LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
cgtcon.f
Go to the documentation of this file.
1 *> \brief \b CGTCON
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/cgtcon.f">
11 *> [TGZ]</a>
12 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cgtcon.f">
13 *> [ZIP]</a>
14 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cgtcon.f">
15 *> [TXT]</a>
16 *> \endhtmlonly
17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE CGTCON( NORM, N, DL, D, DU, DU2, IPIV, ANORM, RCOND,
22 * WORK, INFO )
23 *
24 * .. Scalar Arguments ..
25 * CHARACTER NORM
26 * INTEGER INFO, N
27 * REAL ANORM, RCOND
28 * ..
29 * .. Array Arguments ..
30 * INTEGER IPIV( * )
31 * COMPLEX D( * ), DL( * ), DU( * ), DU2( * ), WORK( * )
32 * ..
33 *
34 *
35 *> \par Purpose:
36 * =============
37 *>
38 *> \verbatim
39 *>
40 *> CGTCON estimates the reciprocal of the condition number of a complex
41 *> tridiagonal matrix A using the LU factorization as computed by
42 *> CGTTRF.
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 array, dimension (N-1)
69 *> The (n-1) multipliers that define the matrix L from the
70 *> LU factorization of A as computed by CGTTRF.
71 *> \endverbatim
72 *>
73 *> \param[in] D
74 *> \verbatim
75 *> D is COMPLEX 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 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 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 REAL
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 REAL
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 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 *> \date September 2012
137 *
138 *> \ingroup complexGTcomputational
139 *
140 * =====================================================================
141  SUBROUTINE cgtcon( NORM, N, DL, D, DU, DU2, IPIV, ANORM, RCOND,
142  \$ work, info )
143 *
144 * -- LAPACK computational routine (version 3.4.2) --
145 * -- LAPACK is a software package provided by Univ. of Tennessee, --
146 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
147 * September 2012
148 *
149 * .. Scalar Arguments ..
150  CHARACTER NORM
151  INTEGER INFO, N
152  REAL ANORM, RCOND
153 * ..
154 * .. Array Arguments ..
155  INTEGER IPIV( * )
156  COMPLEX D( * ), DL( * ), DU( * ), DU2( * ), WORK( * )
157 * ..
158 *
159 * =====================================================================
160 *
161 * .. Parameters ..
162  REAL ONE, ZERO
163  parameter ( one = 1.0e+0, zero = 0.0e+0 )
164 * ..
165 * .. Local Scalars ..
166  LOGICAL ONENRM
167  INTEGER I, KASE, KASE1
168  REAL AINVNM
169 * ..
170 * .. Local Arrays ..
171  INTEGER ISAVE( 3 )
172 * ..
173 * .. External Functions ..
174  LOGICAL LSAME
175  EXTERNAL lsame
176 * ..
177 * .. External Subroutines ..
178  EXTERNAL cgttrs, clacn2, xerbla
179 * ..
180 * .. Intrinsic Functions ..
181  INTRINSIC cmplx
182 * ..
183 * .. Executable Statements ..
184 *
185 * Test the input arguments.
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( anorm.LT.zero ) THEN
194  info = -8
195  END IF
196  IF( info.NE.0 ) THEN
197  CALL xerbla( 'CGTCON', -info )
198  RETURN
199  END IF
200 *
201 * Quick return if possible
202 *
203  rcond = zero
204  IF( n.EQ.0 ) THEN
205  rcond = one
206  RETURN
207  ELSE IF( anorm.EQ.zero ) THEN
208  RETURN
209  END IF
210 *
211 * Check that D(1:N) is non-zero.
212 *
213  DO 10 i = 1, n
214  IF( d( i ).EQ.cmplx( zero ) )
215  \$ RETURN
216  10 CONTINUE
217 *
218  ainvnm = zero
219  IF( onenrm ) THEN
220  kase1 = 1
221  ELSE
222  kase1 = 2
223  END IF
224  kase = 0
225  20 CONTINUE
226  CALL clacn2( n, work( n+1 ), work, ainvnm, kase, isave )
227  IF( kase.NE.0 ) THEN
228  IF( kase.EQ.kase1 ) THEN
229 *
230 * Multiply by inv(U)*inv(L).
231 *
232  CALL cgttrs( 'No transpose', n, 1, dl, d, du, du2, ipiv,
233  \$ work, n, info )
234  ELSE
235 *
236 * Multiply by inv(L**H)*inv(U**H).
237 *
238  CALL cgttrs( 'Conjugate transpose', n, 1, dl, d, du, du2,
239  \$ ipiv, work, n, info )
240  END IF
241  GO TO 20
242  END IF
243 *
244 * Compute the estimate of the reciprocal condition number.
245 *
246  IF( ainvnm.NE.zero )
247  \$ rcond = ( one / ainvnm ) / anorm
248 *
249  RETURN
250 *
251 * End of CGTCON
252 *
253  END
subroutine cgtcon(NORM, N, DL, D, DU, DU2, IPIV, ANORM, RCOND, WORK, INFO)
CGTCON
Definition: cgtcon.f:143
subroutine cgttrs(TRANS, N, NRHS, DL, D, DU, DU2, IPIV, B, LDB, INFO)
CGTTRS
Definition: cgttrs.f:140
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
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:135