LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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ztrcon.f
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1*> \brief \b ZTRCON
2*
3* =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6* http://www.netlib.org/lapack/explore-html/
7*
8*> \htmlonly
9*> Download ZTRCON + dependencies
10*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/ztrcon.f">
11*> [TGZ]</a>
12*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/ztrcon.f">
13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ztrcon.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* SUBROUTINE ZTRCON( NORM, UPLO, DIAG, N, A, LDA, RCOND, WORK,
22* RWORK, INFO )
23*
24* .. Scalar Arguments ..
25* CHARACTER DIAG, NORM, UPLO
26* INTEGER INFO, LDA, N
27* DOUBLE PRECISION RCOND
28* ..
29* .. Array Arguments ..
30* DOUBLE PRECISION RWORK( * )
31* COMPLEX*16 A( LDA, * ), WORK( * )
32* ..
33*
34*
35*> \par Purpose:
36* =============
37*>
38*> \verbatim
39*>
40*> ZTRCON estimates the reciprocal of the condition number of a
41*> triangular matrix A, in either the 1-norm or the infinity-norm.
42*>
43*> The norm of A is computed and an estimate is obtained for
44*> norm(inv(A)), then the reciprocal of the condition number is
45*> 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] UPLO
62*> \verbatim
63*> UPLO is CHARACTER*1
64*> = 'U': A is upper triangular;
65*> = 'L': A is lower triangular.
66*> \endverbatim
67*>
68*> \param[in] DIAG
69*> \verbatim
70*> DIAG is CHARACTER*1
71*> = 'N': A is non-unit triangular;
72*> = 'U': A is unit triangular.
73*> \endverbatim
74*>
75*> \param[in] N
76*> \verbatim
77*> N is INTEGER
78*> The order of the matrix A. N >= 0.
79*> \endverbatim
80*>
81*> \param[in] A
82*> \verbatim
83*> A is COMPLEX*16 array, dimension (LDA,N)
84*> The triangular matrix A. If UPLO = 'U', the leading N-by-N
85*> upper triangular part of the array A contains the upper
86*> triangular matrix, and the strictly lower triangular part of
87*> A is not referenced. If UPLO = 'L', the leading N-by-N lower
88*> triangular part of the array A contains the lower triangular
89*> matrix, and the strictly upper triangular part of A is not
90*> referenced. If DIAG = 'U', the diagonal elements of A are
91*> also not referenced and are assumed to be 1.
92*> \endverbatim
93*>
94*> \param[in] LDA
95*> \verbatim
96*> LDA is INTEGER
97*> The leading dimension of the array A. LDA >= max(1,N).
98*> \endverbatim
99*>
100*> \param[out] RCOND
101*> \verbatim
102*> RCOND is DOUBLE PRECISION
103*> The reciprocal of the condition number of the matrix A,
104*> computed as RCOND = 1/(norm(A) * norm(inv(A))).
105*> \endverbatim
106*>
107*> \param[out] WORK
108*> \verbatim
109*> WORK is COMPLEX*16 array, dimension (2*N)
110*> \endverbatim
111*>
112*> \param[out] RWORK
113*> \verbatim
114*> RWORK is DOUBLE PRECISION array, dimension (N)
115*> \endverbatim
116*>
117*> \param[out] INFO
118*> \verbatim
119*> INFO is INTEGER
120*> = 0: successful exit
121*> < 0: if INFO = -i, the i-th argument had an illegal value
122*> \endverbatim
123*
124* Authors:
125* ========
126*
127*> \author Univ. of Tennessee
128*> \author Univ. of California Berkeley
129*> \author Univ. of Colorado Denver
130*> \author NAG Ltd.
131*
132*> \ingroup trcon
133*
134* =====================================================================
135 SUBROUTINE ztrcon( NORM, UPLO, DIAG, N, A, LDA, RCOND, WORK,
136 \$ RWORK, INFO )
137*
138* -- LAPACK computational routine --
139* -- LAPACK is a software package provided by Univ. of Tennessee, --
140* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
141*
142* .. Scalar Arguments ..
143 CHARACTER DIAG, NORM, UPLO
144 INTEGER INFO, LDA, N
145 DOUBLE PRECISION RCOND
146* ..
147* .. Array Arguments ..
148 DOUBLE PRECISION RWORK( * )
149 COMPLEX*16 A( LDA, * ), WORK( * )
150* ..
151*
152* =====================================================================
153*
154* .. Parameters ..
155 DOUBLE PRECISION ONE, ZERO
156 parameter( one = 1.0d+0, zero = 0.0d+0 )
157* ..
158* .. Local Scalars ..
159 LOGICAL NOUNIT, ONENRM, UPPER
160 CHARACTER NORMIN
161 INTEGER IX, KASE, KASE1
162 DOUBLE PRECISION AINVNM, ANORM, SCALE, SMLNUM, XNORM
163 COMPLEX*16 ZDUM
164* ..
165* .. Local Arrays ..
166 INTEGER ISAVE( 3 )
167* ..
168* .. External Functions ..
169 LOGICAL LSAME
170 INTEGER IZAMAX
171 DOUBLE PRECISION DLAMCH, ZLANTR
172 EXTERNAL lsame, izamax, dlamch, zlantr
173* ..
174* .. External Subroutines ..
175 EXTERNAL xerbla, zdrscl, zlacn2, zlatrs
176* ..
177* .. Intrinsic Functions ..
178 INTRINSIC abs, dble, dimag, max
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*
188* Test the input parameters.
189*
190 info = 0
191 upper = lsame( uplo, 'U' )
192 onenrm = norm.EQ.'1' .OR. lsame( norm, 'O' )
193 nounit = lsame( diag, 'N' )
194*
195 IF( .NOT.onenrm .AND. .NOT.lsame( norm, 'I' ) ) THEN
196 info = -1
197 ELSE IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
198 info = -2
199 ELSE IF( .NOT.nounit .AND. .NOT.lsame( diag, 'U' ) ) THEN
200 info = -3
201 ELSE IF( n.LT.0 ) THEN
202 info = -4
203 ELSE IF( lda.LT.max( 1, n ) ) THEN
204 info = -6
205 END IF
206 IF( info.NE.0 ) THEN
207 CALL xerbla( 'ZTRCON', -info )
208 RETURN
209 END IF
210*
211* Quick return if possible
212*
213 IF( n.EQ.0 ) THEN
214 rcond = one
215 RETURN
216 END IF
217*
218 rcond = zero
219 smlnum = dlamch( 'Safe minimum' )*dble( max( 1, n ) )
220*
221* Compute the norm of the triangular matrix A.
222*
223 anorm = zlantr( norm, uplo, diag, n, n, a, lda, rwork )
224*
225* Continue only if ANORM > 0.
226*
227 IF( anorm.GT.zero ) THEN
228*
229* Estimate the norm of the inverse of A.
230*
231 ainvnm = zero
232 normin = 'N'
233 IF( onenrm ) THEN
234 kase1 = 1
235 ELSE
236 kase1 = 2
237 END IF
238 kase = 0
239 10 CONTINUE
240 CALL zlacn2( n, work( n+1 ), work, ainvnm, kase, isave )
241 IF( kase.NE.0 ) THEN
242 IF( kase.EQ.kase1 ) THEN
243*
244* Multiply by inv(A).
245*
246 CALL zlatrs( uplo, 'No transpose', diag, normin, n, a,
247 \$ lda, work, scale, rwork, info )
248 ELSE
249*
250* Multiply by inv(A**H).
251*
252 CALL zlatrs( uplo, 'Conjugate transpose', diag, normin,
253 \$ n, a, lda, work, scale, rwork, info )
254 END IF
255 normin = 'Y'
256*
257* Multiply by 1/SCALE if doing so will not cause overflow.
258*
259 IF( scale.NE.one ) THEN
260 ix = izamax( n, work, 1 )
261 xnorm = cabs1( work( ix ) )
262 IF( scale.LT.xnorm*smlnum .OR. scale.EQ.zero )
263 \$ GO TO 20
264 CALL zdrscl( n, scale, work, 1 )
265 END IF
266 GO TO 10
267 END IF
268*
269* Compute the estimate of the reciprocal condition number.
270*
271 IF( ainvnm.NE.zero )
272 \$ rcond = ( one / anorm ) / ainvnm
273 END IF
274*
275 20 CONTINUE
276 RETURN
277*
278* End of ZTRCON
279*
280 END
subroutine xerbla(srname, info)
Definition cblat2.f:3285
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
subroutine zlatrs(uplo, trans, diag, normin, n, a, lda, x, scale, cnorm, info)
ZLATRS solves a triangular system of equations with the scale factor set to prevent overflow.
Definition zlatrs.f:239
subroutine zdrscl(n, sa, sx, incx)
ZDRSCL multiplies a vector by the reciprocal of a real scalar.
Definition zdrscl.f:84
subroutine ztrcon(norm, uplo, diag, n, a, lda, rcond, work, rwork, info)
ZTRCON
Definition ztrcon.f:137