Most efficient option for build 3D structures usin

Question

I need a 3D matrix/array structure on my code, and right now I'm relying on Eigen for both my matrices and vectors.

Right now I am creating a 3D structure using new:

MatrixXd* cube= new MatrixXd[60];
for (int i; i<60; i++) cube[i]=MatrixXd(60,60);

and for acessing the values:

double val;
MatrixXd pos;
for (int i; i<60; i++){
    pos=cube[i];
    for (int j; j<60; j++){
        for (int k; k<60; k++){
            val=pos(j,k);
            //...
        }
    }
}

However, right now it is very slow in this part of the code, which makes me beleive that this might not be the most efficient way. Are there any alternatives?

Answer 1

While it was not available, when the question was asked, Eigen has been providing a Tensor module for a while now. It is still in an "unsupported" stage (meaning the API may change), but basic functionality should be mostly stable. The documentation is scattered here and here.

Answer 2

A solution I used is to form a fat matrix containing all the matrices you need stacked.

MatrixXd A(60*60,60);

and then access them with block operations

A0 = A.block<60,60>(0*60,0);
...
A5 = A.block<60,60>(5*60,0);

Answer 3

An alternative is to create a very large chunk of memory ones, and maps Eigen matrices from it:

double* data = new double(60*60 * 60*60*60);

Map<MatrixXd> Mijk(data+60*(60*(60*k)+j)+i), 60, 60);

At this stage you can use Mijk like a MatrixXd object. However, since this not a MatrixXd type, if you want to pass it to a function, your function must either:

• be of the form foo(Map<MatrixXd> mat)
• be a template function: template<typename Der> void foo(const MatrixBase<Der>& mat)
• take a Ref<MatrixXd> object which can handle both Map<> and Matrix<> objects without being a template function and without copies. (doc)