LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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dtrt06.f
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1*> \brief \b DTRT06
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 DTRT06( RCOND, RCONDC, UPLO, DIAG, N, A, LDA, WORK,
12* RAT )
13*
14* .. Scalar Arguments ..
15* CHARACTER DIAG, UPLO
16* INTEGER LDA, N
17* DOUBLE PRECISION RAT, RCOND, RCONDC
18* ..
19* .. Array Arguments ..
20* DOUBLE PRECISION A( LDA, * ), WORK( * )
21* ..
22*
23*
24*> \par Purpose:
25* =============
26*>
27*> \verbatim
28*>
29*> DTRT06 computes a test ratio comparing RCOND (the reciprocal
30*> condition number of a triangular matrix A) and RCONDC, the estimate
31*> computed by DTRCON. Information about the triangular matrix A is
32*> used 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 DOUBLE PRECISION
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 DOUBLE PRECISION
50*> The estimate of the reciprocal condition number computed by
51*> DTRCON.
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] A
77*> \verbatim
78*> A is DOUBLE PRECISION array, dimension (LDA,N)
79*> The triangular matrix A. If UPLO = 'U', the leading n by n
80*> upper triangular part of the array A contains the upper
81*> triangular matrix, and the strictly lower triangular part of
82*> A is not referenced. If UPLO = 'L', the leading n by n lower
83*> triangular part of the array A contains the lower triangular
84*> matrix, and the strictly upper triangular part of A is not
85*> referenced. If DIAG = 'U', the diagonal elements of A are
86*> also not referenced and are assumed to be 1.
87*> \endverbatim
88*>
89*> \param[in] LDA
90*> \verbatim
91*> LDA is INTEGER
92*> The leading dimension of the array A. LDA >= max(1,N).
93*> \endverbatim
94*>
95*> \param[out] WORK
96*> \verbatim
97*> WORK is DOUBLE PRECISION array, dimension (N)
98*> \endverbatim
99*>
100*> \param[out] RAT
101*> \verbatim
102*> RAT is DOUBLE PRECISION
103*> The test ratio. If both RCOND and RCONDC are nonzero,
104*> RAT = MAX( RCOND, RCONDC )/MIN( RCOND, RCONDC ) - 1.
105*> If RAT = 0, the two estimates are exactly the same.
106*> \endverbatim
107*
108* Authors:
109* ========
110*
111*> \author Univ. of Tennessee
112*> \author Univ. of California Berkeley
113*> \author Univ. of Colorado Denver
114*> \author NAG Ltd.
115*
116*> \ingroup double_lin
117*
118* =====================================================================
119 SUBROUTINE dtrt06( RCOND, RCONDC, UPLO, DIAG, N, A, LDA, WORK,
120 $ RAT )
121*
122* -- LAPACK test routine --
123* -- LAPACK is a software package provided by Univ. of Tennessee, --
124* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
125*
126* .. Scalar Arguments ..
127 CHARACTER DIAG, UPLO
128 INTEGER LDA, N
129 DOUBLE PRECISION RAT, RCOND, RCONDC
130* ..
131* .. Array Arguments ..
132 DOUBLE PRECISION A( LDA, * ), WORK( * )
133* ..
134*
135* =====================================================================
136*
137* .. Parameters ..
138 DOUBLE PRECISION ZERO, ONE
139 parameter( zero = 0.0d+0, one = 1.0d+0 )
140* ..
141* .. Local Scalars ..
142 DOUBLE PRECISION ANORM, BIGNUM, EPS, RMAX, RMIN, SMLNUM
143* ..
144* .. External Functions ..
145 DOUBLE PRECISION DLAMCH, DLANTR
146 EXTERNAL dlamch, dlantr
147* ..
148* .. Intrinsic Functions ..
149 INTRINSIC max, min
150* ..
151* .. External Subroutines ..
152 EXTERNAL dlabad
153* ..
154* .. Executable Statements ..
155*
156 eps = dlamch( 'Epsilon' )
157 rmax = max( rcond, rcondc )
158 rmin = min( rcond, rcondc )
159*
160* Do the easy cases first.
161*
162 IF( rmin.LT.zero ) THEN
163*
164* Invalid value for RCOND or RCONDC, return 1/EPS.
165*
166 rat = one / eps
167*
168 ELSE IF( rmin.GT.zero ) THEN
169*
170* Both estimates are positive, return RMAX/RMIN - 1.
171*
172 rat = rmax / rmin - one
173*
174 ELSE IF( rmax.EQ.zero ) THEN
175*
176* Both estimates zero.
177*
178 rat = zero
179*
180 ELSE
181*
182* One estimate is zero, the other is non-zero. If the matrix is
183* ill-conditioned, return the nonzero estimate multiplied by
184* 1/EPS; if the matrix is badly scaled, return the nonzero
185* estimate multiplied by BIGNUM/TMAX, where TMAX is the maximum
186* element in absolute value in A.
187*
188 smlnum = dlamch( 'Safe minimum' )
189 bignum = one / smlnum
190 CALL dlabad( smlnum, bignum )
191 anorm = dlantr( 'M', uplo, diag, n, n, a, lda, work )
192*
193 rat = rmax*( min( bignum / max( one, anorm ), one / eps ) )
194 END IF
195*
196 RETURN
197*
198* End of DTRT06
199*
200 END
subroutine dlabad(SMALL, LARGE)
DLABAD
Definition: dlabad.f:74
subroutine dtrt06(RCOND, RCONDC, UPLO, DIAG, N, A, LDA, WORK, RAT)
DTRT06
Definition: dtrt06.f:121