function p2=euclidean2simplical(p3)
%%function p2=euclidean2simplical(p3)
%%
%% The function computes 2 dimensional coordinate on
%% the simplex given a three dimensional probability vector
%%
%% p3   Matrix whose columns are 3d probability vectors
%% p2   Matrix whose columns are 2d simplical vectors



if size(p3,1)==1,
    p3=p3';
end

p2=zeros(2,size(p3,2));

A=[-1,-.5;1,-.5;0 1];
t=[1;0;0];
for i=1:size(p3,2),
    p2(:,i)=pinv(A)*(p3(:,i)-t);
end
return