How do I do outer product of tensors in Eigen?

问题

In eigen, one can do quite easily tensor contractions using:

Tensor<double, 1> tensor1;
Tensor<double, 2> tensor2;

// fill with data so that
// tensor1 is of dimensions [10] and tensor2 of dimensions [5,10]

std::array<Eigen::IndexPair<int>, 1> product_dims1 = { IndexPair<int>(1, 0) };

auto tensor = tensor2.contract(tensor1, product_dims1);

// now tensor is of dimensions [5]

I am looking for a method that does the opposite of contraction, meaning it takes two tensors A and B, say of dimensions 5 x 10 and 3 x 2 and defines a new tensor C of dimensions 5 x 10 x 3 x 2 such that

  C_ijkl = A_ij * B_kl

I could easily write such a method if necessary, but I get the sense it would be more optimized if I used a native eigen method. I also want to be able to use GPU support which is quite easy with eigen if you use the native methods.

Thanks.

回答1:

The solution is perhaps too simple: You have to contract over no indices.

Eigen::array<Eigen::IndexPair<long>,0> empty_index_list = {};
Tensor<double, 2> A_ij(4, 4);
Tensor<double, 2> B_kl(4, 4);
Tensor<double, 4> C_ijkl = A_ij.contract(B_kl, empty_index_list);

回答2:

You can achieve an outer product by reshaping the the input tensors padding the dimensions with additional one-dimensional ones and then broadcast over the new dimensions.

For the two rank-2 and one rank-4 tensors you have C_ijkl = A_ij * B_kl it would look like:

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

using namespace Eigen;

int main() {

Tensor<double, 2> A_ij(4, 4);
Tensor<double, 2> B_kl(4, 4);
Tensor<double, 4> C_ijkl(4, 4, 4, 4);

Tensor<double, 4>::Dimensions A_pad(4, 4, 1, 1);
array<int, 4> A_bcast(1, 1, 4, 4);

Tensor<double, 4>::Dimensions B_pad(1, 1, 4, 4);
array<int, 4> B_bcast(4, 4, 1, 1);

C_ijkl = A_ij.reshape(A_pad).broadcast(A_bcast) * 
         B_kl.reshape(B_pad).broadcast(B_bcast);

}

来源：https://stackoverflow.com/questions/40829887/how-do-i-do-outer-product-of-tensors-in-eigen

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c++

eigen