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
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
|
/* dpbcon.f -- translated by f2c (version 20061008).
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 "f2c.h"
#include "blaswrap.h"
/* Table of constant values */
static integer c__1 = 1;
/* Subroutine */ int dpbcon_(char *uplo, integer *n, integer *kd, doublereal *
ab, integer *ldab, doublereal *anorm, doublereal *rcond, doublereal *
work, integer *iwork, integer *info)
{
/* System generated locals */
integer ab_dim1, ab_offset, i__1;
doublereal d__1;
/* Local variables */
integer ix, kase;
doublereal scale;
extern logical lsame_(char *, char *);
integer isave[3];
extern /* Subroutine */ int drscl_(integer *, doublereal *, doublereal *,
integer *);
logical upper;
extern /* Subroutine */ int dlacn2_(integer *, doublereal *, doublereal *,
integer *, doublereal *, integer *, integer *);
extern doublereal dlamch_(char *);
doublereal scalel;
extern integer idamax_(integer *, doublereal *, integer *);
extern /* Subroutine */ int dlatbs_(char *, char *, char *, char *,
integer *, integer *, doublereal *, integer *, doublereal *,
doublereal *, doublereal *, integer *);
doublereal scaleu;
extern /* Subroutine */ int xerbla_(char *, integer *);
doublereal ainvnm;
char normin[1];
doublereal smlnum;
/* -- LAPACK routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* Modified to call DLACN2 in place of DLACON, 5 Feb 03, SJH. */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* DPBCON estimates the reciprocal of the condition number (in the */
/* 1-norm) of a real symmetric positive definite band matrix using the */
/* Cholesky factorization A = U**T*U or A = L*L**T computed by DPBTRF. */
/* An estimate is obtained for norm(inv(A)), and the reciprocal of the */
/* condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))). */
/* Arguments */
/* ========= */
/* UPLO (input) CHARACTER*1 */
/* = 'U': Upper triangular factor stored in AB; */
/* = 'L': Lower triangular factor stored in AB. */
/* N (input) INTEGER */
/* The order of the matrix A. N >= 0. */
/* KD (input) INTEGER */
/* The number of superdiagonals of the matrix A if UPLO = 'U', */
/* or the number of subdiagonals if UPLO = 'L'. KD >= 0. */
/* AB (input) DOUBLE PRECISION array, dimension (LDAB,N) */
/* The triangular factor U or L from the Cholesky factorization */
/* A = U**T*U or A = L*L**T of the band matrix A, stored in the */
/* first KD+1 rows of the array. The j-th column of U or L is */
/* stored in the j-th column of the array AB as follows: */
/* if UPLO ='U', AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j; */
/* if UPLO ='L', AB(1+i-j,j) = L(i,j) for j<=i<=min(n,j+kd). */
/* LDAB (input) INTEGER */
/* The leading dimension of the array AB. LDAB >= KD+1. */
/* ANORM (input) DOUBLE PRECISION */
/* The 1-norm (or infinity-norm) of the symmetric band matrix A. */
/* RCOND (output) DOUBLE PRECISION */
/* The reciprocal of the condition number of the matrix A, */
/* computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an */
/* estimate of the 1-norm of inv(A) computed in this routine. */
/* WORK (workspace) DOUBLE PRECISION array, dimension (3*N) */
/* IWORK (workspace) INTEGER array, dimension (N) */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input parameters. */
/* Parameter adjustments */
ab_dim1 = *ldab;
ab_offset = 1 + ab_dim1;
ab -= ab_offset;
--work;
--iwork;
/* Function Body */
*info = 0;
upper = lsame_(uplo, "U");
if (! upper && ! lsame_(uplo, "L")) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*kd < 0) {
*info = -3;
} else if (*ldab < *kd + 1) {
*info = -5;
} else if (*anorm < 0.) {
*info = -6;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("DPBCON", &i__1);
return 0;
}
/* Quick return if possible */
*rcond = 0.;
if (*n == 0) {
*rcond = 1.;
return 0;
} else if (*anorm == 0.) {
return 0;
}
smlnum = dlamch_("Safe minimum");
/* Estimate the 1-norm of the inverse. */
kase = 0;
*(unsigned char *)normin = 'N';
L10:
dlacn2_(n, &work[*n + 1], &work[1], &iwork[1], &ainvnm, &kase, isave);
if (kase != 0) {
if (upper) {
/* Multiply by inv(U'). */
dlatbs_("Upper", "Transpose", "Non-unit", normin, n, kd, &ab[
ab_offset], ldab, &work[1], &scalel, &work[(*n << 1) + 1],
info);
*(unsigned char *)normin = 'Y';
/* Multiply by inv(U). */
dlatbs_("Upper", "No transpose", "Non-unit", normin, n, kd, &ab[
ab_offset], ldab, &work[1], &scaleu, &work[(*n << 1) + 1],
info);
} else {
/* Multiply by inv(L). */
dlatbs_("Lower", "No transpose", "Non-unit", normin, n, kd, &ab[
ab_offset], ldab, &work[1], &scalel, &work[(*n << 1) + 1],
info);
*(unsigned char *)normin = 'Y';
/* Multiply by inv(L'). */
dlatbs_("Lower", "Transpose", "Non-unit", normin, n, kd, &ab[
ab_offset], ldab, &work[1], &scaleu, &work[(*n << 1) + 1],
info);
}
/* Multiply by 1/SCALE if doing so will not cause overflow. */
scale = scalel * scaleu;
if (scale != 1.) {
ix = idamax_(n, &work[1], &c__1);
if (scale < (d__1 = work[ix], abs(d__1)) * smlnum || scale == 0.)
{
goto L20;
}
drscl_(n, &scale, &work[1], &c__1);
}
goto L10;
}
/* Compute the estimate of the reciprocal condition number. */
if (ainvnm != 0.) {
*rcond = 1. / ainvnm / *anorm;
}
L20:
return 0;
/* End of DPBCON */
} /* dpbcon_ */
|
