% This function plots the contours of likelihood values on the scatter plot of a 2 dimensional data.

function [xgrid,ygrid,Z] = biVariateContourPlotsGMMCopula(givenData,gmmObject,~,numMeshPoints,x_dim,y_dim)

%INPUT: givenData (MxN, M=number of points, N=Dimension) % : plo = binary variable (1 plot contour plot, 0 do not plot) %OUTPUT: xgrid,ygrid,Z ( Z contains the likelihood values of the points defined by xgrid and ygrid)

%load general_info;

d = 2;
   if nargin < 5
       x_dim = 1;
       y_dim = 2;
   end

if x_dim == y_dim
    hist(givenData(:,x_dim),10);
    return;
end

numMeshPoints = min(numMeshPoints,256);

givenData = givenData(:,[x_dim y_dim]);
alpha = gmmObject.alpha;
mu = gmmObject.mu(:,[x_dim y_dim]);
sigma = gmmObject.sigma([x_dim y_dim],[x_dim y_dim],:)   0.005*repmat(eye(d),[1 1 numel(alpha)]);

gmmObject = gmdistribution(mu,sigma,alpha);

bin_num = 256;
for j = 1:2
   l_limit = min(gmmObject.mu(:,j))-3*(max(gmmObject.Sigma(j,j,:))^0.5);
   u_limit = max(gmmObject.mu(:,j)) 3*(max(gmmObject.Sigma(j,j,:))^0.5);
   xmesh_inverse_space{j} = (l_limit:(u_limit-l_limit)/(bin_num-1):u_limit);
end

%if isempty(xmesh)||isempty(pdensity)||isempty(cdensity) % Following for loop does the non-parameteric estimation of marginal % densities if not provided

for i = 1:d
    currentVar = givenData(:,i);       

% finding non-parametric PDF values at prespecified mesh points

    [~,pdensity{i},xmesh{i}]=kde(currentVar,numMeshPoints);
    pdensity{i}(pdensity{i}<0) = 0;

% finding non-parametric CDF values cdensity{i} = cumsum(pdensity{i}); cdensity{i} = (cdensity{i}-min(cdensity{i}))/(max(cdensity{i})-min(cdensity{i})); % scaling the cdensity value to be between [0 1] end

%end

[xgrid,ygrid] = meshgrid(xmesh{1}(2:end-1),xmesh{2}(2:end-1));

for k = 1:d
    marginalLogLikelihood_grid{k} = log(pdensity{k}(2:end-1) eps);
    marginalCDFValues_grid{k} = cdensity{k}(2:end-1);
end
[marg1,marg2] = meshgrid(marginalLogLikelihood_grid{1},marginalLogLikelihood_grid{2});

[xg,yg] = meshgrid(marginalCDFValues_grid{1},marginalCDFValues_grid{2});
inputMatrix = [reshape(xg,numel(xg),1) reshape(yg,numel(yg),1)];


copulaLogLikelihoodVals = gmmCopulaPDF(inputMatrix,gmmObject,xmesh_inverse_space);
Z = reshape(copulaLogLikelihoodVals,size(marg1,1),size(marg1,2));
Z = Z marg1 marg2;

% Getting the likelihood value from the log-likelihood.

Z = exp(Z); 

min_level = min(min(Z))
max_level = max(max(Z))

plot(givenData(:,1),givenData(:,2),'b.','MarkerSize',3);hold
contour(xgrid,ygrid,Z,'LevelList',[min_level, max_level],'EdgeColor',[1 0 0]);

%title_string = ['GMCM fit (Log-Likelihood = ',num2str(logLikelihoodVal), ')']; %title(title_string,'FontSize',12,'FontWeight','demi');

axis tight;

plot i want to generate

CodePudding user response：

You can modify the contour line of code and use LevelList to specify the outer levels of z.

min_level = min(min(z))
max_level = max(max(z))

contour(x,y,z, 'LevelList', [min_level, max_level]);

MATLAB Doc for Contour: https://www.mathworks.com/help/matlab/ref/matlab.graphics.chart.primitive.contour-properties.html