wehub-resource-sync
41 lines
1.3 KiB
Matlab
Executable File
41 lines
1.3 KiB
Matlab
Executable File
function y = logSt(X, mu, sigma, v)
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% Compute log pdf of a Student's t distribution.
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% Input:
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% X: d x n data matrix
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% mu: mean
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% sigma: variance
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% v: degree of freedom
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% Output:
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% y: probability density in logrithm scale y=log p(x)
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% Written by mo Chen (sth4nth@gmail.com).
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[d,k] = size(mu);
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if size(sigma,1)==d && size(sigma,2)==d && k==1
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[R,p]= chol(sigma);
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if p ~= 0
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error('ERROR: sigma is not SPD.');
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end
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X = bsxfun(@minus,X,mu);
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Q = R'\X;
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q = dot(Q,Q,1); % quadratic term (M distance)
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o = -log(1+q/v)*((v+d)/2);
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c = gammaln((v+d)/2)-gammaln(v/2)-(d*log(v*pi)+2*sum(log(diag(R))))/2;
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y = c+o;
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elseif size(sigma,1)==d && size(sigma,2)==k
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lambda = 1./sigma;
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ml = mu.*lambda;
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q = bsxfun(@plus,X'.^2*lambda-2*X'*ml,dot(mu,ml,1)); % M distance
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o = bsxfun(@times,log(1+bsxfun(@times,q,1./v)),-(v+d)/2);
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c = gammaln((v+d)/2)-gammaln(v/2)-(d*log(pi*v)+sum(log(sigma),1))/2;
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y = bsxfun(@plus,o,c);
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elseif size(sigma,1)==1 && size(sigma,2)==k
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X2 = repmat(dot(X,X,1)',1,k);
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D = bsxfun(@plus,X2-2*X'*mu,dot(mu,mu,1));
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q = bsxfun(@times,D,1./sigma); % M distance
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o = bsxfun(@times,log(1+bsxfun(@times,q,1./v)),-(v+d)/2);
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c = gammaln((v+d)/2)-gammaln(v/2)-d*log(pi*v.*sigma)/2;
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y = bsxfun(@plus,o,c);
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else
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error('Parameters are mismatched.');
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end
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