clc

seed = 7;
disp(['setting seed ',num2str(seed)])
rng(seed)

nn=1000
dim=2
lambda=2.5
points = zeros(nn,dim);
tic
for i=1:nn
    % random column vector
    p = ranExp(dim,lambda);
    % transpose to get a row vector
    p = p';
    % set the ith row of "points" to be equal to p
    points(i,:) = p;
end
toc
points(1:5,:)

hold off 
% this is how to plot points whose x and y components are the
% first two columns of a matrix
plot( points(:,1),points(:,2), 'ko' )

print -dpdf 'points.pdf' -bestfit

% uncommment the rest to test the importance sampling

% how many points to use ?
n=100000;  
% what dimension ?  (eg try 20 or 30)
dim = 20;
% how many repeats for each value of lambda ?
mm=20;

% values of lambda to try, for importance sampling
lambdaVals = [ 0,1,3,5,8 ]


disp(['dimension ',num2str(dim),', n is ',num2str(n)])
exV = exactVol(dim);
disp(['exact is ',num2str( exV ), ...
    ' fraction of cube ',num2str(exV/2^dim)])

 tic
% this is how we loop over list elements in matlab
for lambda = lambdaVals
    % do the calculation m times and check mean/variance
    estMean  = 0;
    estMean2 = 0;
    for i=1:mm
        [estV,estScaled] = sphereVolMCImpExp(dim,n,lambda);
        estV; 
        estMean = estMean + estV;
        estMean2 = estMean2 + estV*estV;
    end
    estMean  = estMean  / mm;
    estMean2 = estMean2 / mm;
    stdDev = sqrt( estMean2 - estMean*estMean );
    disp(['lambda is ',num2str(lambda),' mean ',num2str(estMean), ...
          ' std dev ',num2str(stdDev)])
end
toc