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sippi_metropolis_gibbs_random_iteration_2d.m
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sippi_metropolis_gibbs_random_iteration_2d.m
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% sippi_metropolis_gibbs_random_iteration(C,mcmc,i);
% computes a 2D marginal (using Nm ranbdom voronois cells)
% and movies to a new realizations
%
% See also: sippi_metropolis_gibbs_random_iteration
%
function [C,mcmc]=sippi_metropolis_gibbs_random_iteration_2d(C,mcmc,i,doPlot);
mcmc.gibbs.null='';
if ~isfield(mcmc.gibbs,'Nm')
mcmc.gibbs.Nm=200;
end
if ~isfield(mcmc.gibbs,'useNN')
mcmc.gibbs.useNN=1;
end
if nargin<3, i=1; end
if nargin<4,
if (i/mcmc.i_plot)==round(i/mcmc.i_plot)
doPlot=1;
else
doPlot=0;
end
end
NC=length(C);
for ic=1:NC;
% CHECK NUMBER OF 1D PRIORS
if isfield(mcmc.gibbs,'i_pert');
usep = mcmc.gibbs.i_pert;
else
usep=[];
for ip=1:length(C{ic}.prior_current)
if (C{ic}.prior_current{ip}.ndim==0)
usep=[usep ip];
end
end
end
if length(usep)>1
% choose a random set of 2D marginal
ip=randomsample(usep,2);
sippi_verbose(sprintf('%s: Running Gibbs sampling of im=[%d,%d] at iteration %d',mfilename,ip(1),ip(2),mcmc.i),0)
prior = C{ic}.prior_current;
m = C{ic}.m_current;
% update which prior parameters to use
for j=1:length(prior);
if sum(ip==j)
prior{j}.perturb=1;
prior{j}.seq_gibbs.step=1;
else
prior{j}.perturb=0;
prior{j}.seq_gibbs.step=1;
end
end
% generate mcmc.gibbs.Nm realizations of the prior, and compute
% the corresponding likelihood of each.
m_arr=zeros(2,mcmc.gibbs.Nm);
logL=zeros(1,mcmc.gibbs.Nm);
pPrior=zeros(1,mcmc.gibbs.Nm);
for im=1:mcmc.gibbs.Nm;
if im==1;
% make sure current model is part of the tested models
m_test{im}=C{ic}.m_current;
prior_test{im}=C{ic}.prior_current;
else
[m_test{im},prior_test{im}]=sippi_prior(prior,m);
end
%[m_test{im},prior_test{im}]=sippi_prior(prior,m);
[d_test{im},forward]=sippi_forward(m_test{im},C{ic}.forward,prior_test{im},C{ic}.data);
[logL(im)]=sippi_likelihood(d_test{im},C{ic}.data);
%m_test{im};
m_arr(:,im) = [m_test{im}{ip}]';
end
% compute the prior probability
for iip=1:length(ip);
if (strcmp(lower(C{ic}.prior_current{ip(iip)}.type),'uniform'))
logPrior(iip,:)=ones(1,mcmc.gibbs.Nm)./mcmc.gibbs.Nm;
elseif (strcmp(lower(C{ic}.prior_current{ip(iip)}.type),'gaussian'))
logPrior(iip,:) = log(normpdf(m_arr(iip,:),C{ic}.prior_current{ip(iip)}.m0,C{ic}.prior_current{ip(iip)}.std));
end
end
if isfield(mcmc,'anneal')
[C{ic}.T_fac,mcmc]=sippi_anneal_temperature(i,mcmc,C{ic}.prior_current);
T=C{ic}.T_fac.*C{ic}.T;
else
T=C{ic}.T; % only use the 'base' temperature.
end
logPost = logL + sum(logPrior);
logPost = logL;
logPost_norm = logPost-max(logPost);
if mcmc.gibbs.useNN==1
%% Nearest Neighbor interpolate
% 1) Interpolate to 2D conditional probabiility
% 2) generate a relazation from the 2D
% 3) find the the precompute set of [m1,m2] closest to the
% simulated set an dchoose that as a realizations!
% Sometimes this measn the chain will move to a place with poor
% data fit!
if isfield(mcmc.gibbs,'Nn1');
Nn1 = mcmc.gibbs.Nn1;
else
Nn1=31;
end
if isfield(mcmc.gibbs,'Nn2');
Nn2 = mcmc.gibbs.Nn2;
else
Nn2=30;
end
m1 = linspace(min(m_arr(1,:)),max(m_arr(1,:)),Nn1);
m2 = linspace(min(m_arr(2,:)),max(m_arr(2,:)),Nn2);
im1=interp1([m1(1) m1(end)],[1 Nn1],m_arr(1,:));
im2=interp1([m2(1) m2(end)],[1 Nn2],m_arr(2,:));
[imm1,imm2]=meshgrid(1:Nn1,1:Nn2);
i_logPost_G=griddata(im1,im2,logPost,imm1,imm2,'nearest');
%logPost_G=griddata(m_arr(1,:),m_arr(2,:),logPost,mm1,mm2,'nearest');
P=exp( (1/T)* (i_logPost_G-max(i_logPost_G(:))) );
%keyboard
% sample from 2D pdf
[m1_sim,m2_sim,ir_1,ir_2]=sample_from_2d_pdf(P,m1,m2);
% Find closest match
w=max(m_arr')-min(m_arr');
%dx = max
for im=1:mcmc.gibbs.Nm;
dis(im) = sqrt( ((m_test{im}{ip(1)}-m1_sim)./(w(1)))^2 + ((m_test{im}{ip(2)}-m2_sim)./(w(2)))^2 );
end
im_use=find(dis==min(dis));
im_use=im_use(1);
else
%% USE A RANDOM ONE FO THE PROPOSED MODELS
P_acc = exp((1/T)*(logPost-max(logPost)));
Cum_P = cumsum(P_acc);
Cum_P = Cum_P./max(Cum_P);
dp=1/mcmc.gibbs.Nm;
p=[1:mcmc.gibbs.Nm]*dp;
r=rand(1);
%r=0.04
im_use = min(find(Cum_P>r));
im_use=im_use(1);
end
% Next line only for debugging
logL_old = C{ic}.logL_current;
% move to current model
prior_ref=C{ic}.prior_current;
C{ic}.prior_current=prior_test{im_use}; % NEEDED FOR GAUSSIAN TYPE PRIOR
% keep step length (all pars in seq Gibbs)
for im=1:length(prior_ref);
C{ic}.prior_current{im}.seq_gibbs=prior_ref{im}.seq_gibbs;
end
C{ic}.m_current=m_test{im_use};
C{ic}.d_current=d_test{im_use};
C{ic}.logL_current=logL(im_use);
C{ic}.L_current=logL(im_use);
C{ic}.iacc=C{ic}.iacc+1;
%C{ic}.mcmc.logL(C{ic}.iacc)=C{ic}.logL_current;
C{ic}.mcmc.acc(ip,mcmc.i)=1;
C{ic}.mcmc.logL(mcmc.i)=C{ic}.logL_current;
% Next 6 lines only for debugging
logL_new = C{ic}.logL_current;
%P_acc = min([2 exp(logL_new-logL_old)]);
%disp(sprintf('logL New/Old %5.3f/%5.3f, Pacc=%1.11f',logL_new, logL_old,P_acc))
%if P_acc<0.00001
% doPlot=1;
% keyboard
%end
%% plot
if mcmc.gibbs.useNN==1
if (doPlot==1)
figure_focus(63);
subplot(1,2,1);
imagesc(m1,m2,i_logPost_G);
hold on
plot(m_arr(1,:),m_arr(2,:),'r.');
plot(m1(ir_1),m2(ir_2),'g*')
hold off
xlabel(sprintf('m_%d',ip(1)))
ylabel(sprintf('m_%d',ip(2)))
title(sprintf('log(f(m_%d,m_%d | not)) at iteration %d',ip(1),ip(2),mcmc.i))
subplot(1,2,2);
imagesc(m1,m2,P);colormap(1-gray)
hold on
plot(m1(ir_1),m2(ir_2),'r.')
plot([m{ip(1)},C{ic}.m_current{ip(1)}],[m{ip(2)},C{ic}.m_current{ip(2)}],'r--')
plot(C{ic}.m_current{ip(1)},C{ic}.m_current{ip(2)},'r*')
plot(m{ip(1)},m{ip(2)},'g*')
hold off
xlabel(sprintf('m_%d',ip(1)))
ylabel(sprintf('m_%d',ip(2)))
title(sprintf('f(m_%d,m_%d | not) at iteration %d, T=%g',ip(1),ip(2),mcmc.i, T))
drawnow;
end
else
if (doPlot==1)
%%
figure_focus(63);
subplot(1,2,1);
plot(m_arr(1,:),m_arr(2,:),'k.','MarkerSize',10);hold on;;scatter(m_arr(1,:),m_arr(2,:),12,logPost,'filled');hold off
hold on
plot(m_arr(1,im_use),m_arr(2,im_use),'b*');
plot(m{ip(1)},m{ip(2)},'g*');
hold off
xlabel(sprintf('m_%d',ip(1)))
ylabel(sprintf('m_%d',ip(2)))
title(sprintf('log(f(m_%d,m_%d | not)) at iteration %d',ip(1),ip(2),mcmc.i))
colormap(gca,flipud(hot));
colorbar
subplot(1,2,2);
plot(m_arr(1,:),m_arr(2,:),'.','MarkerSize',1,'color',[.5 .5 .5]);
hold on;;
try
scatter(m_arr(1,:),m_arr(2,:),P_acc*100+.01,P_acc,'filled');
end
plot(m_arr(1,im_use),m_arr(2,im_use),'b*');
plot(m{ip(1)},m{ip(2)},'g*');
hold off
colormap(gca,flipud(hot));
colorbar
xlabel(sprintf('m_%d',ip(1)))
ylabel(sprintf('m_%d',ip(2)))
title(sprintf('f(m_%d,m_%d | not) at iteration %d, T=%g',ip(1),ip(2),mcmc.i, T))
%hold on
drawnow;
end
end
else
sippi_verbose(sprintf('%s: cannot perfomr Gibbs sampling on selected priors',mfilename));
end
end