LAPACK  3.6.1
LAPACK: Linear Algebra PACKage
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 of 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 of 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 of 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.
[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.
Date
November 2015
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 158 of file sgemv.f.

158 *
159 * -- Reference BLAS level2 routine (version 3.6.0) --
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 * November 2015
163 *
164 * .. Scalar Arguments ..
165  REAL alpha,beta
166  INTEGER incx,incy,lda,m,n
167  CHARACTER trans
168 * ..
169 * .. Array Arguments ..
170  REAL a(lda,*),x(*),y(*)
171 * ..
172 *
173 * =====================================================================
174 *
175 * .. Parameters ..
176  REAL one,zero
177  parameter(one=1.0e+0,zero=0.0e+0)
178 * ..
179 * .. Local Scalars ..
180  REAL temp
181  INTEGER i,info,ix,iy,j,jx,jy,kx,ky,lenx,leny
182 * ..
183 * .. External Functions ..
184  LOGICAL lsame
185  EXTERNAL lsame
186 * ..
187 * .. External Subroutines ..
188  EXTERNAL xerbla
189 * ..
190 * .. Intrinsic Functions ..
191  INTRINSIC max
192 * ..
193 *
194 * Test the input parameters.
195 *
196  info = 0
197  IF (.NOT.lsame(trans,'N') .AND. .NOT.lsame(trans,'T') .AND.
198  + .NOT.lsame(trans,'C')) THEN
199  info = 1
200  ELSE IF (m.LT.0) THEN
201  info = 2
202  ELSE IF (n.LT.0) THEN
203  info = 3
204  ELSE IF (lda.LT.max(1,m)) THEN
205  info = 6
206  ELSE IF (incx.EQ.0) THEN
207  info = 8
208  ELSE IF (incy.EQ.0) THEN
209  info = 11
210  END IF
211  IF (info.NE.0) THEN
212  CALL xerbla('SGEMV ',info)
213  RETURN
214  END IF
215 *
216 * Quick return if possible.
217 *
218  IF ((m.EQ.0) .OR. (n.EQ.0) .OR.
219  + ((alpha.EQ.zero).AND. (beta.EQ.one))) RETURN
220 *
221 * Set LENX and LENY, the lengths of the vectors x and y, and set
222 * up the start points in X and Y.
223 *
224  IF (lsame(trans,'N')) THEN
225  lenx = n
226  leny = m
227  ELSE
228  lenx = m
229  leny = n
230  END IF
231  IF (incx.GT.0) THEN
232  kx = 1
233  ELSE
234  kx = 1 - (lenx-1)*incx
235  END IF
236  IF (incy.GT.0) THEN
237  ky = 1
238  ELSE
239  ky = 1 - (leny-1)*incy
240  END IF
241 *
242 * Start the operations. In this version the elements of A are
243 * accessed sequentially with one pass through A.
244 *
245 * First form y := beta*y.
246 *
247  IF (beta.NE.one) THEN
248  IF (incy.EQ.1) THEN
249  IF (beta.EQ.zero) THEN
250  DO 10 i = 1,leny
251  y(i) = zero
252  10 CONTINUE
253  ELSE
254  DO 20 i = 1,leny
255  y(i) = beta*y(i)
256  20 CONTINUE
257  END IF
258  ELSE
259  iy = ky
260  IF (beta.EQ.zero) THEN
261  DO 30 i = 1,leny
262  y(iy) = zero
263  iy = iy + incy
264  30 CONTINUE
265  ELSE
266  DO 40 i = 1,leny
267  y(iy) = beta*y(iy)
268  iy = iy + incy
269  40 CONTINUE
270  END IF
271  END IF
272  END IF
273  IF (alpha.EQ.zero) RETURN
274  IF (lsame(trans,'N')) THEN
275 *
276 * Form y := alpha*A*x + y.
277 *
278  jx = kx
279  IF (incy.EQ.1) THEN
280  DO 60 j = 1,n
281  temp = alpha*x(jx)
282  DO 50 i = 1,m
283  y(i) = y(i) + temp*a(i,j)
284  50 CONTINUE
285  jx = jx + incx
286  60 CONTINUE
287  ELSE
288  DO 80 j = 1,n
289  temp = alpha*x(jx)
290  iy = ky
291  DO 70 i = 1,m
292  y(iy) = y(iy) + temp*a(i,j)
293  iy = iy + incy
294  70 CONTINUE
295  jx = jx + incx
296  80 CONTINUE
297  END IF
298  ELSE
299 *
300 * Form y := alpha*A**T*x + y.
301 *
302  jy = ky
303  IF (incx.EQ.1) THEN
304  DO 100 j = 1,n
305  temp = zero
306  DO 90 i = 1,m
307  temp = temp + a(i,j)*x(i)
308  90 CONTINUE
309  y(jy) = y(jy) + alpha*temp
310  jy = jy + incy
311  100 CONTINUE
312  ELSE
313  DO 120 j = 1,n
314  temp = zero
315  ix = kx
316  DO 110 i = 1,m
317  temp = temp + a(i,j)*x(ix)
318  ix = ix + incx
319  110 CONTINUE
320  y(jy) = y(jy) + alpha*temp
321  jy = jy + incy
322  120 CONTINUE
323  END IF
324  END IF
325 *
326  RETURN
327 *
328 * End of SGEMV .
329 *
xerbla
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
lsame
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55

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