LAPACK  3.4.2 LAPACK: Linear Algebra PACKage
ctrcon.f
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1 *> \brief \b CTRCON
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
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15 *> [TXT]</a>
16 *> \endhtmlonly
17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE CTRCON( 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 * REAL 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 *> CTRCON 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 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 REAL
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 array, dimension (2*N)
110 *> \endverbatim
111 *>
112 *> \param[out] RWORK
113 *> \verbatim
114 *> RWORK is REAL 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 *> \date November 2011
133 *
134 *> \ingroup complexOTHERcomputational
135 *
136 * =====================================================================
137  SUBROUTINE ctrcon( NORM, UPLO, DIAG, N, A, LDA, RCOND, WORK,
138  \$ rwork, info )
139 *
140 * -- LAPACK computational routine (version 3.4.0) --
141 * -- LAPACK is a software package provided by Univ. of Tennessee, --
142 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
143 * November 2011
144 *
145 * .. Scalar Arguments ..
146  CHARACTER diag, norm, uplo
147  INTEGER info, lda, n
148  REAL rcond
149 * ..
150 * .. Array Arguments ..
151  REAL rwork( * )
152  COMPLEX a( lda, * ), work( * )
153 * ..
154 *
155 * =====================================================================
156 *
157 * .. Parameters ..
158  REAL one, zero
159  parameter( one = 1.0e+0, zero = 0.0e+0 )
160 * ..
161 * .. Local Scalars ..
162  LOGICAL nounit, onenrm, upper
163  CHARACTER normin
164  INTEGER ix, kase, kase1
165  REAL ainvnm, anorm, scale, smlnum, xnorm
166  COMPLEX zdum
167 * ..
168 * .. Local Arrays ..
169  INTEGER isave( 3 )
170 * ..
171 * .. External Functions ..
172  LOGICAL lsame
173  INTEGER icamax
174  REAL clantr, slamch
175  EXTERNAL lsame, icamax, clantr, slamch
176 * ..
177 * .. External Subroutines ..
178  EXTERNAL clacn2, clatrs, csrscl, xerbla
179 * ..
180 * .. Intrinsic Functions ..
181  INTRINSIC abs, aimag, max, real
182 * ..
183 * .. Statement Functions ..
184  REAL cabs1
185 * ..
186 * .. Statement Function definitions ..
187  cabs1( zdum ) = abs( REAL( ZDUM ) ) + abs( aimag( zdum ) )
188 * ..
189 * .. Executable Statements ..
190 *
191 * Test the input parameters.
192 *
193  info = 0
194  upper = lsame( uplo, 'U' )
195  onenrm = norm.EQ.'1' .OR. lsame( norm, 'O' )
196  nounit = lsame( diag, 'N' )
197 *
198  IF( .NOT.onenrm .AND. .NOT.lsame( norm, 'I' ) ) THEN
199  info = -1
200  ELSE IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
201  info = -2
202  ELSE IF( .NOT.nounit .AND. .NOT.lsame( diag, 'U' ) ) THEN
203  info = -3
204  ELSE IF( n.LT.0 ) THEN
205  info = -4
206  ELSE IF( lda.LT.max( 1, n ) ) THEN
207  info = -6
208  END IF
209  IF( info.NE.0 ) THEN
210  CALL xerbla( 'CTRCON', -info )
211  return
212  END IF
213 *
214 * Quick return if possible
215 *
216  IF( n.EQ.0 ) THEN
217  rcond = one
218  return
219  END IF
220 *
221  rcond = zero
222  smlnum = slamch( 'Safe minimum' )*REAL( MAX( 1, N ) )
223 *
224 * Compute the norm of the triangular matrix A.
225 *
226  anorm = clantr( norm, uplo, diag, n, n, a, lda, rwork )
227 *
228 * Continue only if ANORM > 0.
229 *
230  IF( anorm.GT.zero ) THEN
231 *
232 * Estimate the norm of the inverse of A.
233 *
234  ainvnm = zero
235  normin = 'N'
236  IF( onenrm ) THEN
237  kase1 = 1
238  ELSE
239  kase1 = 2
240  END IF
241  kase = 0
242  10 continue
243  CALL clacn2( n, work( n+1 ), work, ainvnm, kase, isave )
244  IF( kase.NE.0 ) THEN
245  IF( kase.EQ.kase1 ) THEN
246 *
247 * Multiply by inv(A).
248 *
249  CALL clatrs( uplo, 'No transpose', diag, normin, n, a,
250  \$ lda, work, scale, rwork, info )
251  ELSE
252 *
253 * Multiply by inv(A**H).
254 *
255  CALL clatrs( uplo, 'Conjugate transpose', diag, normin,
256  \$ n, a, lda, work, scale, rwork, info )
257  END IF
258  normin = 'Y'
259 *
260 * Multiply by 1/SCALE if doing so will not cause overflow.
261 *
262  IF( scale.NE.one ) THEN
263  ix = icamax( n, work, 1 )
264  xnorm = cabs1( work( ix ) )
265  IF( scale.LT.xnorm*smlnum .OR. scale.EQ.zero )
266  \$ go to 20
267  CALL csrscl( n, scale, work, 1 )
268  END IF
269  go to 10
270  END IF
271 *
272 * Compute the estimate of the reciprocal condition number.
273 *
274  IF( ainvnm.NE.zero )
275  \$ rcond = ( one / anorm ) / ainvnm
276  END IF
277 *
278  20 continue
279  return
280 *
281 * End of CTRCON
282 *
283  END