// [[Rcpp::export]]
arma::mat BeQTL2(const arma::mat & A, const arma::mat & B, const arma::umat & Bootmat){
int bsi= Bootmat.n_rows;
arma::mat C(A.n_cols*B.n_cols,Bootmat.n_rows);
arma::mat tC(A.n_rows,B.n_rows);
for(int i=0; i<bsi; i++){
tC = cor(A.rows(Bootmat.row(i)),B.rows(Bootmat.row(i)));
C.col(i) = vectorise(tC,0);
}
C.elem(find_nonfinite(C)).zeros();
return reshape(median(C,1),A.n_cols,B.n_cols);
}
//Script that takes two matrices, performs bootstrapped correlation, and returns the median
// [[Rcpp::export]]
arma::mat BeQTL(const arma::mat & A, const arma::mat & B, const arma::umat & Bootmat){
int bsi= Bootmat.n_rows;
Rcpp::Rcout<<"Starting Bootstrap!"<<std::endl;
arma::mat C(A.n_cols*B.n_cols,Bootmat.n_rows);
arma::mat tA(A.n_rows,A.n_cols);
arma::mat tB(B.n_rows,B.n_cols);
arma::mat tC(A.n_rows,B.n_rows);
for(int i=0; i<bsi; i++){
tA = A.rows(Bootmat.row(i));
tB = B.rows(Bootmat.row(i));
tC = cor(tA,tB);
C.col(i) = vectorise(tC,0);
}
C.elem(find_nonfinite(C)).zeros();
return reshape(median(C,1),A.n_cols,B.n_cols);
}
// bootstrap class
Boot::Boot(const Data& data, Estimator* estimator, const arma::umat& rep)
: data(data), n(data.n), p(data.p), rep(rep), r(rep.n_cols) {
coef.set_size(p, r);
fitted.set_size(n, r);
resid.set_size(n, r);
scale.set_size(1, r);
arma::uvec indices;
Data resamp;
// for each replicate, construct the dataset then estimate
for (int i = 0; i < r; i++) {
indices = rep.col(i);
resamp.x = data.x.rows(indices);
resamp.y = data.y.elem(indices);
(*estimator)(resamp, coef.colptr(i), fitted.colptr(i), resid.colptr(i),
scale.colptr(i));
}
}
List objectivex(const arma::mat& transition, const arma::cube& emission,
const arma::vec& init, const arma::ucube& obs, const arma::umat& ANZ,
const arma::ucube& BNZ, const arma::uvec& INZ, const arma::uvec& nSymbols,
const arma::mat& coef, const arma::mat& X, arma::uvec& numberOfStates,
unsigned int threads) {
unsigned int q = coef.n_rows;
arma::vec grad(
arma::accu(ANZ) + arma::accu(BNZ) + arma::accu(INZ) + (numberOfStates.n_elem- 1) * q,
arma::fill::zeros);
arma::mat weights = exp(X * coef).t();
if (!weights.is_finite()) {
grad.fill(-arma::datum::inf);
return List::create(Named("objective") = arma::datum::inf, Named("gradient") = wrap(grad));
}
weights.each_row() /= sum(weights, 0);
arma::mat initk(emission.n_rows, obs.n_slices);
for (unsigned int k = 0; k < obs.n_slices; k++) {
initk.col(k) = init % reparma(weights.col(k), numberOfStates);
}
arma::uvec cumsumstate = arma::cumsum(numberOfStates);
unsigned int error = 0;
double ll = 0;
#pragma omp parallel for if(obs.n_slices >= threads) schedule(static) reduction(+:ll) num_threads(threads) \
default(none) shared(q, grad, nSymbols, ANZ, BNZ, INZ, \
numberOfStates, cumsumstate, obs, init, initk, X, weights, transition, emission, error)
for (unsigned int k = 0; k < obs.n_slices; k++) {
if (error == 0) {
arma::mat alpha(emission.n_rows, obs.n_cols); //m,n
arma::vec scales(obs.n_cols); //n
arma::sp_mat sp_trans(transition);
uvForward(sp_trans.t(), emission, initk.col(k), obs.slice(k), alpha, scales);
arma::mat beta(emission.n_rows, obs.n_cols); //m,n
uvBackward(sp_trans, emission, obs.slice(k), beta, scales);
int countgrad = 0;
arma::vec grad_k(grad.n_elem, arma::fill::zeros);
// transitionMatrix
if (arma::accu(ANZ) > 0) {
for (unsigned int jj = 0; jj < numberOfStates.n_elem; jj++) {
arma::vec gradArow(numberOfStates(jj));
arma::mat gradA(numberOfStates(jj), numberOfStates(jj));
int ind_jj = cumsumstate(jj) - numberOfStates(jj);
for (unsigned int i = 0; i < numberOfStates(jj); i++) {
arma::uvec ind = arma::find(ANZ.row(ind_jj + i).subvec(ind_jj, cumsumstate(jj) - 1));
if (ind.n_elem > 0) {
gradArow.zeros();
gradA.eye();
gradA.each_row() -= transition.row(ind_jj + i).subvec(ind_jj, cumsumstate(jj) - 1);
gradA.each_col() %= transition.row(ind_jj + i).subvec(ind_jj, cumsumstate(jj) - 1).t();
for (unsigned int j = 0; j < numberOfStates(jj); j++) {
for (unsigned int t = 0; t < (obs.n_cols - 1); t++) {
double tmp = alpha(ind_jj + i, t);
for (unsigned int r = 0; r < obs.n_rows; r++) {
tmp *= emission(ind_jj + j, obs(r, t + 1, k), r);
}
gradArow(j) += tmp * beta(ind_jj + j, t + 1);
}
}
gradArow = gradA * gradArow;
grad_k.subvec(countgrad, countgrad + ind.n_elem - 1) = gradArow.rows(ind);
countgrad += ind.n_elem;
}
}
}
}
if (arma::accu(BNZ) > 0) {
// emissionMatrix
for (unsigned int r = 0; r < obs.n_rows; r++) {
arma::vec gradBrow(nSymbols(r));
arma::mat gradB(nSymbols(r), nSymbols(r));
for (unsigned int i = 0; i < emission.n_rows; i++) {
arma::uvec ind = arma::find(BNZ.slice(r).row(i));
if (ind.n_elem > 0) {
gradBrow.zeros();
gradB.eye();
gradB.each_row() -= emission.slice(r).row(i).subvec(0, nSymbols(r) - 1);
gradB.each_col() %= emission.slice(r).row(i).subvec(0, nSymbols(r) - 1).t();
for (unsigned int j = 0; j < nSymbols(r); j++) {
if (obs(r, 0, k) == j) {
double tmp = initk(i, k);
for (unsigned int r2 = 0; r2 < obs.n_rows; r2++) {
if (r2 != r) {
tmp *= emission(i, obs(r2, 0, k), r2);
}
}
gradBrow(j) += tmp * beta(i, 0);
}
for (unsigned int t = 0; t < (obs.n_cols - 1); t++) {
if (obs(r, t + 1, k) == j) {
double tmp = beta(i, t + 1);
for (unsigned int r2 = 0; r2 < obs.n_rows; r2++) {
if (r2 != r) {
tmp *= emission(i, obs(r2, t + 1, k), r2);
}
}
gradBrow(j) += arma::dot(alpha.col(t), transition.col(i)) * tmp;
}
}
}
gradBrow = gradB * gradBrow;
grad_k.subvec(countgrad, countgrad + ind.n_elem - 1) = gradBrow.rows(ind);
countgrad += ind.n_elem;
}
}
}
}
if (arma::accu(INZ) > 0) {
for (unsigned int i = 0; i < numberOfStates.n_elem; i++) {
int ind_i = cumsumstate(i) - numberOfStates(i);
arma::uvec ind = arma::find(
INZ.subvec(ind_i, cumsumstate(i) - 1));
if (ind.n_elem > 0) {
arma::vec gradIrow(numberOfStates(i), arma::fill::zeros);
for (unsigned int j = 0; j < numberOfStates(i); j++) {
double tmp = weights(i, k);
for (unsigned int r = 0; r < obs.n_rows; r++) {
tmp *= emission(ind_i + j, obs(r, 0, k), r);
}
gradIrow(j) += tmp * beta(ind_i + j, 0);
}
arma::mat gradI(numberOfStates(i), numberOfStates(i), arma::fill::zeros);
gradI.eye();
gradI.each_row() -= init.subvec(ind_i, cumsumstate(i) - 1).t();
gradI.each_col() %= init.subvec(ind_i, cumsumstate(i) - 1);
gradIrow = gradI * gradIrow;
grad_k.subvec(countgrad, countgrad + ind.n_elem - 1) = gradIrow.rows(ind);
countgrad += ind.n_elem;
}
}
}
for (unsigned int jj = 1; jj < numberOfStates.n_elem; jj++) {
unsigned int ind_jj = (cumsumstate(jj) - numberOfStates(jj));
for (unsigned int j = 0; j < emission.n_rows; j++) {
double tmp = 1.0;
for (unsigned int r = 0; r < obs.n_rows; r++) {
tmp *= emission(j, obs(r, 0, k), r);
}
if ((j >= ind_jj) & (j < cumsumstate(jj))) {
grad_k.subvec(countgrad + q * (jj - 1), countgrad + q * jj - 1) += tmp
* beta(j, 0) * initk(j, k) * X.row(k).t() * (1.0 - weights(jj, k));
} else {
grad_k.subvec(countgrad + q * (jj - 1), countgrad + q * jj - 1) -= tmp
* beta(j, 0) * initk(j, k) * X.row(k).t() * weights(jj, k);
}
}
}
if (!scales.is_finite() || !beta.is_finite()) {
#pragma omp atomic
error++;
} else {
ll -= arma::sum(log(scales));
#pragma omp critical
grad += grad_k;
}
}
}
if(error > 0){
ll = -arma::datum::inf;
grad.fill(-arma::datum::inf);
}
return List::create(Named("objective") = -ll, Named("gradient") = wrap(-grad));
}
// [[Rcpp::export]]
Rcpp::List objective(const arma::mat& transition, const arma::cube& emission,
const arma::vec& init, arma::ucube& obs, const arma::umat& ANZ,
const arma::ucube& BNZ, const arma::uvec& INZ, const arma::uvec& nSymbols, unsigned int threads) {
arma::vec grad(arma::accu(ANZ) + arma::accu(BNZ) + arma::accu(INZ), arma::fill::zeros);
unsigned int error = 0;
double ll = 0;
#pragma omp parallel for if(obs.n_slices >= threads) schedule(static) reduction(+:ll) num_threads(threads) \
default(shared) //shared(grad, nSymbols, ANZ, BNZ, INZ, obs, init, transition, emission, error, arma::fill::zeros)
for (unsigned int k = 0; k < obs.n_slices; k++) {
if (error == 0) {
arma::mat alpha(emission.n_rows, obs.n_cols); //m,n
arma::vec scales(obs.n_cols); //n
arma::sp_mat sp_trans(transition);
uvForward(sp_trans.t(), emission, init, obs.slice(k), alpha, scales);
arma::mat beta(emission.n_rows, obs.n_cols); //m,n
uvBackward(sp_trans, emission, obs.slice(k), beta, scales);
int countgrad = 0;
arma::vec grad_k(grad.n_elem, arma::fill::zeros);
// transitionMatrix
arma::vec gradArow(emission.n_rows);
arma::mat gradA(emission.n_rows, emission.n_rows);
for (unsigned int i = 0; i < emission.n_rows; i++) {
arma::uvec ind = arma::find(ANZ.row(i));
if (ind.n_elem > 0) {
gradArow.zeros();
gradA.eye();
gradA.each_row() -= transition.row(i);
gradA.each_col() %= transition.row(i).t();
for (unsigned int t = 0; t < (obs.n_cols - 1); t++) {
for (unsigned int j = 0; j < emission.n_rows; j++) {
double tmp = 1.0;
for (unsigned int r = 0; r < obs.n_rows; r++) {
tmp *= emission(j, obs(r, t + 1, k), r);
}
gradArow(j) += alpha(i, t) * tmp * beta(j, t + 1);
}
}
gradArow = gradA * gradArow;
grad_k.subvec(countgrad, countgrad + ind.n_elem - 1) = gradArow.rows(ind);
countgrad += ind.n_elem;
}
}
// emissionMatrix
for (unsigned int r = 0; r < obs.n_rows; r++) {
arma::vec gradBrow(nSymbols(r));
arma::mat gradB(nSymbols(r), nSymbols(r));
for (unsigned int i = 0; i < emission.n_rows; i++) {
arma::uvec ind = arma::find(BNZ.slice(r).row(i));
if (ind.n_elem > 0) {
gradBrow.zeros();
gradB.eye();
gradB.each_row() -= emission.slice(r).row(i).subvec(0, nSymbols(r) - 1);
gradB.each_col() %= emission.slice(r).row(i).subvec(0, nSymbols(r) - 1).t();
for (unsigned int j = 0; j < nSymbols(r); j++) {
if (obs(r, 0, k) == j) {
double tmp = 1.0;
for (unsigned int r2 = 0; r2 < obs.n_rows; r2++) {
if (r2 != r) {
tmp *= emission(i, obs(r2, 0, k), r2);
}
}
gradBrow(j) += init(i) * tmp * beta(i, 0);
}
for (unsigned int t = 0; t < (obs.n_cols - 1); t++) {
if (obs(r, t + 1, k) == j) {
double tmp = 1.0;
for (unsigned int r2 = 0; r2 < obs.n_rows; r2++) {
if (r2 != r) {
tmp *= emission(i, obs(r2, t + 1, k), r2);
}
}
gradBrow(j) += arma::dot(alpha.col(t), transition.col(i)) * tmp
* beta(i, t + 1);
}
}
}
gradBrow = gradB * gradBrow;
grad_k.subvec(countgrad, countgrad + ind.n_elem - 1) = gradBrow.rows(ind);
countgrad += ind.n_elem;
}
}
}
// InitProbs
arma::uvec ind = arma::find(INZ);
if (ind.n_elem > 0) {
arma::vec gradIrow(emission.n_rows);
arma::mat gradI(emission.n_rows, emission.n_rows);
gradIrow.zeros();
gradI.zeros();
gradI.eye();
gradI.each_row() -= init.t();
gradI.each_col() %= init;
for (unsigned int j = 0; j < emission.n_rows; j++) {
double tmp = 1.0;
for (unsigned int r = 0; r < obs.n_rows; r++) {
tmp *= emission(j, obs(r, 0, k), r);
}
gradIrow(j) += tmp * beta(j, 0);
}
gradIrow = gradI * gradIrow;
grad_k.subvec(countgrad, countgrad + ind.n_elem - 1) = gradIrow.rows(ind);
countgrad += ind.n_elem;
}
if (!scales.is_finite() || !beta.is_finite()) {
#pragma omp atomic
error++;
} else {
ll -= arma::sum(log(scales));
#pragma omp critical
grad += grad_k;
// gradmat.col(k) = grad_k;
}
// for (unsigned int ii = 0; ii < grad_k.n_elem; ii++) {
// #pragma omp atomic
// grad(ii) += grad_k(ii);
// }
}
}
if(error > 0){
ll = -arma::datum::inf;
grad.fill(-arma::datum::inf);
}
// } else {
// grad = sum(gradmat, 1);
// }
return Rcpp::List::create(Rcpp::Named("objective") = -ll, Rcpp::Named("gradient") = Rcpp::wrap(-grad));
}
double ung_ssm::bsf_filter(const unsigned int nsim, arma::cube& alpha,
arma::mat& weights, arma::umat& indices) {
arma::uvec nonzero = arma::find(P1.diag() > 0);
arma::mat L_P1(m, m, arma::fill::zeros);
if (nonzero.n_elem > 0) {
L_P1.submat(nonzero, nonzero) =
arma::chol(P1.submat(nonzero, nonzero), "lower");
}
std::normal_distribution<> normal(0.0, 1.0);
for (unsigned int i = 0; i < nsim; i++) {
arma::vec um(m);
for(unsigned int j = 0; j < m; j++) {
um(j) = normal(engine);
}
alpha.slice(i).col(0) = a1 + L_P1 * um;
}
std::uniform_real_distribution<> unif(0.0, 1.0);
arma::vec normalized_weights(nsim);
double loglik = 0.0;
if(arma::is_finite(y(0))) {
weights.col(0) = log_obs_density(0, alpha);
double max_weight = weights.col(0).max();
weights.col(0) = arma::exp(weights.col(0) - max_weight);
double sum_weights = arma::accu(weights.col(0));
if(sum_weights > 0.0){
normalized_weights = weights.col(0) / sum_weights;
} else {
return -std::numeric_limits<double>::infinity();
}
loglik = max_weight + std::log(sum_weights / nsim);
} else {
weights.col(0).ones();
normalized_weights.fill(1.0 / nsim);
}
for (unsigned int t = 0; t < n; t++) {
arma::vec r(nsim);
for (unsigned int i = 0; i < nsim; i++) {
r(i) = unif(engine);
}
indices.col(t) = stratified_sample(normalized_weights, r, nsim);
arma::mat alphatmp(m, nsim);
for (unsigned int i = 0; i < nsim; i++) {
alphatmp.col(i) = alpha.slice(indices(i, t)).col(t);
}
for (unsigned int i = 0; i < nsim; i++) {
arma::vec uk(k);
for(unsigned int j = 0; j < k; j++) {
uk(j) = normal(engine);
}
alpha.slice(i).col(t + 1) = C.col(t * Ctv) +
T.slice(t * Ttv) * alphatmp.col(i) + R.slice(t * Rtv) * uk;
}
if ((t < (n - 1)) && arma::is_finite(y(t + 1))) {
weights.col(t + 1) = log_obs_density(t + 1, alpha);
double max_weight = weights.col(t + 1).max();
weights.col(t + 1) = arma::exp(weights.col(t + 1) - max_weight);
double sum_weights = arma::accu(weights.col(t + 1));
if(sum_weights > 0.0){
normalized_weights = weights.col(t + 1) / sum_weights;
} else {
return -std::numeric_limits<double>::infinity();
}
loglik += max_weight + std::log(sum_weights / nsim);
} else {
weights.col(t + 1).ones();
normalized_weights.fill(1.0/nsim);
}
}
// constant part of the log-likelihood
switch(distribution) {
case 0 :
loglik += arma::uvec(arma::find_finite(y)).n_elem * norm_log_const(phi);
break;
case 1 : {
arma::uvec finite_y(find_finite(y));
loglik += poisson_log_const(y(finite_y), u(finite_y));
} break;
case 2 : {
arma::uvec finite_y(find_finite(y));
loglik += binomial_log_const(y(finite_y), u(finite_y));
} break;
case 3 : {
arma::uvec finite_y(find_finite(y));
loglik += negbin_log_const(y(finite_y), u(finite_y), phi);
} break;
}
return loglik;
}
double ung_ssm::psi_filter(const ugg_ssm& approx_model,
const double approx_loglik, const arma::vec& scales,
const unsigned int nsim, arma::cube& alpha, arma::mat& weights,
arma::umat& indices) {
arma::mat alphahat(m, n + 1);
arma::cube Vt(m, m, n + 1);
arma::cube Ct(m, m, n + 1);
approx_model.smoother_ccov(alphahat, Vt, Ct);
conditional_cov(Vt, Ct);
std::normal_distribution<> normal(0.0, 1.0);
for (unsigned int i = 0; i < nsim; i++) {
arma::vec um(m);
for(unsigned int j = 0; j < m; j++) {
um(j) = normal(engine);
}
alpha.slice(i).col(0) = alphahat.col(0) + Vt.slice(0) * um;
}
std::uniform_real_distribution<> unif(0.0, 1.0);
arma::vec normalized_weights(nsim);
double loglik = 0.0;
if(arma::is_finite(y(0))) {
weights.col(0) = arma::exp(log_weights(approx_model, 0, alpha) - scales(0));
double sum_weights = arma::accu(weights.col(0));
if(sum_weights > 0.0){
normalized_weights = weights.col(0) / sum_weights;
} else {
return -std::numeric_limits<double>::infinity();
}
loglik = approx_loglik + std::log(sum_weights / nsim);
} else {
weights.col(0).ones();
normalized_weights.fill(1.0 / nsim);
loglik = approx_loglik;
}
for (unsigned int t = 0; t < n; t++) {
arma::vec r(nsim);
for (unsigned int i = 0; i < nsim; i++) {
r(i) = unif(engine);
}
indices.col(t) = stratified_sample(normalized_weights, r, nsim);
arma::mat alphatmp(m, nsim);
// for (unsigned int i = 0; i < nsim; i++) {
// alphatmp.col(i) = alpha.slice(i).col(t);
// }
for (unsigned int i = 0; i < nsim; i++) {
alphatmp.col(i) = alpha.slice(indices(i, t)).col(t);
//alpha.slice(i).col(t) = alphatmp.col(indices(i, t));
}
for (unsigned int i = 0; i < nsim; i++) {
arma::vec um(m);
for(unsigned int j = 0; j < m; j++) {
um(j) = normal(engine);
}
alpha.slice(i).col(t + 1) = alphahat.col(t + 1) +
Ct.slice(t + 1) * (alphatmp.col(i) - alphahat.col(t)) + Vt.slice(t + 1) * um;
}
if ((t < (n - 1)) && arma::is_finite(y(t + 1))) {
weights.col(t + 1) =
arma::exp(log_weights(approx_model, t + 1, alpha) - scales(t + 1));
double sum_weights = arma::accu(weights.col(t + 1));
if(sum_weights > 0.0){
normalized_weights = weights.col(t + 1) / sum_weights;
} else {
return -std::numeric_limits<double>::infinity();
}
loglik += std::log(sum_weights / nsim);
} else {
weights.col(t + 1).ones();
normalized_weights.fill(1.0 / nsim);
}
}
return loglik;
}