//' @title Create a taper setup for an Eigen sparse matrix
//' @description Generate the storage information we'll need to create a sparse eigen matrix
//' @param d A \code{matrix} that is a symmetric distance matrix.
//' @param taprange A \code{double} that is used to specify the gamma.
//' @return A \code{list}
//' \itemize{
//' \item \code{n} - row/col of matrix
//' \item \code{good.dists} - distances that meet tapering requirements
//' \item \code{taps} - results of applying the taper function
//' \item \code{ja} - column index
//' \item \code{ia} - row index
//' }
//' @details This function is meant to be used to create SPAM matrices.
//' The function formats data so that it can be used with a compressed sparse column format.
//' Do not use output for Eigen matrices.
//' @examples
//' data(anom1962)
//' d = rdist_earth1(head(loc))
//' make_tapersetup_eigen(d, 20)
// [[Rcpp::export]]
Rcpp::List make_tapersetup_eigen(arma::mat d, double taprange){
double n = d.n_rows;
// Find elements that are less than taprange and return element ids.
arma::uvec inrange_id = find(d < taprange);
// Approximate how many zero entries exist per columnss
int rescol = floor(double(inrange_id.n_elem) / n);
// Obtain the small distance elements
arma::vec good_dists = d.elem(inrange_id);
// Apply taper function
arma::vec taps = wendland2_1(good_dists, taprange);
// Create a row index matrix and extract out ranges
arma::vec ja = row_arma(d).elem(inrange_id) - 1;
// Create a col index matrix and extract the ranges
arma::vec ia = col_arma(d).elem(inrange_id) - 1;
// Export results as an R list object
return Rcpp::List::create(
Rcpp::Named("n") = n,
Rcpp::Named("good.dists") = good_dists,
Rcpp::Named("taps") = taps,
Rcpp::Named("ja") = ja,
Rcpp::Named("ia") = ia,
Rcpp::Named("rescol") = rescol);
}
//[[Rcpp::export]]
Rcpp::List changeNA(arma::mat X) {
NumericVector x(X.begin(), X.end());
int n = x.size();
IntegerVector y = seq_len(n)-1;//(x.begin(), x.end());
IntegerVector z = y[is_na(x)];
if(z.size()==0){
std::cout << "Nenhum valor faltante.\n";
SEXP xNULL = R_NilValue;
return Rcpp::List::create(xNULL);
} else{
arma::uvec Xna = as<arma::uvec>(z);
NumericVector bx(Xna.n_rows, 100.0);
arma::vec b = as<arma::vec>(bx);
X.elem(Xna) = b;
return Rcpp::List::create(X);
}
}
//' @title Create a taper setup for a SPAM matrix
//' @description Get the storage information we'll need to create a sparse matrix
//' @param d A \code{matrix} that is a symmetric distance matrix.
//' @param taprange A \code{double} that is used to specify the gamma.
//' @return A \code{list}
//' \itemize{
//' \item \code{n} - row/col of matrix
//' \item \code{good.dists} - distances that meet tapering requirements
//' \item \code{taps} - results of applying the taper function
//' \item \code{ja} - ordered column indices
//' \item \code{ia} - pointer to the beginning of each row in the arrays entries and colindices
//' \item \code{index} - element position in matrix
//' }
//' @details This function is meant to be used to create SPAM matrices.
//' Do not use output for Eigen matrices.
//' @examples
//' data(anom1962)
//' d = rdist_earth1(head(loc))
//' make_tapersetup_R(d, 20)
// [[Rcpp::export]]
Rcpp::List make_tapersetup_R(arma::mat d, double taprange){
unsigned int n = d.n_rows;
// Find elements that are less than (logical matrix e.g. 0/1's)
arma::umat inrange = d < taprange;
// Same idea, but return element ids.
arma::uvec inrange_id = find(inrange);
// Convert matrix to allow operations
arma::mat temp = arma::conv_to<arma::mat>::from(inrange);
// Obtain the small distance elements
arma::vec good_dists = d.elem(inrange_id);
// Apply taper function (this cannot be made dynamic)
arma::vec taps = wendland2_1(good_dists, taprange);
// Create ordered column indices of the nonzero values
arma::vec ja = row_arma(d).elem(inrange_id);
// Calculate pointer to the beginning of each row in the arrays' entries and colindices
arma::vec ia(inrange.n_rows + 1);
ia(0) = 1;
ia.rows(1,inrange.n_rows) = 1 + arma::cumsum(arma::sum(temp,1));
// Create a column index matrix and isolate ideal elements
arma::vec index = (col_arma(d).elem(inrange_id) - 1) * n + ja;
// Export results as an R list object
return Rcpp::List::create(
Rcpp::Named("n") = n,
Rcpp::Named("good_dists") = good_dists,
Rcpp::Named("taps") = taps,
Rcpp::Named("ja") = ja,
Rcpp::Named("ia") = ia,
Rcpp::Named("index") = index);
}
void getEystar_endorseIRT (const arma::mat &alpha,
const arma::mat &beta,
const arma::mat &w,
const arma::mat &theta,
const arma::mat &gamma,
const arma::mat &y,
const int N,
const int J,
arma::mat &ystars,
const arma::mat &theta2,
const arma::mat &w2
) {
// arma::mat ystars(N, J, arma::fill::zeros) ;
// Main Calculation
#pragma omp parallel for
for (int n = 0; n < N; n++) {
arma::mat theseystars = arma::mat(1, J, arma::fill::zeros) ;
for (int j = 0; j < J; j++) {
// defaults to untruncated
double low = y(n,j) == 1 ? 0.0 : R_NegInf ;
double high = y(n,j) == 0 ? 0.0 : R_PosInf ;
// mu
double mu =
alpha(j, 0) +
beta(n, 0) -
gamma(0, 0) * (
pow(theta(n, 0), 2) +
pow(w(j, 0), 2) -
2 * theta(n, 0) * w(j, 0)
) ;
double exp = etn1(mu, 1.0, low, high) ;
double exp2 = exp ;
// if (isinf(exp2) || isnan(exp2)) {
// if (low == 0.0) exp2 = .0001 ;
// if (high == 0.0) exp2 = -.0001 ;
// }
// if (isnan(exp2)) {
// exp2 = 0 ;
// }
// if (isinf(exp)) {
// Rcout << n << " " << j << " " << low << " " << high << " " << mu << " " << exp << " " << exp2 << std::endl ;
// }
// if (isnan(exp)) {
// Rcout << n << " " << j << " " << low << " " << high << " " << mu << " " << exp << " " << exp2 << std::endl ;
// }
theseystars(0, j) = exp2 ;
}
ystars.row(n) = theseystars ;
}
arma::uvec check = find_nonfinite(ystars) ;
if (check.n_elem > 0) {
ystars.elem(check).print("ystar check") ;
}
// return(ystars) ;
}
//' Map N(0,1) stochastic perturbations to an LNA path.
//'
//' @param pathmat matrix where the LNA path should be stored
//' @param draws matrix of N(0,1) draws to be mapped to an LNA path
//' @param lna_times vector of interval endpoint times
//' @param lna_pars numeric matrix of parameters, constants, and time-varying
//' covariates at each of the lna_times
//' @param init_start index in the parameter vector where the initial compartment
//' volumes start
//' @param param_update_inds logical vector indicating at which of the times the
//' LNA parameters need to be updated.
//' @param stoich_matrix stoichiometry matrix giving the changes to compartments
//' from each reaction
//' @param forcing_inds logical vector of indicating at which times in the
//' time-varying covariance matrix a forcing is applied.
//' @param forcing_matrix matrix containing the forcings.
//' @param svd_d vector in which to store SVD singular values
//' @param svd_U matrix in which to store the U matrix of the SVD
//' @param svd_V matrix in which to store the V matrix of the SVD
//' @param step_size initial step size for the ODE solver (adapted internally,
//' but too large of an initial step can lead to failure in stiff systems).
//' @param lna_pointer external pointer to LNA integration function.
//' @param set_pars_pointer external pointer to the function for setting the LNA
//' parameters.
//'
//' @return fill out pathmat with the LNA path corresponding to the stochastic
//' perturbations.
//'
//' @export
// [[Rcpp::export]]
void map_draws_2_lna(arma::mat& pathmat,
const arma::mat& draws,
const arma::rowvec& lna_times,
const Rcpp::NumericMatrix& lna_pars,
Rcpp::NumericVector& lna_param_vec,
const Rcpp::IntegerVector& lna_param_inds,
const Rcpp::IntegerVector& lna_tcovar_inds,
const int init_start,
const Rcpp::LogicalVector& param_update_inds,
const arma::mat& stoich_matrix,
const Rcpp::LogicalVector& forcing_inds,
const arma::uvec& forcing_tcov_inds,
const arma::mat& forcings_out,
const arma::cube& forcing_transfers,
arma::vec& svd_d,
arma::mat& svd_U,
arma::mat& svd_V,
double step_size,
SEXP lna_pointer,
SEXP set_pars_pointer) {
// get the dimensions of various objects
int n_events = stoich_matrix.n_cols; // number of transition events, e.g., S2I, I2R
int n_comps = stoich_matrix.n_rows; // number of model compartments (all strata)
int n_odes = n_events + n_events*n_events; // number of ODEs
int n_times = lna_times.n_elem; // number of times at which the LNA must be evaluated
int n_tcovar = lna_tcovar_inds.size(); // number of time-varying covariates or parameters
int n_forcings = forcing_tcov_inds.n_elem; // number of forcings
// for use with forcings
double forcing_flow = 0;
arma::vec forcing_distvec(n_comps, arma::fill::zeros);
// initialize the objects used in each time interval
double t_L = 0;
double t_R = 0;
// vector of parameters, initial compartment columes, constants, and time-varying covariates
std::copy(lna_pars.row(0).begin(), lna_pars.row(0).end(), lna_param_vec.begin());
CALL_SET_ODE_PARAMS(lna_param_vec, set_pars_pointer); // set the parameters in the odeintr namespace
// initial state vector - copy elements from the current parameter vector
arma::vec init_volumes(lna_param_vec.begin() + init_start, n_comps);
// initialize the LNA objects
bool good_svd = true;
Rcpp::NumericVector lna_state_vec(n_odes); // the vector for storing the current state of the LNA ODEs
arma::vec lna_drift(n_events, arma::fill::zeros); // incidence mean vector (log scale)
arma::mat lna_diffusion(n_events, n_events, arma::fill::zeros); // diffusion matrix
arma::vec log_lna(n_events, arma::fill::zeros); // LNA increment, log scale
arma::vec nat_lna(n_events, arma::fill::zeros); // LNA increment, natural scale
// apply forcings if called for - applied after censusing at the first time
if(forcing_inds[0]) {
// distribute the forcings proportionally to the compartment counts in the applicable states
for(int j=0; j < n_forcings; ++j) {
forcing_flow = lna_pars(0, forcing_tcov_inds[j]);
forcing_distvec = forcing_flow * normalise(forcings_out.col(j) % init_volumes, 1);
init_volumes += forcing_transfers.slice(j) * forcing_distvec;
}
}
// iterate over the time sequence, solving the LNA over each interval
for(int j=0; j < (n_times-1); ++j) {
// set the times of the interval endpoints
t_L = lna_times[j];
t_R = lna_times[j+1];
// Reset the LNA state vector and integrate the LNA ODEs over the next interval to 0
std::fill(lna_state_vec.begin(), lna_state_vec.end(), 0.0);
CALL_INTEGRATE_STEM_ODE(lna_state_vec, t_L, t_R, step_size, lna_pointer);
// transfer the elements of the lna_state_vec to the process objects
std::copy(lna_state_vec.begin(), lna_state_vec.begin() + n_events, lna_drift.begin());
std::copy(lna_state_vec.begin() + n_events, lna_state_vec.end(), lna_diffusion.begin());
// ensure symmetry of the diffusion matrix
lna_diffusion = arma::symmatu(lna_diffusion);
// map the stochastic perturbation to the LNA path on its natural scale
try{
if(lna_drift.has_nan() || lna_diffusion.has_nan()) {
good_svd = false;
throw std::runtime_error("Integration failed.");
} else {
good_svd = arma::svd(svd_U, svd_d, svd_V, lna_diffusion); // compute the SVD
}
if(!good_svd) {
throw std::runtime_error("SVD failed.");
} else {
svd_d.elem(arma::find(svd_d < 0)).zeros(); // zero out negative sing. vals
svd_V.each_row() %= arma::sqrt(svd_d).t(); // multiply rows of V by sqrt(d)
svd_U *= svd_V.t(); // complete svd_sqrt
svd_U.elem(arma::find(lna_diffusion == 0)).zeros(); // zero out numerical errors
log_lna = lna_drift + svd_U * draws.col(j); // map the LNA draws
}
} catch(std::exception & err) {
// reinstatiate the SVD objects
arma::vec svd_d(n_events, arma::fill::zeros);
arma::mat svd_U(n_events, n_events, arma::fill::zeros);
arma::mat svd_V(n_events, n_events, arma::fill::zeros);
// forward the exception
forward_exception_to_r(err);
} catch(...) {
::Rf_error("c++ exception (unknown reason)");
}
// compute the LNA increment
nat_lna = arma::vec(expm1(Rcpp::NumericVector(log_lna.begin(), log_lna.end())));
// save the LNA increment
pathmat(j+1, arma::span(1, n_events)) = nat_lna.t();
// update the initial volumes
init_volumes += stoich_matrix * nat_lna;
// if any increments or volumes are negative, throw an error
try{
if(any(nat_lna < 0)) {
throw std::runtime_error("Negative increment.");
}
if(any(init_volumes < 0)) {
throw std::runtime_error("Negative compartment volumes.");
}
} catch(std::runtime_error &err) {
forward_exception_to_r(err);
} catch(...) {
::Rf_error("c++ exception (unknown reason)");
}
// apply forcings if called for - applied after censusing the path
if(forcing_inds[j+1]) {
// distribute the forcings proportionally to the compartment counts in the applicable states
for(int s=0; s < n_forcings; ++s) {
forcing_flow = lna_pars(j+1, forcing_tcov_inds[s]);
forcing_distvec = forcing_flow * normalise(forcings_out.col(s) % init_volumes, 1);
init_volumes += forcing_transfers.slice(s) * forcing_distvec;
}
// throw errors for negative negative volumes
try{
if(any(init_volumes < 0)) {
throw std::runtime_error("Negative compartment volumes.");
}
} catch(std::exception &err) {
forward_exception_to_r(err);
} catch(...) {
::Rf_error("c++ exception (unknown reason)");
}
}
// update the parameters if they need to be updated
if(param_update_inds[j+1]) {
// time-varying covariates and parameters
std::copy(lna_pars.row(j+1).end() - n_tcovar,
lna_pars.row(j+1).end(),
lna_param_vec.end() - n_tcovar);
}
// copy the new initial volumes into the vector of parameters
std::copy(init_volumes.begin(), init_volumes.end(), lna_param_vec.begin() + init_start);
// set the lna parameters and reset the LNA state vector
CALL_SET_ODE_PARAMS(lna_param_vec, set_pars_pointer);
}
}
