LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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zla_gercond_c.f
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1*> \brief \b ZLA_GERCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for general matrices.
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_gercond_c.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_gercond_c.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* DOUBLE PRECISION FUNCTION ZLA_GERCOND_C( TRANS, N, A, LDA, AF,
22* LDAF, IPIV, C, CAPPLY,
23* INFO, WORK, RWORK )
24*
25* .. Scalar Arguments ..
26* CHARACTER TRANS
27* LOGICAL CAPPLY
28* INTEGER N, LDA, LDAF, INFO
29* ..
30* .. Array Arguments ..
31* INTEGER IPIV( * )
32* COMPLEX*16 A( LDA, * ), AF( LDAF, * ), WORK( * )
33* DOUBLE PRECISION C( * ), RWORK( * )
34* ..
35*
36*
37*> \par Purpose:
38* =============
39*>
40*> \verbatim
41*>
42*> ZLA_GERCOND_C computes the infinity norm condition number of
43*> op(A) * inv(diag(C)) where C is a DOUBLE PRECISION 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] A
66*> \verbatim
67*> A is COMPLEX*16 array, dimension (LDA,N)
68*> On entry, the N-by-N matrix A
69*> \endverbatim
70*>
71*> \param[in] LDA
72*> \verbatim
73*> LDA is INTEGER
74*> The leading dimension of the array A. LDA >= max(1,N).
75*> \endverbatim
76*>
77*> \param[in] AF
78*> \verbatim
79*> AF is COMPLEX*16 array, dimension (LDAF,N)
80*> The factors L and U from the factorization
81*> A = P*L*U as computed by ZGETRF.
82*> \endverbatim
83*>
84*> \param[in] LDAF
85*> \verbatim
86*> LDAF is INTEGER
87*> The leading dimension of the array AF. LDAF >= max(1,N).
88*> \endverbatim
89*>
90*> \param[in] IPIV
91*> \verbatim
92*> IPIV is INTEGER array, dimension (N)
93*> The pivot indices from the factorization A = P*L*U
94*> as computed by ZGETRF; row i of the matrix was interchanged
95*> with row IPIV(i).
96*> \endverbatim
97*>
98*> \param[in] C
99*> \verbatim
100*> C is DOUBLE PRECISION array, dimension (N)
101*> The vector C in the formula op(A) * inv(diag(C)).
102*> \endverbatim
103*>
104*> \param[in] CAPPLY
105*> \verbatim
106*> CAPPLY is LOGICAL
107*> If .TRUE. then access the vector C in the formula above.
108*> \endverbatim
109*>
110*> \param[out] INFO
111*> \verbatim
112*> INFO is INTEGER
113*> = 0: Successful exit.
114*> i > 0: The ith argument is invalid.
115*> \endverbatim
116*>
117*> \param[out] WORK
118*> \verbatim
119*> WORK is COMPLEX*16 array, dimension (2*N).
120*> Workspace.
121*> \endverbatim
122*>
123*> \param[out] RWORK
124*> \verbatim
125*> RWORK is DOUBLE PRECISION array, dimension (N).
126*> Workspace.
127*> \endverbatim
128*
129* Authors:
130* ========
131*
132*> \author Univ. of Tennessee
133*> \author Univ. of California Berkeley
134*> \author Univ. of Colorado Denver
135*> \author NAG Ltd.
136*
137*> \ingroup la_gercond
138*
139* =====================================================================
140 DOUBLE PRECISION FUNCTION zla_gercond_c( TRANS, N, A, LDA, AF,
141 \$ LDAF, IPIV, C, CAPPLY,
142 \$ INFO, WORK, RWORK )
143*
144* -- LAPACK computational routine --
145* -- LAPACK is a software package provided by Univ. of Tennessee, --
146* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
147*
148* .. Scalar Arguments ..
149 CHARACTER trans
150 LOGICAL capply
151 INTEGER n, lda, ldaf, info
152* ..
153* .. Array Arguments ..
154 INTEGER ipiv( * )
155 COMPLEX*16 a( lda, * ), af( ldaf, * ), work( * )
156 DOUBLE PRECISION c( * ), rwork( * )
157* ..
158*
159* =====================================================================
160*
161* .. Local Scalars ..
162 LOGICAL notrans
163 INTEGER kase, i, j
164 DOUBLE PRECISION ainvnm, anorm, tmp
165 COMPLEX*16 zdum
166* ..
167* .. Local Arrays ..
168 INTEGER isave( 3 )
169* ..
170* .. External Functions ..
171 LOGICAL lsame
172 EXTERNAL lsame
173* ..
174* .. External Subroutines ..
175 EXTERNAL zlacn2, zgetrs, xerbla
176* ..
177* .. Intrinsic Functions ..
178 INTRINSIC abs, max, real, dimag
179* ..
180* .. Statement Functions ..
181 DOUBLE PRECISION cabs1
182* ..
183* .. Statement Function Definitions ..
184 cabs1( zdum ) = abs( dble( zdum ) ) + abs( dimag( zdum ) )
185* ..
186* .. Executable Statements ..
187 zla_gercond_c = 0.0d+0
188*
189 info = 0
190 notrans = lsame( trans, 'N' )
191 IF ( .NOT. notrans .AND. .NOT. lsame( trans, 'T' ) .AND. .NOT.
192 \$ lsame( trans, 'C' ) ) THEN
193 info = -1
194 ELSE IF( n.LT.0 ) THEN
195 info = -2
196 ELSE IF( lda.LT.max( 1, n ) ) THEN
197 info = -4
198 ELSE IF( ldaf.LT.max( 1, n ) ) THEN
199 info = -6
200 END IF
201 IF( info.NE.0 ) THEN
202 CALL xerbla( 'ZLA_GERCOND_C', -info )
203 RETURN
204 END IF
205*
206* Compute norm of op(A)*op2(C).
207*
208 anorm = 0.0d+0
209 IF ( notrans ) THEN
210 DO i = 1, n
211 tmp = 0.0d+0
212 IF ( capply ) THEN
213 DO j = 1, n
214 tmp = tmp + cabs1( a( i, j ) ) / c( j )
215 END DO
216 ELSE
217 DO j = 1, n
218 tmp = tmp + cabs1( a( i, j ) )
219 END DO
220 END IF
221 rwork( i ) = tmp
222 anorm = max( anorm, tmp )
223 END DO
224 ELSE
225 DO i = 1, n
226 tmp = 0.0d+0
227 IF ( capply ) THEN
228 DO j = 1, n
229 tmp = tmp + cabs1( a( j, i ) ) / c( j )
230 END DO
231 ELSE
232 DO j = 1, n
233 tmp = tmp + cabs1( a( j, i ) )
234 END DO
235 END IF
236 rwork( i ) = tmp
237 anorm = max( anorm, tmp )
238 END DO
239 END IF
240*
241* Quick return if possible.
242*
243 IF( n.EQ.0 ) THEN
244 zla_gercond_c = 1.0d+0
245 RETURN
246 ELSE IF( anorm .EQ. 0.0d+0 ) THEN
247 RETURN
248 END IF
249*
250* Estimate the norm of inv(op(A)).
251*
252 ainvnm = 0.0d+0
253*
254 kase = 0
255 10 CONTINUE
256 CALL zlacn2( n, work( n+1 ), work, ainvnm, kase, isave )
257 IF( kase.NE.0 ) THEN
258 IF( kase.EQ.2 ) THEN
259*
260* Multiply by R.
261*
262 DO i = 1, n
263 work( i ) = work( i ) * rwork( i )
264 END DO
265*
266 IF (notrans) THEN
267 CALL zgetrs( 'No transpose', n, 1, af, ldaf, ipiv,
268 \$ work, n, info )
269 ELSE
270 CALL zgetrs( 'Conjugate transpose', n, 1, af, ldaf, ipiv,
271 \$ work, n, info )
272 ENDIF
273*
274* Multiply by inv(C).
275*
276 IF ( capply ) THEN
277 DO i = 1, n
278 work( i ) = work( i ) * c( i )
279 END DO
280 END IF
281 ELSE
282*
283* Multiply by inv(C**H).
284*
285 IF ( capply ) THEN
286 DO i = 1, n
287 work( i ) = work( i ) * c( i )
288 END DO
289 END IF
290*
291 IF ( notrans ) THEN
292 CALL zgetrs( 'Conjugate transpose', n, 1, af, ldaf, ipiv,
293 \$ work, n, info )
294 ELSE
295 CALL zgetrs( 'No transpose', n, 1, af, ldaf, ipiv,
296 \$ work, n, info )
297 END IF
298*
299* Multiply by R.
300*
301 DO i = 1, n
302 work( i ) = work( i ) * rwork( i )
303 END DO
304 END IF
305 GO TO 10
306 END IF
307*
308* Compute the estimate of the reciprocal condition number.
309*
310 IF( ainvnm .NE. 0.0d+0 )
311 \$ zla_gercond_c = 1.0d+0 / ainvnm
312*
313 RETURN
314*
315* End of ZLA_GERCOND_C
316*
317 END
subroutine xerbla(srname, info)
Definition cblat2.f:3285
subroutine zgetrs(trans, n, nrhs, a, lda, ipiv, b, ldb, info)
ZGETRS
Definition zgetrs.f:121
double precision function zla_gercond_c(trans, n, a, lda, af, ldaf, ipiv, c, capply, info, work, rwork)
ZLA_GERCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for general matrices.
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