pair<double, MatrixXf> TargetProbEstimatorGivenBG::probify(const MatrixXf& scoremat) {
// initial guest at lambda
TargetProbFunction target_func(bgfreq, scoremat);
double lamb;
double fx;
for (lamb = 1. / scoremat.maxCoeff(); lamb < 50.; lamb *= 2.) {
fx = target_func.fx(lamb);
if (fx > 0) break;
}
// use Newton/Raphson method to find the optimal lambda
NewtonRaphsonRootFinder solver;
lamb = solver.find_root(target_func, lamb);
MatrixXf prob(scoremat.rows(), scoremat.cols());
prob = (bgfreq * bgfreq.transpose()).cwiseProduct((lamb * scoremat).unaryExpr(&exp));
return make_pair(lamb, prob);
}