Replicate a column VectorXd in order to construct a MatrixXd in Eigen, C++

Question

Let's assume that we have a 10x20 real matrix:

Eigen::MatrixXd A(10,20);
A.setRandom();

We would like to construct a 10x10 matrix of the form

B = [v v ... v v]

where v is a column vector of length 10. For this vector, v, each element is the squared norm of each row of A, that is:

v = ( ||x_1||^2, ||x_2||^2, ..., ||x_10||^2,)^T,

where x_j denotes the j-th row of A.

What is the most efficient way to construct matrix B?

I could construct v as follows:

Eigen::VectorXd v(10);
for (int i=1; i<10; i++)
{
    v(i) = A.row(i).squaredNorm();
}

I think that this step cannot be solved without a for loop. How could I replicate this column 10 times such that B is filled as discussed above?

Answer 1

Your assumption is wrong. The loop can be avoided by doing a rowwise operation. Then, the replication can be done as follows.

#include <iostream>
#include <Eigen/Core>

int main ()
{
    Eigen::MatrixXd A(10,20), B, C;
    A.setRandom();

    Eigen::VectorXd v(10);
    v = A.rowwise().squaredNorm();

    B = v.replicate(1,10);

    std::cout << B << "\n\n";

    return 0;
}

It can also be written in a single line as

    B =  A.rowwise().squaredNorm().replicate(1,10);

I highly recommend reading the documentation. It's pretty well written.