#include <RcppGSL.h>
#include <gsl/gsl_multifit.h>
#include <cmath>
// [[Rcpp::export]]
Rcpp::List fastLm(const RcppGSL::Matrix &X, const RcppGSL::Vector &y) {
    int n = X.nrow(), k = X.ncol();
    double chisq;
    RcppGSL::Vector coef(k);                // to hold the coefficient vector 
    RcppGSL::Matrix cov(k,k);               // and the covariance matrix
    // the actual fit requires working memory we allocate and free
    gsl_multifit_linear_workspace *work = gsl_multifit_linear_alloc (n, k);
    gsl_multifit_linear (X, y, coef, cov, &chisq, work);
    gsl_multifit_linear_free (work);
    // assign diagonal to a vector, then take square roots to get std.error
    Rcpp::NumericVector std_err;
    std_err = gsl_matrix_diagonal(cov); 	// need two step decl. and assignment
    std_err = Rcpp::sqrt(std_err);         	// sqrt() is an Rcpp sugar function
    return Rcpp::List::create(Rcpp::Named("coefficients") = coef,
                              Rcpp::Named("stderr")       = std_err,
                              Rcpp::Named("df.residual")  = n - k);
}

#include <RcppGSL.h>
#include <gsl/gsl_matrix.h>
#include <gsl/gsl_blas.h>
// [[Rcpp::export]]
Rcpp::NumericVector colNorm(const RcppGSL::Matrix & G) {
    int k = G.ncol();
    Rcpp::NumericVector n(k);           // to store results
    for (int j = 0; j < k; j++) {
        RcppGSL::VectorView colview = gsl_matrix_const_column (G, j);
        n[j] = gsl_blas_dnrm2(colview);
    }
    return n;                           // return vector
}