LAPACK  3.8.0
LAPACK: Linear Algebra PACKage
stpt06.f
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1 *> \brief \b STPT06
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 STPT06( RCOND, RCONDC, UPLO, DIAG, N, AP, WORK, RAT )
12 *
13 * .. Scalar Arguments ..
14 * CHARACTER DIAG, UPLO
15 * INTEGER N
16 * REAL RAT, RCOND, RCONDC
17 * ..
18 * .. Array Arguments ..
19 * REAL AP( * ), WORK( * )
20 * ..
21 *
22 *
23 *> \par Purpose:
24 * =============
25 *>
26 *> \verbatim
27 *>
28 *> STPT06 computes a test ratio comparing RCOND (the reciprocal
29 *> condition number of a triangular matrix A) and RCONDC, the estimate
30 *> computed by STPCON. Information about the triangular matrix A is
31 *> used if one estimate is zero and the other is non-zero to decide if
32 *> underflow in the estimate is justified.
33 *> \endverbatim
34 *
35 * Arguments:
36 * ==========
37 *
38 *> \param[in] RCOND
39 *> \verbatim
40 *> RCOND is REAL
41 *> The estimate of the reciprocal condition number obtained by
42 *> forming the explicit inverse of the matrix A and computing
43 *> RCOND = 1/( norm(A) * norm(inv(A)) ).
44 *> \endverbatim
45 *>
46 *> \param[in] RCONDC
47 *> \verbatim
48 *> RCONDC is REAL
49 *> The estimate of the reciprocal condition number computed by
50 *> STPCON.
51 *> \endverbatim
52 *>
53 *> \param[in] UPLO
54 *> \verbatim
55 *> UPLO is CHARACTER
56 *> Specifies whether the matrix A is upper or lower triangular.
57 *> = 'U': Upper triangular
58 *> = 'L': Lower triangular
59 *> \endverbatim
60 *>
61 *> \param[in] DIAG
62 *> \verbatim
63 *> DIAG is CHARACTER
64 *> Specifies whether or not the matrix A is unit triangular.
65 *> = 'N': Non-unit triangular
66 *> = 'U': Unit triangular
67 *> \endverbatim
68 *>
69 *> \param[in] N
70 *> \verbatim
71 *> N is INTEGER
72 *> The order of the matrix A. N >= 0.
73 *> \endverbatim
74 *>
75 *> \param[in] AP
76 *> \verbatim
77 *> AP is REAL array, dimension (N*(N+1)/2)
78 *> The upper or lower triangular matrix A, packed columnwise in
79 *> a linear array. The j-th column of A is stored in the array
80 *> AP as follows:
81 *> if UPLO = 'U', AP((j-1)*j/2 + i) = A(i,j) for 1<=i<=j;
82 *> if UPLO = 'L',
83 *> AP((j-1)*(n-j) + j*(j+1)/2 + i-j) = A(i,j) for j<=i<=n.
84 *> \endverbatim
85 *>
86 *> \param[out] WORK
87 *> \verbatim
88 *> WORK is REAL array, dimension (N)
89 *> \endverbatim
90 *>
91 *> \param[out] RAT
92 *> \verbatim
93 *> RAT is REAL
94 *> The test ratio. If both RCOND and RCONDC are nonzero,
95 *> RAT = MAX( RCOND, RCONDC )/MIN( RCOND, RCONDC ) - 1.
96 *> If RAT = 0, the two estimates are exactly the same.
97 *> \endverbatim
98 *
99 * Authors:
100 * ========
101 *
102 *> \author Univ. of Tennessee
103 *> \author Univ. of California Berkeley
104 *> \author Univ. of Colorado Denver
105 *> \author NAG Ltd.
106 *
107 *> \date December 2016
108 *
109 *> \ingroup single_lin
110 *
111 * =====================================================================
112  SUBROUTINE stpt06( RCOND, RCONDC, UPLO, DIAG, N, AP, WORK, RAT )
113 *
114 * -- LAPACK test routine (version 3.7.0) --
115 * -- LAPACK is a software package provided by Univ. of Tennessee, --
116 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
117 * December 2016
118 *
119 * .. Scalar Arguments ..
120  CHARACTER DIAG, UPLO
121  INTEGER N
122  REAL RAT, RCOND, RCONDC
123 * ..
124 * .. Array Arguments ..
125  REAL AP( * ), WORK( * )
126 * ..
127 *
128 * =====================================================================
129 *
130 * .. Parameters ..
131  REAL ZERO, ONE
132  parameter( zero = 0.0e+0, one = 1.0e+0 )
133 * ..
134 * .. Local Scalars ..
135  REAL ANORM, BIGNUM, EPS, RMAX, RMIN, SMLNUM
136 * ..
137 * .. External Functions ..
138  REAL SLAMCH, SLANTP
139  EXTERNAL slamch, slantp
140 * ..
141 * .. Intrinsic Functions ..
142  INTRINSIC max, min
143 * ..
144 * .. External Subroutines ..
145  EXTERNAL slabad
146 * ..
147 * .. Executable Statements ..
148 *
149  eps = slamch( 'Epsilon' )
150  rmax = max( rcond, rcondc )
151  rmin = min( rcond, rcondc )
152 *
153 * Do the easy cases first.
154 *
155  IF( rmin.LT.zero ) THEN
156 *
157 * Invalid value for RCOND or RCONDC, return 1/EPS.
158 *
159  rat = one / eps
160 *
161  ELSE IF( rmin.GT.zero ) THEN
162 *
163 * Both estimates are positive, return RMAX/RMIN - 1.
164 *
165  rat = rmax / rmin - one
166 *
167  ELSE IF( rmax.EQ.zero ) THEN
168 *
169 * Both estimates zero.
170 *
171  rat = zero
172 *
173  ELSE
174 *
175 * One estimate is zero, the other is non-zero. If the matrix is
176 * ill-conditioned, return the nonzero estimate multiplied by
177 * 1/EPS; if the matrix is badly scaled, return the nonzero
178 * estimate multiplied by BIGNUM/TMAX, where TMAX is the maximum
179 * element in absolute value in A.
180 *
181  smlnum = slamch( 'Safe minimum' )
182  bignum = one / smlnum
183  CALL slabad( smlnum, bignum )
184  anorm = slantp( 'M', uplo, diag, n, ap, work )
185 *
186  rat = rmax*( min( bignum / max( one, anorm ), one / eps ) )
187  END IF
188 *
189  RETURN
190 *
191 * End of STPT06
192 *
193  END
subroutine slabad(SMALL, LARGE)
SLABAD
Definition: slabad.f:76
subroutine stpt06(RCOND, RCONDC, UPLO, DIAG, N, AP, WORK, RAT)
STPT06
Definition: stpt06.f:113