151692/Uniform_PDFs_pruned.m at master · ModelDBRepository/151692 · GitHub

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

%% Symbolic calculation and numeric simulation for uniform distriutions with pruning

clear all
close all

%% Parameters
N = 10000000;   %number of pair connections
a = 0.1;        %pruning value. 0.1 is good to see the effect in sum and abs_diff but for the joint we need a lower value, for instance 0.01

%% Plotting parameters
numericFontSize = 25;
axesFontSize = 30;
lineThickness = 2;
markLine = 1;
markSize = 12;

n_bins = 200;                   %bins for the histogram

%% Parameters and variables for symbolic calculation
syms u;

%% Simulation samples
x_unp = rand(N,1) .* (rand(N,1) > a);
y_unp = rand(N,1) .* (rand(N,1) > a);

x = x_unp((x_unp+y_unp)~=0);    %uses logical index to cut away the zero elements from the distributions when they have the same index in x and y (w_{ij}=w_{ji}=0)
y = y_unp((x_unp+y_unp)~=0);    %uses logical index to cut away the zero elements from the distributions when they have the same index in x and y (w_{ij}=w_{ji}=0)

%% Single distributions
sum_var = x + y;
abs_diff_var = abs(x-y);

%% Plots

% Initial Distribution
bin_dim = 1 / n_bins;
[counts,bin_location] = hist(x_unp, n_bins);               %Note: bin_location==sample
figure(1);
bar(bin_location, counts/(sum(bin_dim*counts)));
hold on
x_ax = 0:0.001:1;
y_ax = (1-a) * ones(1, size(x_ax,2));
h = plot(x_ax,y_ax);
set(h, 'color', 'k', 'LineWidth', lineThickness);

set(gca,'fontsize',numericFontSize);
xlabel('w','fontsize',axesFontSize);
ylabel('f(w)','fontsize',axesFontSize);
axis([-0.2 1.2 0 22]);
colormap(gray);
caxis([-1 1.4]);
title('');

print(gcf, '-depsc2', '-loose', 'Uniform_initialPDF_prune0_1'); % Print the figure in eps (first option) and uncropped (second object)


% Sum
bin_dim = 2 / n_bins;
[counts,bin_location] = hist(sum_var, n_bins);         %Note: bin_location==sample
figure(2);
bar(bin_location, counts/(sum(bin_dim*counts)));
hold on
h1 = ezplot( ((1-a)/(1+a))*u + (2*a)/(1+a), [0,1] );
set(h1,'color', 'k', 'LineWidth', lineThickness);
hold on
h2 = ezplot( -((1-a)/(1+a))*u + 2*((1-a)/(1+a)), [1,2] );
set(h2,'color','k', 'LineWidth', lineThickness);

set(gca,'fontsize',numericFontSize);
xlabel('Z_2','fontsize',axesFontSize);
ylabel('f(Z_2)','fontsize',axesFontSize);
axis([-0.2 2.2 0 1.5]);
colormap(gray);
caxis([-1 1.4]);
title('');

print(gcf, '-depsc2', '-loose', 'Uniform_sumPDF_prune0_1'); % Print the figure in eps (first option) and uncropped (second object)


% Difference
bin_dim = 2 / n_bins;
[counts,bin_location] = hist(x-y, n_bins);            %Note: bin_location==sample
figure(3);
bar(bin_location, counts/(sum(bin_dim*counts)));
hold on
h1 = ezplot( ((1-a)/(1+a))*u + 1/(1+a), [-1,0]);
set(h1,'color', 'k', 'LineWidth', lineThickness);
hold on
h2 = ezplot( -((1-a)/(1+a))*u + 1/(1+a), [0,1]);
set(h2,'color', 'k', 'LineWidth', lineThickness);

set(gca,'fontsize',numericFontSize);
xlabel('diff','fontsize',axesFontSize);
ylabel('f(diff)','fontsize',axesFontSize);
axis([-1.2 1.2 0 1.5]);
colormap(gray);
caxis([-1 1.4]);
title('');


% Absolute difference
bin_dim = 1 / n_bins;
[counts,bin_location] = hist(abs_diff_var, n_bins);    %Note: bin_location==sample
figure(4);
bar(bin_location, counts/(sum(bin_dim*counts)));
hold on
h = ezplot( -2*((1-a)/(1+a))*u + 2/(1+a), [0,1]);
set(h,'color','k', 'LineWidth', lineThickness);

set(gca,'fontsize',numericFontSize);
xlabel('Z_1','fontsize',axesFontSize);
ylabel('f(Z_1)','fontsize',axesFontSize);
axis([-0.2 1.2 0 2.5]);
colormap(gray);
caxis([-1 1.4]);
title('');

print(gcf, '-depsc2', '-loose', 'Uniform_absdiffPDF_prune0_1'); % Print the figure in eps (first option) and uncropped (second object)


% Joint Distribution
bin_dim_x = 1 / n_bins;
bin_dim_y = 2 / n_bins;
[bidim_counts,Cell_location] = hist3([sum_var, abs_diff_var], [n_bins,n_bins]);
figure(5);
mesh(Cell_location{1},Cell_location{2},bidim_counts'/(sum(sum(bin_dim_x*bin_dim_y*bidim_counts))))      %simulation
%hold on
%surf(Cell_location{1},Cell_location{2}, ((1-a)/(1+a))*ones(size(Cell_location{1},2),size(Cell_location{2},2))')

set(gca,'fontsize',numericFontSize);
axis on
%xlabel('Z_2','fontsize',axesFontSize);
%ylabel('Z_1','fontsize',axesFontSize);
%zlabel('f(Z_1,Z_2)','fontsize',axesFontSize);
%set(gca, 'ZTick',[0:(1-a)/(1+a):3]);
colormap(gray);
caxis([-2 6]);
view([145 45]);
title('');

print(gcf, '-depsc2', '-loose', 'Uniform_jointPDF_prune0_01'); % Print the figure in eps (first option) and uncropped (second object)