LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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strt06.f
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1*> \brief \b STRT06
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 STRT06( RCOND, RCONDC, UPLO, DIAG, N, A, LDA, WORK,
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 A( LDA, * ), WORK( * )
21* ..
22*
23*
24*> \par Purpose:
25* =============
26*>
27*> \verbatim
28*>
29*> STRT06 computes a test ratio comparing RCOND (the reciprocal
30*> condition number of a triangular matrix A) and RCONDC, the estimate
31*> computed by STRCON. 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 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*> STRCON.
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 REAL 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 REAL array, dimension (N)
98*> \endverbatim
99*>
100*> \param[out] RAT
101*> \verbatim
102*> RAT is REAL
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 single_lin
117*
118* =====================================================================
119 SUBROUTINE strt06( 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 REAL RAT, RCOND, RCONDC
130* ..
131* .. Array Arguments ..
132 REAL A( LDA, * ), WORK( * )
133* ..
134*
135* =====================================================================
136*
137* .. Parameters ..
138 REAL ZERO, ONE
139 parameter( zero = 0.0e+0, one = 1.0e+0 )
140* ..
141* .. Local Scalars ..
142 REAL ANORM, BIGNUM, EPS, RMAX, RMIN, SMLNUM
143* ..
144* .. External Functions ..
145 REAL SLAMCH, SLANTR
146 EXTERNAL slamch, slantr
147* ..
148* .. Intrinsic Functions ..
149 INTRINSIC max, min
150* ..
151* .. Executable Statements ..
152*
153 eps = slamch( 'Epsilon' )
154 rmax = max( rcond, rcondc )
155 rmin = min( rcond, rcondc )
156*
157* Do the easy cases first.
158*
159 IF( rmin.LT.zero ) THEN
160*
161* Invalid value for RCOND or RCONDC, return 1/EPS.
162*
163 rat = one / eps
164*
165 ELSE IF( rmin.GT.zero ) THEN
166*
167* Both estimates are positive, return RMAX/RMIN - 1.
168*
169 rat = rmax / rmin - one
170*
171 ELSE IF( rmax.EQ.zero ) THEN
172*
173* Both estimates zero.
174*
175 rat = zero
176*
177 ELSE
178*
179* One estimate is zero, the other is non-zero. If the matrix is
180* ill-conditioned, return the nonzero estimate multiplied by
181* 1/EPS; if the matrix is badly scaled, return the nonzero
182* estimate multiplied by BIGNUM/TMAX, where TMAX is the maximum
183* element in absolute value in A.
184*
185 smlnum = slamch( 'Safe minimum' )
186 bignum = one / smlnum
187 anorm = slantr( 'M', uplo, diag, n, n, a, lda, work )
188*
189 rat = rmax*( min( bignum / max( one, anorm ), one / eps ) )
190 END IF
191*
192 RETURN
193*
194* End of STRT06
195*
196 END
subroutine strt06(rcond, rcondc, uplo, diag, n, a, lda, work, rat)
STRT06
Definition strt06.f:121