rowvec dF2du(unsigned row, irowvec causes, const DataPairs &data, const gmat &sigma, vec u){
// Attaining variance covariance matrix etc. (conditional on u)
vmat cond_sig = sigma(causes);
vec cond_mean = cond_sig.proj*u;
rowvec alp = data.alpha_get(row, causes);
rowvec gam = data.gamma_get(row, causes);
colvec alpgam = alp.t() - gam.t();
double cdf = pn(alpgam, cond_mean, cond_sig.vcov);
vec ll = sqrt(diagvec(cond_sig.vcov));
mat Lambda = diagmat(ll);
mat iLambda = diagmat(1/ll);
mat R = iLambda*cond_sig.vcov*iLambda;
mat LR = Lambda*R;
double r = R(0,1);
vec ytilde = iLambda*(alpgam - cond_mean);
vecmat D = Dbvn(ytilde(0),ytilde(1),r);
mat M = -LR*D.V;
vec dcdfdu = trans(cond_sig.proj)*cond_sig.inv*M;
rowvec dF2du_1 = data.dpiduMarg_get(row, causes(0), 0)*data.piMarg_get(row, causes(1), 1)*cdf ;
rowvec dF2du_2 = data.dpiduMarg_get(row, causes(1), 1)*data.piMarg_get(row, causes(0), 0)*cdf;
vec dF2du_3 = data.piMarg_get(row, causes(0), 0)*data.piMarg_get(row, causes(1), 1)*dcdfdu;
rowvec dF2du = dF2du_1 + dF2du_2 + dF2du_3.t();
return(dF2du);
};
arma::rowvec bs_optim_calc(const arma::vec& theta,
const std::vector<std::string>& desc, const arma::field<arma::vec>& objdesc,
std::string model_type, const arma::vec& scales, const arma::mat& omega, unsigned int N,
double obj_value, double alpha,
std::string compute_v,
unsigned int K, unsigned int H, unsigned int G,
bool robust, double eff){
arma::field<arma::mat> bso = opt_n_gof_bootstrapper(theta,
desc, objdesc,
scales, model_type,
N, robust, eff, alpha,
H);
arma::mat cov_nu_nu_theta = bso(0);
arma::mat bs_obj_values = bso(1);
double optimism = 2*sum(diagvec(cov_nu_nu_theta * omega));
arma::rowvec temp(4);
temp(0) = obj_value;
temp(1) = optimism;
temp(2) = obj_value + optimism;
temp(3) = arma::as_scalar(bootstrap_gof_test(obj_value, bs_obj_values, alpha, false).row(0));
return temp;
}
void expectedArmaDiagvec() {
if(_colInd >= _genMat.n_cols) {
return;
}
cout << "- Compute expectedArmaDiagvec() ... ";
save<double>("Arma.diagvecSuper", diagvec(_genMat, _colInd));
cout << "done." << endl;
}
//' @title Generate the Confidence Interval for Theta Estimates
//' @description Create an Asymptotic CI for the Theta Estimates.
//' @param theta A \code{vec} containing the estimates
//' @param A A \code{mat} that is the first derivative matrix.
//' @param v_hat A \code{mat} that is the bootstrapped V matrix
//' @param omega A \code{mat} that is the inverse of the diagonal V matrix.
//' @param alpha A \code{double} that contains the confidence level.
//' @return A \code{mat} that has the first column
//' @backref src/inference.cpp
//' @backref src/inference.h
//' @keywords internal
// [[Rcpp::export]]
arma::mat theta_ci(const arma::vec& theta,
const arma::mat& A,
const arma::mat& v_hat, const arma::mat& omega, double alpha){
arma::mat psi = calculate_psi_matrix(A, v_hat, omega);
arma::vec se = sqrt(diagvec(psi));
return format_ci(theta, se, alpha);
}
rowvec Connectome::clusteringCoeff(const mat &W)
{
/*
The weighted clustering coefficient is the average "intensity" of
triangles around a node.
Input: NW, weighted undirected connection matrix
Output: C, clustering coefficient vector
Reference: Onnela et al. (2005) Phys Rev E 71:065103
*/
rowvec K = degree(W);
mat t = arma::pow(W,(1.0/3.0));
rowvec cyc3 = conv_to<rowvec>::from(diagvec(t*t*t));
K(find(cyc3 == 0)).fill(datum::inf);
return cyc3/(K%(K-1));
}
double Connectome::transitivity(const mat &W)
{
/*
Transitivity is the ratio of 'triangles to triplets' in the network.
(A classical version of the clustering coefficient).
Input: W weighted undirected connection matrix
Output: T transitivity scalar
Reference: Onnela et al. (2005) Phys Rev E 71:065103
*/
rowvec K = degree(W);
mat t = arma::pow(W,(1.0/3.0));
vec cyc3 = diagvec(t*t*t);
return accu(cyc3)/sum(K%(K-1));
}
AD::SXMatrix CasadiSystem::gauss_likelihood(const AD::SXMatrix& v) {
mat Sf = chol(this->R);
mat Sf_inv = inv(Sf);
int r_size = this->R.n_cols;
float C = pow(2*M_PI, r_size/2)*prod(diagvec(Sf));
AD::SXMatrix Sf_inv_casadi(r_size,r_size);
for(int i=0; i < r_size; ++i) {
for(int j=0; j < r_size; ++j) {
Sf_inv_casadi(i,j) = Sf_inv(i,j);
}
}
AD::SXMatrix M = mul(Sf_inv_casadi, v);
AD::SXMatrix E_exp_sum = exp(-0.5*mul(trans(M),M));
AD::SXMatrix w = E_exp_sum / C; // no need to normalize here because normalized later on anyways
return w;
}
