This is a good place for numba if performance and memory use are a concern. Good NumPy 125 ms ± 2.42 ms per loop (mean ± std. dev. of 7 runs, 10 loops each) Naive numba (memory efficient) 386 ms ± 1.83 ms per loop (mean ± std. dev. of 7 runs, 1 loop each) Parallel numba (memory efficient, cpu bounded) 46.8 ms ± 1.12 ms per loop (mean ± std. dev. of 7 runs, 10 loops each) Here is a gist that produced the timings: https://gist.github.com/bashtage/39c50b223580b9bc3f763a3b1be3e478 All were on a 12 core Ryzen. Kevin On Mon, Aug 18, 2025 at 12:35 PM Christian Lorentzen via NumPy-Discussion < numpy-discussion@python.org> wrote:

If W is just a vector, i.e. my main use case, than what you write is what I wanted to imply and actually how I implemented it in several cases. The point is that X.T * weights[None, :] still doubles memory (same size as X) and this solution doesn't exploit the symmetry. Best Christian

On 17.08.2025 22:13, Kevin Jacobs wrote:

Why not:

XTWX = (X.T * weights[None, :]) @ X

if `weights` is a vector? Allocating `diag(weights)` is the big memory and CPU hog at least for my generally long and skinny X matrices.

-Kevin

On Fri, Aug 15, 2025 at 10:08 AM Christian Lorentzen via NumPy-Discussion < numpy-discussion@python.org> wrote:

...

Dear numpy community

I would like to propose a mew feature in np.linalg to compute weighted gram matrix (sandwich product), see https://github.com/numpy/numpy/issues/29559. Proposed new feature or change:

The solvers for many important statistical models like Generalized Linear Models often need to compute X.T @ W @ X where X is a 2-dimensional array of features (features in columns, observations in rows) and W is very often a diagonal array of (current) weights. This computation is usually the main computational bottleneck.

It would be great if numpy could provide an efficient implementation of it, e.g. np.linalg.sandwicht_product(X, weight=w).

Why numpy? It seems even more unrealistic to me, to get it into BLAS implementations. Numpy has support for SIMD via Highways. Computational alternatives

Drawbacks of (X.T * diag(W)) @ X:

- Additional memory allocation to compute X.T @ diag(W) , same size as (usually large) X. - The result is symmetric, but this fact is not used. So at least a factor of 2 is possible. Note that without weights, X.T @ X uses BLAS syrk. But the weights are crucial.

Drawback of Z = np.sqrt(diag(W))[:, None] * X and then Z @ Z:

- Additional memory allocation for Z, same size as (usually large) X. - Taking square roots for possibly large diag(W)

Additional information

https://github.com/Quantco/tabmat has an implementation of it with XSIMD.

Best Christian Lorentzen _______________________________________________ NumPy-Discussion mailing list -- numpy-discussion@python.org To unsubscribe send an email to numpy-discussion-leave@python.org https://mail.python.org/mailman3//lists/numpy-discussion.python.org Member address: jacobs@bioinformed.com

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