Armadillo - no member named i in matrix expression - c++

Question

According to Armadillo docs:
.i()
Member function of any matrix expression
Provides an inverse of the matrix expression
...
However, when I try to compile this snippet:
#include <armadillo>
#include <iostream>
arma::sp_mat linReg(arma::sp_mat X, arma::sp_mat Y) {
return (X.t() * X).i() * X.t() * Y;
}
int main() {
arma::sp_mat X = arma::sprandu(1000, 10, 0.3);
arma::sp_mat y = arma::sprandu(1000, 10, 0.3);
std::cout << linReg(X,y).t() << std::endl;
}
I get the following error
lreg.cpp: In function ‘arma::sp_mat linReg(arma::sp_mat,
arma::sp_mat)’: lreg.cpp:6:24: error: ‘arma::enable_if2<true, const
arma::SpGluearma::SpOp<arma::SpMat<double, arma::spop_htrans>,
arma::SpMat, arma::spglue_times> >::result’ {aka ‘const class
arma::SpGluearma::SpOp<arma::SpMat<double, arma::spop_htrans>,
arma::SpMat, arma::spglue_times>’} has no member named ‘i’
6 | return (X.t() * X).i() * X.t() * Y;
|
I already tried with mat and it works fine. Any clue why it's not working with sparse matrix? And if so, how can we calculate the inverse of a sparse matrix?

Answer 1

Taking the inverse of a sparse matrix is often not desired as you end up with a dense matrix. Often the explicit inverse is not required.
Instead of taking the inverse here, maybe treat the problem as solving a system of linear equations. Then reformulate using solve() or spsolve(). Below is an untested example for demonstrating the general approach:
arma::mat linReg(const arma::sp_mat& X, const arma::sp_mat& Y) {
arma::sp_mat A = X.t() * X;
arma::mat B = arma::mat(X.t() * Y); // convert to dense matrix
arma::mat result;
bool ok = arma::spsolve(result, A, B);
if(ok == false) {
// handle failure here
}
return result;
}