refined ch02. logMn needs to be checked

chapter02/logDirichlet.m

@@ -1,9 +1,11 @@
 function y = logDirichlet(X, a)
 % Compute log pdf of a Dirichlet distribution.
 % Input:
-%   X: d x n data matrix satifying (sum(X,1)==ones(1,n) && X>=0)
-%   a: d x k parameters
+%   X: d x n data matrix, each column sums to one (sum(X,1)==ones(1,n) && X>=0)
+%   a: d x k parameter of Dirichlet
 %   y: k x n probability density
+% Output:
+%   y: k x n probability density in logrithm scale y=log p(x)
 % Written by Mo Chen ([email protected]).
 X = bsxfun(@times,X,1./sum(X,1));
 if size(a,1) == 1

chapter02/logGauss.m

@@ -1,5 +1,11 @@
 function y = logGauss(X, mu, sigma)
 % Compute log pdf of a Gaussian distribution.
+% Input:
+%   X: d x n data matrix
+%   mu: mean of Gaussian
+%   sigma: variance of Gaussian
+% Output:
+%   y: probability density in logrithm scale y=log p(x)
 % Written by Mo Chen ([email protected]).
 
 [d,n] = size(X);

chapter02/logKde.m

@@ -1,5 +1,10 @@
 function z = logKde (X, Y, sigma)
 % Compute log pdf of kernel density estimator.
+% Input:
+%   X: d x n data matrix to be evaluate
+%   Y: d x k data matrix served as database
+% Output:
+%   z: probability density in logrithm scale z=log p(x|y)
 % Written by Mo Chen ([email protected]).
 D = bsxfun(@plus,full(dot(X,X,1)),full(dot(Y,Y,1))')-full(2*(Y'*X));
-z = logSumExp(D/(-2*sigma^2),1)-0.5*log(2*pi)-log(sigma*size(Y,2));
+z = logsumexp(D/(-2*sigma^2),1)-0.5*log(2*pi)-log(sigma*size(Y,2),1);

chapter02/logMn.m

@@ -1,11 +1,16 @@
 function z = logMn (x, p)
 % Compute log pdf of a multinomial distribution.
+% Input:
+%   x: d x n data matrix
+%   p: 1 x k probability
+% Output:
+%   z: probability density in logrithm scale z=log p(x)
 % Written by Mo Chen ([email protected]).    
-    if numel(x) ~= numel(p)
-        n = numel(x);
-        x = reshape(x,1,n);
-        [u,~,label] = unique(x);
-        x = full(sum(sparse(label,1:n,1,n,numel(u),n),2));
-    end
-    z = gammaln(sum(x)+1)-sum(gammaln(x+1))+dot(x,log(p));
-endfunction
+if numel(x) ~= numel(p)
+    n = numel(x);
+    x = reshape(x,1,n);
+    label = zeros(1,n);
+    [u,~,label(:)] = unique(x);
+    x = full(sum(sparse(label,1:n,1,n,numel(u),n),2));
+end
+z = gammaln(sum(x)+1)-sum(gammaln(x+1))+dot(x,log(p));

chapter02/logMvGamma.m

@@ -1,7 +1,13 @@
 function y = logMvGamma(x,d)
-% Compute logarithm multivariate Gamma function.
-% Gamma_p(x) = pi^(d(d-1)/4) \prod_(j=1)^d Gamma(x+(1-j)/2)
-% log(Gamma_p(x)) = d(d-1)/4 log(pi) + \sum_(j=1)^d log(Gamma(x+(1-j)/2))
+% Compute logarithm multivariate Gamma function 
+% which is used in the probability density function of the Wishart and inverse Wishart distributions.
+% Gamma_d(x) = pi^(d(d-1)/4) \prod_(j=1)^d Gamma(x+(1-j)/2)
+% log(Gamma_d(x)) = d(d-1)/4 log(pi) + \sum_(j=1)^d log(Gamma(x+(1-j)/2))
+% Input:
+%   x: m x n data matrix
+%   d: dimension
+% Output:
+%   y: m x n logarithm multivariate Gamma
 % Written by Michael Chen ([email protected]).
 s = size(x);
 x = reshape(x,1,prod(s));

chapter02/logSt.m

@@ -1,5 +1,12 @@
 function y = logSt(X, mu, sigma, v)
 % Compute log pdf of a Student's t distribution.
+% Input:
+%   X: d x n data matrix
+%   mu: mean
+%   sigma: variance
+%   v: degree of freedom
+% Output:
+%   y: probability density in logrithm scale y=log p(x)
 % Written by mo Chen ([email protected]).
 [d,k] = size(mu);
 

chapter02/logVmf.m

@@ -1,5 +1,11 @@
 function y = logVmf(X, mu, kappa)
 % Compute log pdf of a von Mises-Fisher distribution.
+% Input:
+%   X: d x n data matrix
+%   mu: d x k mean
+%   kappa: 1 x k variance
+% Output:
+%   y: k x n probability density in logrithm scale y=log p(x)
 % Written by Mo Chen ([email protected]).
 d = size(X,1);
 c = (d/2-1)*log(kappa)-(d/2)*log(2*pi)-logbesseli(d/2-1,kappa);

chapter02/logWishart.m

@@ -1,5 +1,11 @@
-function y = logWishart(Sigma, v, W)
+function y = logWishart(Sigma, W, v)
 % Compute log pdf of a Wishart distribution.
+% Input:
+%   Sigma: d x d covariance matrix
+%   W: d x d covariance parameter
+%   v: degree of freedom
+% Output:
+%   y: probability density in logrithm scale y=log p(Sigma)
 % Written by Mo Chen ([email protected]).
 d = length(Sigma);
 B = -0.5*v*logdet(W)-0.5*v*d*log(2)-logmvgamma(0.5*v,d);