LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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dtbt06.f
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1*> \brief \b DTBT06
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 DTBT06( RCOND, RCONDC, UPLO, DIAG, N, KD, AB, LDAB,
12* WORK, RAT )
13*
14* .. Scalar Arguments ..
15* CHARACTER DIAG, UPLO
16* INTEGER KD, LDAB, N
17* DOUBLE PRECISION RAT, RCOND, RCONDC
18* ..
19* .. Array Arguments ..
20* DOUBLE PRECISION AB( LDAB, * ), WORK( * )
21* ..
22*
23*
24*> \par Purpose:
25* =============
26*>
27*> \verbatim
28*>
29*> DTBT06 computes a test ratio comparing RCOND (the reciprocal
30*> condition number of a triangular matrix A) and RCONDC, the estimate
31*> computed by DTBCON. 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*> DTBCON.
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] KD
77*> \verbatim
78*> KD is INTEGER
79*> The number of superdiagonals or subdiagonals of the
80*> triangular band matrix A. KD >= 0.
81*> \endverbatim
82*>
83*> \param[in] AB
84*> \verbatim
85*> AB is DOUBLE PRECISION array, dimension (LDAB,N)
86*> The upper or lower triangular band matrix A, stored in the
87*> first kd+1 rows of the array. The j-th column of A is stored
88*> in the j-th column of the array AB as follows:
89*> if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
90*> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).
91*> \endverbatim
92*>
93*> \param[in] LDAB
94*> \verbatim
95*> LDAB is INTEGER
96*> The leading dimension of the array AB. LDAB >= KD+1.
97*> \endverbatim
98*>
99*> \param[out] WORK
100*> \verbatim
101*> WORK is DOUBLE PRECISION array, dimension (N)
102*> \endverbatim
103*>
104*> \param[out] RAT
105*> \verbatim
106*> RAT is DOUBLE PRECISION
107*> The test ratio. If both RCOND and RCONDC are nonzero,
108*> RAT = MAX( RCOND, RCONDC )/MIN( RCOND, RCONDC ) - 1.
109*> If RAT = 0, the two estimates are exactly the same.
110*> \endverbatim
111*
112* Authors:
113* ========
114*
115*> \author Univ. of Tennessee
116*> \author Univ. of California Berkeley
117*> \author Univ. of Colorado Denver
118*> \author NAG Ltd.
119*
120*> \ingroup double_lin
121*
122* =====================================================================
123 SUBROUTINE dtbt06( RCOND, RCONDC, UPLO, DIAG, N, KD, AB, LDAB,
124 \$ WORK, RAT )
125*
126* -- LAPACK test routine --
127* -- LAPACK is a software package provided by Univ. of Tennessee, --
128* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
129*
130* .. Scalar Arguments ..
131 CHARACTER DIAG, UPLO
132 INTEGER KD, LDAB, N
133 DOUBLE PRECISION RAT, RCOND, RCONDC
134* ..
135* .. Array Arguments ..
136 DOUBLE PRECISION AB( LDAB, * ), WORK( * )
137* ..
138*
139* =====================================================================
140*
141* .. Parameters ..
142 DOUBLE PRECISION ZERO, ONE
143 parameter( zero = 0.0d+0, one = 1.0d+0 )
144* ..
145* .. Local Scalars ..
146 DOUBLE PRECISION ANORM, BIGNUM, EPS, RMAX, RMIN, SMLNUM
147* ..
148* .. External Functions ..
149 DOUBLE PRECISION DLAMCH, DLANTB
150 EXTERNAL dlamch, dlantb
151* ..
152* .. Intrinsic Functions ..
153 INTRINSIC max, min
154* ..
155* .. Executable Statements ..
156*
157 eps = dlamch( 'Epsilon' )
158 rmax = max( rcond, rcondc )
159 rmin = min( rcond, rcondc )
160*
161* Do the easy cases first.
162*
163 IF( rmin.LT.zero ) THEN
164*
165* Invalid value for RCOND or RCONDC, return 1/EPS.
166*
167 rat = one / eps
168*
169 ELSE IF( rmin.GT.zero ) THEN
170*
171* Both estimates are positive, return RMAX/RMIN - 1.
172*
173 rat = rmax / rmin - one
174*
175 ELSE IF( rmax.EQ.zero ) THEN
176*
177* Both estimates zero.
178*
179 rat = zero
180*
181 ELSE
182*
183* One estimate is zero, the other is non-zero. If the matrix is
184* ill-conditioned, return the nonzero estimate multiplied by
185* 1/EPS; if the matrix is badly scaled, return the nonzero
186* estimate multiplied by BIGNUM/TMAX, where TMAX is the maximum
187* element in absolute value in A.
188*
189 smlnum = dlamch( 'Safe minimum' )
190 bignum = one / smlnum
191 anorm = dlantb( 'M', uplo, diag, n, kd, ab, ldab, work )
192*
193 rat = rmax*( min( bignum / max( one, anorm ), one / eps ) )
194 END IF
195*
196 RETURN
197*
198* End of DTBT06
199*
200 END
subroutine dtbt06(rcond, rcondc, uplo, diag, n, kd, ab, ldab, work, rat)
DTBT06
Definition dtbt06.f:125