LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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cgecon.f
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1*> \brief \b CGECON
2*
3* =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6* http://www.netlib.org/lapack/explore-html/
7*
8*> \htmlonly
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13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cgecon.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* SUBROUTINE CGECON( NORM, N, A, LDA, ANORM, RCOND, WORK, RWORK,
22* INFO )
23*
24* .. Scalar Arguments ..
25* CHARACTER NORM
26* INTEGER INFO, LDA, N
27* REAL ANORM, RCOND
28* ..
29* .. Array Arguments ..
30* REAL RWORK( * )
31* COMPLEX A( LDA, * ), WORK( * )
32* ..
33*
34*
35*> \par Purpose:
36* =============
37*>
38*> \verbatim
39*>
40*> CGECON estimates the reciprocal of the condition number of a general
41*> complex matrix A, in either the 1-norm or the infinity-norm, using
42*> the LU factorization computed by CGETRF.
43*>
44*> An estimate is obtained for norm(inv(A)), and the reciprocal of the
45*> condition number is computed as
46*> RCOND = 1 / ( norm(A) * norm(inv(A)) ).
47*> \endverbatim
48*
49* Arguments:
50* ==========
51*
52*> \param[in] NORM
53*> \verbatim
54*> NORM is CHARACTER*1
55*> Specifies whether the 1-norm condition number or the
56*> infinity-norm condition number is required:
57*> = '1' or 'O': 1-norm;
58*> = 'I': Infinity-norm.
59*> \endverbatim
60*>
61*> \param[in] N
62*> \verbatim
63*> N is INTEGER
64*> The order of the matrix A. N >= 0.
65*> \endverbatim
66*>
67*> \param[in] A
68*> \verbatim
69*> A is COMPLEX array, dimension (LDA,N)
70*> The factors L and U from the factorization A = P*L*U
71*> as computed by CGETRF.
72*> \endverbatim
73*>
74*> \param[in] LDA
75*> \verbatim
76*> LDA is INTEGER
77*> The leading dimension of the array A. LDA >= max(1,N).
78*> \endverbatim
79*>
80*> \param[in] ANORM
81*> \verbatim
82*> ANORM is REAL
83*> If NORM = '1' or 'O', the 1-norm of the original matrix A.
84*> If NORM = 'I', the infinity-norm of the original matrix A.
85*> \endverbatim
86*>
87*> \param[out] RCOND
88*> \verbatim
89*> RCOND is REAL
90*> The reciprocal of the condition number of the matrix A,
91*> computed as RCOND = 1/(norm(A) * norm(inv(A))).
92*> \endverbatim
93*>
94*> \param[out] WORK
95*> \verbatim
96*> WORK is COMPLEX array, dimension (2*N)
97*> \endverbatim
98*>
99*> \param[out] RWORK
100*> \verbatim
101*> RWORK is REAL array, dimension (2*N)
102*> \endverbatim
103*>
104*> \param[out] INFO
105*> \verbatim
106*> INFO is INTEGER
107*> = 0: successful exit
108*> < 0: if INFO = -i, the i-th argument had an illegal value.
109*> NaNs are illegal values for ANORM, and they propagate to
110*> the output parameter RCOND.
111*> Infinity is illegal for ANORM, and it propagates to the output
112*> parameter RCOND as 0.
113*> = 1: if RCOND = NaN, or
114*> RCOND = Inf, or
115*> the computed norm of the inverse of A is 0.
116*> In the latter, RCOND = 0 is returned.
117*> \endverbatim
118*
119* Authors:
120* ========
121*
122*> \author Univ. of Tennessee
123*> \author Univ. of California Berkeley
124*> \author Univ. of Colorado Denver
125*> \author NAG Ltd.
126*
127*> \ingroup gecon
128*
129* =====================================================================
130 SUBROUTINE cgecon( NORM, N, A, LDA, ANORM, RCOND, WORK, RWORK,
131 \$ INFO )
132*
133* -- LAPACK computational routine --
134* -- LAPACK is a software package provided by Univ. of Tennessee, --
135* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
136*
137* .. Scalar Arguments ..
138 CHARACTER NORM
139 INTEGER INFO, LDA, N
140 REAL ANORM, RCOND
141* ..
142* .. Array Arguments ..
143 REAL RWORK( * )
144 COMPLEX A( LDA, * ), WORK( * )
145* ..
146*
147* =====================================================================
148*
149* .. Parameters ..
150 REAL ONE, ZERO
151 parameter( one = 1.0e+0, zero = 0.0e+0 )
152* ..
153* .. Local Scalars ..
154 LOGICAL ONENRM
155 CHARACTER NORMIN
156 INTEGER IX, KASE, KASE1
157 REAL AINVNM, SCALE, SL, SMLNUM, SU, HUGEVAL
158 COMPLEX ZDUM
159* ..
160* .. Local Arrays ..
161 INTEGER ISAVE( 3 )
162* ..
163* .. External Functions ..
164 LOGICAL LSAME, SISNAN
165 INTEGER ICAMAX
166 REAL SLAMCH
167 EXTERNAL lsame, icamax, slamch, sisnan
168* ..
169* .. External Subroutines ..
170 EXTERNAL clacn2, clatrs, csrscl, xerbla
171* ..
172* .. Intrinsic Functions ..
173 INTRINSIC abs, aimag, max, real
174* ..
175* .. Statement Functions ..
176 REAL CABS1
177* ..
178* .. Statement Function definitions ..
179 cabs1( zdum ) = abs( real( zdum ) ) + abs( aimag( zdum ) )
180* ..
181* .. Executable Statements ..
182*
183 hugeval = slamch( 'Overflow' )
184*
185* Test the input parameters.
186*
187 info = 0
188 onenrm = norm.EQ.'1' .OR. lsame( norm, 'O' )
189 IF( .NOT.onenrm .AND. .NOT.lsame( norm, 'I' ) ) THEN
190 info = -1
191 ELSE IF( n.LT.0 ) THEN
192 info = -2
193 ELSE IF( lda.LT.max( 1, n ) ) THEN
194 info = -4
195 ELSE IF( anorm.LT.zero ) THEN
196 info = -5
197 END IF
198 IF( info.NE.0 ) THEN
199 CALL xerbla( 'CGECON', -info )
200 RETURN
201 END IF
202*
203* Quick return if possible
204*
205 rcond = zero
206 IF( n.EQ.0 ) THEN
207 rcond = one
208 RETURN
209 ELSE IF( anorm.EQ.zero ) THEN
210 RETURN
211 ELSE IF( sisnan( anorm ) ) THEN
212 rcond = anorm
213 info = -5
214 RETURN
215 ELSE IF( anorm.GT.hugeval ) THEN
216 info = -5
217 RETURN
218 END IF
219*
220 smlnum = slamch( 'Safe minimum' )
221*
222* Estimate the norm of inv(A).
223*
224 ainvnm = zero
225 normin = 'N'
226 IF( onenrm ) THEN
227 kase1 = 1
228 ELSE
229 kase1 = 2
230 END IF
231 kase = 0
232 10 CONTINUE
233 CALL clacn2( n, work( n+1 ), work, ainvnm, kase, isave )
234 IF( kase.NE.0 ) THEN
235 IF( kase.EQ.kase1 ) THEN
236*
237* Multiply by inv(L).
238*
239 CALL clatrs( 'Lower', 'No transpose', 'Unit', normin, n, a,
240 \$ lda, work, sl, rwork, info )
241*
242* Multiply by inv(U).
243*
244 CALL clatrs( 'Upper', 'No transpose', 'Non-unit', normin, n,
245 \$ a, lda, work, su, rwork( n+1 ), info )
246 ELSE
247*
248* Multiply by inv(U**H).
249*
250 CALL clatrs( 'Upper', 'Conjugate transpose', 'Non-unit',
251 \$ normin, n, a, lda, work, su, rwork( n+1 ),
252 \$ info )
253*
254* Multiply by inv(L**H).
255*
256 CALL clatrs( 'Lower', 'Conjugate transpose', 'Unit', normin,
257 \$ n, a, lda, work, sl, rwork, info )
258 END IF
259*
260* Divide X by 1/(SL*SU) if doing so will not cause overflow.
261*
262 scale = sl*su
263 normin = 'Y'
264 IF( scale.NE.one ) THEN
265 ix = icamax( n, work, 1 )
266 IF( scale.LT.cabs1( work( ix ) )*smlnum .OR. scale.EQ.zero )
267 \$ GO TO 20
268 CALL csrscl( n, scale, work, 1 )
269 END IF
270 GO TO 10
271 END IF
272*
273* Compute the estimate of the reciprocal condition number.
274*
275 IF( ainvnm.NE.zero ) THEN
276 rcond = ( one / ainvnm ) / anorm
277 ELSE
278 info = 1
279 RETURN
280 END IF
281*
282* Check for NaNs and Infs
283*
284 IF( sisnan( rcond ) .OR. rcond.GT.hugeval )
285 \$ info = 1
286*
287 20 CONTINUE
288 RETURN
289*
290* End of CGECON
291*
292 END
subroutine xerbla(srname, info)
Definition cblat2.f:3285
subroutine cgecon(norm, n, a, lda, anorm, rcond, work, rwork, info)
CGECON
Definition cgecon.f:132
subroutine clacn2(n, v, x, est, kase, isave)
CLACN2 estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vec...
Definition clacn2.f:133
subroutine clatrs(uplo, trans, diag, normin, n, a, lda, x, scale, cnorm, info)
CLATRS solves a triangular system of equations with the scale factor set to prevent overflow.
Definition clatrs.f:239
subroutine csrscl(n, sa, sx, incx)
CSRSCL multiplies a vector by the reciprocal of a real scalar.
Definition csrscl.f:84