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
|
/*
* This file is part of MAMMULT: Metrics And Models for Multilayer Networks
*
* This program is free software: you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation, either version 3 of the License, or (at
* your option) any later version.
*
* This program is distributed in the hope that it will be useful, but
* WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
* General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program. If not, see <http://www.gnu.org/licenses/>.
*/
/**
*
* Tune the inter-layer degree correlation function \bar{q}(k) of a
* two-layer multiplex, in order to make it as similar as possible to
* a power law with exponent $\mu$, where $\mu$ is given as input
*
* This version of the program is (or, better, "shoud be") able to
* tune also the value of the pre-factor "a"
*
*/
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <strings.h>
#include <time.h>
#include "rank_utils.h"
inline double compute_delta(double q, double k, double mu, double a){
return fabs(log(q) - mu * log(k) - log(a));
//return fabs (q - a*pow(k,mu));
}
void tune_qnn_adaptive(double *R1, double *R2, int N, int *pairing, double eps,
double beta, double mu_target){
double act_mu, test_mu, F, F_new, F_old;
double delta1_old, delta2_old, delta1_new, delta2_new;
double val, prob;
double mu, a, err, dummy_a;
int *new_pairing;
int p1, p2, tmp_val;
int tot;
char swap = 0;
new_pairing = malloc(N * sizeof(int));
copy_pairing(pairing, new_pairing, N);
a = 1.0;
F = 10000;
fit_current_trend(R1, R2, N, pairing, &mu, &a, &err);
fprintf(stderr, "Initial mu: %g a: %g corr: %g\n", mu, a, err);
//fprintf("%f %f %f %f %f\n", eps, beta, mu_target, act_mu, F);
tot = 0;
while (F > eps){
/* sample two positions of "pairing" and shuffle them in "new_pairing" */
p1 = rand() % N;
p2 = rand() % N;
while (p2 == p1){
p2 = rand() % N;
}
tmp_val = new_pairing[p1];
new_pairing[p1] = new_pairing[p2];
new_pairing[p2] = tmp_val;
delta1_old = compute_delta(R2[pairing[p1]], R1[p1], mu_target, a);
delta2_old = compute_delta(R2[pairing[p2]], R1[p2], mu_target, a);
delta1_new = compute_delta(R2[new_pairing[p1]], R1[p1], mu_target, a);
delta2_new = compute_delta(R2[new_pairing[p2]], R1[p2], mu_target, a);
//F_new = log(delta1_new * delta2_new);
//F_old = log(delta1_old * delta2_old);
F_new = delta1_new + delta2_new;
F_old = delta1_old + delta2_old;
if (F_new <= F_old){/* Accept this swap with probability 1 */
tmp_val = pairing[p1];
pairing[p1] = pairing[p2];
pairing[p2] = tmp_val;
//act_mu = test_mu;
swap = 1;
}
else{/* Accept the swap with a certain probability */
val = 1.0 * rand() / RAND_MAX;
//prob = pow(fabs(F - F_new)/(F+F_new), beta);
prob = exp(-(F_new - F_old)/beta);
//fprintf(stderr, "-- %g %g %g -> %f \n", F_new, F_old, F_new - F_old, prob);
if (val < prob){ /* Accept the swap */
tmp_val = pairing[p1];
pairing[p1] = pairing[p2];
pairing[p2] = tmp_val;
//act_mu = test_mu;
swap = 1;
}
else{ /* Rollback the swap */
tmp_val = new_pairing[p1];
new_pairing[p1] = new_pairing[p2];
new_pairing[p2] = tmp_val;
swap = 0;
}
}
///F = fabs(act_mu - mu_target);
///if (tot % 200 == 0){
//fprintf(stderr, "%d %g\n", tot, act_mu);
//fprintf(stderr, "%d: %f %f ---- %f %f ---- %f %f ---- %d \n",
//tot, delta1_old, delta2_old, delta1_new, delta2_new, F_old, F_new, swap);
///}
tot += 1;
if (tot %200 == 0){
fit_current_trend(R1, R2, N, pairing, &mu, &a, &err);
fprintf(stderr, "mu: %g a: %g corr: %g\n", mu, a, err);
//a = a - 0.01 *(a - exp(a));
a = exp(a);
}
fit_current_trend(R1, R2, N, pairing, &mu, &dummy_a, &err);
F = fabs(mu - mu_target);
}
fit_current_trend(R1, R2, N, pairing, &mu, &a, &err);
fprintf(stderr, "Final mu: %g a: %g corr: %g\n", mu, a, err);
}
void dump_qnn(double *R1, double *R2, int N, int *pairing){
int i;
int *qnn, *num;
qnn = malloc(N * sizeof(int));
num = malloc(N * sizeof(int));
for (i=0; i<N; i++){
qnn[i]=0;
num[i]=0;
}
for (i=0; i<N; i++){
qnn[(int)(R1[i])] += R2[pairing[i]];
num[(int)(R1[i])] += 1;
}
for(i=0; i<N; i++){
if (num[i] >0){
printf("%d %f\n", i, 1.0*qnn[i]/num[i]);
}
}
free(num);
free(qnn);
}
void dump_degs(double *R1, double *R2, int N, int *pairing){
int i;
for(i=0; i<N; i++){
printf("%g %g\n", R1[i], R2[pairing[i]]);
}
}
int main (int argc, char *argv[]){
int N1, N2;
double *R1 = NULL;
double *R2 = NULL;
double eps, beta, mu_target;
int *pairing = NULL;
srand(time(NULL));
if (argc < 6){
printf("Usage: %s <degs1> <degs2> <mu> <eps> <beta> [RND|NAT|INV]\n", argv[0]);
exit(1);
}
mu_target = atof(argv[3]);
eps = atof(argv[4]);
beta = atof(argv[5]);
load_ranking(argv[1], &N1, &R1);
load_ranking(argv[2], &N2, &R2);
if (N1 != N2){
printf("Error!!!! The two files must have the same number of lines!!!! Exiting...\n");
exit(1);
}
pairing = malloc(N1 * sizeof(int));
select_pairing(pairing, N1, argc, argv, 6);
tune_qnn_adaptive(R1, R2, N1, pairing, eps, beta, mu_target);
dump_pairing(pairing, N1);
//dump_qnn(R1, R2, N1, pairing);
//dump_degs(R1, R2, N1, pairing);
}
|
