如果本征中两个张量相等，该如何比较？

Question

There is this:

https://codeyarns.com/2016/02/16/how-to-compare-eigen-matrices-for-equality/

But there is no isApprox for tensors.

The following doesn't do what I want:

#include <Eigen/Core>
#include <unsupported/Eigen/CXX11/Tensor>
#include <array>
#include <iostream>

using namespace Eigen;
using namespace std;

int main()
{
// Create 2 matrices using tensors of rank 2
Eigen::Tensor<int, 2> a(2, 3);
Eigen::Tensor<int, 2>* b = &a;

cerr<<(*b==*b)<<endl;
}

because it does coordinate wise comparison and returns a tensor of the same dimension instead of a true/false vale.

How do I check if two tensors are identical? No isApprox for tensors.

I could write my own function, but I want to be able to use GPU power when available, and it seems like Eigen has built-in GPU support.

Answer 1

For an exact comparison of 2 tensors A and B, you can use the comparison operator followed by a boolean reduction: Tensor<bool, 0> eq = (A==B).all();

This will return a tensor of rank 0 (ie a scalar) that contains a boolean value that's true iff each coefficient of A is equal to the corresponding coefficient of B.

There is no approximate comparison at the moment, although it wouldn't be difficult to add.

Answer 2

You can always use a couple of Eigen::Map s to do the isApprox checks.

#include <iostream>
#include <unsupported/Eigen/CXX11/Tensor>

using namespace Eigen;

int main()
{

    Tensor<double, 3> t(2, 3, 4);
    Tensor<double, 3> r(2, 3, 4);

    t.setConstant(2.1);
    r.setConstant(2.1);
    t(1, 2, 3) = 2.2;
    std::cout << "Size: " << r.size() << "\n";
    std::cout << "t: " << t << "\n";
    std::cout << "r: " << r << "\n";

    Map<VectorXd> mt(t.data(), t.size());
    Map<VectorXd> mr(r.data(), r.size());

    std::cout << "Default isApprox: " << mt.isApprox(mr) << "\n";
    std::cout << "Coarse isApprox: " << mt.isApprox(mr, 0.11) << "\n";

    return 0;
}

PS/NB Regarding Eigen's built in GPU support... Last I checked it is fairly limited and with good reason. It is/was limited to fixed size matrices as dynamic allocation on a GPU is really something you want to avoid like the common cold (if not like the plague). I take it back. It looks like the Tensor module supports GPUs pretty well.