Eigen: Is there an inbuilt way to calculate sample covariance

Question

I am using the Eigen library in C++: I am currently calculating the covariance matrix myself as follows:

Eigen::MatrixXd covariance_matrix = Eigen::MatrixXd::Constant(21, 21, 0);
data mean = calc_mean(all_data)
for(int j = 0; j < 21; j++){
    for(int k = 0; k < 21; k++){
        for(std::vector<data>::iterator it = all_data.begin(); it!= all_data.end(); it++){
            covariance_matrix(j,k) += ((*it)[j] - mean[j]) * ((*it)[k] - mean[k]);
        }
        covariance_matrix(j,k) /= all_data.size() - 1;
    }
}

Is there an inbuilt/more optimized way to do this with the Eigen library? For example if I store my data in a MatrixXd where each row is an observation and each column a feature?

Thanks

Answer 1

Using Eigen expressions will leverage SIMD and cache optimized algorithms, so yes it should definitely be faster, and in any case, much simpler to write:

MatrixXd centered = mat.rowwise() - mat.colwise().mean();
MatrixXd cov = (centered.adjoint() * centered) / double(mat.rows() - 1);

Moreover, assuming "data" is a typedef for a double[21], then you can use the Map<> feature to view your std::vector as an Eigen object:

Map<Matrix<double,Dynamic,21,RowMajor> > mat(&(all_data[0][0], all_data.size(), 21);