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
234
235
236
237
238
239
|
/*! \file
Copyright (c) 2003, The Regents of the University of California, through
Lawrence Berkeley National Laboratory (subject to receipt of any required
approvals from U.S. Dept. of Energy)
All rights reserved.
The source code is distributed under BSD license, see the file License.txt
at the top-level directory.
*/
/*! @file clacon2.c
* \brief Estimates the 1-norm
*
* <pre>
* -- SuperLU routine (version 5.0) --
* Univ. of California Berkeley, Xerox Palo Alto Research Center,
* and Lawrence Berkeley National Lab.
* July 25, 2015
* </pre>
*/
#include <math.h>
#include "slu_Cnames.h"
#include "slu_scomplex.h"
/*! \brief
*
* <pre>
* Purpose
* =======
*
* CLACON2 estimates the 1-norm of a square matrix A.
* Reverse communication is used for evaluating matrix-vector products.
*
* This is a thread safe version of CLACON, which uses the array ISAVE
* in place of a STATIC variables, as follows:
*
* CLACON CLACON2
* jump isave[0]
* j isave[1]
* iter isave[2]
*
*
* Arguments
* =========
*
* N (input) INT
* The order of the matrix. N >= 1.
*
* V (workspace) COMPLEX PRECISION array, dimension (N)
* On the final return, V = A*W, where EST = norm(V)/norm(W)
* (W is not returned).
*
* X (input/output) COMPLEX PRECISION array, dimension (N)
* On an intermediate return, X should be overwritten by
* A * X, if KASE=1,
* A' * X, if KASE=2,
* where A' is the conjugate transpose of A,
* and CLACON must be re-called with all the other parameters
* unchanged.
*
*
* EST (output) FLOAT PRECISION
* An estimate (a lower bound) for norm(A).
*
* KASE (input/output) INT
* On the initial call to CLACON, KASE should be 0.
* On an intermediate return, KASE will be 1 or 2, indicating
* whether X should be overwritten by A * X or A' * X.
* On the final return from CLACON, KASE will again be 0.
*
* isave (input/output) int [3]
* ISAVE is INTEGER array, dimension (3)
* ISAVE is used to save variables between calls to CLACON2
*
* Further Details
* ===============
*
* Contributed by Nick Higham, University of Manchester.
* Originally named CONEST, dated March 16, 1988.
*
* Reference: N.J. Higham, "FORTRAN codes for estimating the one-norm of
* a real or complex matrix, with applications to condition estimation",
* ACM Trans. Math. Soft., vol. 14, no. 4, pp. 381-396, December 1988.
* =====================================================================
* </pre>
*/
int
clacon2_(int *n, complex *v, complex *x, float *est, int *kase, int isave[3])
{
/* Table of constant values */
int c__1 = 1;
complex zero = {0.0, 0.0};
complex one = {1.0, 0.0};
/* System generated locals */
float d__1;
/* Local variables */
int jlast;
float altsgn, estold;
int i;
float temp;
float safmin;
extern float smach(char *);
extern int icmax1_slu(int *, complex *, int *);
extern double scsum1_slu(int *, complex *, int *);
safmin = smach("Safe minimum"); /* lamch_("Safe minimum"); */
if ( *kase == 0 ) {
for (i = 0; i < *n; ++i) {
x[i].r = 1. / (float) (*n);
x[i].i = 0.;
}
*kase = 1;
isave[0] = 1; /* jump = 1; */
return 0;
}
switch (isave[0]) {
case 1: goto L20;
case 2: goto L40;
case 3: goto L70;
case 4: goto L110;
case 5: goto L140;
}
/* ................ ENTRY (isave[0] = 1)
FIRST ITERATION. X HAS BEEN OVERWRITTEN BY A*X. */
L20:
if (*n == 1) {
v[0] = x[0];
*est = c_abs(&v[0]);
/* ... QUIT */
goto L150;
}
*est = scsum1_slu(n, x, &c__1);
for (i = 0; i < *n; ++i) {
d__1 = c_abs(&x[i]);
if (d__1 > safmin) {
d__1 = 1 / d__1;
x[i].r *= d__1;
x[i].i *= d__1;
} else {
x[i] = one;
}
}
*kase = 2;
isave[0] = 2; /* jump = 2; */
return 0;
/* ................ ENTRY (isave[0] = 2)
FIRST ITERATION. X HAS BEEN OVERWRITTEN BY TRANSPOSE(A)*X. */
L40:
isave[1] = icmax1_slu(n, &x[0], &c__1); /* j */
--isave[1]; /* --j; */
isave[2] = 2; /* iter = 2; */
/* MAIN LOOP - ITERATIONS 2,3,...,ITMAX. */
L50:
for (i = 0; i < *n; ++i) x[i] = zero;
x[isave[1]] = one;
*kase = 1;
isave[0] = 3; /* jump = 3; */
return 0;
/* ................ ENTRY (isave[0] = 3)
X HAS BEEN OVERWRITTEN BY A*X. */
L70:
#ifdef _CRAY
CCOPY(n, x, &c__1, v, &c__1);
#else
ccopy_(n, x, &c__1, v, &c__1);
#endif
estold = *est;
*est = scsum1_slu(n, v, &c__1);
L90:
/* TEST FOR CYCLING. */
if (*est <= estold) goto L120;
for (i = 0; i < *n; ++i) {
d__1 = c_abs(&x[i]);
if (d__1 > safmin) {
d__1 = 1 / d__1;
x[i].r *= d__1;
x[i].i *= d__1;
} else {
x[i] = one;
}
}
*kase = 2;
isave[0] = 4; /* jump = 4; */
return 0;
/* ................ ENTRY (isave[0] = 4)
X HAS BEEN OVERWRITTEN BY TRANDPOSE(A)*X. */
L110:
jlast = isave[1]; /* j; */
isave[1] = icmax1_slu(n, &x[0], &c__1); /* j */
isave[1] = isave[1] - 1; /* --j; */
if (x[jlast].r != (d__1 = x[isave[1]].r, fabs(d__1)) && isave[2] < 5) {
isave[2] = isave[2] + 1; /* ++iter; */
goto L50;
}
/* ITERATION COMPLETE. FINAL STAGE. */
L120:
altsgn = 1.;
for (i = 1; i <= *n; ++i) {
x[i-1].r = altsgn * ((float)(i - 1) / (float)(*n - 1) + 1.);
x[i-1].i = 0.;
altsgn = -altsgn;
}
*kase = 1;
isave[0] = 5; /* jump = 5; */
return 0;
/* ................ ENTRY (isave[0] = 5)
X HAS BEEN OVERWRITTEN BY A*X. */
L140:
temp = scsum1_slu(n, x, &c__1) / (float)(*n * 3) * 2.;
if (temp > *est) {
#ifdef _CRAY
CCOPY(n, &x[0], &c__1, &v[0], &c__1);
#else
ccopy_(n, &x[0], &c__1, &v[0], &c__1);
#endif
*est = temp;
}
L150:
*kase = 0;
return 0;
} /* clacon_ */
|
