sim-numerics/tests/test_revision_points.py

"""Pins the corrections the revision made.

Each of these replaced a statement in the paper that was wrong or too broad.
They are asserted here so a later edit cannot quietly restore the old claim.
"""
from __future__ import annotations

from simroot.baselines import _opposite, _same_sign  # 2026-09-21 fix

import math
import os
import sys

import pytest

sys.path.insert(0, os.path.dirname(os.path.dirname(os.path.abspath(__file__))))

from simroot.pure import PURE_SIMS, pure_root
from stage5_three_point import PROBLEMS, order_of

R2 = math.sqrt(2.0)
F = lambda x: x * x - 2.0
XTOL, MAXFEV = 1e-12, 200


def iterate(S, n, sigma=2.0, x0=0.0, xfar=2.0):
    x, errs = x0, []
    for _ in range(n):
        x = x + (1.0 - S(F(x) / sigma)) * (xfar - x)
        errs.append(abs(x - R2))
    return errs


# --------------------------------------------------------------------------
# the naming contradiction: the proposed similarity is the tent, and its
# degeneracy is a property of the CHOSEN scale only
# --------------------------------------------------------------------------
def test_the_tent_is_captured_under_the_chosen_scale():
    """Table 1's last row.  Not a slow rate - capture at the far end on the
    first step."""
    e = iterate(PURE_SIMS["ratio"], 200)
    assert abs(e[0] - e[-1]) < 1e-15, (e[0], e[-1])
    assert abs(e[0] - 0.5858) < 1e-3, e[0]


def test_the_tent_is_the_best_similarity_under_the_derived_scale():
    """The same function, the other scale.  If these two tests ever agree in
    sign, the paper's central thesis - that the content is in the scale - has
    been broken."""
    tot = {}
    for sim in PURE_SIMS:
        s = 0
        for _n, f, a, b, root in PROBLEMS:
            x, n, conv = pure_root(f, a, b, XTOL, MAXFEV, similarity=sim,
                                   scale="derived3", guard="project")
            s += n if (conv and abs(x - root) <= 1e-8) else MAXFEV
        tot[sim] = s
    assert min(tot, key=lambda k: tot[k]) == "ratio", tot


def test_the_tent_never_clips_under_the_derived_scale():
    """Why the degeneracy disappears: |f|/sigma stays below 1, so the
    truncation in max(0, 1-|z|) never engages."""
    from simroot.pure import _slope3
    a, b = 0.0, 2.0
    fa, fb = F(a), F(b)
    A, FA, B = a, fa, b
    x, fx, xp, fp = a, fa, b, fb
    xp2 = fp2 = None
    clipped = steps = 0
    for _ in range(40):
        if abs(B - A) <= XTOL:
            break
        far = B if abs(B - x) >= abs(A - x) else A
        sc = abs(_slope3(x, fx, xp, fp, xp2, fp2)) * abs(far - x)
        if sc == 0.0:
            break
        steps += 1
        clipped += abs(fx) / sc >= 1.0
        xn = x + min(1.0, abs(fx) / sc) * (far - x)
        if not (min(A, B) < xn < max(A, B)):
            xn = 0.5 * (A + B)
        fn = F(xn)
        xp2, fp2, xp, fp, x, fx = xp, fp, x, fx, xn, fn
        if _opposite(FA, fn):
            B = xn
        else:
            A, FA = xn, fn
    assert steps > 0
    assert clipped == 0, f"{clipped} of {steps} steps clipped"


# --------------------------------------------------------------------------
# Proposition 1 is specific; Proposition 1' locates the boundary
# --------------------------------------------------------------------------
def test_only_the_ratio_form_reproduces_regula_falsi():
    a, b = 1.0, 4.0
    fa, fb = F(a), F(b)
    falsi = (a * fb - b * fa) / (fb - fa)
    matches = []
    for name, S in (("rational", PURE_SIMS["rational"]),
                    ("exp_abs", PURE_SIMS["exp_abs"]),
                    ("rat_sq", PURE_SIMS["rat_sq"]),
                    ("cosine", PURE_SIMS["cosine"]),
                    ("ratio", PURE_SIMS["ratio"])):
        pt = a + (1.0 - S(F(a) / abs(fb))) * (b - a)
        if abs(pt - falsi) < 1e-12:
            matches.append(name)
    assert matches == ["rational"], matches


def test_the_bracket_end_difference_gives_regula_falsi_exactly():
    """Proposition 1'.  This is why 'most recent' in the definition of the
    divided difference is load-bearing."""
    a, b = 1.0, 4.0
    fa, fb = F(a), F(b)
    falsi = (a * fb - b * fa) / (fb - fa)
    sigma = abs((fb - fa) / (b - a)) * abs(b - a)
    pt = a + min(1.0, abs(fa) / sigma) * (b - a)
    assert pt == falsi


# --------------------------------------------------------------------------
# Table 1's c = 0 rows: a sublinear law with a predicted coefficient
# --------------------------------------------------------------------------
@pytest.mark.parametrize("sim,want", [("rat_sq", 0.8536), ("exp_sq", 0.8536),
                                      ("cosine", 1.7071)])
def test_the_quadratic_similarities_are_sublinear_with_a_predicted_constant(sim, want):
    S = PURE_SIMS[sim]
    h = 1e-4
    c2 = (1.0 - S(h)) / (h * h)
    fp, D, sigma = 2.0 * R2, 2.0 - R2, 2.0
    predicted = sigma * sigma / (c2 * fp * fp * D)
    assert abs(predicted - want) < 1e-3, predicted
    e = iterate(S, 4001)
    assert abs(4000 * e[4000] - predicted) < 0.02, (4000 * e[4000], predicted)


def test_there_is_no_rate_to_measure_for_those_rows():
    """The old table reported 0.93-0.94 as a 'measured rate'; the ratio
    creeps to 1, so that number was the window's end, not a rate."""
    e = iterate(PURE_SIMS["rat_sq"], 4001)
    ratios = [e[n] / e[n - 1] for n in (10, 100, 1000, 4000)]
    assert ratios == sorted(ratios), ratios
    assert ratios[0] < 0.94 < ratios[-1]
    assert ratios[-1] > 0.999


# --------------------------------------------------------------------------
# the order is 2, not Muller's 1.84
# --------------------------------------------------------------------------
def test_the_three_point_order_is_two():
    ps = [order_of(lambda f_, a_, b_, xt, mx: pure_root(
        f_, a_, b_, XTOL, MAXFEV, scale="derived3", guard="project"),
        f, a, b, root) for _n, f, a, b, root in PROBLEMS]
    ps = [p for p in ps if math.isfinite(p) and 0.5 < p < 5.0]
    med = sorted(ps)[len(ps) // 2]
    assert abs(med - 2.0) < 0.1, med


# --------------------------------------------------------------------------
# the two evaluation-count conventions must both be reported and must differ
# in the direction the paper says
# --------------------------------------------------------------------------
@pytest.mark.skipif(not os.path.exists(os.path.join(
    os.path.dirname(os.path.dirname(os.path.abspath(__file__))),
    "sweep_full.json")), reason="sweep not present")
def test_charged_totals_are_what_section_5_reports():
    import json
    root = os.path.dirname(os.path.dirname(os.path.abspath(__file__)))
    with open(os.path.join(root, "sweep_full.json"), encoding="utf8") as fh:
        rows = {r["label"]: r for r in json.load(fh)}
    # since 2026-09-21 the competitors are the library alone: brent is
    # scipy.brentq (7004; our pure-Python implementation, timed in section 5.2,
    # is 6991) and chandrupatla is scipy's elementwise.find_root (5228; the
    # earlier 5208 came from a per-problem best of ours and the library, with
    # ours stopping on a bracket twice as wide)
    for lbl, want in (("pure.ratio.derived3.project", 6026),
                      ("brent", 7004), ("bisection", 10620),
                      ("chandrupatla", 5228)):
        got = rows[lbl]["APS"]["total"] + rows[lbl]["CHA"]["total"]
        assert got == want, (lbl, got, want)