LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
Loading...
Searching...
No Matches
dtpt06.f
Go to the documentation of this file.
1*> \brief \b DTPT06
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 DTPT06( RCOND, RCONDC, UPLO, DIAG, N, AP, WORK, RAT )
12*
13* .. Scalar Arguments ..
14* CHARACTER DIAG, UPLO
15* INTEGER N
16* DOUBLE PRECISION RAT, RCOND, RCONDC
17* ..
18* .. Array Arguments ..
19* DOUBLE PRECISION AP( * ), WORK( * )
20* ..
21*
22*
23*> \par Purpose:
24* =============
25*>
26*> \verbatim
27*>
28*> DTPT06 computes a test ratio comparing RCOND (the reciprocal
29*> condition number of a triangular matrix A) and RCONDC, the estimate
30*> computed by DTPCON. 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 DOUBLE PRECISION
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 DOUBLE PRECISION
49*> The estimate of the reciprocal condition number computed by
50*> DTPCON.
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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (N)
89*> \endverbatim
90*>
91*> \param[out] RAT
92*> \verbatim
93*> RAT is DOUBLE PRECISION
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*> \ingroup double_lin
108*
109* =====================================================================
110 SUBROUTINE dtpt06( RCOND, RCONDC, UPLO, DIAG, N, AP, WORK, RAT )
111*
112* -- LAPACK test routine --
113* -- LAPACK is a software package provided by Univ. of Tennessee, --
114* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
115*
116* .. Scalar Arguments ..
117 CHARACTER DIAG, UPLO
118 INTEGER N
119 DOUBLE PRECISION RAT, RCOND, RCONDC
120* ..
121* .. Array Arguments ..
122 DOUBLE PRECISION AP( * ), WORK( * )
123* ..
124*
125* =====================================================================
126*
127* .. Parameters ..
128 DOUBLE PRECISION ZERO, ONE
129 parameter( zero = 0.0d+0, one = 1.0d+0 )
130* ..
131* .. Local Scalars ..
132 DOUBLE PRECISION ANORM, BIGNUM, EPS, RMAX, RMIN, SMLNUM
133* ..
134* .. External Functions ..
135 DOUBLE PRECISION DLAMCH, DLANTP
136 EXTERNAL dlamch, dlantp
137* ..
138* .. Intrinsic Functions ..
139 INTRINSIC max, min
140* ..
141* .. Executable Statements ..
142*
143 eps = dlamch( 'Epsilon' )
144 rmax = max( rcond, rcondc )
145 rmin = min( rcond, rcondc )
146*
147* Do the easy cases first.
148*
149 IF( rmin.LT.zero ) THEN
150*
151* Invalid value for RCOND or RCONDC, return 1/EPS.
152*
153 rat = one / eps
154*
155 ELSE IF( rmin.GT.zero ) THEN
156*
157* Both estimates are positive, return RMAX/RMIN - 1.
158*
159 rat = rmax / rmin - one
160*
161 ELSE IF( rmax.EQ.zero ) THEN
162*
163* Both estimates zero.
164*
165 rat = zero
166*
167 ELSE
168*
169* One estimate is zero, the other is non-zero. If the matrix is
170* ill-conditioned, return the nonzero estimate multiplied by
171* 1/EPS; if the matrix is badly scaled, return the nonzero
172* estimate multiplied by BIGNUM/TMAX, where TMAX is the maximum
173* element in absolute value in A.
174*
175 smlnum = dlamch( 'Safe minimum' )
176 bignum = one / smlnum
177 anorm = dlantp( 'M', uplo, diag, n, ap, work )
178*
179 rat = rmax*( min( bignum / max( one, anorm ), one / eps ) )
180 END IF
181*
182 RETURN
183*
184* End of DTPT06
185*
186 END
subroutine dtpt06(rcond, rcondc, uplo, diag, n, ap, work, rat)
DTPT06
Definition dtpt06.f:111