LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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zla_gbamv.f
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1*> \brief \b ZLA_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
10*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zla_gbamv.f">
11*> [TGZ]</a>
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13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zla_gbamv.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* SUBROUTINE ZLA_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* COMPLEX*16 AB( LDAB, * ), X( * )
30* DOUBLE PRECISION Y( * )
31* ..
32*
33*
34*> \par Purpose:
35* =============
36*>
37*> \verbatim
38*>
39*> ZLA_GBAMV performs one of the matrix-vector operations
40*>
41*> y := alpha*abs(A)*abs(x) + beta*abs(y),
42*> or y := alpha*abs(A)**T*abs(x) + beta*abs(y),
43*>
44*> where alpha and beta are scalars, x and y are vectors and A is an
45*> m by n matrix.
46*>
47*> This function is primarily used in calculating error bounds.
48*> To protect against underflow during evaluation, components in
49*> the resulting vector are perturbed away from zero by (N+1)
50*> times the underflow threshold. To prevent unnecessarily large
51*> errors for block-structure embedded in general matrices,
52*> "symbolically" zero components are not perturbed. A zero
53*> entry is considered "symbolic" if all multiplications involved
54*> in computing that entry have at least one zero multiplicand.
55*> \endverbatim
56*
57* Arguments:
58* ==========
59*
60*> \param[in] TRANS
61*> \verbatim
62*> TRANS is INTEGER
63*> On entry, TRANS specifies the operation to be performed as
64*> follows:
65*>
66*> BLAS_NO_TRANS y := alpha*abs(A)*abs(x) + beta*abs(y)
67*> BLAS_TRANS y := alpha*abs(A**T)*abs(x) + beta*abs(y)
68*> BLAS_CONJ_TRANS y := alpha*abs(A**T)*abs(x) + beta*abs(y)
69*>
70*> Unchanged on exit.
71*> \endverbatim
72*>
73*> \param[in] M
74*> \verbatim
75*> M is INTEGER
76*> On entry, M specifies the number of rows of the matrix A.
77*> M must be at least zero.
78*> Unchanged on exit.
79*> \endverbatim
80*>
81*> \param[in] N
82*> \verbatim
83*> N is INTEGER
84*> On entry, N specifies the number of columns of the matrix A.
85*> N must be at least zero.
86*> Unchanged on exit.
87*> \endverbatim
88*>
89*> \param[in] KL
90*> \verbatim
91*> KL is INTEGER
92*> The number of subdiagonals within the band of A. KL >= 0.
93*> \endverbatim
94*>
95*> \param[in] KU
96*> \verbatim
97*> KU is INTEGER
98*> The number of superdiagonals within the band of A. KU >= 0.
99*> \endverbatim
100*>
101*> \param[in] ALPHA
102*> \verbatim
103*> ALPHA is DOUBLE PRECISION
104*> On entry, ALPHA specifies the scalar alpha.
105*> Unchanged on exit.
106*> \endverbatim
107*>
108*> \param[in] AB
109*> \verbatim
110*> AB is COMPLEX*16 array, dimension ( LDAB, n )
111*> Before entry, the leading m by n part of the array AB must
112*> contain the matrix of coefficients.
113*> Unchanged on exit.
114*> \endverbatim
115*>
116*> \param[in] LDAB
117*> \verbatim
118*> LDAB is INTEGER
119*> On entry, LDAB specifies the first dimension of AB as declared
120*> in the calling (sub) program. LDAB must be at least
121*> max( 1, m ).
122*> Unchanged on exit.
123*> \endverbatim
124*>
125*> \param[in] X
126*> \verbatim
127*> X is COMPLEX*16 array, dimension
128*> ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n'
129*> and at least
130*> ( 1 + ( m - 1 )*abs( INCX ) ) otherwise.
131*> Before entry, the incremented array X must contain the
132*> vector x.
133*> Unchanged on exit.
134*> \endverbatim
135*>
136*> \param[in] INCX
137*> \verbatim
138*> INCX is INTEGER
139*> On entry, INCX specifies the increment for the elements of
140*> X. INCX must not be zero.
141*> Unchanged on exit.
142*> \endverbatim
143*>
144*> \param[in] BETA
145*> \verbatim
146*> BETA is DOUBLE PRECISION
147*> On entry, BETA specifies the scalar beta. When BETA is
148*> supplied as zero then Y need not be set on input.
149*> Unchanged on exit.
150*> \endverbatim
151*>
152*> \param[in,out] Y
153*> \verbatim
154*> Y is DOUBLE PRECISION array, dimension
155*> ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n'
156*> and at least
157*> ( 1 + ( n - 1 )*abs( INCY ) ) otherwise.
158*> Before entry with BETA non-zero, the incremented array Y
159*> must contain the vector y. On exit, Y is overwritten by the
160*> updated vector y.
161*> \endverbatim
162*>
163*> \param[in] INCY
164*> \verbatim
165*> INCY is INTEGER
166*> On entry, INCY specifies the increment for the elements of
167*> Y. INCY must not be zero.
168*> Unchanged on exit.
169*>
170*> Level 2 Blas routine.
171*> \endverbatim
172*
173* Authors:
174* ========
175*
176*> \author Univ. of Tennessee
177*> \author Univ. of California Berkeley
178*> \author Univ. of Colorado Denver
179*> \author NAG Ltd.
180*
181*> \ingroup complex16GBcomputational
182*
183* =====================================================================
184 SUBROUTINE zla_gbamv( TRANS, M, N, KL, KU, ALPHA, AB, LDAB, X,
185 \$ INCX, BETA, Y, INCY )
186*
187* -- LAPACK computational routine --
188* -- LAPACK is a software package provided by Univ. of Tennessee, --
189* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
190*
191* .. Scalar Arguments ..
192 DOUBLE PRECISION ALPHA, BETA
193 INTEGER INCX, INCY, LDAB, M, N, KL, KU, TRANS
194* ..
195* .. Array Arguments ..
196 COMPLEX*16 AB( LDAB, * ), X( * )
197 DOUBLE PRECISION Y( * )
198* ..
199*
200* =====================================================================
201*
202* .. Parameters ..
203 COMPLEX*16 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 COMPLEX*16 CDUM
211* ..
212* .. External Subroutines ..
213 EXTERNAL xerbla, dlamch
214 DOUBLE PRECISION DLAMCH
215* ..
216* .. External Functions ..
217 EXTERNAL ilatrans
218 INTEGER ILATRANS
219* ..
220* .. Intrinsic Functions ..
221 INTRINSIC max, abs, real, dimag, sign
222* ..
223* .. Statement Functions
224 DOUBLE PRECISION CABS1
225* ..
226* .. Statement Function Definitions ..
227 cabs1( cdum ) = abs( dble( cdum ) ) + abs( dimag( cdum ) )
228* ..
229* .. Executable Statements ..
230*
231* Test the input parameters.
232*
233 info = 0
234 IF ( .NOT.( ( trans.EQ.ilatrans( 'N' ) )
235 \$ .OR. ( trans.EQ.ilatrans( 'T' ) )
236 \$ .OR. ( trans.EQ.ilatrans( 'C' ) ) ) ) THEN
237 info = 1
238 ELSE IF( m.LT.0 )THEN
239 info = 2
240 ELSE IF( n.LT.0 )THEN
241 info = 3
242 ELSE IF( kl.LT.0 .OR. kl.GT.m-1 ) THEN
243 info = 4
244 ELSE IF( ku.LT.0 .OR. ku.GT.n-1 ) THEN
245 info = 5
246 ELSE IF( ldab.LT.kl+ku+1 )THEN
247 info = 6
248 ELSE IF( incx.EQ.0 )THEN
249 info = 8
250 ELSE IF( incy.EQ.0 )THEN
251 info = 11
252 END IF
253 IF( info.NE.0 )THEN
254 CALL xerbla( 'ZLA_GBAMV ', info )
255 RETURN
256 END IF
257*
258* Quick return if possible.
259*
260 IF( ( m.EQ.0 ).OR.( n.EQ.0 ).OR.
261 \$ ( ( alpha.EQ.zero ).AND.( beta.EQ.one ) ) )
262 \$ RETURN
263*
264* Set LENX and LENY, the lengths of the vectors x and y, and set
265* up the start points in X and Y.
266*
267 IF( trans.EQ.ilatrans( 'N' ) )THEN
268 lenx = n
269 leny = m
270 ELSE
271 lenx = m
272 leny = n
273 END IF
274 IF( incx.GT.0 )THEN
275 kx = 1
276 ELSE
277 kx = 1 - ( lenx - 1 )*incx
278 END IF
279 IF( incy.GT.0 )THEN
280 ky = 1
281 ELSE
282 ky = 1 - ( leny - 1 )*incy
283 END IF
284*
285* Set SAFE1 essentially to be the underflow threshold times the
286* number of additions in each row.
287*
288 safe1 = dlamch( 'Safe minimum' )
289 safe1 = (n+1)*safe1
290*
291* Form y := alpha*abs(A)*abs(x) + beta*abs(y).
292*
293* The O(M*N) SYMB_ZERO tests could be replaced by O(N) queries to
294* the inexact flag. Still doesn't help change the iteration order
295* to per-column.
296*
297 kd = ku + 1
298 ke = kl + 1
299 iy = ky
300 IF ( incx.EQ.1 ) THEN
301 IF( trans.EQ.ilatrans( 'N' ) )THEN
302 DO i = 1, leny
303 IF ( beta .EQ. 0.0d+0 ) THEN
304 symb_zero = .true.
305 y( iy ) = 0.0d+0
306 ELSE IF ( y( iy ) .EQ. 0.0d+0 ) 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. 0.0d+0 ) THEN
313 DO j = max( i-kl, 1 ), min( i+ku, lenx )
314 temp = cabs1( ab( kd+i-j, j ) )
315 symb_zero = symb_zero .AND.
316 \$ ( x( j ) .EQ. zero .OR. temp .EQ. zero )
317
318 y( iy ) = y( iy ) + alpha*cabs1( 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 ELSE
328 DO i = 1, leny
329 IF ( beta .EQ. 0.0d+0 ) THEN
330 symb_zero = .true.
331 y( iy ) = 0.0d+0
332 ELSE IF ( y( iy ) .EQ. 0.0d+0 ) THEN
333 symb_zero = .true.
334 ELSE
335 symb_zero = .false.
336 y( iy ) = beta * abs( y( iy ) )
337 END IF
338 IF ( alpha .NE. 0.0d+0 ) THEN
339 DO j = max( i-kl, 1 ), min( i+ku, lenx )
340 temp = cabs1( ab( ke-i+j, i ) )
341 symb_zero = symb_zero .AND.
342 \$ ( x( j ) .EQ. zero .OR. temp .EQ. zero )
343
344 y( iy ) = y( iy ) + alpha*cabs1( x( j ) )*temp
345 END DO
346 END IF
347
348 IF ( .NOT.symb_zero)
349 \$ y( iy ) = y( iy ) + sign( safe1, y( iy ) )
350
351 iy = iy + incy
352 END DO
353 END IF
354 ELSE
355 IF( trans.EQ.ilatrans( 'N' ) )THEN
356 DO i = 1, leny
357 IF ( beta .EQ. 0.0d+0 ) THEN
358 symb_zero = .true.
359 y( iy ) = 0.0d+0
360 ELSE IF ( y( iy ) .EQ. 0.0d+0 ) THEN
361 symb_zero = .true.
362 ELSE
363 symb_zero = .false.
364 y( iy ) = beta * abs( y( iy ) )
365 END IF
366 IF ( alpha .NE. 0.0d+0 ) THEN
367 jx = kx
368 DO j = max( i-kl, 1 ), min( i+ku, lenx )
369 temp = cabs1( ab( kd+i-j, j ) )
370 symb_zero = symb_zero .AND.
371 \$ ( x( jx ) .EQ. zero .OR. temp .EQ. zero )
372
373 y( iy ) = y( iy ) + alpha*cabs1( x( jx ) )*temp
374 jx = jx + incx
375 END DO
376 END IF
377
378 IF ( .NOT.symb_zero )
379 \$ y( iy ) = y( iy ) + sign( safe1, y( iy ) )
380
381 iy = iy + incy
382 END DO
383 ELSE
384 DO i = 1, leny
385 IF ( beta .EQ. 0.0d+0 ) THEN
386 symb_zero = .true.
387 y( iy ) = 0.0d+0
388 ELSE IF ( y( iy ) .EQ. 0.0d+0 ) THEN
389 symb_zero = .true.
390 ELSE
391 symb_zero = .false.
392 y( iy ) = beta * abs( y( iy ) )
393 END IF
394 IF ( alpha .NE. 0.0d+0 ) THEN
395 jx = kx
396 DO j = max( i-kl, 1 ), min( i+ku, lenx )
397 temp = cabs1( ab( ke-i+j, i ) )
398 symb_zero = symb_zero .AND.
399 \$ ( x( jx ) .EQ. zero .OR. temp .EQ. zero )
400
401 y( iy ) = y( iy ) + alpha*cabs1( x( jx ) )*temp
402 jx = jx + incx
403 END DO
404 END IF
405
406 IF ( .NOT.symb_zero )
407 \$ y( iy ) = y( iy ) + sign( safe1, y( iy ) )
408
409 iy = iy + incy
410 END DO
411 END IF
412
413 END IF
414*
415 RETURN
416*
417* End of ZLA_GBAMV
418*
419 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 zla_gbamv(TRANS, M, N, KL, KU, ALPHA, AB, LDAB, X, INCX, BETA, Y, INCY)
ZLA_GBAMV performs a matrix-vector operation to calculate error bounds.
Definition: zla_gbamv.f:186