[Marc-Antoine Schmidt (MarcAntoineSchmidtQC)]

Fixes #414, as an alternative to #540 that does not copy the data.

StandardizedMatrix computes its products by expanding X * mult + shift into uncentered terms. These cancel when a column's mean is large relative to its std, which can lose all significant digits. This PR subtracts the column means inside the C++ kernels while they read the dense data, so the products are computed on centered data without a copy:

• sandwich: the dense sandwich kernel centers while packing its panels. For a SplitMatrix, the sparse × dense and categorical × dense cross kernels do the same.
• matvec / transpose_matvec: the dense matrix-vector kernels take a center and are vectorized along the unrestricted direction, so restricted products also get faster.
• standardize() keeps the exact means. For a StandardizedMatrix built directly, they are recovered from shift / mult.

Also fixes StandardizedMatrix.astype dropping mult, and transpose_matvec ignoring the order of cols when it lists all columns in a different order.

Benchmarks

float64 on an M1 Pro, against main and #540 with materialize_shift=True.

Accuracy at mean/std = 1e6 (max error / max |value|, against data centered in float64):

	main	#540 + flag	this PR
dense sandwich	3.6e-3	2.9e-11	5.8e-16
dense transpose_matvec	3.2e-9	3.2e-10	1.4e-15
split sandwich	2.0e-3	4.6e-11	4.1e-15
split transpose_matvec	3.3e-9	2.7e-10	3.7e-15
StandardizedMatrix built directly, sandwich	9.9e-3	9.9e-3	2.3e-11

Speed (ms) and memory, 1M×50 unless noted:

	main	#540 + flag	this PR
standardize	16	75	17
sandwich, F / C order	30 / 57	23 / 27	25 / 28
matvec, F order	6.0	4.6	7.4
transpose_matvec, F / C order	8.1 / 32	5.9 / 33	7.7 / 6.8
matvec with cols, 100k×500	5.4	5.8	2.7
split sandwich (50 dense, 20 sparse, 2 categoricals)	104	103	108
extra memory held	0	381 MB	0

#540 is faster for unrestricted matvec / transpose_matvec on F-order data, because it can call BLAS on its copy. On C-order data, OpenBLAS's X.T @ v is slow; this PR's kernel avoids it.

glum fits (time / iterations / coefficient error against a fit on centered data):

	main	#540 + flag	this PR
dense 1M×50 binomial, means ~1e6, irls-ls	fails (singular Hessian)	0.57 s / 3 / 1e-12	0.30 s / 3 / 3e-16
same, irls-cd	42 s / 200, no convergence	0.57 s / 3 / 1e-12	0.30 s / 3 / 6e-16
mixed DataFrame poisson, dense means ~1e6, irls-ls	0.51 s / 9 / 4e-9	0.44 s / 8 / 4e-11	0.43 s / 8 / 2e-15

#540 only helps if glum passes the flag; this PR fixes glum's current call. The reproducer from Quantco/glum#872 converges in 12 IRLS iterations (0.9 s) instead of hitting the 100-iteration cap (300 s). glum's test suite, including the golden masters, passes against this branch.

Checklist

• Added a CHANGELOG.rst entry

[Copilot]

🟡 Changes recommended

Active correctness bugs discard meaningful shift residuals, break products on standardized dense slices, and return columns in the wrong order for unsigned indexers.

4 open issues

• Handle unsigned descending indices in identity check · New
• Squeeze selected center before applying at least_1d · New
• Do not discard meaningful shift updates · New
• Preserve float32 center rounding residual in shift · New

What changed in this PR

Improves numerical stability of standardized matrix products by centering dense data inside the kernels, addressing #414 without copying the matrix.

Changes:

• Adds in-kernel centering for dense products and sparse/categorical cross-products.
• Vectorizes dense matrix-vector kernels and fixes scaling preservation and permuted-column ordering.
• Adds numerical-accuracy and regression tests, plus release notes.

File	Description
tests/​test_standardized_mat.py	Tests accuracy, slicing, casting, and column ordering.
tests/​test_fast_sandwich.py	Tests centered kernels across layouts and restrictions.
src/​tabmat/​standardized_mat.py	Tracks centers and dispatches centered products.
src/​tabmat/​split_matrix.py	Routes centers through dense blocks and cross-products.
src/​tabmat/​sparse_matrix.py	Passes dense centers into sparse cross-products.
src/​tabmat/​matrix_base.py	Adds centered-product hooks and preserves exact means.
src/​tabmat/​ext/​split.pyx	Exposes centering for categorical–dense kernels.
src/​tabmat/​ext/​sparse.pyx	Exposes centering for sparse–dense kernels.
src/​tabmat/​ext/​sparse_helpers-tmpl.cpp	Centers dense values during cross-product packing.
src/​tabmat/​ext/​dense.pyx	Validates centers and dispatches dense kernels.
src/​tabmat/​ext/​dense_helpers-tmpl.cpp	Implements centering and vectorized matrix-vector operations.
src/​tabmat/​ext/​cat_split_helpers-tmpl.cpp	Centers dense values in categorical cross-products.
src/​tabmat/​dense_matrix.py	Adds centered-product dispatch and column-order handling.
src/​tabmat/​categorical_matrix.py	Forwards centers to categorical–dense kernels.
CHANGELOG.rst	Documents accuracy fixes and performance changes.

_{Review effort: Balanced}