kalmanFilter::kalmanFilter(arma::vec state, arma::mat transistion, arma::mat meas, arma::mat mNoise, arma::mat pNoise) {
stateEstimation = state;
transistionMatrix = transistion;
transistionMatrixT = transistion.i();
measurementMatrix = meas;
transistionMatrixT = meas.i();
measNoise = mNoise;
processNoise = pNoise;
sanityChecks();
std::cout << "Kalman filter object is created.\n";
}
void QUIC_SVD::ExtractSVD(arma::mat& u,
arma::mat& v,
arma::mat& sigma)
{
// Calculate A * V_hat, necessary for further calculations.
arma::mat projectedMat;
if (dataset.n_cols > dataset.n_rows)
projectedMat = dataset.t() * basis;
else
projectedMat = dataset * basis;
// Calculate the squared projected matrix.
arma::mat projectedMatSquared = projectedMat.t() * projectedMat;
// Calculate the SVD of the above matrix.
arma::mat uBar, vBar;
arma::vec sigmaBar;
arma::svd(uBar, sigmaBar, vBar, projectedMatSquared);
// Calculate the approximate SVD of the original matrix, using the SVD of the
// squared projected matrix.
v = basis * vBar;
sigma = arma::sqrt(diagmat(sigmaBar));
u = projectedMat * vBar * sigma.i();
// Since columns are sampled, the unitary matrices have to be exchanged, if
// the transposed matrix is not passed.
if (dataset.n_cols > dataset.n_rows)
{
arma::mat tempMat = u;
u = v;
v = tempMat;
}
}
// [[Rcpp::export]]
arma::vec Mahalanobis(arma::mat x, arma::rowvec center, arma::mat cov){
int n = x.n_rows;
arma::mat x_cen;
x_cen.copy_size(x);
for (int i=0; i < n; i++) {
x_cen.row(i) = x.row(i) - center;
}
return sum((x_cen * cov.i()) % x_cen, 1);
}
double mahalanobis(const arma::rowvec& x, const arma::rowvec& mu, const arma::mat& sigma) {
const arma::rowvec err = x - mu;
return arma::as_scalar(err * sigma.i() * err.t());
}
// [[Rcpp::export]]
List PCspatregMCMC(const arma::vec& y, const arma::mat& X, const arma::mat& K, const arma::uvec& sampleIndex,
const arma::vec& betaMean, const arma::mat& betaSig, const double& phiScale, const int& burn, const int& iter) {
int na = K.n_cols;
int nsite = X.n_rows;
int nb = X.n_cols;
int ns = y.n_elem;
arma::uvec idx = sampleIndex-1;
arma::mat Xsmp = X.rows(idx);
arma::mat Ksmp = K.rows(idx);
arma::mat betaStor(iter, nb, fill::zeros);
arma::mat alphaStor(iter, na, fill::zeros);
arma::vec phiStor(iter, fill::zeros);
arma::vec sigStor(iter, fill::zeros);
arma::mat predStor(iter, nsite);
// Beta items
arma::mat betaPrec = betaSig.i();
arma::mat V_beta_inv(nb, nb);
arma::vec v_beta(nb);
// Alpha items
arma::mat I(na,na, fill::eye);
arma::mat V_alpha_inv(na, na);
arma::vec v_alpha(na);
// phi items
arma::vec Kbar(ns);
double V_phi_inv;
double v_phi;
// Initial values
arma::vec beta(nb);
beta = solve(Xsmp.t() * Xsmp, Xsmp.t()*y);
double tau = (ns-1)/as_scalar((y - Xsmp*beta).t()*(y - Xsmp*beta));
double phi = 0;
arma::vec alpha(na, fill::zeros);
for(int i=0; i<iter+burn; i++){
// update beta
V_beta_inv = tau*Xsmp.t()*Xsmp + betaPrec;
v_beta = tau * Xsmp.t() * (y - phi*Ksmp*alpha) + betaPrec*betaMean;
beta = GCN(V_beta_inv, v_beta);
if(i>=burn){betaStor.row(i-burn) = beta.t();}
// update alpha
V_alpha_inv = phi*phi*tau*Ksmp.t()*Ksmp + I;
v_alpha = phi*tau*Ksmp.t()*(y-Xsmp*beta);
alpha = GCN(V_alpha_inv, v_alpha);
if(i>=burn){alphaStor.row(i-burn) = phi*alpha.t();}
// update phi
Kbar = Ksmp*alpha;
V_phi_inv = tau*as_scalar(Kbar.t()*Kbar) + 1/(phiScale*phiScale);
v_phi = tau*dot(Kbar, y-Xsmp*beta);
phi = as<double>(rnorm(1, v_phi/V_phi_inv, 1/sqrt(V_phi_inv)));
if(i>=burn) phiStor(i-burn) = phi;
// update tau
tau = as<double>(rgamma(1, ns/2, as_scalar((y-Xsmp*beta-phi*Ksmp*alpha).t()*(y-Xsmp*beta-phi*Ksmp*alpha))/2));
if(i>=burn) sigStor(i-burn) = 1/sqrt(tau);
// make prediction
if(i>=burn){
predStor.row(i-burn) = (X*beta + phi*K*alpha).t();
}
}
return Rcpp::List::create(
Rcpp::Named("beta") = betaStor,
Rcpp::Named("alpha") = alphaStor,
Rcpp::Named("phi")=phiStor,
Rcpp::Named("sigma")=sigStor,
Rcpp::Named("pred")=predStor
);
}