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-le...@python.org >> https://mail.python.org/mailman3//lists/numpy-discussion.python.org >> Member address: jac...@bioinformed.com >> > > _______________________________________________ > NumPy-Discussion mailing list -- numpy-discussion@python.org > To unsubscribe send an email to > numpy-discussion-leave@python.orghttps://mail.python.org/mailman3//lists/numpy-discussion.python.org > Member address: lorentzen...@gmail.com > > _______________________________________________ > NumPy-Discussion mailing list -- numpy-discussion@python.org > To unsubscribe send an email to numpy-discussion-le...@python.org > https://mail.python.org/mailman3//lists/numpy-discussion.python.org > Member address: kevin.k.shepp...@gmail.com >
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