//' Fast addition of vector to each row of matrix
//'
//' @description Fast addition of vector to each row of a matrix. This corresponds to t(t(x) + v)
//' @param x A matrix with dimensions n*k.
//' @param v A vector of length k.
//' @return A matrix of dimension n*k where v is added to each row of x
//' @author Claus Ekstrom <claus@@rprimer.dk>
//' @examples
//'
//' A <- matrix(1:12, ncol=3)
//' B <- c(1, 2, 3)
//'
//' add_torows(A, B)
//'
//' @export
// [[Rcpp::export]]
arma::mat add_torows(const arma::mat &x, const arma::rowvec &v) {
if (x.n_cols != v.n_elem) {
stop("Non-conformable objects. Length of v does not match columns in x");
}
arma::mat m = x.each_row() + v;
return (m);
}
arma::cx_mat generate_visibilities_from_local_skymodel(arma::mat& skymodel, arma::mat& uvw_baselines)
{
arma::cx_mat model_vis(uvw_baselines.n_rows, 1);
model_vis.zeros();
skymodel.each_row([&](arma::rowvec& src_entry) {
model_vis += visibilities_for_point_source(uvw_baselines, src_entry[0], src_entry[1], src_entry[2]);
});
return std::move(model_vis);
}
unsigned int optCoef(arma::mat& weights, const arma::icube& obs, const arma::cube& emission,
const arma::mat& initk, const arma::cube& beta, const arma::mat& scales, arma::mat& coef,
const arma::mat& X, const arma::ivec& cumsumstate, const arma::ivec& numberOfStates,
int trace) {
int iter = 0;
double change = 1.0;
while ((change > 1e-10) & (iter < 100)) {
arma::vec tmpvec(X.n_cols * (weights.n_rows - 1));
bool solve_ok = arma::solve(tmpvec, hCoef(weights, X),
gCoef(obs, beta, scales, emission, initk, weights, X, cumsumstate, numberOfStates));
if (solve_ok == false) {
return (4);
}
arma::mat coefnew(coef.n_rows, coef.n_cols - 1);
for (unsigned int i = 0; i < (weights.n_rows - 1); i++) {
coefnew.col(i) = coef.col(i + 1) - tmpvec.subvec(i * X.n_cols, (i + 1) * X.n_cols - 1);
}
change = arma::accu(arma::abs(coef.submat(0, 1, coef.n_rows - 1, coef.n_cols - 1) - coefnew))
/ coefnew.n_elem;
coef.submat(0, 1, coef.n_rows - 1, coef.n_cols - 1) = coefnew;
iter++;
if (trace == 3) {
Rcout << "coefficient optimization iter: " << iter;
Rcout << " new coefficients: " << std::endl << coefnew << std::endl;
Rcout << " relative change: " << change << std::endl;
}
weights = exp(X * coef).t();
if (!weights.is_finite()) {
return (5);
}
weights.each_row() /= sum(weights, 0);
}
return (0);
}
///
/// \brief Vespucci::MathDimensionReduction::plsregress PLS Regression Using SIMPLS algorithm.
/// This is essentially a line-for-line rewrite of plsregress from the Octave
/// statistics package.
/// Copyright (C) 2012 Fernando Damian Nieuwveldt <*****@*****.**>
/// This is an implementation of the SIMPLS algorithm:
/// Reference: SIMPLS: An alternative approach to partial least squares regression.
/// Chemometrics and Intelligent Laboratory Systems (1993)
/// \param x
/// \param y
/// \param components Number of PLS components
/// \param x_loadings "Output" values
/// \param y_loadings
/// \param x_scores
/// \param y_scores
/// \param coefficients
/// \param fitted_data
/// \return
///
bool Vespucci::Math::DimensionReduction::plsregress(arma::mat X, arma::mat Y,
int components, arma::mat &X_loadings,
arma::mat &Y_loadings,
arma::mat &X_scores,
arma::mat &Y_scores,
arma::mat &coefficients,
arma::mat &percent_variance,
arma::mat &fitted)
{
using namespace arma;
uword observations = X.n_rows;
uword predictors = X.n_cols;
uword responses = Y.n_cols;
//Mean centering
mat Xmeans = arma::mean(X);
mat Ymeans = arma::mean(Y);
//Octave does below with bsxfun. After optimization, this should hopefully not
// be slower.
X.each_row() -= Xmeans; //element-wise subtraction of mean
Y.each_row() -= Ymeans; //same
mat S = trans(X) * Y;
mat R = zeros(predictors, components);
mat P = R;
mat V = R;
mat T = zeros(observations, components);
mat U = T;
mat Q = zeros(responses, components);
mat eigvec;
vec eigval;
mat q;
mat r;
mat t;
mat nt;
mat p;
mat u;
mat v;
double max_eigval;
for (int i = 0; i < components; ++i){
eig_sym(eigval, eigvec, (trans(S) * S));
max_eigval = eigval.max();
uvec dom_index = find(eigval >= max_eigval);
uword dominant_index = dom_index(0);
q = eigvec.col(dominant_index);
r = S*q; //X block factor weights
t = X*r; //X block factor weights
t.each_row() -= mean(t); //center t
nt = arma::sqrt(t.t()*t); //compute norm (is arma::norm() the same?)
t.each_row() /= nt;
r.each_row() /= nt; //normalize
p = X.t()*t; //X block factor loadings
q = Y.t()*t; //Y block factor loadings
u = Y*q; //Y block factor scores
v = p;
//Ensure orthogonality
if (i > 0){
v = v - V*(V.t()*p);
u = u - T*(T.t()*u);
}
v.each_row() /= arma::sqrt(trans(v) * v); //normalize orthogonal loadings
S = S - v * (trans(v)*S); //deflate S wrt loadings
R.col(i) = r;
T.col(i) = t;
P.col(i) = p;
Q.col(i) = q;
U.col(i) = u;
V.col(i) = v;
}
//Regression coefficients
mat B = R*trans(Q);
fitted = T*trans(Q);
fitted.each_row() += Ymeans;
//Octave creates copies from inputs before sending to output. Doing same
//here just to be safe.
coefficients = B;
X_scores = T;
X_loadings = P;
Y_scores = U;
Y_loadings = Q;
//projection = R;
percent_variance.set_size(2, coefficients.n_cols);
percent_variance.row(0) = sum(arma::abs(P)%arma::abs(P)) / sum(sum(arma::abs(X)%arma::abs(X)));
percent_variance.row(1) = sum(arma::abs(Q)%arma::abs(Q)) / sum(sum(arma::abs(Y)%arma::abs(Y)));
return true;
}
//[[Rcpp::export(.emplik_intern)]]
List emplik_intern(arma::mat z, arma::colvec mu, arma::vec lam, double eps,
double M = 1e30, double thresh = 1e-12, int itermax = 1000){
//(arma::mat z, arma::vec mu = vec(z.n_cols,fill::zeros), double eps = 1/z.nrows, double M = datum::inf);
// # Backtracking line search parameters [Tweak only with extreme caution.]
// # See Boyd and Vandenberghe, pp 464-466.
double ALPHA = 0.3; // seems better than 0.01 on some 2d test data (sometimes fewer iters)
double BETA = 0.8;
// # We need 0 < ALPHA < 1/2 and 0 < BETA < 1
// # Backtrack threshold: you can miss by this much.
double BACKEPS = 0;
// # Consider replacing 0 by 1e-10 if backtracking seems to be
// # failing due to round off.
int n = z.n_rows;
int d = z.n_cols;
z.each_row() -= trans(mu);
// Use lam = 0 or initial lam, whichever is best
arma::vec onen = arma::vec(n,arma::fill::ones);
arma::mat init0 = mllog(onen, eps, M, 2);
arma::mat init(init0.n_rows, init0.n_cols);
if(!any(lam)){
init = init0;
} else {
init = mllog(onen+z*lam, eps, M, 2);
if(sum(init0.col(0) < sum(init.col(0)))){
lam = arma::rowvec(z.n_cols,arma::fill::zeros);
init = init0;
}
}
// # Initial f, g
double fold = sum(init.col(0));
arma::rowvec gold = sum(z.each_col() % init.col(1),0);
bool converged = false;
int iter = 0;
arma::mat oldvals = init;
arma::mat newvals(oldvals.n_rows, oldvals.n_cols);
arma::vec rootllpp;
arma::mat zt(z.n_rows, z.n_cols);
arma::vec yt(z.n_rows);
arma::vec wts;
double fnew; double targ;
double logelr;
arma::vec step(z.n_cols);
int s; double ndec; double gradnorm;
bool backtrack = false;
while(!converged){
iter += 1;
// # Get Newton Step
rootllpp = sqrt(oldvals.col(2)); //# sqrt 2nd deriv of -llog lik
zt = z;
for(int j=0; j<d; j++){
zt.col(j) %= rootllpp;
}
yt = oldvals.col(1) / rootllpp;
step = -svdlm(zt,yt);
backtrack = false;
s = 1;
while(!backtrack){
newvals = mllog(onen + z * (lam+s*step), eps, M, 2);
fnew = sum(newvals.col(0));
targ = fold + ALPHA * s * sum(trans(gold) % step) + BACKEPS; // (BACKEPS for roundoff, should not be needed)
if(fnew <= targ){ // backtracking has converged
backtrack = true;
oldvals = newvals;
fold = fnew;
gold = sum(z.each_col() % oldvals.col(1),0);
lam = lam + s*step;
} else{
s = s * BETA;
}
}
// # Newton decrement and gradient norm
ndec = sqrt(sum(square(step % trans(gold))));
gradnorm = sqrt(sum(square(gold)));
converged = (ndec * ndec <= thresh);
if( iter > itermax )
break;
}
wts = pow(1 + z * lam, -1)/n;
logelr = sum(mllog(onen + z * lam, eps, M, 0).col(0));
return Rcpp::List::create(Named("logelr")=logelr, Named("lam") = lam, Named("wts") = wts,
Named("conv") = converged, Named("niter") = iter,Named("ndec") = ndec, Named("gradnorm") = gradnorm);
}
//' 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);
}
}
// [[Rcpp::export]]
List solveHierBasis(arma::mat design_mat,
arma::vec y,
arma::vec ak,arma::mat weights,
int n, double lam_min_ratio, int nlam,
double max_lambda) {
// This function returns the argmin of the following function:
// (0.5) * ||y - X %*% beta||_2^2 + P(beta), where
// P(\beta) = \sum_{j=1}^{J_n} weights[j, lam_indx] * norm(beta[j:J_n])
// where j indexes the basis function and lam_indx indexes the different
// lambda values.
//
// Args:
// design_mat: A design matrix of size n * J_n, where J_n is number of
// basis functions. This matrix should be centered.
// y: The centered response vector.
// ak: A J_n-vector of weights where ak[j] = j^m - (j-1)^m for a smoothness
// level m.
// weights: A J_n * nlam matrix which is simply the concatenation [ak,ak,...,ak].
// n: The number of observations, equal to length(y).
// lam_min_ratio: Ratio of min_lambda to max_lambda.
// nlam: Number of lambda values.
// max_lambda: A double specifying the maximum lambda, if NA then function
// selects a max_lambda.
// Returns:
// beta_hat2: The solution matrix, a J_n * nlam matrix.
// lambdas: Sequence of lambda values used for fitting.
// Generate the x_mat, this is our orthonormal design matrix.
arma::mat x_mat, R_mat;
arma::qr_econ(x_mat, R_mat, design_mat);
x_mat = x_mat * sqrt(n);
R_mat = R_mat / sqrt(n);
// arma::sp_mat R_mat2 = sp_mat(R_mat / sqrt(n));
// Note that for a orthogonal design with X^T %*% X = nI the
// two problems are equivalent:
// 1. (1/2n)*|Y - X %*% beta|^2 + lambda * Pen(beta),
// 2. (1/2)*|t(X) %*% Y/n - beta|^2 + lambda * Pen(beta).
//
// Thus all we need, is to solve the proximal problem.
// Define v_temp = t(X) %*% Y/n for the prox problem.
arma::vec v_temp = x_mat.t() * (y /n);
// We evaluate a max_lambda value if not specified by user.
if(R_IsNA(max_lambda)) {
// Followed by the maximum lambda value.
max_lambda = max(abs(v_temp) / ak);
// max_lambda = norm(v_temp, 2);
}
// Generate the full lambda sequence.
arma::vec lambdas = linspace<vec>(log10(max_lambda),
log10(max_lambda * lam_min_ratio),
nlam);
lambdas = exp10(lambdas);
// Generate matrix of weights.
weights.each_row() %= lambdas.t();
// Obtain beta.hat, solve prox problem.
arma::sp_mat beta_hat = GetProx(v_temp, weights);
// Take the inverse of the R_mat to obtain solution on the original scale
arma::mat beta_hat2 = solve(trimatu(R_mat), mat(beta_hat));
///////////// Removed after version 0.7.1, moved to a different R function.//////////
// We also obtain the DOF for the different methods.
//arma::vec dof = getDof(x_mat, weights, beta_hat, nlam, n);
//////////// Removed after version 0.7.1, moved to a different R function.//////////
// Return fitted values.
arma::mat yhat = x_mat * mat(beta_hat);
return List::create(Named("beta") = beta_hat2,
Named("lambdas") = lambdas,
//Named("dof") = dof,
Named("yhat") = yhat,
Named(".beta_ortho") = beta_hat);
}
// [[Rcpp::export]]
List solveHierLogistic(arma::mat design_mat,
arma::vec y,
arma::vec ak,arma::mat weights,
int n, int nlam, int J,
double max_lambda, double lam_min_ratio,
double tol, int max_iter,
double tol_inner, int max_iter_inner) {
// This function returns the argmin of the following function:
// -L(beta) + P(beta), where
// P(\beta) = \sum_{j=1}^{J_n} weights[j, lam_indx] * norm(beta[j:J_n])
// where j indexes the basis function and lam_indx indexes the different
// lambda values. 'L' in this case is the log-likelihood for a binomial model.
//
// Args:
// design_mat: A design matrix of size n * J_n, where J_n is number of
// basis functions.
// y: The response vector.
// ak: A J_n-vector of weights where ak[j] = j^m - (j-1)^m for a smoothness
// level m.
// weights: A J_n * nlam matrix which is simply the concatenation [ak,ak,...,ak].
// n: The number of observations, equal to length(y).
// lam_min_ratio: Ratio of min_lambda to max_lambda.
// nlam: Number of lambda values.
// max_lambda: A double specifying the maximum lambda. A max lambda needs to
// be specified for logistic regression.
// tol, tol_inner: The tolerance for the outer and inner loop respectively.
// max_iter, max_iter_inner: The maximum number of iterations for outer and
// inner loops respectively.
// Returns:
// beta_final: The sparse solution matrix, a J_n * nlam matrix.
// intercept: The vector of fitted intercepts of size nlam.
// lambdas: Sequence of lambda values used for fitting.
// fitted: The fitted probabilities.
//
// Generate the x_mat, this is our orthonormal design matrix.
arma::mat x_mat, R_mat;
arma::qr_econ(x_mat, R_mat, design_mat);
x_mat = x_mat * sqrt(n);
R_mat = R_mat / sqrt(n);
// We evaluate a max_lambda value if not specified by user.
if(R_IsNA(max_lambda)) {
// A simple calculation to evelaute the max lambda,
// If we wish to find a max lambda, then beta = 0 and hence the
// temp fitted probabilities are 0.5. The current quadratic approximation
// is given by
// y_tilde = intercept + X * beta + (y - p_hat)/(p_jhat * (1 - p_hat)).
// In this case this is simply 4 * (y - 0.5).
// Finally max_lambda is give first finding
// v_temp = t(x_mat) * (4 * (y - 0.5))/n followed by
// max(abs(v_temp)) / (4*ak).
arma::vec v_temp = x_mat.t() * ((y - 0.5) / n);
// Followed by the maximum lambda value.
max_lambda = max(abs(v_temp) / ak);
}
// Generate the full lambda sequence.
arma::vec lambdas = linspace<vec>(log10(max_lambda),
log10(max_lambda * lam_min_ratio),
nlam);
lambdas = exp10(lambdas);
// Generate matrix of weights.
weights.each_row() %= lambdas.t();
// The final matrix we will use to store beta values.
arma::mat beta_ans(J, nlam);
// The final vector to store values for the intercept.
arma::vec intercept_ans(nlam);
// The vectors we will use to check convergence.
// We also use this for the sake of warm starts.
arma::vec beta(J, fill::zeros);
// arma::vec beta_new(J, fill::zeros);
double intercept = 0;
// double intercept_new = 0;
// The full parameter vector which containts the intercept + covariates.
arma::vec pars(J + 1, fill::zeros);
arma::vec pars_new(J + 1, fill::zeros);
// For each lambda and each middle iteration number,
// We design a new vector of probabilities and consequently a new
// response vector.
arma::vec temp_prob;
arma::vec temp_resp;
// We also store a temporary linear part, given by X * beta.
arma::vec temp_xbeta;
// Begin outer loop to decrement lambdas.
for(int i = 0; i < nlam; ++i) {
//Rcout << "Solving for Lambda num: " << i <<"\n";
// Begin middle loop to update quadratic approximation of
// log-likelihood.
bool converge = false;
int counter = 0;
while(!converge && counter < max_iter) {
temp_xbeta = x_mat * beta;
temp_prob = 1 / (1 + exp(-1 * (intercept + temp_xbeta)));
// Note that the optimization problem is actually given by
// (1/4) * (1/2) * ||y - beta_inter - X %*% beta||_2^2 + lam * Pen(beta),
// where the 1/4 comes from the weighted least squares part and beta_inter
// is the intercept term. Unlike linear models, we cannot ignore the intercept
// term now.
// Hence we use a simple coordinate descent algorithm.
temp_resp = intercept + temp_xbeta +
(y - temp_prob) / (temp_prob % (1 - temp_prob));
pars(0) = intercept;
pars.subvec(1, J) = beta;
// Obtain updated parameter.
pars_new = innerLoop(temp_resp, beta, intercept,
tol_inner, max_iter_inner,
x_mat, n, weights.col(i));
// Rcout << "Lambda"<< i<< ": "<< norm(pars_new - pars)/norm(pars_new) << "\n";
if(norm(pars_new - pars) / norm(pars_new) < tol) {
beta_ans.col(i) = pars_new.subvec(1, J);
intercept_ans(i) = pars_new(0);
beta = beta_ans.col(i);
intercept = pars_new(0);
converge = true;
} else {
beta = pars_new.subvec(1, J);
intercept = pars_new(0);
counter = counter + 1;
if(counter == max_iter) {
beta_ans.col(i) = beta;
intercept_ans(i) = intercept;
Function warning("warning");
warning("Function did not converge for some lambda.");
}
}
}
}
// Generate matrix of intercepts, this will be a n*nlam martrix for the
// nlam different fitted models.
arma::mat inters_mat(n, nlam, fill::eye);
inters_mat.each_row() %= trans(intercept_ans);
arma::mat fit_xbeta = inters_mat + x_mat * beta_ans;
arma::mat fit_prob = 1 / (1 + exp(-1 * fit_xbeta));
// Now return beta to the original scale.
arma::mat beta_hat2 = solve(trimatu(R_mat), beta_ans);
arma::sp_mat beta_final = sp_mat(beta_hat2);
return List::create(Named("beta") = beta_final,
Named("intercept") = intercept_ans,
Named("lambdas") = lambdas,
Named("fitted") = fit_prob);
}
