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phi_comp_bf.m
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phi_comp_bf.m
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function [phi_MIP prob prob_prod_MIP MIP network] = phi_comp_bf(subsystem,numerator,denom_past,denom_future,whole_sys_state,network)
% compute small phi of a given purview...?
%
% 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
op_normalize = network.options(14);
op_small_phi = network.options(16);
% global FRs, global b_table
% global BRs_check, global FRs_check
% global BRs_check2, global FRs_check2
% eps = 1e-10;
% global func_time, global inline_time
% global cpt_time tpm_time
% global nodes
num_nodes_denom_past = length(denom_past);
num_nodes_numerator = length(numerator);
num_nodes_denom_future = length(denom_future);
%% unpartitioned transition repertoire
% BRs = cell(2^N,2^N);
% current_convi = convi(numerator); past_convi = convi(denom_past); future_convi = convi(denom_future);
current = sum(2.^(numerator-1))+1; past = sum(2.^(denom_past-1))+1; future = sum(2.^(denom_future-1))+1;
% if (current_convi ~= current) || (past_convi ~= past) || (future_convi ~= future)
% disp('ERROR!')
% end
% current = numerator; past = denom_past; future = denom_future;
if isempty(network.BRs{current,past})
% tic
network.BRs{current,past} = comp_pers_cpt(network.nodes,numerator,denom_past,whole_sys_state,'backward');
% cpt_time = cpt_time + toc;
% disp('old')
% tic
% network.BRs_check{current,past} = comp_pers_single(numerator,denom_past,whole_sys_state,p,1);
% tpm_time = tpm_time + toc;
% BRs{current,past} = comp_pers_single(numerator,denom_past,whole_sys_state,p,1);
% if ~all(abs(BRs{current,past} - BRs_check{current,past}) <= eps)
% disp('BR CHECK:')
% disp(numerator)
% disp(denom_past)
% disp(BRs{current,past})
% disp(BRs_check{current,past})
% disp(BRs{current,past}(:) == BRs_check{current,past}(:))
% end
end
prob_bw = network.BRs{current,past};
if isempty(network.FRs{current,future})
% tic
network.FRs{current,future} = comp_pers_cpt(network.nodes,numerator,denom_future,whole_sys_state,'forward');
% cpt_time = cpt_time + toc;
% tic
% FRs_check{current,future} = comp_pers_single(numerator,denom_future,whole_sys_state,p,2);
% tpm_time = tpm_time + toc;
% disp('new result:')
% disp(size(FRs{current,future}))
% % disp(FRs{current,future}(:))
% disp('check result:')
% disp(size(FRs_check{current,future}))
% disp(FRs_check{current,future})
% if ~all(abs(FRs{current,future} - FRs_check{current,future}) <= eps)
% disp('FR CHECK:')
% disp(numerator)
% disp(denom_past)
% disp(FRs{current,future})
% disp(FRs_check{current,future})
% disp(FRs_check2{current,future})
% disp(FRs{current,future}(:) == FRs_check{current,future}(:))
% end
end
prob_fw = network.FRs{current,future};
prob = cell(2,1);
prob{1} = prob_bw(:);
prob{2} = prob_fw(:);
%% more than one
if num_nodes_denom_past ~= 0
[denom_past_partitions_1 denom_past_partitions_2 num_denom_partitions] = bipartition(denom_past,num_nodes_denom_past); % partition of denom_past
else
denom_past_partitions_1{1} = []; denom_past_partitions_2{1} = []; num_denom_partitions = 1;
end
% if num_nodes_denom_future ~= 0
% [xf_b1 xf_b2 Nf_b] = bipartition(denom_future,num_nodes_denom_future); % partition of denom_future
% else
% xf_b1{1} = []; xf_b2{1} = []; Nf_b = 1;
% end
[num_numerator_partitions1 num_numerator_partitions2 num_numerator_partitions] = bipartition(numerator,num_nodes_numerator,1); % partition of numerator
MIP = cell(2,2,2);
phi_MIP = zeros(1,2);
prob_prod_MIP = cell(2,1);
phi_cand = zeros(num_denom_partitions,num_numerator_partitions,2,2);
prob_prod_vec = cell(num_denom_partitions,num_numerator_partitions,2);
for bf = 1:2 % past and future
phi_zero_found = 0;
for i = 1:num_denom_partitions % past or future
denom_part1 = denom_past_partitions_1{i};
denom_part2 = denom_past_partitions_2{i};
for j = 1:num_numerator_partitions % present
numerator_part1 = num_numerator_partitions1{j};
numerator_part2 = num_numerator_partitions2{j};
Norm = Normalization(denom_part1,denom_part2,numerator_part1,numerator_part2);
% if (all(numerator == [1 2]) && all(denom_past == [1 2]))
% disp('numerator_part1:')
% disp(numerator_part1)
% disp('numerator_part2:')
% disp(numerator_part2)
% disp('denom_part1:')
% disp(denom_part1)
% disp('denom_part2:')
% disp(denom_part2)
% disp('Norm:')
% disp(Norm)
% end
% current_1_convi = convi(numerator_part1);
% current_2_convi = convi(numerator_part2);
% other_1_convi = convi(denom_part1);
% other_2_convi = convi(denom_part2);
current_1 = sum(2.^(numerator_part1-1))+1;
current_2 = sum(2.^(numerator_part2-1))+1;
other_1 = sum(2.^(denom_part1-1))+1;
other_2 = sum(2.^(denom_part2-1))+1;
% if (current_1_convi ~= current_1) || (current_2_convi ~= current_2) || (other_1_convi ~= other_1) || (other_2 ~= other_2_convi)
% disp('ERROR!')
% end
% current_1 = numerator_part1;
% current_2 = numerator_part2;
% other_1 = denom_part1;
% other_2 = denom_part2;
if Norm ~= 0
if bf == 1
if isempty(network.BRs{current_1,other_1})
% tic
network.BRs{current_1,other_1} = comp_pers_cpt(network.nodes,numerator_part1,denom_part1,whole_sys_state,'backward');
% cpt_time = cpt_time + toc;
% % disp('old')
% tic
% BRs_check{current_1,other_1} = comp_pers_single(numerator_part1,denom_part1,whole_sys_state,p,1);
% tpm_time = tpm_time + toc;
% if ~all(abs(BRs{current_1,other_1} - BRs_check{current_1,other_1}) <= eps)
% disp('BR CHECK:')
% disp(numerator_part1)
% disp(denom_part1)
% disp(BRs{current_1,other_1})
% disp(BRs_check{current_1,other_1})
% disp(BRs{current_1,other_1}(:) == BRs_check{current_1,other_1}(:))
% end
end
prob_p1 = network.BRs{current_1,other_1};
if isempty(network.BRs{current_2,other_2})
% tic
network.BRs{current_2,other_2} = comp_pers_cpt(network.nodes,numerator_part2,denom_part2,whole_sys_state,'backward');
% cpt_time = cpt_time + toc;
% % disp('old')
% tic
% BRs_check{current_2,other_2} = comp_pers_single(numerator_part2,denom_part2,whole_sys_state,p,1);
% tpm_time = tpm_time + toc;
% if ~all(abs(BRs{current_2,other_2} - BRs_check{current_2,other_2}) <= eps)
% disp('BR CHECK:')
% disp(numerator_part2)
% disp(denom_part2)
% disp(BRs{current_2,other_2})
% disp(BRs_check{current_2,other_2})
% disp(BRs{current_2,other_2}(:) == BRs_check{current_2,other_2}(:))
% end
end
prob_p2 = network.BRs{current_2,other_2};
else
if isempty(network.FRs{current_1,other_1})
% tic
network.FRs{current_1,other_1} = comp_pers_cpt(network.nodes,numerator_part1,denom_part1,whole_sys_state,'forward');
% cpt_time = cpt_time + toc;
% tic
% FRs_check{current_1,other_1} = comp_pers_single(numerator_part1,denom_part1,whole_sys_state,p,2);
% tpm_time = tpm_time + toc;
%
% if ~all(abs(FRs{current_1,other_1} - FRs_check{current_1,other_1}) <= eps)
% disp('FR CHECK:')
% disp(numerator_part1)
% disp(denom_part1)
% % disp('new result')
% disp(FRs{current_1,other_1})
% % disp('old result')
% disp(FRs_check{current_1,other_1})
% disp(FRs_check2{current_1,other_1})
% disp(FRs{current_1,other_1}(:) == FRs_check{current_1,other_1}(:))
% end
end
prob_p1 = network.FRs{current_1,other_1};
if isempty(network.FRs{current_2,other_2})
% tic
network.FRs{current_2,other_2} = comp_pers_cpt(network.nodes,numerator_part2,denom_part2,whole_sys_state,'forward');
% cpt_time = cpt_time + toc;
% tic
% FRs_check{current_2,other_2} = comp_pers_single(numerator_part2,denom_part2,whole_sys_state,p,2);
% tpm_time = tpm_time + toc;
%
% if ~all(abs(FRs{current_2,other_2} - FRs_check{current_2,other_2}) <= eps)
% disp('FR CHECK:')
% disp(numerator_part2)
% disp(denom_part2)
% disp(FRs{current_2,other_2})
% disp(FRs_check{current_2,other_2})
% disp(FRs_check2{current_2,other_2})
% disp(FRs{current_2,other_2}(:) == FRs_check{current_2,other_2}(:))
% end
end
prob_p2 = network.FRs{current_2,other_2};
end
% if exist('prob_prod_comp','file') == 3
% % tic
% prob_p = prob_prod_comp(prob_p1(:),prob_p2(:),denom_past,denom_part1,0); % ADDED (:)
% % func_time = func_time + toc;
%
% else
% tic
if isempty(prob_p1)
prob_p = prob_p2(:);
elseif isempty(prob_p2)
prob_p = prob_p1(:);
else
% prob_p_test = (expand_prob(prob_p1,denom_past,denom_part1) .* expand_prob(prob_p2,denom_past,denom_part2));
% prob_p_test = prob_p_test(:)/sum(prob_p_test);
% prob_p1_reshape = reshape(prob_p1,
% repmat_vec = ones(1,N);
% repmat_vec(denom_part2) = 2;
% prob_p1_rep = repmat(prob_p1,repmat_vec);
% repmat_vec = ones(1,N);
% repmat_vec(denom_part1) = 2;
% prob_p2_rep = repmat(prob_p2,repmat_vec) ;
% prob_p_test = prob_p1_rep .* prob_p2_rep;
% prob_p_test = prob_p_test(:);
prob_p_test = bsxfun(@times,prob_p1,prob_p2);
prob_p = prob_p_test(:);
% if ~all(prob_p_test == prob_p_test2(:))
% disp('***NOPE***')
% end
% prob_p_test = prob_p1(:) * prob_p2(:)';
% prob_p_test = prob_p_test(:)
end
% cpt_time = cpt_time + toc;
% end
% if ~all(abs(prob_p - prob_p_test) <= 1e-5)
% disp('PROB CHECK:')
% disp(abs(prob_p - prob_p_test) <= 1e-5)
% disp('****************')
% disp('****************')
% disp('present part 1:')
% disp(numerator_part1)
% disp('other part 1:')
% disp(denom_part1)
% disp('present part 2:')
% disp(numerator_part2)
% disp('other part 2:')
% disp(denom_part2)
% disp(prob_p1)
% disp(prob_p2)
% disp(prob_p)
% disp(prob_p_test)
% disp('****************')
% % else
% % disp('present part 1:')
% % disp(numerator_part1)
% % disp('other part 1:')
% % disp(denom_part1)
% % disp('present part 2:')
% % disp(numerator_part2)
% % disp('other part 2:')
% % disp(denom_part2)
% % disp(prob_p1)
% % disp(prob_p2)
% % disp(prob_p)
% % disp(prob_p_test)
% end
prob_prod_vec{i,j,bf} = prob_p;
if (op_small_phi == 0)
phi = KLD(prob{bf},prob_p);
% phi2 = KLD_old(prob{bf},prob_p);
% if (phi ~= phi2)
% disp('ERRROR')
% disp(phi)
% disp(phi2)
% disp(prob{bf})
% disp(prob_p)
% end
% % prob_whole = prob{bf};
% prob_p(prob_p==0) = 1; % avoid log0 when computing entropy
% H1 = - sum(prob_whole.*log2(prob_p)) ;
%
% prob_whole(prob_whole==0) = 1;
% H2 = - sum(prob_whole.*log2(prob_whole));
% phi = H1 - H2;
elseif (op_small_phi == 1)
phi = emd_hat_gd_metric_mex(prob{bf},prob_p,gen_dist_matrix(length(prob_p)));
elseif op_small_phi == 2
phi = k_distance(prob{bf},prob_p);
elseif (op_small_phi == 3)
phi = L1norm(prob{bf},prob_p);
end
else
prob_prod_vec{i,j,bf} = [];
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;
% if (all(numerator == [1 2]) && all(denom_past == [1 2])) && (Norm ~= 0)
% disp('bf:')
% disp(bf)
% disp('full dist')
% disp(prob{bf})
% disp('part dist')
% disp(prob_p)
% disp('phi:')
% disp(phi)
% disp('phi_norm')
% disp(phi/Norm)
% end
end
if phi_zero_found
break
end
end
if phi_zero_found
phi_MIP(bf) = 0;
else
[phi_MIP(bf) 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
end
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 [X_min i_min j_min k_min] = min3(X,X2,op_normalize)
X_min = Inf; % minimum of normalized phi (or unnormalized if op_normalize == 0)
X_min2 = Inf; % minimum of phi
i_min = 1;
j_min = 1;
k_min = 1;
if (op_normalize == 1)
for i=1: size(X,1)
for j=1: size(X,2)
for k=1: size(X,3)
if X(i,j,k) <= X_min && X2(i,j,k) <= X_min2
X_min = X(i,j,k);
X_min2 = X2(i,j,k);
i_min = i;
j_min = j;
k_min = k;
end
end
end
end
else
for i=1: size(X,1)
for j=1: size(X,2)
for k=1: size(X,3)
if X2(i,j,k) <= X_min
% X_min = X(i,j,k);
X_min = X2(i,j,k);
i_min = i;
j_min = j;
k_min = k;
end
end
end
end
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