Copying upper MatrixXd to lower MatrixXd (Eigen3) C++ library

Question

I've got a lower triangular MatrixXd and I want to copy its lower values to the upper side as it'll become a symmetric matrix. How can I do it?

So far I've done:

 MatrixXd m(n,n); 
 .....
 //do something with m
 for(j=0; j < n; j++)
       {
         for(i=0; i<j; i++)
           {
             m(i,j) = m(j,i);

           }
       }

Is there a fastest way to do it? I was thinking of some internal method that is able to "copy" the lower triangular matrix to the upper. Say I've got this matrix, we call m:

1 2 3
4 5 6
7 8 9

what I need to obtain in m is :

1 4 7
4 5 8
7 8 9

I also know you can get the upper or the lower part of the matrix to do something:

MatrixXd m1(n,n);
 m1 = m.triangularView<Eigen::Upper>();
cout << m1 <<endl;

1 2 3
0 5 6
0 0 9

But I can't yet get what I want...

Answer 1

I assume here that you are referring to working with the Eigen3 c++ library. This is not clear from your question. if not, you should consider it. In any case, within Eigen, there is no need to actually copy the triangular part, to get a selfadjoint matrix. Eigen has the concept of views, and you can use a self adjoint view in order to perform an operation like e.g.

using namespace Eigen;
MatrixXd m(m,n);
...
(generate uppper triangular entries in m)
...
VectorXd r(n), p(n);
r = m.selfadjointView<Upper>() * p;

here is a small example to illustrate using fixed size matrices:

#include <Eigen/Core>

using namespace std;
using namespace Eigen;

int main()
{
    Matrix2d m,c;
    m << 1, 2,
         0, 1;

    Vector2d x(0,2), r;

    // perform copy operation 
    c = m.selfadjointView<Upper>(); 
    cout << c << endl;

    // directly apply selfadjoint view in matrix operation
    // (no entries are copied)
    r = m.selfadjointView<Upper>() * x;
} 

the output will be [1, 2, 2, 1]. now, the result in r is the same as if you had used c * x instead. Just that there is no need for copying the values in the original matrix to make it selfadjoint.

Answer 2

In case the selfadjointView is not an option for you, the solution is to use triangularView on the destination matrix:

m.triangularView<Lower>() = m.transpose();