LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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dla_gbamv.f
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1*> \brief \b DLA_GBAMV performs a matrix-vector operation to calculate error bounds.
2*
3* =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6* http://www.netlib.org/lapack/explore-html/
7*
8*> \htmlonly
9*> Download DLA_GBAMV + dependencies
10*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dla_gbamv.f">
11*> [TGZ]</a>
12*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dla_gbamv.f">
13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dla_gbamv.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* SUBROUTINE DLA_GBAMV( TRANS, M, N, KL, KU, ALPHA, AB, LDAB, X,
22* INCX, BETA, Y, INCY )
23*
24* .. Scalar Arguments ..
25* DOUBLE PRECISION ALPHA, BETA
26* INTEGER INCX, INCY, LDAB, M, N, KL, KU, TRANS
27* ..
28* .. Array Arguments ..
29* DOUBLE PRECISION AB( LDAB, * ), X( * ), Y( * )
30* ..
31*
32*
33*> \par Purpose:
34* =============
35*>
36*> \verbatim
37*>
38*> DLA_GBAMV performs one of the matrix-vector operations
39*>
40*> y := alpha*abs(A)*abs(x) + beta*abs(y),
41*> or y := alpha*abs(A)**T*abs(x) + beta*abs(y),
42*>
43*> where alpha and beta are scalars, x and y are vectors and A is an
44*> m by n matrix.
45*>
46*> This function is primarily used in calculating error bounds.
47*> To protect against underflow during evaluation, components in
48*> the resulting vector are perturbed away from zero by (N+1)
49*> times the underflow threshold. To prevent unnecessarily large
50*> errors for block-structure embedded in general matrices,
51*> "symbolically" zero components are not perturbed. A zero
52*> entry is considered "symbolic" if all multiplications involved
53*> in computing that entry have at least one zero multiplicand.
54*> \endverbatim
55*
56* Arguments:
57* ==========
58*
59*> \param[in] TRANS
60*> \verbatim
61*> TRANS is INTEGER
62*> On entry, TRANS specifies the operation to be performed as
63*> follows:
64*>
65*> BLAS_NO_TRANS y := alpha*abs(A)*abs(x) + beta*abs(y)
66*> BLAS_TRANS y := alpha*abs(A**T)*abs(x) + beta*abs(y)
67*> BLAS_CONJ_TRANS y := alpha*abs(A**T)*abs(x) + beta*abs(y)
68*>
69*> Unchanged on exit.
70*> \endverbatim
71*>
72*> \param[in] M
73*> \verbatim
74*> M is INTEGER
75*> On entry, M specifies the number of rows of the matrix A.
76*> M must be at least zero.
77*> Unchanged on exit.
78*> \endverbatim
79*>
80*> \param[in] N
81*> \verbatim
82*> N is INTEGER
83*> On entry, N specifies the number of columns of the matrix A.
84*> N must be at least zero.
85*> Unchanged on exit.
86*> \endverbatim
87*>
88*> \param[in] KL
89*> \verbatim
90*> KL is INTEGER
91*> The number of subdiagonals within the band of A. KL >= 0.
92*> \endverbatim
93*>
94*> \param[in] KU
95*> \verbatim
96*> KU is INTEGER
97*> The number of superdiagonals within the band of A. KU >= 0.
98*> \endverbatim
99*>
100*> \param[in] ALPHA
101*> \verbatim
102*> ALPHA is DOUBLE PRECISION
103*> On entry, ALPHA specifies the scalar alpha.
104*> Unchanged on exit.
105*> \endverbatim
106*>
107*> \param[in] AB
108*> \verbatim
109*> AB is DOUBLE PRECISION array, dimension ( LDAB, n )
110*> Before entry, the leading m by n part of the array AB must
111*> contain the matrix of coefficients.
112*> Unchanged on exit.
113*> \endverbatim
114*>
115*> \param[in] LDAB
116*> \verbatim
117*> LDAB is INTEGER
118*> On entry, LDA specifies the first dimension of AB as declared
119*> in the calling (sub) program. LDAB must be at least
120*> max( 1, m ).
121*> Unchanged on exit.
122*> \endverbatim
123*>
124*> \param[in] X
125*> \verbatim
126*> X is DOUBLE PRECISION array, dimension
127*> ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n'
128*> and at least
129*> ( 1 + ( m - 1 )*abs( INCX ) ) otherwise.
130*> Before entry, the incremented array X must contain the
131*> vector x.
132*> Unchanged on exit.
133*> \endverbatim
134*>
135*> \param[in] INCX
136*> \verbatim
137*> INCX is INTEGER
138*> On entry, INCX specifies the increment for the elements of
139*> X. INCX must not be zero.
140*> Unchanged on exit.
141*> \endverbatim
142*>
143*> \param[in] BETA
144*> \verbatim
145*> BETA is DOUBLE PRECISION
146*> On entry, BETA specifies the scalar beta. When BETA is
147*> supplied as zero then Y need not be set on input.
148*> Unchanged on exit.
149*> \endverbatim
150*>
151*> \param[in,out] Y
152*> \verbatim
153*> Y is DOUBLE PRECISION array, dimension
154*> ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n'
155*> and at least
156*> ( 1 + ( n - 1 )*abs( INCY ) ) otherwise.
157*> Before entry with BETA non-zero, the incremented array Y
158*> must contain the vector y. On exit, Y is overwritten by the
159*> updated vector y.
160*> If either m or n is zero, then Y not referenced and the function
161*> performs a quick return.
162*> \endverbatim
163*>
164*> \param[in] INCY
165*> \verbatim
166*> INCY is INTEGER
167*> On entry, INCY specifies the increment for the elements of
168*> Y. INCY must not be zero.
169*> Unchanged on exit.
170*>
171*> Level 2 Blas routine.
172*> \endverbatim
173*
174* Authors:
175* ========
176*
177*> \author Univ. of Tennessee
178*> \author Univ. of California Berkeley
179*> \author Univ. of Colorado Denver
180*> \author NAG Ltd.
181*
182*> \ingroup la_gbamv
183*
184* =====================================================================
185 SUBROUTINE dla_gbamv( TRANS, M, N, KL, KU, ALPHA, AB, LDAB, X,
186 $ INCX, BETA, Y, INCY )
187*
188* -- LAPACK computational routine --
189* -- LAPACK is a software package provided by Univ. of Tennessee, --
190* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
191*
192* .. Scalar Arguments ..
193 DOUBLE PRECISION ALPHA, BETA
194 INTEGER INCX, INCY, LDAB, M, N, KL, KU, TRANS
195* ..
196* .. Array Arguments ..
197 DOUBLE PRECISION AB( LDAB, * ), X( * ), Y( * )
198* ..
199*
200* =====================================================================
201*
202* .. Parameters ..
203 DOUBLE PRECISION ONE, ZERO
204 parameter( one = 1.0d+0, zero = 0.0d+0 )
205* ..
206* .. Local Scalars ..
207 LOGICAL SYMB_ZERO
208 DOUBLE PRECISION TEMP, SAFE1
209 INTEGER I, INFO, IY, J, JX, KX, KY, LENX, LENY, KD, KE
210* ..
211* .. External Subroutines ..
212 EXTERNAL xerbla, dlamch
213 DOUBLE PRECISION DLAMCH
214* ..
215* .. External Functions ..
216 EXTERNAL ilatrans
217 INTEGER ILATRANS
218* ..
219* .. Intrinsic Functions ..
220 INTRINSIC max, abs, sign
221* ..
222* .. Executable Statements ..
223*
224* Test the input parameters.
225*
226 info = 0
227 IF ( .NOT.( ( trans.EQ.ilatrans( 'N' ) )
228 $ .OR. ( trans.EQ.ilatrans( 'T' ) )
229 $ .OR. ( trans.EQ.ilatrans( 'C' ) ) ) ) THEN
230 info = 1
231 ELSE IF( m.LT.0 )THEN
232 info = 2
233 ELSE IF( n.LT.0 )THEN
234 info = 3
235 ELSE IF( kl.LT.0 .OR. kl.GT.m-1 ) THEN
236 info = 4
237 ELSE IF( ku.LT.0 .OR. ku.GT.n-1 ) THEN
238 info = 5
239 ELSE IF( ldab.LT.kl+ku+1 )THEN
240 info = 6
241 ELSE IF( incx.EQ.0 )THEN
242 info = 8
243 ELSE IF( incy.EQ.0 )THEN
244 info = 11
245 END IF
246 IF( info.NE.0 )THEN
247 CALL xerbla( 'DLA_GBAMV ', info )
248 RETURN
249 END IF
250*
251* Quick return if possible.
252*
253 IF( ( m.EQ.0 ).OR.( n.EQ.0 ).OR.
254 $ ( ( alpha.EQ.zero ).AND.( beta.EQ.one ) ) )
255 $ RETURN
256*
257* Set LENX and LENY, the lengths of the vectors x and y, and set
258* up the start points in X and Y.
259*
260 IF( trans.EQ.ilatrans( 'N' ) )THEN
261 lenx = n
262 leny = m
263 ELSE
264 lenx = m
265 leny = n
266 END IF
267 IF( incx.GT.0 )THEN
268 kx = 1
269 ELSE
270 kx = 1 - ( lenx - 1 )*incx
271 END IF
272 IF( incy.GT.0 )THEN
273 ky = 1
274 ELSE
275 ky = 1 - ( leny - 1 )*incy
276 END IF
277*
278* Set SAFE1 essentially to be the underflow threshold times the
279* number of additions in each row.
280*
281 safe1 = dlamch( 'Safe minimum' )
282 safe1 = (n+1)*safe1
283*
284* Form y := alpha*abs(A)*abs(x) + beta*abs(y).
285*
286* The O(M*N) SYMB_ZERO tests could be replaced by O(N) queries to
287* the inexact flag. Still doesn't help change the iteration order
288* to per-column.
289*
290 kd = ku + 1
291 ke = kl + 1
292 iy = ky
293 IF ( incx.EQ.1 ) THEN
294 IF( trans.EQ.ilatrans( 'N' ) )THEN
295 DO i = 1, leny
296 IF ( beta .EQ. zero ) THEN
297 symb_zero = .true.
298 y( iy ) = 0.0d+0
299 ELSE IF ( y( iy ) .EQ. zero ) THEN
300 symb_zero = .true.
301 ELSE
302 symb_zero = .false.
303 y( iy ) = beta * abs( y( iy ) )
304 END IF
305 IF ( alpha .NE. zero ) THEN
306 DO j = max( i-kl, 1 ), min( i+ku, lenx )
307 temp = abs( ab( kd+i-j, j ) )
308 symb_zero = symb_zero .AND.
309 $ ( x( j ) .EQ. zero .OR. temp .EQ. zero )
310
311 y( iy ) = y( iy ) + alpha*abs( x( j ) )*temp
312 END DO
313 END IF
314
315 IF ( .NOT.symb_zero )
316 $ y( iy ) = y( iy ) + sign( safe1, y( iy ) )
317 iy = iy + incy
318 END DO
319 ELSE
320 DO i = 1, leny
321 IF ( beta .EQ. zero ) THEN
322 symb_zero = .true.
323 y( iy ) = 0.0d+0
324 ELSE IF ( y( iy ) .EQ. zero ) THEN
325 symb_zero = .true.
326 ELSE
327 symb_zero = .false.
328 y( iy ) = beta * abs( y( iy ) )
329 END IF
330 IF ( alpha .NE. zero ) THEN
331 DO j = max( i-kl, 1 ), min( i+ku, lenx )
332 temp = abs( ab( ke-i+j, i ) )
333 symb_zero = symb_zero .AND.
334 $ ( x( j ) .EQ. zero .OR. temp .EQ. zero )
335
336 y( iy ) = y( iy ) + alpha*abs( x( j ) )*temp
337 END DO
338 END IF
339
340 IF ( .NOT.symb_zero )
341 $ y( iy ) = y( iy ) + sign( safe1, y( iy ) )
342 iy = iy + incy
343 END DO
344 END IF
345 ELSE
346 IF( trans.EQ.ilatrans( 'N' ) )THEN
347 DO i = 1, leny
348 IF ( beta .EQ. zero ) THEN
349 symb_zero = .true.
350 y( iy ) = 0.0d+0
351 ELSE IF ( y( iy ) .EQ. zero ) THEN
352 symb_zero = .true.
353 ELSE
354 symb_zero = .false.
355 y( iy ) = beta * abs( y( iy ) )
356 END IF
357 IF ( alpha .NE. zero ) THEN
358 jx = kx
359 DO j = max( i-kl, 1 ), min( i+ku, lenx )
360 temp = abs( ab( kd+i-j, j ) )
361 symb_zero = symb_zero .AND.
362 $ ( x( jx ) .EQ. zero .OR. temp .EQ. zero )
363
364 y( iy ) = y( iy ) + alpha*abs( x( jx ) )*temp
365 jx = jx + incx
366 END DO
367 END IF
368
369 IF ( .NOT.symb_zero )
370 $ y( iy ) = y( iy ) + sign( safe1, y( iy ) )
371
372 iy = iy + incy
373 END DO
374 ELSE
375 DO i = 1, leny
376 IF ( beta .EQ. zero ) THEN
377 symb_zero = .true.
378 y( iy ) = 0.0d+0
379 ELSE IF ( y( iy ) .EQ. zero ) THEN
380 symb_zero = .true.
381 ELSE
382 symb_zero = .false.
383 y( iy ) = beta * abs( y( iy ) )
384 END IF
385 IF ( alpha .NE. zero ) THEN
386 jx = kx
387 DO j = max( i-kl, 1 ), min( i+ku, lenx )
388 temp = abs( ab( ke-i+j, i ) )
389 symb_zero = symb_zero .AND.
390 $ ( x( jx ) .EQ. zero .OR. temp .EQ. zero )
391
392 y( iy ) = y( iy ) + alpha*abs( x( jx ) )*temp
393 jx = jx + incx
394 END DO
395 END IF
396
397 IF ( .NOT.symb_zero )
398 $ y( iy ) = y( iy ) + sign( safe1, y( iy ) )
399
400 iy = iy + incy
401 END DO
402 END IF
403
404 END IF
405*
406 RETURN
407*
408* End of DLA_GBAMV
409*
410 END
xerbla
subroutine xerbla(srname, info)
Definition cblat2.f:3285
ilatrans
integer function ilatrans(trans)
ILATRANS
Definition ilatrans.f:58
dla_gbamv
subroutine dla_gbamv(trans, m, n, kl, ku, alpha, ab, ldab, x, incx, beta, y, incy)
DLA_GBAMV performs a matrix-vector operation to calculate error bounds.
Definition dla_gbamv.f:187
dlamch
double precision function dlamch(cmach)
DLAMCH
Definition dlamch.f:69