LAPACK  3.8.0
LAPACK: Linear Algebra PACKage
ctrt06.f
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1 *> \brief \b CTRT06
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
7 *
8 * Definition:
9 * ===========
10 *
11 * SUBROUTINE CTRT06( RCOND, RCONDC, UPLO, DIAG, N, A, LDA, RWORK,
12 * RAT )
13 *
14 * .. Scalar Arguments ..
15 * CHARACTER DIAG, UPLO
16 * INTEGER LDA, N
17 * REAL RAT, RCOND, RCONDC
18 * ..
19 * .. Array Arguments ..
20 * REAL RWORK( * )
21 * COMPLEX A( LDA, * )
22 * ..
23 *
24 *
25 *> \par Purpose:
26 * =============
27 *>
28 *> \verbatim
29 *>
30 *> CTRT06 computes a test ratio comparing RCOND (the reciprocal
31 *> condition number of a triangular matrix A) and RCONDC, the estimate
32 *> computed by CTRCON. Information about the triangular matrix A is
33 *> used if one estimate is zero and the other is non-zero to decide if
34 *> underflow in the estimate is justified.
35 *> \endverbatim
36 *
37 * Arguments:
38 * ==========
39 *
40 *> \param[in] RCOND
41 *> \verbatim
42 *> RCOND is REAL
43 *> The estimate of the reciprocal condition number obtained by
44 *> forming the explicit inverse of the matrix A and computing
45 *> RCOND = 1/( norm(A) * norm(inv(A)) ).
46 *> \endverbatim
47 *>
48 *> \param[in] RCONDC
49 *> \verbatim
50 *> RCONDC is REAL
51 *> The estimate of the reciprocal condition number computed by
52 *> CTRCON.
53 *> \endverbatim
54 *>
55 *> \param[in] UPLO
56 *> \verbatim
57 *> UPLO is CHARACTER
58 *> Specifies whether the matrix A is upper or lower triangular.
59 *> = 'U': Upper triangular
60 *> = 'L': Lower triangular
61 *> \endverbatim
62 *>
63 *> \param[in] DIAG
64 *> \verbatim
65 *> DIAG is CHARACTER
66 *> Specifies whether or not the matrix A is unit triangular.
67 *> = 'N': Non-unit triangular
68 *> = 'U': Unit triangular
69 *> \endverbatim
70 *>
71 *> \param[in] N
72 *> \verbatim
73 *> N is INTEGER
74 *> The order of the matrix A. N >= 0.
75 *> \endverbatim
76 *>
77 *> \param[in] A
78 *> \verbatim
79 *> A is COMPLEX array, dimension (LDA,N)
80 *> The triangular matrix A. If UPLO = 'U', the leading n by n
81 *> upper triangular part of the array A contains the upper
82 *> triangular matrix, and the strictly lower triangular part of
83 *> A is not referenced. If UPLO = 'L', the leading n by n lower
84 *> triangular part of the array A contains the lower triangular
85 *> matrix, and the strictly upper triangular part of A is not
86 *> referenced. If DIAG = 'U', the diagonal elements of A are
87 *> also not referenced and are assumed to be 1.
88 *> \endverbatim
89 *>
90 *> \param[in] LDA
91 *> \verbatim
92 *> LDA is INTEGER
93 *> The leading dimension of the array A. LDA >= max(1,N).
94 *> \endverbatim
95 *>
96 *> \param[out] RWORK
97 *> \verbatim
98 *> RWORK is REAL array, dimension (N)
99 *> \endverbatim
100 *>
101 *> \param[out] RAT
102 *> \verbatim
103 *> RAT is REAL
104 *> The test ratio. If both RCOND and RCONDC are nonzero,
105 *> RAT = MAX( RCOND, RCONDC )/MIN( RCOND, RCONDC ) - 1.
106 *> If RAT = 0, the two estimates are exactly the same.
107 *> \endverbatim
108 *
109 * Authors:
110 * ========
111 *
112 *> \author Univ. of Tennessee
113 *> \author Univ. of California Berkeley
114 *> \author Univ. of Colorado Denver
115 *> \author NAG Ltd.
116 *
117 *> \date December 2016
118 *
119 *> \ingroup complex_lin
120 *
121 * =====================================================================
122  SUBROUTINE ctrt06( RCOND, RCONDC, UPLO, DIAG, N, A, LDA, RWORK,
123  $ RAT )
124 *
125 * -- LAPACK test routine (version 3.7.0) --
126 * -- LAPACK is a software package provided by Univ. of Tennessee, --
127 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
128 * December 2016
129 *
130 * .. Scalar Arguments ..
131  CHARACTER DIAG, UPLO
132  INTEGER LDA, N
133  REAL RAT, RCOND, RCONDC
134 * ..
135 * .. Array Arguments ..
136  REAL RWORK( * )
137  COMPLEX A( lda, * )
138 * ..
139 *
140 * =====================================================================
141 *
142 * .. Parameters ..
143  REAL ZERO, ONE
144  parameter( zero = 0.0e+0, one = 1.0e+0 )
145 * ..
146 * .. Local Scalars ..
147  REAL ANORM, BIGNUM, EPS, RMAX, RMIN
148 * ..
149 * .. External Functions ..
150  REAL CLANTR, SLAMCH
151  EXTERNAL clantr, slamch
152 * ..
153 * .. Intrinsic Functions ..
154  INTRINSIC max, min
155 * ..
156 * .. Executable Statements ..
157 *
158  eps = slamch( 'Epsilon' )
159  rmax = max( rcond, rcondc )
160  rmin = min( rcond, rcondc )
161 *
162 * Do the easy cases first.
163 *
164  IF( rmin.LT.zero ) THEN
165 *
166 * Invalid value for RCOND or RCONDC, return 1/EPS.
167 *
168  rat = one / eps
169 *
170  ELSE IF( rmin.GT.zero ) THEN
171 *
172 * Both estimates are positive, return RMAX/RMIN - 1.
173 *
174  rat = rmax / rmin - one
175 *
176  ELSE IF( rmax.EQ.zero ) THEN
177 *
178 * Both estimates zero.
179 *
180  rat = zero
181 *
182  ELSE
183 *
184 * One estimate is zero, the other is non-zero. If the matrix is
185 * ill-conditioned, return the nonzero estimate multiplied by
186 * 1/EPS; if the matrix is badly scaled, return the nonzero
187 * estimate multiplied by BIGNUM/TMAX, where TMAX is the maximum
188 * element in absolute value in A.
189 *
190  bignum = one / slamch( 'Safe minimum' )
191  anorm = clantr( 'M', uplo, diag, n, n, a, lda, rwork )
192 *
193  rat = rmax*( min( bignum / max( one, anorm ), one / eps ) )
194  END IF
195 *
196  RETURN
197 *
198 * End of CTRT06
199 *
200  END
subroutine ctrt06(RCOND, RCONDC, UPLO, DIAG, N, A, LDA, RWORK, RAT)
CTRT06
Definition: ctrt06.f:124