-
Notifications
You must be signed in to change notification settings - Fork 0
/
Copy pathSLPCDforgrass.m
executable file
·189 lines (175 loc) · 5.69 KB
/
SLPCDforgrass.m
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
clear
kappa_grid=0:0.002:2;
Z=imread('grass.tiff');
Z=im2double(Z);
Z=Z(1:256,1:256);
observation=Z;
m=512/2;n=512/2;
N=[m,n];
q=2;
%chess=zeros(m,n);
%chess=conschess(chess);
G_start=q;
%% priors and starting points
mu_0=mean(mean(observation)); %prior of mean parameter is normal distribution
mu=normrnd(mu_0,0.2,[1,q]); %starting points
sigma=(unifrnd(0,0.1,[1,q])).^2;
iteration=6000;
burnin=2000;
alpha=1;tau=0.01;
data=observation;
clear('observation');
Z_start=randi(G_start,N);
% pi_start=sample_dirichlet(ones(1,G_start),1);
% pi_start=sample_dirichlet(ones(1,G_start),1);
kappa_start=0.3;
R=max(data(:))-min(data(:));
invp1=0.001;invp2=0.001;
mu_sig=100^2;
%% Chess
threedeye=eye(2);
chess = repmat(threedeye,N/2);
kappa_upper=4;
Zshell=Z;
Zshell(:)=1:m*n;
%% (1 item)
p1=dlmread(strcat('p1tableCT=1','q=',num2str(q),'.txt'));
%% Conditional type(2 items)
nCT=min(2,q);
p2=[];
for i=1:nCT
p2(:,:,i)=dlmread(strcat('p2tableCT=',num2str(i),'q=',num2str(q),'.txt'));
end
p1(:,2:end)=log(p1(:,2:end));
p2(:,2:end,:)=log(p2(:,2:end,:));
p1(p1==-Inf)=0;
p2(p2==-Inf)=0;
iteration=6000;
burnin=2000;
%% MCMC
for iter=1:iteration
chess=1-chess;
%% update Z
Z_new=(1-chess).*Z_start + chess.*prop_new_potts(Z_start,q); %propose new value
neighbors_new = findneighbour(Z_new);
neighbors_start =findneighbour(Z_start);
likelihood_start=log(normpdf(data,mu(Z_start),sqrt(sigma(Z_start))));
likelihood_new=log(normpdf(data,mu(Z_new),sqrt(sigma(Z_new))));
Z_prob=likelihood_new-likelihood_start+...
(neighbors_new-neighbors_start)*kappa_start;
transitions = (log(rand(N)) < Z_prob ).* chess .* (Z_new - Z_start);
Z_start=Z_start+transitions;
chess=1-chess;
%% update Z
Z_new=((1-chess).*Z_start+chess.*prop_new_potts(Z_start,q)); %propose new value
neighbors_new = findneighbour(Z_new);
neighbors_start =findneighbour(Z_start);
likelihood_start=log(normpdf(data,mu(Z_start),sqrt(sigma(Z_start))));
likelihood_new=log(normpdf(data,mu(Z_new),sqrt(sigma(Z_new))));
Z_prob=likelihood_new-likelihood_start+...
(neighbors_new-neighbors_start)*kappa_start;
transitions = (log(rand(N)) < Z_prob ).* chess .* (Z_new - Z_start);
Z_start=Z_start+transitions;
%% ============ update kappa
d=(Z_start==circshift(Z_start, [1 0]));
cnt1=d(2:end,1)+0;
d=(Z_start==circshift(Z_start, [0 1]));
cnt2=d(1,2:end)+0;
tem=tabulate([cnt1;cnt2']);
counts1=tem(:,2)';
d=(Z_start==circshift(Z_start, [1 0]))+0;
d=d+(Z_start==circshift(Z_start, [0 1]));
d(1,:)=[];
d(:,1)=[];
nCT=min(2,q); CTmat=zeros(size(Z_start)-1);
for ii=2:size(Z_start,1)
for jj=2:size(Z_start,2)
neib=[Z_start(minuspos(ii,m),jj),Z_start(ii,minuspos(jj,n))];
CTmat(ii-1,jj-1)= length(unique(neib));
end
end
p2tableCT=zeros(nCT,2+1);
for ii=1:nCT
tem=tabulate(d(CTmat==ii));
p2tableCT(ii,tem(:,1)+1)=p2tableCT(ii,tem(:,1)+1)+tem(:,2)';
end
kappa_new=kappa_start+0.02*randn(1);
if kappa_new >0 && kappa_new<kappa_upper
kappa_start_r=abs(kappa_start-kappa_grid);
kappa_new_r=abs(kappa_new-kappa_grid);
rnk_start=find(kappa_start_r==min(kappa_start_r),1);
rnk_new=find(kappa_new_r==min(kappa_new_r),1);
like_p1start=sum(counts1.*p1(rnk_start,2:end));
like_p1new=sum(counts1.*p1(rnk_new,2:end));
like_p2start=0;
for ii=1:nCT
like_p2start=like_p2start+sum(p2tableCT(ii,:).*p2(rnk_start,2:4,ii));
end
like_p2new=0;
for ii=1:nCT
like_p2new=like_p2new+sum(p2tableCT(ii,:).*p2(rnk_new,2:4,ii));
end
like_new=like_p1new+like_p2new;
like_start=like_p1start+like_p2start;
if like_new-like_start>log(rand(1))
kappa_start=kappa_new;
end
end
%% update mu
for i=1:G_start
a=(Z_start==i);
aa=sum(a(:));
block=data(a);
mu_new=normrnd(mu(i),0.002);
mu_prob=sum(log(normpdf(block,mu_new,sqrt(sigma(i))))-...
log(normpdf(block,mu(i),sqrt(sigma(i)))))...
+log(normpdf(mu_new,mu_0,sqrt(mu_sig)))-log(normpdf(mu(i),mu_0,sqrt(mu_sig)));
if mu_prob>log(rand(1))
mu(i)=mu_new;
end
% ave=(sum(block)+tau*mu_0)/(aa+tau);
% sig=sigma(i)/(aa+tau);
% mu(i)=normrnd(ave,sqrt(sig));
end
%% update of mean parameter is over
for i=1:G_start
a=(Z_start==i);
block=data(a);
sigma_new=(normrnd(sqrt(sigma(i)),0.001))^2;
sigma_prob=sum(log(normpdf(block,mu(i),sqrt(sigma_new)))-log(normpdf(block,mu(i),sqrt(sigma(i)))))...
+inversegampdf(sigma_new,invp1,invp2)-inversegampdf(sigma(i),invp1,invp2);
if sigma_prob>log(rand(1))
sigma(i)=sigma_new;
end
end
% sigma=1./phi;
%% update of sigma is over. need to update \kappa
mu_mat(iter,:)=mu;
sigma_mat(iter,:)=sigma;
kappa_mat(iter)=kappa_start;
if iter>burnin
Z_cell{iter-burnin}=Z_start;
end
end
save(strcat('SLPCDforgrass','q=',num2str(q),'.mat'));
exit;
plot(kappa_mat(2001:end))
mean(mu_mat(2001:end,:))
std(mu_mat(2001:end,:))
mean(sigma_mat(2001:end,:))
std(sigma_mat(2001:end,:))
mean(kappa_mat(2001:end))
std(kappa_mat(2001:end))
MSE=0;
for i=1:4000
mu_sim=mu_mat(i+2000,:);
sigma_sim=sqrt(sigma_mat(i+2000,:));
Zsim=normrnd(mu_sim(Z_cell{i}),sigma(Z_cell{i}));
MSE=MSE+mean((Zsim(:)-Z(:)).^2);
end
MSE=MSE/4000
imshow(Z_start-1)
set(gca,'position',[0,0,1,1])
set(gcf, 'PaperPosition', [0 0 15 15]); %Position plot at left hand corner with width 5 and height 5.
set(gcf, 'PaperSize', [15 15]); %Set the paper to have width 5 and height 5.
saveas(gcf, 'grass_SLPCD', 'jpg') %Save figure