LAPACK  3.8.0
LAPACK: Linear Algebra PACKage
ctpt06.f
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1 *> \brief \b CTPT06
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 CTPT06( RCOND, RCONDC, UPLO, DIAG, N, AP, RWORK, RAT )
12 *
13 * .. Scalar Arguments ..
14 * CHARACTER DIAG, UPLO
15 * INTEGER N
16 * REAL RAT, RCOND, RCONDC
17 * ..
18 * .. Array Arguments ..
19 * REAL RWORK( * )
20 * COMPLEX AP( * )
21 * ..
22 *
23 *
24 *> \par Purpose:
25 * =============
26 *>
27 *> \verbatim
28 *>
29 *> CTPT06 computes a test ratio comparing RCOND (the reciprocal
30 *> condition number of the triangular matrix A) and RCONDC, the estimate
31 *> computed by CTPCON. Information about the triangular matrix is used
32 *> if one estimate is zero and the other is non-zero to decide if
33 *> underflow in the estimate is justified.
34 *> \endverbatim
35 *
36 * Arguments:
37 * ==========
38 *
39 *> \param[in] RCOND
40 *> \verbatim
41 *> RCOND is REAL
42 *> The estimate of the reciprocal condition number obtained by
43 *> forming the explicit inverse of the matrix A and computing
44 *> RCOND = 1/( norm(A) * norm(inv(A)) ).
45 *> \endverbatim
46 *>
47 *> \param[in] RCONDC
48 *> \verbatim
49 *> RCONDC is REAL
50 *> The estimate of the reciprocal condition number computed by
51 *> CTPCON.
52 *> \endverbatim
53 *>
54 *> \param[in] UPLO
55 *> \verbatim
56 *> UPLO is CHARACTER
57 *> Specifies whether the matrix A is upper or lower triangular.
58 *> = 'U': Upper triangular
59 *> = 'L': Lower triangular
60 *> \endverbatim
61 *>
62 *> \param[in] DIAG
63 *> \verbatim
64 *> DIAG is CHARACTER
65 *> Specifies whether or not the matrix A is unit triangular.
66 *> = 'N': Non-unit triangular
67 *> = 'U': Unit triangular
68 *> \endverbatim
69 *>
70 *> \param[in] N
71 *> \verbatim
72 *> N is INTEGER
73 *> The order of the matrix A. N >= 0.
74 *> \endverbatim
75 *>
76 *> \param[in] AP
77 *> \verbatim
78 *> AP is COMPLEX array, dimension (N*(N+1)/2)
79 *> The upper or lower triangular matrix A, packed columnwise in
80 *> a linear array. The j-th column of A is stored in the array
81 *> AP as follows:
82 *> if UPLO = 'U', AP((j-1)*j/2 + i) = A(i,j) for 1<=i<=j;
83 *> if UPLO = 'L',
84 *> AP((j-1)*(n-j) + j*(j+1)/2 + i-j) = A(i,j) for j<=i<=n.
85 *> \endverbatim
86 *>
87 *> \param[out] RWORK
88 *> \verbatim
89 *> RWORK is REAL array, dimension (N)
90 *> \endverbatim
91 *>
92 *> \param[out] RAT
93 *> \verbatim
94 *> RAT is REAL
95 *> The test ratio. If both RCOND and RCONDC are nonzero,
96 *> RAT = MAX( RCOND, RCONDC )/MIN( RCOND, RCONDC ) - 1.
97 *> If RAT = 0, the two estimates are exactly the same.
98 *> \endverbatim
99 *
100 * Authors:
101 * ========
102 *
103 *> \author Univ. of Tennessee
104 *> \author Univ. of California Berkeley
105 *> \author Univ. of Colorado Denver
106 *> \author NAG Ltd.
107 *
108 *> \date December 2016
109 *
110 *> \ingroup complex_lin
111 *
112 * =====================================================================
113  SUBROUTINE ctpt06( RCOND, RCONDC, UPLO, DIAG, N, AP, RWORK, RAT )
114 *
115 * -- LAPACK test routine (version 3.7.0) --
116 * -- LAPACK is a software package provided by Univ. of Tennessee, --
117 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
118 * December 2016
119 *
120 * .. Scalar Arguments ..
121  CHARACTER DIAG, UPLO
122  INTEGER N
123  REAL RAT, RCOND, RCONDC
124 * ..
125 * .. Array Arguments ..
126  REAL RWORK( * )
127  COMPLEX AP( * )
128 * ..
129 *
130 * =====================================================================
131 *
132 * .. Parameters ..
133  REAL ZERO, ONE
134  parameter( zero = 0.0e+0, one = 1.0e+0 )
135 * ..
136 * .. Local Scalars ..
137  REAL ANORM, BIGNUM, EPS, RMAX, RMIN
138 * ..
139 * .. External Functions ..
140  REAL CLANTP, SLAMCH
141  EXTERNAL clantp, slamch
142 * ..
143 * .. Intrinsic Functions ..
144  INTRINSIC max, min
145 * ..
146 * .. Executable Statements ..
147 *
148  eps = slamch( 'Epsilon' )
149  rmax = max( rcond, rcondc )
150  rmin = min( rcond, rcondc )
151 *
152 * Do the easy cases first.
153 *
154  IF( rmin.LT.zero ) THEN
155 *
156 * Invalid value for RCOND or RCONDC, return 1/EPS.
157 *
158  rat = one / eps
159 *
160  ELSE IF( rmin.GT.zero ) THEN
161 *
162 * Both estimates are positive, return RMAX/RMIN - 1.
163 *
164  rat = rmax / rmin - one
165 *
166  ELSE IF( rmax.EQ.zero ) THEN
167 *
168 * Both estimates zero.
169 *
170  rat = zero
171 *
172  ELSE
173 *
174 * One estimate is zero, the other is non-zero. If the matrix is
175 * ill-conditioned, return the nonzero estimate multiplied by
176 * 1/EPS; if the matrix is badly scaled, return the nonzero
177 * estimate multiplied by BIGNUM/TMAX, where TMAX is the maximum
178 * element in absolute value in A.
179 *
180  bignum = one / slamch( 'Safe minimum' )
181  anorm = clantp( 'M', uplo, diag, n, ap, rwork )
182 *
183  rat = rmax*( min( bignum / max( one, anorm ), one / eps ) )
184  END IF
185 *
186  RETURN
187 *
188 * End of CTPT06
189 *
190  END
subroutine ctpt06(RCOND, RCONDC, UPLO, DIAG, N, AP, RWORK, RAT)
CTPT06
Definition: ctpt06.f:114