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
|
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
void differentiate(double* f, double** df, int D, int K){
df[0] = f;
int i;
for(int k=1; k<=K; k++){
for(i=0; i<D-k; i++){
df[k][i] = df[k-1][i+1] - df[k-1][i];
}
}
}
double integrate(double* f, double p, int D){
double sum = 0.0;
for(int i=0;i<D;i++){
sum += pow(fabs(f[i]),p);
}
return pow(sum,1/p);
}
double compute_derivatives(int* f, int** Sf, double** Af, double* Mf, double** df, double** dMf, double p, double* intdf, double* intdMf, int N, int D, int K){
for(int i=0;i<D;i++) df[0][i] = (double) f[i];
int r=0;
for(int i=0;i<D;i++) {
Sf[i][i] = f[i];
Af[i][i] = 1.0*Sf[i][i];
}
for(int n=1;n<D;n++){
for(int i=0;i+n<D;i++){
Sf[i][i+n] = Sf[i][i+n-1]+f[i+n];
Sf[i+n][i] = Sf[i][i+n];
Af[i][i+n] = 1.0*Sf[i][i+n]/(n+1);
Af[i+n][i] = Af[i][i+n];
}
}
for(int i=0;i<D;i++){
Mf[i] = Af[i][i];
for(int j=0;j<D;j++){
if(Af[i][j] > Mf[i]) Mf[i] = Af[i][j];
}
}
//printf("Mf ");
//for(int i=0;i<D;i++) printf("%+0.1f ",Mf[i]);
//printf("\n");
for(int i=0;i<D;i++){
//for(int j=0;j<D;j++) printf("%0.1f ",Af[i][j]);
//printf("\n");
}
differentiate(df[0],df,D,K);
differentiate(dMf[0],dMf,D,K);
//for(int k=0;k<=K;k++){
//printf("f %d: ",k);
//for(int i=0;i<D;i++) printf("%+0.1f ",df[k][i]);
//printf("\n");
//printf("Mf %d: ",k);
//for(int i=0;i<D;i++) printf("%+0.1f ",dMf[k][i]);
//printf("\n");
//}
//for(int k=0;k<=K;k++){
int k=K;
intdf[k] = integrate(df[k],p,D);
intdMf[k] = integrate(dMf[k],p,D);
//printf("%d: %f / %f = %f\n",k,intdMf[k],intdf[k],intdMf[k]/intdf[k]);
return intdMf[k]/intdf[k];
//}
}
int main() {
int N=16;
int D=5*N;
int K=3;
double p = 1.0;
int* f = malloc(D*sizeof(int));
int** Sf = malloc(D*sizeof(int*));
double** Af = malloc(D*sizeof(double*));
double* Mf = malloc(D*sizeof(double));
for(int i=0;i<D;i++){
Sf[i] = malloc(D*sizeof(int));
Af[i] = malloc(D*sizeof(double));
}
double** df = malloc(D*sizeof(double*));
double** dMf = malloc(D*sizeof(double*));
for(int k=0;k<=K;k++){
df[k] = malloc(D*sizeof(double));
dMf[k] = malloc(D*sizeof(double));
for(int i=0;i<D;i++){
df[k][i] = 0;
dMf[k][i] = 0;
}
}
dMf[0] = Mf;
double* intdf = malloc(sizeof(double)*K);
double* intdMf = malloc(sizeof(double)*K);
double r = 0.0;
for(int t=1; t<=(1 << N)-1; t++){
for(int i=0;i<D;i++) f[i]=0;
//for(int i=0;i<N;i++) f[N+i] = rand() %2;
for(int i=0;i<N;i++){
f[2*N+i+K/2] = (t >> i) & 1;
//if(i%3==0) f[2*N+i+K/2] = 1;
}
r = compute_derivatives(f, Sf, Af, Mf, df, dMf, p, intdf, intdMf, N, D, K);
//printf("%.3d: %.3f \n",t,r);
if(r>.4997){
printf("f: ");
for(int i=0;i<D;i++) printf("%.1d ",f[i]);
printf("\n");
printf("%.4f\n",r);
}
}
return 0;
}
|
