function [pfa, vt] = threshold (nfa, np)
% This function calculates the threshold value from nfa and np.
% The newton-Raphson  recursive formula is used
% This function uses "incomplete_gamma.m".
delmax = .00001;
eps = 0.000000001;
delta =10000.;
pfa = np * log(2) / nfa;
sqrtpfa = sqrt(-log10(pfa));
sqrtnp = sqrt(np); 
vt0 = np - sqrtnp + 2.3 * sqrtpfa * (sqrtpfa + sqrtnp - 1.0);
vt = vt0;
while (abs(delta) >= vt0)
   igf = incomplete_gamma(vt0,np);
   num = 0.5^(np/nfa) - igf;
   temp = (np-1) * log(vt0+eps) - vt0 - factor(np-1);
   deno = exp(temp);
   vt = vt0 + (num / (deno+eps));
   delta = abs(vt - vt0) * 10000.0; 
   vt0 = vt;
end