function [ estV,estFrac ] = sphereVolMC( dim,nn )
%sphereVolMC : MC for hypersphere volume
%   Monte Carlo estimate of volume of hypersphere in d dimensions
%   outputs the volume and the fraction of the corresponding hypercube
estV = 0.0;
for i=1:nn
    x = rand(dim,1);  % column vector with 'dim' random numbers
    xNorm2 = x' * x;  % squared norm of vector 
                      % (remember x' is transpose of x)
    if ( xNorm2  < 1 )
       estV = estV + 1;
    end
end
estV = estV/nn;
% this is the integral (volume of one "quadrant")
estFrac = estV;
% mult by 2^dim to get the vol of the full hypersphere
estV = estV * 2^dim;
end