Eigen Contraction与Numpy Dot结果不一致问题咨询

Hey there! Let’s dig into why your tensor dot product results aren’t lining up between NumPy and Eigen, and how to replicate NumPy’s behavior exactly in C++.

First, Let’s Recap NumPy’s Default Behavior #

When you run a tensor dot in NumPy (like np.tensordot(a, b, axes)), the outcome depends entirely on how you specify the axes to contract:

• If you skip the axes argument, NumPy flattens both tensors into 1D arrays and computes a simple inner product.
• If you pass something like axes=([2], [2]), it contracts the third (depth) dimension of both tensors—meaning it multiplies corresponding elements along that axis and sums them up, which sounds exactly like what you’re aiming for (since you mentioned needing three multiplication operations per depth component).

Yes, the product_dims Parameter Is Almost Certainly the Issue! #

Eigen doesn’t guess which axes you want to contract—you have to tell it explicitly via the dimension arguments in contract() (which ties directly to the product_dims concept). If you don’t set this correctly, Eigen will contract the wrong axes, leading to mismatched shapes or values compared to NumPy.

Another easy-to-miss detail: memory layout. NumPy defaults to row-major ordering, while Eigen uses column-major by default. If your tensors are stored in different layouts, even with the right axes, you’ll get wonky results.

How to Replicate NumPy’s Tensor Dot in Eigen #

Let’s say you’re working with two 3D tensors (shape (height, width, 3)) in NumPy, and you’re running:

result = np.tensordot(a, b, axes=([2], [2]))

This gives a 2D tensor where each element is the sum of the three depth-component products (e.g., a[i,j,0]*b[i,j,0] + a[i,j,1]*b[i,j,1] + a[i,j,2]*b[i,j,2]).

Here’s how to do the exact same thing in Eigen:

1. Match the memory layout: Declare your Eigen tensors with row-major ordering to match NumPy’s default.
2. Explicitly contract the depth axis: Use Eigen’s contract() method and specify that you want to contract the third (0-based index 2) dimension of both tensors.

Example code snippet:

#include <Eigen/Tensor>

using namespace Eigen;

int main() {
    // Create two 3D tensors (2x2x3 as an example) with row-major layout
    Tensor<float, 3, RowMajor> a(2, 2, 3);
    Tensor<float, 3, RowMajor> b(2, 2, 3);
    
    // Fill your tensors with values matching your NumPy input here
    
    // Define which axes to contract: the 3rd dimension (index 2) for both tensors
    array<int, 1> contract_dims_a = {2};
    array<int, 1> contract_dims_b = {2};
    
    // Perform the contract operation—result will be a 2x2 tensor
    Tensor<float, 2, RowMajor> result = a.contract(b, contract_dims_a, contract_dims_b);

    // Alternatively, you can do element-wise multiply then sum over the depth axis (same result):
    // Tensor<float, 2, RowMajor> result = (a * b).sum(2);
    
    return 0;
}

Quick Checks to Ensure Alignment #

• Double-check the axis indices: Eigen uses 0-based indexing, so the depth axis (third dimension in NumPy) is index 2 in Eigen.
• Verify memory layout: If you’re loading data from NumPy into Eigen, make sure to use RowMajor to avoid shape misinterpretation.
• Test with small, known values: Use simple tensors (like all 1s or a small set of numbers) to confirm that both NumPy and Eigen return the same result.

Wrapping Up #

The core difference is that NumPy has implicit defaults for tensor contraction, while Eigen requires you to be explicit about which axes to pair up. By setting the correct contraction dimensions (or using the sum-after-element-wise-multiply shortcut) and matching memory layouts, you’ll get exactly the depth-component dot product you need, identical to NumPy.

内容的提问来源于stack exchange，提问作者raaj