-
Notifications
You must be signed in to change notification settings - Fork 2
/
phi_comp_bORf_unidir.m
293 lines (249 loc) · 11.8 KB
/
phi_comp_bORf_unidir.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
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
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
function [phi_MIP prob network] = phi_comp_bORf_unidir(M1,M2,numerator,denom,whole_sys_state,network,bf_option,bfcut_option)
% compute small phi of a given higher order purview...?
% if the system is cut unidirectionally
% options = the options
% subsystem = a system
% numerator = state of the system??
% denom_past =
% denom_future =
% whole_sys_state =
% p = TPM as a 2^N x N matrix
% b_table
% BRs
% FRs
bf = 1; %Larissa: That's only there to keep the dimensions as before, should be updated!
op_normalize = network.options(14);
op_small_phi = network.options(16);
num_nodes_denom = length(denom);
num_nodes_numerator = length(numerator);
%% unpartitioned transition repertoire
denomM1 = denom(ismember(denom,M1));
denomM2 = denom(ismember(denom,M2));
otherM1 = sum(2.^(denomM1-1))+1; %will be 1 if empty!
otherM2 = sum(2.^(denomM2-1))+1;
%M1 <- M2 noised and past, or M1 -> M2 noised and future
if (strcmp(bfcut_option,'BRcut') && strcmp(bf_option,'backward')) || (strcmp(bfcut_option,'FRcut') && strcmp(bf_option,'forward'))
numeratorM1 = numerator;
numeratorM2 = numerator(ismember(numerator, M2));
%M1 <- M2 noised and future, or M1 -> M2 noised and past
elseif (strcmp(bfcut_option,'BRcut') && strcmp(bf_option,'forward')) || (strcmp(bfcut_option,'FRcut') && strcmp(bf_option,'backward'))
numeratorM1 = numerator(ismember(numerator, M1));
numeratorM2 = numerator;
end
currentM1 = sum(2.^(numeratorM1-1))+1;
currentM2 = sum(2.^(numeratorM2-1))+1;
if strcmp(bf_option,'backward')
if isempty(network.BRs{currentM1,otherM1}) && otherM1 > 1
network.BRs{currentM1,otherM1} = comp_pers_cpt(network.nodes,numeratorM1,denomM1,whole_sys_state,bf_option);
end
prob_M1 = network.BRs{currentM1,otherM1};
if isempty(network.BRs{currentM2,otherM2}) && otherM2 > 1
network.BRs{currentM2,otherM2} = comp_pers_cpt(network.nodes,numeratorM2,denomM2,whole_sys_state,bf_option);
end
prob_M2 = network.BRs{currentM2,otherM2};
elseif strcmp(bf_option,'forward')
if isempty(network.FRs{currentM1,otherM1}) && otherM1 > 1
network.FRs{currentM1,otherM1} = comp_pers_cpt(network.nodes,numeratorM1,denomM1,whole_sys_state,bf_option);
end
prob_M1 = network.FRs{currentM1,otherM1};
if isempty(network.FRs{currentM2,otherM2}) && otherM2 > 1
network.FRs{currentM2,otherM2} = comp_pers_cpt(network.nodes,numeratorM2,denomM2,whole_sys_state,bf_option);
end
prob_M2 = network.FRs{currentM2,otherM2};
end
if isempty(prob_M1)
prob = prob_M2(:);
elseif isempty(prob_M2)
prob = prob_M1(:);
else
prob_test = bsxfun(@times,prob_M1,prob_M2);
prob = prob_test(:);
end
%% more than one
if num_nodes_denom ~= 0
[denom_partitions1 denom_partitions2 num_denom_partitions] = bipartition(denom,num_nodes_denom); % partition of xp
else
denom_partitions1{1} = []; denom_partitions2{1} = []; num_denom_partitions = 1;
end
[numerator_partitions1 numerator_partitions2 num_numerator_partitions] = bipartition(numerator,num_nodes_numerator,1); % partition of numerator
phi_cand = zeros(num_denom_partitions,num_numerator_partitions,2,2);
prob_prod_vec = cell(num_denom_partitions,num_numerator_partitions,2,2);
phi_zero_found = 0;
for i = 1:num_denom_partitions % past or future
denom_part1 = denom_partitions1{i};
denom_part2 = denom_partitions2{i};
denomM1_part1 = denom_part1(ismember(denom_part1,M1));
denomM2_part1 = denom_part1(ismember(denom_part1,M2));
denomM1_part2 = denom_part2(ismember(denom_part2,M1));
denomM2_part2 = denom_part2(ismember(denom_part2,M2));
for j=1: num_numerator_partitions % present
numerator_part1 = numerator_partitions1{j};
numerator_part2 = numerator_partitions2{j};
Norm = Normalization(denom_part1,denom_part2,numerator_part1,numerator_part2);
if Norm ~= 0
%M1 <- M2 noised and past, or M1 -> M2 noised and future
if (strcmp(bfcut_option,'BRcut') && strcmp(bf_option,'backward')) || (strcmp(bfcut_option,'FRcut') && strcmp(bf_option,'forward'))
numeratorM1_part1 = numerator_part1;
numeratorM2_part1 = numerator_part1(ismember(numerator_part1, M2));
numeratorM1_part2 = numerator_part2;
numeratorM2_part2 = numerator_part2(ismember(numerator_part2, M2));
%M1 <- M2 noised and future, or M1 -> M2 noised and past
elseif (strcmp(bfcut_option,'BRcut') && strcmp(bf_option,'forward')) || (strcmp(bfcut_option,'FRcut') && strcmp(bf_option,'backward'))
numeratorM1_part1 = numerator_part1(ismember(numerator_part1, M1));
numeratorM2_part1 = numerator_part1;
numeratorM1_part2 = numerator_part2(ismember(numerator_part2, M1));
numeratorM2_part2 = numerator_part2;
end
currentM1_1 = sum(2.^(numeratorM1_part1-1))+1;
currentM2_1 = sum(2.^(numeratorM2_part1-1))+1;
currentM1_2 = sum(2.^(numeratorM1_part2-1))+1;
currentM2_2 = sum(2.^(numeratorM2_part2-1))+1;
otherM1_1 = sum(2.^(denomM1_part1-1))+1;
otherM2_1 = sum(2.^(denomM2_part1-1))+1;
otherM1_2 = sum(2.^(denomM1_part2-1))+1;
otherM2_2 = sum(2.^(denomM2_part2-1))+1;
if strcmp(bf_option,'backward')
if isempty(network.BRs{currentM1_1,otherM1_1}) && otherM1_1 > 1
network.BRs{currentM1_1,otherM1_1} = comp_pers_cpt(network.nodes,numeratorM1_part1,denomM1_part1,whole_sys_state,bf_option);
end
probM1_p1 = network.BRs{currentM1_1,otherM1_1};
if isempty(network.BRs{currentM1_2,otherM1_2}) && otherM1_2 > 1
network.BRs{currentM1_2,otherM1_2} = comp_pers_cpt(network.nodes,numeratorM1_part2,denomM1_part2,whole_sys_state,bf_option);
end
probM1_p2 = network.BRs{currentM1_2,otherM1_2};
if isempty(network.BRs{currentM2_1,otherM2_1}) && otherM2_1 > 1
network.BRs{currentM2_1,otherM2_1} = comp_pers_cpt(network.nodes,numeratorM2_part1,denomM2_part1,whole_sys_state,bf_option);
end
probM2_p1 = network.BRs{currentM2_1,otherM2_1};
if isempty(network.BRs{currentM2_2,otherM2_2}) && otherM2_2 > 1
network.BRs{currentM2_2,otherM2_2} = comp_pers_cpt(network.nodes,numeratorM2_part2,denomM2_part2,whole_sys_state,bf_option);
end
probM2_p2 = network.BRs{currentM2_2,otherM2_2};
elseif strcmp(bf_option,'forward')
if isempty(network.FRs{currentM1_1,otherM1_1}) && otherM1_1 > 1
network.FRs{currentM1_1,otherM1_1} = comp_pers_cpt(network.nodes,numeratorM1_part1,denomM1_part1,whole_sys_state,bf_option);
end
probM1_p1 = network.FRs{currentM1_1,otherM1_1};
if isempty(network.FRs{currentM1_2,otherM1_2}) && otherM1_2 > 1
network.FRs{currentM1_2,otherM1_2} = comp_pers_cpt(network.nodes,numeratorM1_part2,denomM1_part2,whole_sys_state,bf_option);
end
probM1_p2 = network.FRs{currentM1_2,otherM1_2};
if isempty(network.FRs{currentM2_1,otherM2_1}) && otherM2_1 > 1
network.FRs{currentM2_1,otherM2_1} = comp_pers_cpt(network.nodes,numeratorM2_part1,denomM2_part1,whole_sys_state,bf_option);
end
probM2_p1 = network.FRs{currentM2_1,otherM2_1};
if isempty(network.FRs{currentM2_2,otherM2_2}) && otherM2_2 > 1
network.FRs{currentM2_2,otherM2_2} = comp_pers_cpt(network.nodes,numeratorM2_part2,denomM2_part2,whole_sys_state,bf_option);
end
probM2_p2 = network.FRs{currentM2_2,otherM2_2};
end
% first find part 1
%Don't flatten matrices here, because bsxfun below needs it in high dimension
if isempty(probM1_p1)
prob_p1 = probM2_p1;
elseif isempty(probM2_p1)
prob_p1 = probM1_p1;
else
prob_p1 = bsxfun(@times,probM1_p1,probM2_p1);
end
% then part 2
%Don't flatten matrices here, because bsxfun below needs it in high dimension
if isempty(probM1_p2)
prob_p2 = probM2_p2;
elseif isempty(probM2_p2)
prob_p2 = probM1_p2;
else
prob_p2 = bsxfun(@times,probM1_p2,probM2_p2);
end
% then multiply partition
if isempty(prob_p1)
prob_p = prob_p2(:);
elseif isempty(prob_p2)
prob_p = prob_p1(:);
else
prob_p_test = bsxfun(@times,prob_p1,prob_p2);
prob_p = prob_p_test(:);
end
prob_prod_vec{i,j,bf} = prob_p;
if (op_small_phi == 0)
phi = KLD(prob,prob_p);
elseif (op_small_phi == 1)
phi = emd_hat_gd_metric_mex(prob,prob_p,gen_dist_matrix(length(prob_p)));
elseif op_small_phi == 2
phi = k_distance(prob,prob_p);
elseif (op_small_phi == 3)
phi = L1norm(prob,prob_p);
end
else
phi = Inf;
end
if phi == 0
phi_zero_found = 1;
break
end
phi_cand(i,j,bf,1) = phi;
phi_cand(i,j,bf,2) = phi/Norm;
end
if phi_zero_found
break
end
end
if phi_zero_found
phi_MIP = 0;
else
[phi_MIP i j] = min2(phi_cand(:,:,bf,1),phi_cand(:,:,bf,2),op_normalize);
% prob_prod_MIP{bf} = prob_prod_vec{i,j,bf};
%
% MIP{1,1,bf} = denom_past_partitions_1{i};
% MIP{2,1,bf} = denom_past_partitions_2{i};
% MIP{1,2,bf} = num_numerator_partitions1{j};
% MIP{2,2,bf} = num_numerator_partitions2{j};
end
end
%% subfunctions
function Norm = Normalization(denom_part1,denom_part2,numerator_part1,numerator_part2,xf_1,xf_2)
if nargin == 4
Norm = min(length(numerator_part1),length(denom_part2)) + min(length(numerator_part2),length(denom_part1));
else
Norm = min(length(numerator_part1),length(denom_part2)) + min(length(numerator_part2),length(denom_part1)) ...
+ min(length(numerator_part1),length(xf_2)) + min(length(numerator_part2),length(xf_1));
end
end
function [phi_min_choice i_min j_min] = min2(phi,phi_norm,op_normalize)
phi_norm_min = Inf; % minimum of normalized phi
phi_min = Inf; % minimum of phi
i_min = 1;
j_min = 1;
epsilon = 10^-10;
if (op_normalize == 1 || op_normalize == 2)
for i=1: size(phi,1)
for j=1: size(phi,2)
% if phi_norm(i,j) <= phi_norm_min && phi(i,j) <= phi_min
dif = phi_norm_min - phi_norm(i,j);
if dif > epsilon || abs(dif) < epsilon %Larissa: instead of phi <= phi_min
phi_min = phi(i,j);
phi_norm_min = phi_norm(i,j);
i_min = i;
j_min = j;
end
end
end
else
for i=1: size(phi,1)
for j=1: size(phi,2)
dif = phi_min - phi(i,j);
if dif > epsilon || abs(dif) < epsilon
phi_min = phi(i,j);
phi_norm_min = phi_norm(i,j);
i_min = i;
j_min = j;
end
end
end
end
if (op_normalize == 0 || op_normalize == 1)
phi_min_choice = phi_min;
else
phi_min_choice = phi_norm_min;
end
end