LAPACK  3.10.0 LAPACK: Linear Algebra PACKage

## ◆ sla_geamv()

 subroutine sla_geamv ( integer 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 )

SLA_GEAMV computes a matrix-vector product using a general matrix to calculate error bounds.

Download SLA_GEAMV + dependencies [TGZ] [ZIP] [TXT]

Purpose:
``` SLA_GEAMV  performs one of the matrix-vector operations

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

where alpha and beta are scalars, x and y are vectors and A is an
m by n matrix.

This function is primarily used in calculating error bounds.
To protect against underflow during evaluation, components in
the resulting vector are perturbed away from zero by (N+1)
times the underflow threshold.  To prevent unnecessarily large
errors for block-structure embedded in general matrices,
"symbolically" zero components are not perturbed.  A zero
entry is considered "symbolic" if all multiplications involved
in computing that entry have at least one zero multiplicand.```
Parameters
 [in] TRANS ``` TRANS is INTEGER On entry, TRANS specifies the operation to be performed as follows: BLAS_NO_TRANS y := alpha*abs(A)*abs(x) + beta*abs(y) BLAS_TRANS y := alpha*abs(A**T)*abs(x) + beta*abs(y) BLAS_CONJ_TRANS y := alpha*abs(A**T)*abs(x) + beta*abs(y) Unchanged on exit.``` [in] M ``` M is INTEGER On entry, M specifies the number of rows of the matrix A. M must be at least zero. Unchanged on exit.``` [in] N ``` N is INTEGER On entry, N specifies the number of columns of the matrix A. N must be at least zero. Unchanged on exit.``` [in] ALPHA ``` ALPHA is REAL On entry, ALPHA specifies the scalar alpha. Unchanged on exit.``` [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. Unchanged on exit.``` [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 ). Unchanged on exit.``` [in] X ``` X is REAL array, dimension ( 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. Unchanged on exit.``` [in] INCX ``` INCX is INTEGER On entry, INCX specifies the increment for the elements of X. INCX must not be zero. Unchanged on exit.``` [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. Unchanged on exit.``` [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.``` [in] INCY ``` INCY is INTEGER On entry, INCY specifies the increment for the elements of Y. INCY must not be zero. Unchanged on exit. Level 2 Blas routine.```

Definition at line 172 of file sla_geamv.f.

174 *
175 * -- LAPACK computational routine --
176 * -- LAPACK is a software package provided by Univ. of Tennessee, --
177 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
178 *
179 * .. Scalar Arguments ..
180  REAL ALPHA, BETA
181  INTEGER INCX, INCY, LDA, M, N, TRANS
182 * ..
183 * .. Array Arguments ..
184  REAL A( LDA, * ), X( * ), Y( * )
185 * ..
186 *
187 * =====================================================================
188 *
189 * .. Parameters ..
190  REAL ONE, ZERO
191  parameter( one = 1.0e+0, zero = 0.0e+0 )
192 * ..
193 * .. Local Scalars ..
194  LOGICAL SYMB_ZERO
195  REAL TEMP, SAFE1
196  INTEGER I, INFO, IY, J, JX, KX, KY, LENX, LENY
197 * ..
198 * .. External Subroutines ..
199  EXTERNAL xerbla, slamch
200  REAL SLAMCH
201 * ..
202 * .. External Functions ..
203  EXTERNAL ilatrans
204  INTEGER ILATRANS
205 * ..
206 * .. Intrinsic Functions ..
207  INTRINSIC max, abs, sign
208 * ..
209 * .. Executable Statements ..
210 *
211 * Test the input parameters.
212 *
213  info = 0
214  IF ( .NOT.( ( trans.EQ.ilatrans( 'N' ) )
215  \$ .OR. ( trans.EQ.ilatrans( 'T' ) )
216  \$ .OR. ( trans.EQ.ilatrans( 'C' )) ) ) THEN
217  info = 1
218  ELSE IF( m.LT.0 )THEN
219  info = 2
220  ELSE IF( n.LT.0 )THEN
221  info = 3
222  ELSE IF( lda.LT.max( 1, m ) )THEN
223  info = 6
224  ELSE IF( incx.EQ.0 )THEN
225  info = 8
226  ELSE IF( incy.EQ.0 )THEN
227  info = 11
228  END IF
229  IF( info.NE.0 )THEN
230  CALL xerbla( 'SLA_GEAMV ', info )
231  RETURN
232  END IF
233 *
234 * Quick return if possible.
235 *
236  IF( ( m.EQ.0 ).OR.( n.EQ.0 ).OR.
237  \$ ( ( alpha.EQ.zero ).AND.( beta.EQ.one ) ) )
238  \$ RETURN
239 *
240 * Set LENX and LENY, the lengths of the vectors x and y, and set
241 * up the start points in X and Y.
242 *
243  IF( trans.EQ.ilatrans( 'N' ) )THEN
244  lenx = n
245  leny = m
246  ELSE
247  lenx = m
248  leny = n
249  END IF
250  IF( incx.GT.0 )THEN
251  kx = 1
252  ELSE
253  kx = 1 - ( lenx - 1 )*incx
254  END IF
255  IF( incy.GT.0 )THEN
256  ky = 1
257  ELSE
258  ky = 1 - ( leny - 1 )*incy
259  END IF
260 *
261 * Set SAFE1 essentially to be the underflow threshold times the
262 * number of additions in each row.
263 *
264  safe1 = slamch( 'Safe minimum' )
265  safe1 = (n+1)*safe1
266 *
267 * Form y := alpha*abs(A)*abs(x) + beta*abs(y).
268 *
269 * The O(M*N) SYMB_ZERO tests could be replaced by O(N) queries to
270 * the inexact flag. Still doesn't help change the iteration order
271 * to per-column.
272 *
273  iy = ky
274  IF ( incx.EQ.1 ) THEN
275  IF( trans.EQ.ilatrans( 'N' ) )THEN
276  DO i = 1, leny
277  IF ( beta .EQ. zero ) THEN
278  symb_zero = .true.
279  y( iy ) = 0.0
280  ELSE IF ( y( iy ) .EQ. zero ) THEN
281  symb_zero = .true.
282  ELSE
283  symb_zero = .false.
284  y( iy ) = beta * abs( y( iy ) )
285  END IF
286  IF ( alpha .NE. zero ) THEN
287  DO j = 1, lenx
288  temp = abs( a( i, j ) )
289  symb_zero = symb_zero .AND.
290  \$ ( x( j ) .EQ. zero .OR. temp .EQ. zero )
291
292  y( iy ) = y( iy ) + alpha*abs( x( j ) )*temp
293  END DO
294  END IF
295
296  IF ( .NOT.symb_zero )
297  \$ y( iy ) = y( iy ) + sign( safe1, y( iy ) )
298
299  iy = iy + incy
300  END DO
301  ELSE
302  DO i = 1, leny
303  IF ( beta .EQ. zero ) THEN
304  symb_zero = .true.
305  y( iy ) = 0.0
306  ELSE IF ( y( iy ) .EQ. zero ) THEN
307  symb_zero = .true.
308  ELSE
309  symb_zero = .false.
310  y( iy ) = beta * abs( y( iy ) )
311  END IF
312  IF ( alpha .NE. zero ) THEN
313  DO j = 1, lenx
314  temp = abs( a( j, i ) )
315  symb_zero = symb_zero .AND.
316  \$ ( x( j ) .EQ. zero .OR. temp .EQ. zero )
317
318  y( iy ) = y( iy ) + alpha*abs( x( j ) )*temp
319  END DO
320  END IF
321
322  IF ( .NOT.symb_zero )
323  \$ y( iy ) = y( iy ) + sign( safe1, y( iy ) )
324
325  iy = iy + incy
326  END DO
327  END IF
328  ELSE
329  IF( trans.EQ.ilatrans( 'N' ) )THEN
330  DO i = 1, leny
331  IF ( beta .EQ. zero ) THEN
332  symb_zero = .true.
333  y( iy ) = 0.0
334  ELSE IF ( y( iy ) .EQ. zero ) THEN
335  symb_zero = .true.
336  ELSE
337  symb_zero = .false.
338  y( iy ) = beta * abs( y( iy ) )
339  END IF
340  IF ( alpha .NE. zero ) THEN
341  jx = kx
342  DO j = 1, lenx
343  temp = abs( a( i, j ) )
344  symb_zero = symb_zero .AND.
345  \$ ( x( jx ) .EQ. zero .OR. temp .EQ. zero )
346
347  y( iy ) = y( iy ) + alpha*abs( x( jx ) )*temp
348  jx = jx + incx
349  END DO
350  END IF
351
352  IF (.NOT.symb_zero)
353  \$ y( iy ) = y( iy ) + sign( safe1, y( iy ) )
354
355  iy = iy + incy
356  END DO
357  ELSE
358  DO i = 1, leny
359  IF ( beta .EQ. zero ) THEN
360  symb_zero = .true.
361  y( iy ) = 0.0
362  ELSE IF ( y( iy ) .EQ. zero ) THEN
363  symb_zero = .true.
364  ELSE
365  symb_zero = .false.
366  y( iy ) = beta * abs( y( iy ) )
367  END IF
368  IF ( alpha .NE. zero ) THEN
369  jx = kx
370  DO j = 1, lenx
371  temp = abs( a( j, i ) )
372  symb_zero = symb_zero .AND.
373  \$ ( x( jx ) .EQ. zero .OR. temp .EQ. zero )
374
375  y( iy ) = y( iy ) + alpha*abs( x( jx ) )*temp
376  jx = jx + incx
377  END DO
378  END IF
379
380  IF (.NOT.symb_zero)
381  \$ y( iy ) = y( iy ) + sign( safe1, y( iy ) )
382
383  iy = iy + incy
384  END DO
385  END IF
386
387  END IF
388 *
389  RETURN
390 *
391 * End of SLA_GEAMV
392 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
integer function ilatrans(TRANS)
ILATRANS
Definition: ilatrans.f:58
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
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