 CONTINUE
284 jx = jx + incx
285 60 CONTINUE
286 ELSE
287 DO 80 j = 1,n
288 temp = alpha*x(jx)
289 iy = ky
290 DO 70 i = 1,m
291 y(iy) = y(iy) + temp*a(i,j)
292 iy = iy + incy
293 70 CONTINUE
294 jx = jx + incx
295 80 CONTINUE
296 END IF
297 ELSE
298*
299* Form y := alpha*A**T*x + y.
300*
301 jy = ky
302 IF (incx.EQ.1) THEN
303 DO 100 j = 1,n
304 temp = zero
305 DO 90 i = 1,m
306 temp = temp + a(i,j)*x(i)
307 90 CONTINUE
308 y(jy) = y(jy) + alpha*temp
309 jy = jy + incy
310 100 CONTINUE
311 ELSE
312 DO 120 j = 1,n
313 temp = zero
314 ix = kx
315 DO 110 i = 1,m
316 temp = temp + a(i,j)*x(ix)
317 ix = ix + incx
318 110 CONTINUE
319 y(jy) = y(jy) + alpha*temp
320 jy = jy + incy
321 120 CONTINUE
322 END IF
323 END IF
324*
325 RETURN
326*
327* End of SGEMV
328*
xerbla
subroutine xerbla(srname, info)
Definition cblat2.f:3285
lsame
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
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