``LogisticGroupLasso`` is not equivalent to ``scikit-learn`` ``LogisticRegression`` with groups of size 1

Problem

LogisticGroupLasso doesn't give the same regression coefficient as scikit-learn LogisticRegression when fitted on groups with size 1.

Expected behavior

Group logistic regression with groups of size one should be equivalent to logistic regression.

Script to reproduce

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```python import numpy as np from sklearn.linear_model import LogisticRegression from group_lasso import LogisticGroupLasso n_samples, n_features = 20, 60 # generate dummy data rng = np.random.RandomState(123) X = rng.randn(n_samples, n_features) y = np.sign(rng.randn(n_samples)) # max regularization parameter alpha_max = np.linalg.norm(X.T @ y, ord=np.inf) / (2 * n_samples) alpha = 0.1 * alpha_max # fit scikit-learn log reg sk_model = LogisticRegression( penalty='l1', C=1/(n_samples * alpha), # scikit-learn uses an un-normalized loss fit_intercept=False, tol=1e-9, solver='liblinear' ).fit(X, y) sk_coef = sk_model.coef_.flatten() # group log reg yn_model = LogisticGroupLasso( group_reg=alpha, groups=np.arange(n_features), fit_intercept=False, subsampling_scheme=None, tol=1e-9, l1_reg=0., ).fit(X, y) coef_ = yn_model.coef_ yn_coef = coef_[:, 1] np.testing.assert_allclose(yn_coef, sk_coef) ```

output

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```shell AssertionError: Not equal to tolerance rtol=1e-07, atol=0 Mismatched elements: 10 / 60 (16.7%) Max absolute difference: 0.96593495 Max relative difference: 1. x: array([ 0. , -0. , -0.010529, 0. , 0. , 0.43878 , 0. , 0.337345, 0.15179 , -0. , 0.066626, 0. , -0. , 0. , -0. , 0. , 0. , -0. ,... y: array([ 0. , 0. , -0.034694, 0. , 0. , 1.111946, 0. , 0.840564, 0.309066, 0. , 0.15613 , 0. , 0. , 0. , 0. , 0. , 0. , 0. ,... ```

yngvem / group-lasso