LAPACK  3.10.0 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 *> \ingroup complex_lin
109 *
110 * =====================================================================
111  SUBROUTINE ctpt06( RCOND, RCONDC, UPLO, DIAG, N, AP, RWORK, RAT )
112 *
113 * -- LAPACK test routine --
114 * -- LAPACK is a software package provided by Univ. of Tennessee, --
115 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
116 *
117 * .. Scalar Arguments ..
118  CHARACTER DIAG, UPLO
119  INTEGER N
120  REAL RAT, RCOND, RCONDC
121 * ..
122 * .. Array Arguments ..
123  REAL RWORK( * )
124  COMPLEX AP( * )
125 * ..
126 *
127 * =====================================================================
128 *
129 * .. Parameters ..
130  REAL ZERO, ONE
131  parameter( zero = 0.0e+0, one = 1.0e+0 )
132 * ..
133 * .. Local Scalars ..
134  REAL ANORM, BIGNUM, EPS, RMAX, RMIN
135 * ..
136 * .. External Functions ..
137  REAL CLANTP, SLAMCH
138  EXTERNAL clantp, slamch
139 * ..
140 * .. Intrinsic Functions ..
141  INTRINSIC max, min
142 * ..
143 * .. Executable Statements ..
144 *
145  eps = slamch( 'Epsilon' )
146  rmax = max( rcond, rcondc )
147  rmin = min( rcond, rcondc )
148 *
149 * Do the easy cases first.
150 *
151  IF( rmin.LT.zero ) THEN
152 *
153 * Invalid value for RCOND or RCONDC, return 1/EPS.
154 *
155  rat = one / eps
156 *
157  ELSE IF( rmin.GT.zero ) THEN
158 *
159 * Both estimates are positive, return RMAX/RMIN - 1.
160 *
161  rat = rmax / rmin - one
162 *
163  ELSE IF( rmax.EQ.zero ) THEN
164 *
165 * Both estimates zero.
166 *
167  rat = zero
168 *
169  ELSE
170 *
171 * One estimate is zero, the other is non-zero. If the matrix is
172 * ill-conditioned, return the nonzero estimate multiplied by
173 * 1/EPS; if the matrix is badly scaled, return the nonzero
174 * estimate multiplied by BIGNUM/TMAX, where TMAX is the maximum
175 * element in absolute value in A.
176 *
177  bignum = one / slamch( 'Safe minimum' )
178  anorm = clantp( 'M', uplo, diag, n, ap, rwork )
179 *
180  rat = rmax*( min( bignum / max( one, anorm ), one / eps ) )
181  END IF
182 *
183  RETURN
184 *
185 * End of CTPT06
186 *
187  END
subroutine ctpt06(RCOND, RCONDC, UPLO, DIAG, N, AP, RWORK, RAT)
CTPT06
Definition: ctpt06.f:112