Vector4d compute_grad(Vector4d beta, VectorXd x, VectorXd y){
Vector4d grad;
ArrayXd tmp;
ArrayXd pred = model_fun(beta, x);
assert(x.size()==y.size());
// beta(0)
tmp = 1 / (1 + exp(-(x.array()-beta(2))/abs(beta(3))));
tmp *= pred - y.array();
grad(0) = tmp.sum() / x.size();
// beta(1)
tmp = 1 / (1 + exp(-(x.array()-beta(2))/abs(beta(3))));
tmp = 1 - tmp;
tmp *= pred - y.array();
grad(1) = tmp.sum() / x.size();
// beta(2)
tmp = -(beta(0)- beta(1)) * (exp((beta(2)-x.array())/abs(beta(3)))/abs(beta(3))) \
/ (1+exp((beta(2)-x.array())/abs(beta(3)))).pow(2);
tmp *= pred - y.array();
grad(2) = tmp.sum() / x.size();
// beta(3)
tmp = (beta(0) - beta(1)) * (beta(2)-x.array()).pow(2) * sgn(beta(3)) \
/ (abs(beta(3))*pow(beta(3), 2)*(1+exp((beta(2)-x.array())/abs(beta(3)))).pow(2));
tmp *= pred - y.array();
grad(3) = tmp.sum() / x.size();
return grad;
}
//@{
double gammaDist::aic (const ArrayXd& y, const ArrayXd& n, const ArrayXd& mu,
const ArrayXd& wt, double dev) const {
double nn(wt.sum());
double disp(dev/nn);
double ans(0), invdisp(1./disp);
for (int i = 0; i < mu.size(); ++i)
ans += wt[i] * ::Rf_dgamma(y[i], invdisp, mu[i] * disp, true);
return -2. * ans + 2.;
}
double MeanNormalLikelihood::logValue(RefArrayXd modelParameters)
{
unsigned long n = observations.size();
double lambda0;
double lambda;
ArrayXd argument;
ArrayXd predictions;
predictions.resize(n);
predictions.setZero();
model.predict(predictions, modelParameters);
argument = (observations - predictions);
argument = argument.square()*weights;
lambda0 = lgammal(n/2.) - log(2) - (n/2.)*log(Functions::PI) + 0.5*weights.log().sum();
lambda = lambda0 - (n/2.)*log(argument.sum());
return lambda;
}
double Functions::logGaussLikelihood(const RefArrayXd observations, const RefArrayXd predictions, const RefArrayXd uncertainties)
{
if ((observations.size() != predictions.size()) || (observations.size() != uncertainties.size()))
{
cerr << "Array dimensions do not match. Quitting program." << endl;
exit(EXIT_FAILURE);
}
ArrayXd delta;
ArrayXd lambda0;
ArrayXd lambda;
delta = ((observations - predictions)*(observations - predictions)) / (uncertainties*uncertainties);
lambda0 = -1.*log(sqrt(2.*PI) * uncertainties);
lambda = lambda0 -0.5*delta;
return lambda.sum();
}
//@{
double inverseGaussianDist::aic (const ArrayXd& y, const ArrayXd& n, const ArrayXd& mu,
const ArrayXd& wt, double dev) const {
double wtsum(wt.sum());
return wtsum * (std::log(dev/wtsum * 2. * M_PI) + 1.) + 3. * (y.log() * wt).sum() + 2.;
}