fix(splines): evaluate the I-spline basis in closed form

[ChrisW09]

Fixes #53.

ISplineTransformer returned inaccurate and sometimes identically zero basis columns whenever an M-spline's support was narrow compared to the knot range. This happens on skewed data under the default quantile placement and with a larger output_dim, also through Preprocessor, and without a warning.

Root cause

ISplineTransformer._ispline_basis integrated each M-spline with the trapezoid rule on a fixed 200-point grid over the whole knot range, then interpolated the cumulative integral linearly with np.interp. A basis function whose support spans only a few grid cells ramped up over whole cells instead of over its support. One whose support falls between two grid points integrated to 0, and since normalization only ran if max_integral > 1e-10, its column stayed all zeros. Such rows also break the ordering I_0 ≥ I_1 ≥ … ≥ I_{K-1} that every I-spline row satisfies.

Fix

• New ISplineTransformer._ispline_columns evaluates every I-spline column in closed form. The antiderivative of the B-spline basis, BSpline(knots, np.eye(n_coef), degree).antiderivative(), is itself a B-spline of degree p + 1. Each column is that antiderivative minus its value at the left boundary, divided by the analytic integral (t_{k+p+1} - t_k) / (p + 1).
• x is clipped to the knot range, so values below and above it are 0 and 1. At the right boundary the value is pinned to the full integral instead of being evaluated, so a repeated boundary knot cannot put the evaluation on a zero-width interval. A basis function with zero-width support (a repeated knot) becomes the step function at that knot, its limit as the support shrinks.
• _ispline_basis delegates to _ispline_columns, and _design_matrix builds the whole design in one call instead of one call per column.

Behaviour changes

• I-spline values change wherever the quadrature was inaccurate: narrow knot spans on skewed data or with a larger output_dim. On benign data (normal, output_dim=6) the old values were within about 2e-4 of the exact ones. The golden regression baselines pass unchanged.
• A basis function with zero-width support, which on main arises when an interior knot coincides with a boundary knot on tied data, is now the step function at that knot instead of an all-zero column.

Documentation

• The class docstring ("the integral of an M-spline over the fitted range ... normalized to [0, 1]") and docs/representations/spline_expansions.md (I_k(x) = ∫_{τ_k}^{x} M_k(t) dt) already describe the fixed behaviour; the implementation now matches them exactly, so they are unchanged.
• The new private _ispline_columns has a docstring describing the closed form, the boundary values and the zero-width case; _ispline_basis refers to it.

Tests

• test_ispline_matches_exact_integral_on_tight_knots[lognormal(0, 2)-{6,10,30}, normal-{20,50}, lognormal(0, 1)-20, exponential-20]: the transform equals the normalized antiderivative of each B-spline basis function to 1e-10, no column is all zero, and every row is ordered I_0 ≥ I_1 ≥ …. The cases cover the issue's reproduction and every row of its error table. Fails on main (all 7 cases), passes here.
• test_ispline_reaches_zero_and_one_at_the_range_boundaries: on lognormal(0, 2) data with output_dim=10, every column is exactly 0 at the training minimum and exactly 1 at the training maximum. Fails on main, passes here.

Reproduction

Output of the script from #53 on this branch:

all-zero columns: []
max |pretab - exact| per column: [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]

Checks

• just test: 1446 passed, 59 skipped, 7 xfailed; coverage 93.54% (gate 90%).
• Minimum dependencies (CI job: Python 3.10, numpy 1.24.4, pandas 2.0.3, scipy 1.10.1, scikit-learn 1.6.0): 1433 passed, 72 skipped, 7 xfailed; scripts/quickstart.py passes.
• just docs: strict build succeeds.
• just check: all pre-commit and pre-push hooks pass (ruff format, ruff lint, prettier, file hygiene, pyright with 0 errors).
• Import direction between subpackages is unchanged.

Merge notes

• Base: main.
• No other per-issue PR changes pretab/expansion/spline/i_spline.py. The PRs for MSplineTransformer: absolute clipping thresholds make the basis depend on feature scale #63 (fix(splines): drop absolute clipping thresholds from the M-spline basis #107), Target-aware splines trim selector knots by position, dropping the dominant split, and cap adaptive width at 15 #69 (fix(splines): search the resolved knot window in target-aware placement #109), B/M/I spline knot_locations are sized by output_dim and clipped to the data range instead of used as given #81 (fix(splines): honour explicit knot_locations regardless of output_dim #118), B/M/I spline and two-feature thin-plate spline transformers encode a missing value as an all-zero row #87 (fix(splines): expand a missing value to a NaN row in the B/M/I and thin-plate bases #122) and A 2-D y (multi-output target) crashes the B/M/I splines even when unsupervised, and target-aware methods with unrelated errors #88 (fix(splines): ignore y when unsupervised and reject a multi-output target #123) add tests to tests/expansion/spline/test_spline_expansions.py in other places, and each merges cleanly with this branch.
• The PR for B/M/I spline and two-feature thin-plate spline transformers encode a missing value as an all-zero row #87 (fix(splines): expand a missing value to a NaN row in the B/M/I and thin-plate bases #122) passes only the observed rows to _design_matrix, so the np.nan_to_num kept in ISplineTransformer._design_matrix becomes a no-op there. The PR for A partial spline policy mapping drops the "clip" default, and "extrapolate"/"warn" give all-zero basis rows #84 (fix(splines): keep family policy defaults and extrapolate out-of-range rows #121) documents that under "extrapolate" and "warn" an I-spline stays at 0 below and 1 above the range, which the clipping in _ispline_columns provides. With this branch and the branches for MSplineTransformer: absolute clipping thresholds make the basis depend on feature scale #63, A partial spline policy mapping drops the "clip" default, and "extrapolate"/"warn" give all-zero basis rows #84 and B/M/I spline and two-feature thin-plate spline transformers encode a missing value as an all-zero row #87 combined, the full test suite passes (1499 passed, 59 skipped, 7 xfailed).
• The PR for Spline knots on tied data land on the range boundary or repeat, producing dead columns and all-zero rows #56 (fix(splines): keep knots unique and strictly interior on tied data #101) drops repeated and boundary knots on tied data, which removes the usual source of the zero-width basis functions handled here. It does not touch this file.

This change was previously part of #75, which is closed in favour of one pull request per issue.