gam-sae 0.3.141

//! `collapse_bar_uses_reachable_dictionary_rank_not_nominal_count_1610`, split
//! verbatim out of `tests.rs` to keep that tracked file under the #780 10k-line
//! gate. Declared as a sibling `#[cfg(test)] mod` in `mod.rs`; the shared
//! `periodic_basis` fixture helper is sourced from the sibling `tests` module.

use super::*;
use super::tests::periodic_basis;
use ndarray::{Array2, Array3, array};

/// #1610 — the co-collapse acceptance bar must be calibrated against the
/// dictionary's GEOMETRICALLY REACHABLE rank `Σ_k rank(Φ_k)`, NOT the nominal
/// coefficient count `Σ_k basis_size_k` (the owner's audit: "nonlinear dict vs
/// linear PCA ceiling (biased high)"). The PCA ceiling the `0.5` fraction is
/// taken against is the best EV a rank-`q` LINEAR dictionary reaches; using the
/// nominal coefficient count for `q` over-states what a curved/degenerate
/// dictionary can actually span, biasing the bar high.
///
/// Fixture: a K=2 dictionary on a rank-2 (unit-circle) target.
///   * atom A — a `[1, sin, cos]` periodic chart on 4 distinct angles: full
///     chart rank `rank(Φ_A) = 3 = basis_size`.
///   * atom B — the SAME chart but evaluated at a SINGLE repeated coordinate, so
///     every row of `Φ_B` is identical: `rank(Φ_B) = 1 ≪ basis_size = 3` — a
///     geometrically degenerate atom that linearly spans only ONE direction.
///
/// Properties asserted (each fails if someone reverts to the nominal count):
///   1. `reachable_dictionary_rank = rank(Φ_A) + rank(Φ_B) = 3 + 1 = 4`, capped
///      at `min(n,p)`, strictly BELOW the nominal `Σ basis_size = 6`.
///   2. the reachable rank is read from the chart design ALONE, so a co-collapsed
///      decoder (`B → 0`) reports the SAME reachable rank (the guard does not
///      lower its own bar at the very collapse it must catch).
///   3. the live `collapse_ev_bar` at the reachable rank is ≤ the bar at the
///      nominal count (the bias is corrected DOWNWARD, never up).
#[test]
pub(crate) fn collapse_bar_uses_reachable_dictionary_rank_not_nominal_count_1610() {
    use crate::manifold::outer_objective::{collapse_ev_bar, reachable_dictionary_rank};

    // A target with genuine spectral spread across >= 6 directions, so the rank-q
    // PCA ceiling STRICTLY increases with q over the range that separates the
    // reachable rank (3) from the nominal count (6). n=8 rows, p=8 cols with
    // geometrically decaying singular values along distinct coordinate axes: the
    // captured-variance fraction at rank 3 is strictly below that at rank 6, so
    // the two bars differ and the cap (min(n,p)=8) never masks the difference.
    let (n, p) = (8usize, 8usize);
    let mut target = Array2::<f64>::zeros((n, p));
    // Row r, axis a: value sigma_a on the a-th axis when r == a, else 0 — a
    // diagonal-ish design whose centered singular values are the sigma_a, strictly
    // decreasing, so each extra rank adds a strictly positive variance increment.
    let sigma = [8.0_f64, 4.0, 2.0, 1.0, 0.5, 0.25, 0.125, 0.0625];
    for a in 0..p {
        target[[a, a]] = sigma[a];
    }

    // atom A: full-rank periodic chart on 4 distinct angles → rank(Φ_A) = 3.
    let coords_a = array![[0.0_f64], [0.25], [0.5], [0.75]];
    let (phi_a, jet_a) = periodic_basis(&coords_a);
    // atom B: SAME chart evaluated at one repeated coordinate → every Φ row equal
    // → rank(Φ_B) = 1, even though basis_size = 3.
    let coords_b = array![[0.3_f64], [0.3], [0.3], [0.3]];
    let (phi_b, jet_b) = periodic_basis(&coords_b);

    let make = |name: &str, phi: Array2<f64>, jet: Array3<f64>, decoder: Array2<f64>| {
        SaeManifoldAtom::new(
            name,
            SaeAtomBasisKind::Periodic,
            1,
            phi,
            jet,
            decoder,
            Array2::<f64>::eye(3),
        )
        .unwrap()
    };

    // Healthy (nonzero) decoders for both atoms.
    let atom_a = make("full", phi_a.clone(), jet_a.clone(), Array2::<f64>::ones((3, p)));
    let atom_b = make("degenerate", phi_b.clone(), jet_b.clone(), Array2::<f64>::ones((3, p)));

    // Per-atom realized chart image rank (capped at output dim p=8, so no cap
    // bites here): full chart spans rank 3; the repeated-coordinate chart rank 1.
    assert_eq!(
        atom_a.realized_chart_image_rank().unwrap(),
        3,
        "full periodic chart on 4 distinct angles spans rank 3 in [1,sin,cos]"
    );
    assert_eq!(
        atom_b.realized_chart_image_rank().unwrap(),
        1,
        "a chart evaluated at ONE repeated coordinate has identical rows → rank 1, \
         far below its basis_size 3"
    );

    let atoms = vec![atom_a, atom_b];
    let nominal: usize = atoms
        .iter()
        .map(|a| a.basis_size())
        .sum::<usize>()
        .min(n)
        .min(p);
    let reachable = reachable_dictionary_rank(&atoms, n, p);

    // (1) reachable rank = rank(Φ_A) + rank(Φ_B) = 3 + 1 = 4, STRICTLY below the
    // nominal Σ basis_size = 6 — the biased-high count is corrected.
    assert_eq!(reachable, 4, "reachable rank must be rank(Φ_A) + rank(Φ_B) = 3 + 1");
    assert_eq!(nominal, 6, "nominal Σ basis_size (capped) must be 6 on this fixture");
    assert!(
        reachable < nominal,
        "reachable rank {reachable} must be strictly below the nominal count \
         {nominal} (this fails if someone reverts to Σ basis_size)"
    );

    // (2) decoder-magnitude independence: a co-collapsed dictionary (decoders → 0)
    // reports the SAME reachable rank, so the guard keeps its full bar at the
    // collapse it must catch.
    let collapsed: Vec<SaeManifoldAtom> = vec![
        make("full0", phi_a, jet_a, Array2::<f64>::zeros((3, p))),
        make("degenerate0", phi_b, jet_b, Array2::<f64>::zeros((3, p))),
    ];
    assert_eq!(
        reachable_dictionary_rank(&collapsed, n, p),
        reachable,
        "reachable rank must read the chart design alone and be invariant to the \
         decoder magnitude (a co-collapsed decoder still reports full geometric reach)"
    );

    // (3) the live collapse bar at the reachable rank is STRICTLY BELOW the bar at
    // the nominal count on this spread target: calibrating against reachable
    // geometry corrects the (biased-high) bar DOWNWARD. This is the behavioral
    // consequence — it fails if the call sites revert to the nominal count.
    let bar_reachable = collapse_ev_bar(target.view(), reachable);
    let bar_nominal = collapse_ev_bar(target.view(), nominal);
    assert!(
        bar_reachable < bar_nominal,
        "collapse bar at reachable rank ({bar_reachable}) must be strictly below the \
         bar at the nominal count ({bar_nominal}) on a spectrally-spread target"
    );
    // Both finite and in [0,1] — a real, usable bar, not the degenerate fallback.
    assert!(
        bar_reachable.is_finite() && (0.0..=1.0).contains(&bar_reachable),
        "reachable-rank collapse bar must be a finite EV fraction, got {bar_reachable}"
    );
}