1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
|
/* ../netlib/sptcon.f -- translated by f2c (version 20100827). You must link the resulting object file with libf2c: on Microsoft Windows system, link with libf2c.lib;
on Linux or Unix systems, link with .../path/to/libf2c.a -lm or, if you install libf2c.a in a standard place, with -lf2c -lm -- in that order, at the end of the command line, as in cc *.o -lf2c -lm Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., http://www.netlib.org/f2c/libf2c.zip */
#include "FLA_f2c.h" /* Table of constant values */
static integer c__1 = 1;
/* > \brief \b SPTCON */
/* =========== DOCUMENTATION =========== */
/* Online html documentation available at */
/* http://www.netlib.org/lapack/explore-html/ */
/* > \htmlonly */
/* > Download SPTCON + dependencies */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/sptcon. f"> */
/* > [TGZ]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/sptcon. f"> */
/* > [ZIP]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/sptcon. f"> */
/* > [TXT]</a> */
/* > \endhtmlonly */
/* Definition: */
/* =========== */
/* SUBROUTINE SPTCON( N, D, E, ANORM, RCOND, WORK, INFO ) */
/* .. Scalar Arguments .. */
/* INTEGER INFO, N */
/* REAL ANORM, RCOND */
/* .. */
/* .. Array Arguments .. */
/* REAL D( * ), E( * ), WORK( * ) */
/* .. */
/* > \par Purpose: */
/* ============= */
/* > */
/* > \verbatim */
/* > */
/* > SPTCON computes the reciprocal of the condition number (in the */
/* > 1-norm) of a real symmetric positive definite tridiagonal matrix */
/* > using the factorization A = L*D*L**T or A = U**T*D*U computed by */
/* > SPTTRF. */
/* > */
/* > Norm(inv(A)) is computed by a direct method, and the reciprocal of */
/* > the condition number is computed as */
/* > RCOND = 1 / (ANORM * norm(inv(A))). */
/* > \endverbatim */
/* Arguments: */
/* ========== */
/* > \param[in] N */
/* > \verbatim */
/* > N is INTEGER */
/* > The order of the matrix A. N >= 0. */
/* > \endverbatim */
/* > */
/* > \param[in] D */
/* > \verbatim */
/* > D is REAL array, dimension (N) */
/* > The n diagonal elements of the diagonal matrix D from the */
/* > factorization of A, as computed by SPTTRF. */
/* > \endverbatim */
/* > */
/* > \param[in] E */
/* > \verbatim */
/* > E is REAL array, dimension (N-1) */
/* > The (n-1) off-diagonal elements of the unit bidiagonal factor */
/* > U or L from the factorization of A, as computed by SPTTRF. */
/* > \endverbatim */
/* > */
/* > \param[in] ANORM */
/* > \verbatim */
/* > ANORM is REAL */
/* > The 1-norm of the original matrix A. */
/* > \endverbatim */
/* > */
/* > \param[out] RCOND */
/* > \verbatim */
/* > RCOND is REAL */
/* > The reciprocal of the condition number of the matrix A, */
/* > computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is the */
/* > 1-norm of inv(A) computed in this routine. */
/* > \endverbatim */
/* > */
/* > \param[out] WORK */
/* > \verbatim */
/* > WORK is REAL array, dimension (N) */
/* > \endverbatim */
/* > */
/* > \param[out] INFO */
/* > \verbatim */
/* > INFO is INTEGER */
/* > = 0: successful exit */
/* > < 0: if INFO = -i, the i-th argument had an illegal value */
/* > \endverbatim */
/* Authors: */
/* ======== */
/* > \author Univ. of Tennessee */
/* > \author Univ. of California Berkeley */
/* > \author Univ. of Colorado Denver */
/* > \author NAG Ltd. */
/* > \date September 2012 */
/* > \ingroup realPTcomputational */
/* > \par Further Details: */
/* ===================== */
/* > */
/* > \verbatim */
/* > */
/* > The method used is described in Nicholas J. Higham, "Efficient */
/* > Algorithms for Computing the Condition Number of a Tridiagonal */
/* > Matrix", SIAM J. Sci. Stat. Comput., Vol. 7, No. 1, January 1986. */
/* > \endverbatim */
/* > */
/* ===================================================================== */
/* Subroutine */
int sptcon_(integer *n, real *d__, real *e, real *anorm, real *rcond, real *work, integer *info)
{
/* System generated locals */
integer i__1;
real r__1;
/* Local variables */
integer i__, ix;
extern /* Subroutine */
int xerbla_(char *, integer *);
extern integer isamax_(integer *, real *, integer *);
real ainvnm;
/* -- LAPACK computational routine (version 3.4.2) -- */
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
/* September 2012 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input arguments. */
/* Parameter adjustments */
--work;
--e;
--d__;
/* Function Body */
*info = 0;
if (*n < 0)
{
*info = -1;
}
else if (*anorm < 0.f)
{
*info = -4;
}
if (*info != 0)
{
i__1 = -(*info);
xerbla_("SPTCON", &i__1);
return 0;
}
/* Quick return if possible */
*rcond = 0.f;
if (*n == 0)
{
*rcond = 1.f;
return 0;
}
else if (*anorm == 0.f)
{
return 0;
}
/* Check that D(1:N) is positive. */
i__1 = *n;
for (i__ = 1;
i__ <= i__1;
++i__)
{
if (d__[i__] <= 0.f)
{
return 0;
}
/* L10: */
}
/* Solve M(A) * x = e, where M(A) = (m(i,j)) is given by */
/* m(i,j) = f2c_abs(A(i,j)); i = j; */
/* m(i,j) = -f2c_abs(A(i,j)), i .ne. j, */
/* and e = [ 1, 1, ..., 1 ]**T. Note M(A) = M(L)*D*M(L)**T. */
/* Solve M(L) * x = e. */
work[1] = 1.f;
i__1 = *n;
for (i__ = 2;
i__ <= i__1;
++i__)
{
work[i__] = work[i__ - 1] * (r__1 = e[i__ - 1], f2c_abs(r__1)) + 1.f;
/* L20: */
}
/* Solve D * M(L)**T * x = b. */
work[*n] /= d__[*n];
for (i__ = *n - 1;
i__ >= 1;
--i__)
{
work[i__] = work[i__] / d__[i__] + work[i__ + 1] * (r__1 = e[i__], f2c_abs(r__1));
/* L30: */
}
/* Compute AINVNM = max(x(i)), 1<=i<=n. */
ix = isamax_(n, &work[1], &c__1);
ainvnm = (r__1 = work[ix], f2c_abs(r__1));
/* Compute the reciprocal condition number. */
if (ainvnm != 0.f)
{
*rcond = 1.f / ainvnm / *anorm;
}
return 0;
/* End of SPTCON */
}
/* sptcon_ */
|
