validation check for precomputed gram matrix fails erroneously when using float32 data

Describe the bug

A validation check for the precomputed gram matrix has been introduced in version 1.0.0 (https://github.com/scikit-learn/scikit-learn/pull/19004).

This check sometimes misleadingly fails when the matrix has dtype float32 and the arbitrary selected feature columns are sparse.

Code snippet to reproduce attached.

I could add a pr in the following days to fix that if wanted.

Steps/Code to Reproduce

from sklearn.linear_model import LassoCV
import numpy as np

m = LassoCV()

np.random.seed(seed=3)

X = np.random.random((10000, 50)).astype(np.float32)
X[:, 25] = np.where(X[:, 25] < 0.98, 0, 1)
X[:, 26] = np.where(X[:, 26] < 0.98, 0, 1)
y = np.random.random((10000, 1)).astype(np.float32)

m.fit(X, y)

Expected Results

No Exception thrown

Actual Results

ValueError: Gram matrix passed in via ‘precompute’ parameter did not pass validation when a single element was checked - please check that it was computed properly. For element (25,26) we computed -0.4163646101951599 but the user-supplied value was -0.41635191440582275.

Versions

1.0.1

[derHeinzer]

I created a pr to fix this issue: https://github.com/scikit-learn/scikit-learn/pull/22008 The check of gram matrix is unnecessary in case it has not been provided by the user, but calculated by coordinate descent itself. Additionally it would make sense to increase tolerance values when the dtype of the matrices are float32.

[agramfort]

@QuantHao #22208 is stalled as there is no test added. Can you take over the PR and add the necessary tests so we can consider merging? 🙏