UniformDistribution

   Uniform probability on a continuous space.

   Generates a uniform distribution on the bounds defining the given
   continuous space.
   Right now, the output is a Gaussian mixture with a single component
   with a spherical covariance defined given the bounds of the space in
   each dimension.
   
   Parameters:
     CS: The continuous space where to define the probability
         distribution.
   Outputs:
     p: The Gaussian mixture.
     v: Value for the distribution in the continuous space. This is lower
        as the space gets larger. In principle this is the same value as
        that returned by UniformProbability but it could be slightly
        different since the returned distribution is only an approximation 
        of the uniform distribution and not the real one.

   See also @CSpace/UniformProbability.

0001 function [p v]=UniformDistribution(CS)
0002 %   Uniform probability on a continuous space.
0003 %
0004 %   Generates a uniform distribution on the bounds defining the given
0005 %   continuous space.
0006 %   Right now, the output is a Gaussian mixture with a single component
0007 %   with a spherical covariance defined given the bounds of the space in
0008 %   each dimension.
0009 %
0010 %   Parameters:
0011 %     CS: The continuous space where to define the probability
0012 %         distribution.
0013 %   Outputs:
0014 %     p: The Gaussian mixture.
0015 %     v: Value for the distribution in the continuous space. This is lower
0016 %        as the space gets larger. In principle this is the same value as
0017 %        that returned by UniformProbability but it could be slightly
0018 %        different since the returned distribution is only an approximation
0019 %        of the uniform distribution and not the real one.
0020 %
0021 %   See also @CSpace/UniformProbability.
0022 
0023   d=CS.max-CS.min;
0024   md=max(d);
0025   c=CS.min+d/2;
0026   g1=Gaussian(c,ones(CS.dim)*200*md);
0027   p=GMixture(1,{g1});
0028   v=Value(g1,CS.min);
0029