LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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zgtcon.f
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1*> \brief \b ZGTCON
2*
3* =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6* http://www.netlib.org/lapack/explore-html/
7*
8*> \htmlonly
9*> Download ZGTCON + dependencies
10*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zgtcon.f">
11*> [TGZ]</a>
12*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zgtcon.f">
13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zgtcon.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* SUBROUTINE ZGTCON( NORM, N, DL, D, DU, DU2, IPIV, ANORM, RCOND,
22* WORK, INFO )
23*
24* .. Scalar Arguments ..
25* CHARACTER NORM
26* INTEGER INFO, N
27* DOUBLE PRECISION ANORM, RCOND
28* ..
29* .. Array Arguments ..
30* INTEGER IPIV( * )
31* COMPLEX*16 D( * ), DL( * ), DU( * ), DU2( * ), WORK( * )
32* ..
33*
34*
35*> \par Purpose:
36* =============
37*>
38*> \verbatim
39*>
40*> ZGTCON estimates the reciprocal of the condition number of a complex
41*> tridiagonal matrix A using the LU factorization as computed by
42*> ZGTTRF.
43*>
44*> An estimate is obtained for norm(inv(A)), and the reciprocal of the
45*> condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
46*> \endverbatim
47*
48* Arguments:
49* ==========
50*
51*> \param[in] NORM
52*> \verbatim
53*> NORM is CHARACTER*1
54*> Specifies whether the 1-norm condition number or the
55*> infinity-norm condition number is required:
56*> = '1' or 'O': 1-norm;
57*> = 'I': Infinity-norm.
58*> \endverbatim
59*>
60*> \param[in] N
61*> \verbatim
62*> N is INTEGER
63*> The order of the matrix A. N >= 0.
64*> \endverbatim
65*>
66*> \param[in] DL
67*> \verbatim
68*> DL is COMPLEX*16 array, dimension (N-1)
69*> The (n-1) multipliers that define the matrix L from the
70*> LU factorization of A as computed by ZGTTRF.
71*> \endverbatim
72*>
73*> \param[in] D
74*> \verbatim
75*> D is COMPLEX*16 array, dimension (N)
76*> The n diagonal elements of the upper triangular matrix U from
77*> the LU factorization of A.
78*> \endverbatim
79*>
80*> \param[in] DU
81*> \verbatim
82*> DU is COMPLEX*16 array, dimension (N-1)
83*> The (n-1) elements of the first superdiagonal of U.
84*> \endverbatim
85*>
86*> \param[in] DU2
87*> \verbatim
88*> DU2 is COMPLEX*16 array, dimension (N-2)
89*> The (n-2) elements of the second superdiagonal of U.
90*> \endverbatim
91*>
92*> \param[in] IPIV
93*> \verbatim
94*> IPIV is INTEGER array, dimension (N)
95*> The pivot indices; for 1 <= i <= n, row i of the matrix was
96*> interchanged with row IPIV(i). IPIV(i) will always be either
97*> i or i+1; IPIV(i) = i indicates a row interchange was not
98*> required.
99*> \endverbatim
100*>
101*> \param[in] ANORM
102*> \verbatim
103*> ANORM is DOUBLE PRECISION
104*> If NORM = '1' or 'O', the 1-norm of the original matrix A.
105*> If NORM = 'I', the infinity-norm of the original matrix A.
106*> \endverbatim
107*>
108*> \param[out] RCOND
109*> \verbatim
110*> RCOND is DOUBLE PRECISION
111*> The reciprocal of the condition number of the matrix A,
112*> computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
113*> estimate of the 1-norm of inv(A) computed in this routine.
114*> \endverbatim
115*>
116*> \param[out] WORK
117*> \verbatim
118*> WORK is COMPLEX*16 array, dimension (2*N)
119*> \endverbatim
120*>
121*> \param[out] INFO
122*> \verbatim
123*> INFO is INTEGER
124*> = 0: successful exit
125*> < 0: if INFO = -i, the i-th argument had an illegal value
126*> \endverbatim
127*
128* Authors:
129* ========
130*
131*> \author Univ. of Tennessee
132*> \author Univ. of California Berkeley
133*> \author Univ. of Colorado Denver
134*> \author NAG Ltd.
135*
136*> \ingroup complex16GTcomputational
137*
138* =====================================================================
139 SUBROUTINE zgtcon( NORM, N, DL, D, DU, DU2, IPIV, ANORM, RCOND,
140 $ WORK, INFO )
141*
142* -- LAPACK computational routine --
143* -- LAPACK is a software package provided by Univ. of Tennessee, --
144* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
145*
146* .. Scalar Arguments ..
147 CHARACTER NORM
148 INTEGER INFO, N
149 DOUBLE PRECISION ANORM, RCOND
150* ..
151* .. Array Arguments ..
152 INTEGER IPIV( * )
153 COMPLEX*16 D( * ), DL( * ), DU( * ), DU2( * ), WORK( * )
154* ..
155*
156* =====================================================================
157*
158* .. Parameters ..
159 DOUBLE PRECISION ONE, ZERO
160 parameter( one = 1.0d+0, zero = 0.0d+0 )
161* ..
162* .. Local Scalars ..
163 LOGICAL ONENRM
164 INTEGER I, KASE, KASE1
165 DOUBLE PRECISION AINVNM
166* ..
167* .. Local Arrays ..
168 INTEGER ISAVE( 3 )
169* ..
170* .. External Functions ..
171 LOGICAL LSAME
172 EXTERNAL lsame
173* ..
174* .. External Subroutines ..
175 EXTERNAL xerbla, zgttrs, zlacn2
176* ..
177* .. Intrinsic Functions ..
178 INTRINSIC dcmplx
179* ..
180* .. Executable Statements ..
181*
182* Test the input arguments.
183*
184 info = 0
185 onenrm = norm.EQ.'1' .OR. lsame( norm, 'O' )
186 IF( .NOT.onenrm .AND. .NOT.lsame( norm, 'I' ) ) THEN
187 info = -1
188 ELSE IF( n.LT.0 ) THEN
189 info = -2
190 ELSE IF( anorm.LT.zero ) THEN
191 info = -8
192 END IF
193 IF( info.NE.0 ) THEN
194 CALL xerbla( 'ZGTCON', -info )
195 RETURN
196 END IF
197*
198* Quick return if possible
199*
200 rcond = zero
201 IF( n.EQ.0 ) THEN
202 rcond = one
203 RETURN
204 ELSE IF( anorm.EQ.zero ) THEN
205 RETURN
206 END IF
207*
208* Check that D(1:N) is non-zero.
209*
210 DO 10 i = 1, n
211 IF( d( i ).EQ.dcmplx( zero ) )
212 $ RETURN
213 10 CONTINUE
214*
215 ainvnm = zero
216 IF( onenrm ) THEN
217 kase1 = 1
218 ELSE
219 kase1 = 2
220 END IF
221 kase = 0
222 20 CONTINUE
223 CALL zlacn2( n, work( n+1 ), work, ainvnm, kase, isave )
224 IF( kase.NE.0 ) THEN
225 IF( kase.EQ.kase1 ) THEN
226*
227* Multiply by inv(U)*inv(L).
228*
229 CALL zgttrs( 'No transpose', n, 1, dl, d, du, du2, ipiv,
230 $ work, n, info )
231 ELSE
232*
233* Multiply by inv(L**H)*inv(U**H).
234*
235 CALL zgttrs( 'Conjugate transpose', n, 1, dl, d, du, du2,
236 $ ipiv, work, n, info )
237 END IF
238 GO TO 20
239 END IF
240*
241* Compute the estimate of the reciprocal condition number.
242*
243 IF( ainvnm.NE.zero )
244 $ rcond = ( one / ainvnm ) / anorm
245*
246 RETURN
247*
248* End of ZGTCON
249*
250 END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine zgtcon(NORM, N, DL, D, DU, DU2, IPIV, ANORM, RCOND, WORK, INFO)
ZGTCON
Definition: zgtcon.f:141
subroutine zgttrs(TRANS, N, NRHS, DL, D, DU, DU2, IPIV, B, LDB, INFO)
ZGTTRS
Definition: zgttrs.f:138
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