LAPACK  3.10.0 LAPACK: Linear Algebra PACKage
stbt06.f
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1 *> \brief \b STBT06
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 STBT06( 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 * REAL RAT, RCOND, RCONDC
18 * ..
19 * .. Array Arguments ..
20 * REAL AB( LDAB, * ), WORK( * )
21 * ..
22 *
23 *
24 *> \par Purpose:
25 * =============
26 *>
27 *> \verbatim
28 *>
29 *> STBT06 computes a test ratio comparing RCOND (the reciprocal
30 *> condition number of a triangular matrix A) and RCONDC, the estimate
31 *> computed by STBCON. 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 *> STBCON.
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 REAL 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 REAL array, dimension (N)
102 *> \endverbatim
103 *>
104 *> \param[out] RAT
105 *> \verbatim
106 *> RAT is REAL
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 single_lin
121 *
122 * =====================================================================
123  SUBROUTINE stbt06( 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  REAL RAT, RCOND, RCONDC
134 * ..
135 * .. Array Arguments ..
136  REAL AB( LDAB, * ), WORK( * )
137 * ..
138 *
139 * =====================================================================
140 *
141 * .. Parameters ..
142  REAL ZERO, ONE
143  parameter( zero = 0.0e+0, one = 1.0e+0 )
144 * ..
145 * .. Local Scalars ..
146  REAL ANORM, BIGNUM, EPS, RMAX, RMIN, SMLNUM
147 * ..
148 * .. External Functions ..
149  REAL SLAMCH, SLANTB
150  EXTERNAL slamch, slantb
151 * ..
152 * .. Intrinsic Functions ..
153  INTRINSIC max, min
154 * ..
155 * .. External Subroutines ..
157 * ..
158 * .. Executable Statements ..
159 *
160  eps = slamch( 'Epsilon' )
161  rmax = max( rcond, rcondc )
162  rmin = min( rcond, rcondc )
163 *
164 * Do the easy cases first.
165 *
166  IF( rmin.LT.zero ) THEN
167 *
168 * Invalid value for RCOND or RCONDC, return 1/EPS.
169 *
170  rat = one / eps
171 *
172  ELSE IF( rmin.GT.zero ) THEN
173 *
174 * Both estimates are positive, return RMAX/RMIN - 1.
175 *
176  rat = rmax / rmin - one
177 *
178  ELSE IF( rmax.EQ.zero ) THEN
179 *
180 * Both estimates zero.
181 *
182  rat = zero
183 *
184  ELSE
185 *
186 * One estimate is zero, the other is non-zero. If the matrix is
187 * ill-conditioned, return the nonzero estimate multiplied by
188 * 1/EPS; if the matrix is badly scaled, return the nonzero
189 * estimate multiplied by BIGNUM/TMAX, where TMAX is the maximum
190 * element in absolute value in A.
191 *
192  smlnum = slamch( 'Safe minimum' )
193  bignum = one / smlnum
194  CALL slabad( smlnum, bignum )
195  anorm = slantb( 'M', uplo, diag, n, kd, ab, ldab, work )
196 *
197  rat = rmax*( min( bignum / max( one, anorm ), one / eps ) )
198  END IF
199 *
200  RETURN
201 *
202 * End of STBT06
203 *
204  END