// -*- mode: C++; c-indent-level: 4; c-basic-offset: 4; indent-tabs-mode: nil; -*-
//
// fastLm.cpp: Rcpp/Armadillo glue example of a simple lm() alternative
//
// Copyright (C)  2010 - 2024  Dirk Eddelbuettel, Romain Francois and Douglas Bates
//
// This file is part of RcppArmadillo.
//
// RcppArmadillo is free software: you can redistribute it and/or modify it
// under the terms of the GNU General Public License as published by
// the Free Software Foundation, either version 2 of the License, or
// (at your option) any later version.
//
// RcppArmadillo is distributed in the hope that it will be useful, but
// WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU General Public License
// along with RcppArmadillo.  If not, see <http://www.gnu.org/licenses/>.

#include <RcppArmadillo/Lighter>

// [[Rcpp::export]]
Rcpp::List fastLm_impl(const arma::mat& X, const arma::colvec& y) {
    int n = X.n_rows, k = X.n_cols;

    arma::colvec coef = arma::solve(X, y);     // fit model y ~ X
    arma::colvec res  = y - X*coef;            // residuals
    double s2 = arma::dot(res, res) / (n - k); // std.errors of coefficients
    arma::colvec std_err = arma::sqrt(s2 * arma::diagvec(arma::pinv(arma::trans(X)*X)));

    return Rcpp::List::create(Rcpp::Named("coefficients") = coef,
                              Rcpp::Named("stderr")       = std_err,
                              Rcpp::Named("df.residual")  = n - k);
}
