fix(basis): B-spline LS round-trip transpose + point-wise nbasis CV (GH #33)

[sipemu]

Fixes #33.

Two independent defects in the 1-D B-spline basis path.

Bug 1 — fdata_to_basis / basis_to_fdata transpose the result for n > 1

Both functions built a curve-major flat buffer ([i*K + k], [i*m + j]) and passed it to FdMatrix::from_column_major, which reads it column-major ([row + col*n]). For a single curve the two layouts coincide (why a smooth 1-curve round-trip was perfect), but for multiple curves the coefficients and reconstruction were transposed/scrambled — hence residuals worse than a constant fit, flat in n_basis, and outside the data range on the 35×365 weather matrix. The least-squares solve (BᵀB)⁻¹Bᵀ itself is correct.

Fix: collect per-curve rows and scatter them into the matrix via [(i, k)] / [(i, j)] indexing (column-major-correct), preserving parallelism.

Bug 2 — basis_nbasis_cv (Cv) always selects the maximum n_basis

evaluate_nbasis_cv fit each fold's training curves but threw those coefficients away, then projected every test curve onto the basis using its own data and scored it against itself — a pure in-sample residual with no hold-out, monotone-decreasing in n_basis. (Leaving out whole curves is ill-posed for per-curve basis fitting: a held-out curve can't be predicted from other curves' coefficients.)

Fix: cross-validate over time points — fit coefficients on the retained points, predict the held-out points, score the prediction error. This is a genuine predictive criterion that penalizes overfitting and shows an interior minimum. The GCV/AIC/BIC paths were already correct and are unchanged.

Tests

• test_bspline_roundtrip_multi_curve_is_least_squares: multi-curve round-trip beats a constant fit, improves with n_basis, stays in range.
• test_basis_nbasis_cv_penalizes_overfitting: CV no longer selects the max n_basis (and scores aren't monotone) on smooth+noise data.
• Full basis (149) + smooth_basis (106) + R-validation (173) + validate_new_modules (56) pass; clippy --all-targets + rustfmt clean.

🤖 Generated with Claude Code

[codecov]

Codecov Report

❌ Patch coverage is 98.57143% with 1 line in your changes missing coverage. Please review.
✅ Project coverage is 89.02%. Comparing base (fca0a0e) to head (e768b72).
⚠️ Report is 3 commits behind head on main.

Files with missing lines	Patch %	Lines
fdars-core/src/smooth_basis.rs	98.14%	1 Missing ⚠️

Additional details and impacted files

@@           Coverage Diff           @@
##             main      #36   +/-   ##
=======================================
  Coverage   89.01%   89.02%           
=======================================
  Files         200      200           
  Lines       44099    44124   +25     
=======================================
+ Hits        39255    39281   +26     
+ Misses       4844     4843    -1     

Flag	Coverage Δ
rust	89.02% <98.57%> (+<0.01%)	⬆️

Flags with carried forward coverage won't be shown. Click here to find out more.

Files with missing lines	Coverage Δ
fdars-core/src/basis/projection.rs	95.76% <100.00%> (+0.34%)	⬆️
fdars-core/src/smooth_basis.rs	97.59% <98.14%> (+0.07%)	⬆️

🚀 New features to boost your workflow:

• ❄️ Test Analytics: Detect flaky tests, report on failures, and find test suite problems.