LAPACK 3.12.1
LAPACK: Linear Algebra PACKage
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◆ sla_gbamv()

subroutine sla_gbamv ( integer trans,
integer m,
integer n,
integer kl,
integer ku,
real alpha,
real, dimension( ldab, * ) ab,
integer ldab,
real, dimension( * ) x,
integer incx,
real beta,
real, dimension( * ) y,
integer incy )

SLA_GBAMV performs a matrix-vector operation to calculate error bounds.

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

Purpose:
!>
!> SLA_GBAMV  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,
!>  zero components are not perturbed.  A zero
!> entry is considered  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]KL
!>          KL is INTEGER
!>           The number of subdiagonals within the band of A.  KL >= 0.
!>
[in]KU
!>          KU is INTEGER
!>           The number of superdiagonals within the band of A.  KU >= 0.
!>
[in]ALPHA
!>          ALPHA is REAL
!>           On entry, ALPHA specifies the scalar alpha.
!>           Unchanged on exit.
!>
[in]AB
!>          AB is REAL array, dimension ( LDAB, n )
!>           Before entry, the leading m by n part of the array AB must
!>           contain the matrix of coefficients.
!>           Unchanged on exit.
!>
[in]LDAB
!>          LDAB is INTEGER
!>           On entry, LDA specifies the first dimension of AB as declared
!>           in the calling (sub) program. LDAB 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
!>           ( 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.
!>           Unchanged on exit.
!>
!>  Level 2 Blas routine.
!>
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

Definition at line 183 of file sla_gbamv.f.

185*
186* -- LAPACK computational routine --
187* -- LAPACK is a software package provided by Univ. of Tennessee, --
188* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
189*
190* .. Scalar Arguments ..
191 REAL ALPHA, BETA
192 INTEGER INCX, INCY, LDAB, M, N, KL, KU, TRANS
193* ..
194* .. Array Arguments ..
195 REAL AB( LDAB, * ), X( * ), Y( * )
196* ..
197*
198* =====================================================================
199* .. Parameters ..
200 REAL ONE, ZERO
201 parameter( one = 1.0e+0, zero = 0.0e+0 )
202* ..
203* .. Local Scalars ..
204 LOGICAL SYMB_ZERO
205 REAL TEMP, SAFE1
206 INTEGER I, INFO, IY, J, JX, KX, KY, LENX, LENY, KD, KE
207* ..
208* .. External Subroutines ..
209 EXTERNAL xerbla, slamch
210 REAL SLAMCH
211* ..
212* .. External Functions ..
213 EXTERNAL ilatrans
214 INTEGER ILATRANS
215* ..
216* .. Intrinsic Functions ..
217 INTRINSIC max, abs, sign
218* ..
219* .. Executable Statements ..
220*
221* Test the input parameters.
222*
223 info = 0
224 IF ( .NOT.( ( trans.EQ.ilatrans( 'N' ) )
225 $ .OR. ( trans.EQ.ilatrans( 'T' ) )
226 $ .OR. ( trans.EQ.ilatrans( 'C' ) ) ) ) THEN
227 info = 1
228 ELSE IF( m.LT.0 )THEN
229 info = 2
230 ELSE IF( n.LT.0 )THEN
231 info = 3
232 ELSE IF( kl.LT.0 .OR. kl.GT.m-1 ) THEN
233 info = 4
234 ELSE IF( ku.LT.0 .OR. ku.GT.n-1 ) THEN
235 info = 5
236 ELSE IF( ldab.LT.kl+ku+1 )THEN
237 info = 6
238 ELSE IF( incx.EQ.0 )THEN
239 info = 8
240 ELSE IF( incy.EQ.0 )THEN
241 info = 11
242 END IF
243 IF( info.NE.0 )THEN
244 CALL xerbla( 'SLA_GBAMV ', info )
245 RETURN
246 END IF
247*
248* Quick return if possible.
249*
250 IF( ( m.EQ.0 ).OR.( n.EQ.0 ).OR.
251 $ ( ( alpha.EQ.zero ).AND.( beta.EQ.one ) ) )
252 $ RETURN
253*
254* Set LENX and LENY, the lengths of the vectors x and y, and set
255* up the start points in X and Y.
256*
257 IF( trans.EQ.ilatrans( 'N' ) )THEN
258 lenx = n
259 leny = m
260 ELSE
261 lenx = m
262 leny = n
263 END IF
264 IF( incx.GT.0 )THEN
265 kx = 1
266 ELSE
267 kx = 1 - ( lenx - 1 )*incx
268 END IF
269 IF( incy.GT.0 )THEN
270 ky = 1
271 ELSE
272 ky = 1 - ( leny - 1 )*incy
273 END IF
274*
275* Set SAFE1 essentially to be the underflow threshold times the
276* number of additions in each row.
277*
278 safe1 = slamch( 'Safe minimum' )
279 safe1 = (n+1)*safe1
280*
281* Form y := alpha*abs(A)*abs(x) + beta*abs(y).
282*
283* The O(M*N) SYMB_ZERO tests could be replaced by O(N) queries to
284* the inexact flag. Still doesn't help change the iteration order
285* to per-column.
286*
287 kd = ku + 1
288 ke = kl + 1
289 iy = ky
290 IF ( incx.EQ.1 ) THEN
291 IF( trans.EQ.ilatrans( 'N' ) )THEN
292 DO i = 1, leny
293 IF ( beta .EQ. zero ) THEN
294 symb_zero = .true.
295 y( iy ) = 0.0
296 ELSE IF ( y( iy ) .EQ. zero ) THEN
297 symb_zero = .true.
298 ELSE
299 symb_zero = .false.
300 y( iy ) = beta * abs( y( iy ) )
301 END IF
302 IF ( alpha .NE. zero ) THEN
303 DO j = max( i-kl, 1 ), min( i+ku, lenx )
304 temp = abs( ab( kd+i-j, j ) )
305 symb_zero = symb_zero .AND.
306 $ ( x( j ) .EQ. zero .OR. temp .EQ. zero )
307
308 y( iy ) = y( iy ) + alpha*abs( x( j ) )*temp
309 END DO
310 END IF
311
312 IF ( .NOT.symb_zero )
313 $ y( iy ) = y( iy ) + sign( safe1, y( iy ) )
314 iy = iy + incy
315 END DO
316 ELSE
317 DO i = 1, leny
318 IF ( beta .EQ. zero ) THEN
319 symb_zero = .true.
320 y( iy ) = 0.0
321 ELSE IF ( y( iy ) .EQ. zero ) THEN
322 symb_zero = .true.
323 ELSE
324 symb_zero = .false.
325 y( iy ) = beta * abs( y( iy ) )
326 END IF
327 IF ( alpha .NE. zero ) THEN
328 DO j = max( i-kl, 1 ), min( i+ku, lenx )
329 temp = abs( ab( ke-i+j, i ) )
330 symb_zero = symb_zero .AND.
331 $ ( x( j ) .EQ. zero .OR. temp .EQ. zero )
332
333 y( iy ) = y( iy ) + alpha*abs( x( j ) )*temp
334 END DO
335 END IF
336
337 IF ( .NOT.symb_zero )
338 $ y( iy ) = y( iy ) + sign( safe1, y( iy ) )
339 iy = iy + incy
340 END DO
341 END IF
342 ELSE
343 IF( trans.EQ.ilatrans( 'N' ) )THEN
344 DO i = 1, leny
345 IF ( beta .EQ. zero ) THEN
346 symb_zero = .true.
347 y( iy ) = 0.0
348 ELSE IF ( y( iy ) .EQ. zero ) THEN
349 symb_zero = .true.
350 ELSE
351 symb_zero = .false.
352 y( iy ) = beta * abs( y( iy ) )
353 END IF
354 IF ( alpha .NE. zero ) THEN
355 jx = kx
356 DO j = max( i-kl, 1 ), min( i+ku, lenx )
357 temp = abs( ab( kd+i-j, j ) )
358 symb_zero = symb_zero .AND.
359 $ ( x( jx ) .EQ. zero .OR. temp .EQ. zero )
360
361 y( iy ) = y( iy ) + alpha*abs( x( jx ) )*temp
362 jx = jx + incx
363 END DO
364 END IF
365
366 IF ( .NOT.symb_zero )
367 $ y( iy ) = y( iy ) + sign( safe1, y( iy ) )
368
369 iy = iy + incy
370 END DO
371 ELSE
372 DO i = 1, leny
373 IF ( beta .EQ. zero ) THEN
374 symb_zero = .true.
375 y( iy ) = 0.0
376 ELSE IF ( y( iy ) .EQ. zero ) THEN
377 symb_zero = .true.
378 ELSE
379 symb_zero = .false.
380 y( iy ) = beta * abs( y( iy ) )
381 END IF
382 IF ( alpha .NE. zero ) THEN
383 jx = kx
384 DO j = max( i-kl, 1 ), min( i+ku, lenx )
385 temp = abs( ab( ke-i+j, i ) )
386 symb_zero = symb_zero .AND.
387 $ ( x( jx ) .EQ. zero .OR. temp .EQ. zero )
388
389 y( iy ) = y( iy ) + alpha*abs( x( jx ) )*temp
390 jx = jx + incx
391 END DO
392 END IF
393
394 IF ( .NOT.symb_zero )
395 $ y( iy ) = y( iy ) + sign( safe1, y( iy ) )
396
397 iy = iy + incy
398 END DO
399 END IF
400
401 END IF
402*
403 RETURN
404*
405* End of SLA_GBAMV
406*
xerbla
subroutine xerbla(srname, info)
Definition cblat2.f:3285
ilatrans
integer function ilatrans(trans)
ILATRANS
Definition ilatrans.f:56
slamch
real function slamch(cmach)
SLAMCH
Definition slamch.f:68
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