LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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zla_gbrcond_x.f
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1*> \brief \b ZLA_GBRCOND_X computes the infinity norm condition number of op(A)*diag(x) for general banded matrices.
2*
3* =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6* http://www.netlib.org/lapack/explore-html/
7*
8*> \htmlonly
9*> Download ZLA_GBRCOND_X + dependencies
10*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zla_gbrcond_x.f">
11*> [TGZ]</a>
12*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zla_gbrcond_x.f">
13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zla_gbrcond_x.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* DOUBLE PRECISION FUNCTION ZLA_GBRCOND_X( TRANS, N, KL, KU, AB,
22* LDAB, AFB, LDAFB, IPIV,
23* X, INFO, WORK, RWORK )
24*
25* .. Scalar Arguments ..
26* CHARACTER TRANS
27* INTEGER N, KL, KU, KD, KE, LDAB, LDAFB, INFO
28* ..
29* .. Array Arguments ..
30* INTEGER IPIV( * )
31* COMPLEX*16 AB( LDAB, * ), AFB( LDAFB, * ), WORK( * ),
32* $ X( * )
33* DOUBLE PRECISION RWORK( * )
34*
35*
36*
37*> \par Purpose:
38* =============
39*>
40*> \verbatim
41*>
42*> ZLA_GBRCOND_X Computes the infinity norm condition number of
43*> op(A) * diag(X) where X is a COMPLEX*16 vector.
44*> \endverbatim
45*
46* Arguments:
47* ==========
48*
49*> \param[in] TRANS
50*> \verbatim
51*> TRANS is CHARACTER*1
52*> Specifies the form of the system of equations:
53*> = 'N': A * X = B (No transpose)
54*> = 'T': A**T * X = B (Transpose)
55*> = 'C': A**H * X = B (Conjugate Transpose = Transpose)
56*> \endverbatim
57*>
58*> \param[in] N
59*> \verbatim
60*> N is INTEGER
61*> The number of linear equations, i.e., the order of the
62*> matrix A. N >= 0.
63*> \endverbatim
64*>
65*> \param[in] KL
66*> \verbatim
67*> KL is INTEGER
68*> The number of subdiagonals within the band of A. KL >= 0.
69*> \endverbatim
70*>
71*> \param[in] KU
72*> \verbatim
73*> KU is INTEGER
74*> The number of superdiagonals within the band of A. KU >= 0.
75*> \endverbatim
76*>
77*> \param[in] AB
78*> \verbatim
79*> AB is COMPLEX*16 array, dimension (LDAB,N)
80*> On entry, the matrix A in band storage, in rows 1 to KL+KU+1.
81*> The j-th column of A is stored in the j-th column of the
82*> array AB as follows:
83*> AB(KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+kl)
84*> \endverbatim
85*>
86*> \param[in] LDAB
87*> \verbatim
88*> LDAB is INTEGER
89*> The leading dimension of the array AB. LDAB >= KL+KU+1.
90*> \endverbatim
91*>
92*> \param[in] AFB
93*> \verbatim
94*> AFB is COMPLEX*16 array, dimension (LDAFB,N)
95*> Details of the LU factorization of the band matrix A, as
96*> computed by ZGBTRF. U is stored as an upper triangular
97*> band matrix with KL+KU superdiagonals in rows 1 to KL+KU+1,
98*> and the multipliers used during the factorization are stored
99*> in rows KL+KU+2 to 2*KL+KU+1.
100*> \endverbatim
101*>
102*> \param[in] LDAFB
103*> \verbatim
104*> LDAFB is INTEGER
105*> The leading dimension of the array AFB. LDAFB >= 2*KL+KU+1.
106*> \endverbatim
107*>
108*> \param[in] IPIV
109*> \verbatim
110*> IPIV is INTEGER array, dimension (N)
111*> The pivot indices from the factorization A = P*L*U
112*> as computed by ZGBTRF; row i of the matrix was interchanged
113*> with row IPIV(i).
114*> \endverbatim
115*>
116*> \param[in] X
117*> \verbatim
118*> X is COMPLEX*16 array, dimension (N)
119*> The vector X in the formula op(A) * diag(X).
120*> \endverbatim
121*>
122*> \param[out] INFO
123*> \verbatim
124*> INFO is INTEGER
125*> = 0: Successful exit.
126*> i > 0: The ith argument is invalid.
127*> \endverbatim
128*>
129*> \param[out] WORK
130*> \verbatim
131*> WORK is COMPLEX*16 array, dimension (2*N).
132*> Workspace.
133*> \endverbatim
134*>
135*> \param[out] RWORK
136*> \verbatim
137*> RWORK is DOUBLE PRECISION array, dimension (N).
138*> Workspace.
139*> \endverbatim
140*
141* Authors:
142* ========
143*
144*> \author Univ. of Tennessee
145*> \author Univ. of California Berkeley
146*> \author Univ. of Colorado Denver
147*> \author NAG Ltd.
148*
149*> \ingroup la_gbrcond
150*
151* =====================================================================
152 DOUBLE PRECISION FUNCTION zla_gbrcond_x( TRANS, N, KL, KU, AB,
153 $ LDAB, AFB, LDAFB, IPIV,
154 $ X, INFO, WORK, RWORK )
155*
156* -- LAPACK computational routine --
157* -- LAPACK is a software package provided by Univ. of Tennessee, --
158* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
159*
160* .. Scalar Arguments ..
161 CHARACTER trans
162 INTEGER n, kl, ku, kd, ke, ldab, ldafb, info
163* ..
164* .. Array Arguments ..
165 INTEGER ipiv( * )
166 COMPLEX*16 ab( ldab, * ), afb( ldafb, * ), work( * ),
167 $ x( * )
168 DOUBLE PRECISION rwork( * )
169*
170*
171* =====================================================================
172*
173* .. Local Scalars ..
174 LOGICAL notrans
175 INTEGER kase, i, j
176 DOUBLE PRECISION ainvnm, anorm, tmp
177 COMPLEX*16 zdum
178* ..
179* .. Local Arrays ..
180 INTEGER isave( 3 )
181* ..
182* .. External Functions ..
183 LOGICAL lsame
184 EXTERNAL lsame
185* ..
186* .. External Subroutines ..
187 EXTERNAL zlacn2, zgbtrs, xerbla
188* ..
189* .. Intrinsic Functions ..
190 INTRINSIC abs, max
191* ..
192* .. Statement Functions ..
193 DOUBLE PRECISION cabs1
194* ..
195* .. Statement Function Definitions ..
196 cabs1( zdum ) = abs( dble( zdum ) ) + abs( dimag( zdum ) )
197* ..
198* .. Executable Statements ..
199*
200 zla_gbrcond_x = 0.0d+0
201*
202 info = 0
203 notrans = lsame( trans, 'N' )
204 IF ( .NOT. notrans .AND. .NOT. lsame(trans, 'T') .AND. .NOT.
205 $ lsame( trans, 'C' ) ) THEN
206 info = -1
207 ELSE IF( n.LT.0 ) THEN
208 info = -2
209 ELSE IF( kl.LT.0 .OR. kl.GT.n-1 ) THEN
210 info = -3
211 ELSE IF( ku.LT.0 .OR. ku.GT.n-1 ) THEN
212 info = -4
213 ELSE IF( ldab.LT.kl+ku+1 ) THEN
214 info = -6
215 ELSE IF( ldafb.LT.2*kl+ku+1 ) THEN
216 info = -8
217 END IF
218 IF( info.NE.0 ) THEN
219 CALL xerbla( 'ZLA_GBRCOND_X', -info )
220 RETURN
221 END IF
222*
223* Compute norm of op(A)*op2(C).
224*
225 kd = ku + 1
226 ke = kl + 1
227 anorm = 0.0d+0
228 IF ( notrans ) THEN
229 DO i = 1, n
230 tmp = 0.0d+0
231 DO j = max( i-kl, 1 ), min( i+ku, n )
232 tmp = tmp + cabs1( ab( kd+i-j, j) * x( j ) )
233 END DO
234 rwork( i ) = tmp
235 anorm = max( anorm, tmp )
236 END DO
237 ELSE
238 DO i = 1, n
239 tmp = 0.0d+0
240 DO j = max( i-kl, 1 ), min( i+ku, n )
241 tmp = tmp + cabs1( ab( ke-i+j, i ) * x( j ) )
242 END DO
243 rwork( i ) = tmp
244 anorm = max( anorm, tmp )
245 END DO
246 END IF
247*
248* Quick return if possible.
249*
250 IF( n.EQ.0 ) THEN
251 zla_gbrcond_x = 1.0d+0
252 RETURN
253 ELSE IF( anorm .EQ. 0.0d+0 ) THEN
254 RETURN
255 END IF
256*
257* Estimate the norm of inv(op(A)).
258*
259 ainvnm = 0.0d+0
260*
261 kase = 0
262 10 CONTINUE
263 CALL zlacn2( n, work( n+1 ), work, ainvnm, kase, isave )
264 IF( kase.NE.0 ) THEN
265 IF( kase.EQ.2 ) THEN
266*
267* Multiply by R.
268*
269 DO i = 1, n
270 work( i ) = work( i ) * rwork( i )
271 END DO
272*
273 IF ( notrans ) THEN
274 CALL zgbtrs( 'No transpose', n, kl, ku, 1, afb, ldafb,
275 $ ipiv, work, n, info )
276 ELSE
277 CALL zgbtrs( 'Conjugate transpose', n, kl, ku, 1, afb,
278 $ ldafb, ipiv, work, n, info )
279 ENDIF
280*
281* Multiply by inv(X).
282*
283 DO i = 1, n
284 work( i ) = work( i ) / x( i )
285 END DO
286 ELSE
287*
288* Multiply by inv(X**H).
289*
290 DO i = 1, n
291 work( i ) = work( i ) / x( i )
292 END DO
293*
294 IF ( notrans ) THEN
295 CALL zgbtrs( 'Conjugate transpose', n, kl, ku, 1, afb,
296 $ ldafb, ipiv, work, n, info )
297 ELSE
298 CALL zgbtrs( 'No transpose', n, kl, ku, 1, afb, ldafb,
299 $ ipiv, work, n, info )
300 END IF
301*
302* Multiply by R.
303*
304 DO i = 1, n
305 work( i ) = work( i ) * rwork( i )
306 END DO
307 END IF
308 GO TO 10
309 END IF
310*
311* Compute the estimate of the reciprocal condition number.
312*
313 IF( ainvnm .NE. 0.0d+0 )
314 $ zla_gbrcond_x = 1.0d+0 / ainvnm
315*
316 RETURN
317*
318* End of ZLA_GBRCOND_X
319*
320 END
subroutine xerbla(srname, info)
Definition cblat2.f:3285
subroutine zgbtrs(trans, n, kl, ku, nrhs, ab, ldab, ipiv, b, ldb, info)
ZGBTRS
Definition zgbtrs.f:138
double precision function zla_gbrcond_x(trans, n, kl, ku, ab, ldab, afb, ldafb, ipiv, x, info, work, rwork)
ZLA_GBRCOND_X computes the infinity norm condition number of op(A)*diag(x) for general banded matrice...
subroutine zlacn2(n, v, x, est, kase, isave)
ZLACN2 estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vec...
Definition zlacn2.f:133
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48