LAPACK 3.11.0
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*> \endverbatim
161*>
162*> \param[in] INCY
163*> \verbatim
164*> INCY is INTEGER
165*> On entry, INCY specifies the increment for the elements of
166*> Y. INCY must not be zero.
167*> Unchanged on exit.
168*>
169*> Level 2 Blas routine.
170*> \endverbatim
171*
172* Authors:
173* ========
174*
175*> \author Univ. of Tennessee
176*> \author Univ. of California Berkeley
177*> \author Univ. of Colorado Denver
178*> \author NAG Ltd.
179*
180*> \ingroup doubleGBcomputational
181*
182* =====================================================================
183 SUBROUTINE dla_gbamv( TRANS, M, N, KL, KU, ALPHA, AB, LDAB, X,
184 $ INCX, BETA, Y, INCY )
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 DOUBLE PRECISION ALPHA, BETA
192 INTEGER INCX, INCY, LDAB, M, N, KL, KU, TRANS
193* ..
194* .. Array Arguments ..
195 DOUBLE PRECISION AB( LDAB, * ), X( * ), Y( * )
196* ..
197*
198* =====================================================================
199*
200* .. Parameters ..
201 DOUBLE PRECISION ONE, ZERO
202 parameter( one = 1.0d+0, zero = 0.0d+0 )
203* ..
204* .. Local Scalars ..
205 LOGICAL SYMB_ZERO
206 DOUBLE PRECISION TEMP, SAFE1
207 INTEGER I, INFO, IY, J, JX, KX, KY, LENX, LENY, KD, KE
208* ..
209* .. External Subroutines ..
210 EXTERNAL xerbla, dlamch
211 DOUBLE PRECISION DLAMCH
212* ..
213* .. External Functions ..
214 EXTERNAL ilatrans
215 INTEGER ILATRANS
216* ..
217* .. Intrinsic Functions ..
218 INTRINSIC max, abs, sign
219* ..
220* .. Executable Statements ..
221*
222* Test the input parameters.
223*
224 info = 0
225 IF ( .NOT.( ( trans.EQ.ilatrans( 'N' ) )
226 $ .OR. ( trans.EQ.ilatrans( 'T' ) )
227 $ .OR. ( trans.EQ.ilatrans( 'C' ) ) ) ) THEN
228 info = 1
229 ELSE IF( m.LT.0 )THEN
230 info = 2
231 ELSE IF( n.LT.0 )THEN
232 info = 3
233 ELSE IF( kl.LT.0 .OR. kl.GT.m-1 ) THEN
234 info = 4
235 ELSE IF( ku.LT.0 .OR. ku.GT.n-1 ) THEN
236 info = 5
237 ELSE IF( ldab.LT.kl+ku+1 )THEN
238 info = 6
239 ELSE IF( incx.EQ.0 )THEN
240 info = 8
241 ELSE IF( incy.EQ.0 )THEN
242 info = 11
243 END IF
244 IF( info.NE.0 )THEN
245 CALL xerbla( 'DLA_GBAMV ', info )
246 RETURN
247 END IF
248*
249* Quick return if possible.
250*
251 IF( ( m.EQ.0 ).OR.( n.EQ.0 ).OR.
252 $ ( ( alpha.EQ.zero ).AND.( beta.EQ.one ) ) )
253 $ RETURN
254*
255* Set LENX and LENY, the lengths of the vectors x and y, and set
256* up the start points in X and Y.
257*
258 IF( trans.EQ.ilatrans( 'N' ) )THEN
259 lenx = n
260 leny = m
261 ELSE
262 lenx = m
263 leny = n
264 END IF
265 IF( incx.GT.0 )THEN
266 kx = 1
267 ELSE
268 kx = 1 - ( lenx - 1 )*incx
269 END IF
270 IF( incy.GT.0 )THEN
271 ky = 1
272 ELSE
273 ky = 1 - ( leny - 1 )*incy
274 END IF
275*
276* Set SAFE1 essentially to be the underflow threshold times the
277* number of additions in each row.
278*
279 safe1 = dlamch( 'Safe minimum' )
280 safe1 = (n+1)*safe1
281*
282* Form y := alpha*abs(A)*abs(x) + beta*abs(y).
283*
284* The O(M*N) SYMB_ZERO tests could be replaced by O(N) queries to
285* the inexact flag. Still doesn't help change the iteration order
286* to per-column.
287*
288 kd = ku + 1
289 ke = kl + 1
290 iy = ky
291 IF ( incx.EQ.1 ) THEN
292 IF( trans.EQ.ilatrans( 'N' ) )THEN
293 DO i = 1, leny
294 IF ( beta .EQ. zero ) THEN
295 symb_zero = .true.
296 y( iy ) = 0.0d+0
297 ELSE IF ( y( iy ) .EQ. zero ) THEN
298 symb_zero = .true.
299 ELSE
300 symb_zero = .false.
301 y( iy ) = beta * abs( y( iy ) )
302 END IF
303 IF ( alpha .NE. zero ) THEN
304 DO j = max( i-kl, 1 ), min( i+ku, lenx )
305 temp = abs( ab( kd+i-j, j ) )
306 symb_zero = symb_zero .AND.
307 $ ( x( j ) .EQ. zero .OR. temp .EQ. zero )
308
309 y( iy ) = y( iy ) + alpha*abs( x( j ) )*temp
310 END DO
311 END IF
312
313 IF ( .NOT.symb_zero )
314 $ y( iy ) = y( iy ) + sign( safe1, y( iy ) )
315 iy = iy + incy
316 END DO
317 ELSE
318 DO i = 1, leny
319 IF ( beta .EQ. zero ) THEN
320 symb_zero = .true.
321 y( iy ) = 0.0d+0
322 ELSE IF ( y( iy ) .EQ. zero ) THEN
323 symb_zero = .true.
324 ELSE
325 symb_zero = .false.
326 y( iy ) = beta * abs( y( iy ) )
327 END IF
328 IF ( alpha .NE. zero ) THEN
329 DO j = max( i-kl, 1 ), min( i+ku, lenx )
330 temp = abs( ab( ke-i+j, i ) )
331 symb_zero = symb_zero .AND.
332 $ ( x( j ) .EQ. zero .OR. temp .EQ. zero )
333
334 y( iy ) = y( iy ) + alpha*abs( x( j ) )*temp
335 END DO
336 END IF
337
338 IF ( .NOT.symb_zero )
339 $ y( iy ) = y( iy ) + sign( safe1, y( iy ) )
340 iy = iy + incy
341 END DO
342 END IF
343 ELSE
344 IF( trans.EQ.ilatrans( 'N' ) )THEN
345 DO i = 1, leny
346 IF ( beta .EQ. zero ) THEN
347 symb_zero = .true.
348 y( iy ) = 0.0d+0
349 ELSE IF ( y( iy ) .EQ. zero ) THEN
350 symb_zero = .true.
351 ELSE
352 symb_zero = .false.
353 y( iy ) = beta * abs( y( iy ) )
354 END IF
355 IF ( alpha .NE. zero ) THEN
356 jx = kx
357 DO j = max( i-kl, 1 ), min( i+ku, lenx )
358 temp = abs( ab( kd+i-j, j ) )
359 symb_zero = symb_zero .AND.
360 $ ( x( jx ) .EQ. zero .OR. temp .EQ. zero )
361
362 y( iy ) = y( iy ) + alpha*abs( x( jx ) )*temp
363 jx = jx + incx
364 END DO
365 END IF
366
367 IF ( .NOT.symb_zero )
368 $ y( iy ) = y( iy ) + sign( safe1, y( iy ) )
369
370 iy = iy + incy
371 END DO
372 ELSE
373 DO i = 1, leny
374 IF ( beta .EQ. zero ) THEN
375 symb_zero = .true.
376 y( iy ) = 0.0d+0
377 ELSE IF ( y( iy ) .EQ. zero ) THEN
378 symb_zero = .true.
379 ELSE
380 symb_zero = .false.
381 y( iy ) = beta * abs( y( iy ) )
382 END IF
383 IF ( alpha .NE. zero ) THEN
384 jx = kx
385 DO j = max( i-kl, 1 ), min( i+ku, lenx )
386 temp = abs( ab( ke-i+j, i ) )
387 symb_zero = symb_zero .AND.
388 $ ( x( jx ) .EQ. zero .OR. temp .EQ. zero )
389
390 y( iy ) = y( iy ) + alpha*abs( x( jx ) )*temp
391 jx = jx + incx
392 END DO
393 END IF
394
395 IF ( .NOT.symb_zero )
396 $ y( iy ) = y( iy ) + sign( safe1, y( iy ) )
397
398 iy = iy + incy
399 END DO
400 END IF
401
402 END IF
403*
404 RETURN
405*
406* End of DLA_GBAMV
407*
408 END
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
integer function ilatrans(TRANS)
ILATRANS
Definition: ilatrans.f:58
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:185