%function [f,y] = varsketchpad(N)
function [f,y] = varsketchpad(N,v,tau,delta)
% minimize P{|X| > delta*N}
% given that the pdf > tau
% and var[X] > v

global X X2 del1 ix v0
X = -N:1:N;
X2 = X.^2;

del1 = delta*N
ix = find(abs(X)>=del1)
v = v0

xdim = length(X);
LB = zeros(xdim,1)+1e-9;
%UB = LB + 1;
UB = LB + tau;

Aeq = [];
% normalization
Aeq(1,:) = ones(1,xdim);
Beq(1,1) = 1;
% zero mean
Aeq(2,:) = X;
Beq(2,1) = 0;

f = ones(xdim,1)/xdim;
if any(f>tau)
  fprintf('tau = %1.5f is too small; must be at least %1.5f \n\n',tau,f(1));
  return
end

f = f + rand(size(f))*1e-5;
f = f/sum(f);

%[f,y] = fmincon(@myobj,f,[],[],Aeq,Beq,LB,UB,@mycon);
[f,y] = fmincon(@myobj,f,[],[],Aeq,Beq,LB,UB);
v = X2*f
return

% maximum variance
[f,y] = linprog(-X(:).^2,[],[],Aeq,Beq,LB,UB);
y = -y;
return


function y = myobj(f)
global ix
y = sum(f(ix));
return

function [C, Ceq] = mycon(f)
global X2 v0
C = v0-X2*f;
Ceq = 0;
return