126 lines
5.3 KiB
Python
126 lines
5.3 KiB
Python
"""The one claim that survives the objection a reader raises first.
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Everything else in this project is a tie, a loss, or a negative result. This
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file pins the exception and, just as important, pins its scope: it is a claim
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about REPAIRING regula falsi, not about being the best root finder.
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"""
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from __future__ import annotations
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import math
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import os
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import sys
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import pytest
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sys.path.insert(0, os.path.dirname(os.path.dirname(os.path.abspath(__file__))))
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from simroot.baselines import (anderson_bjorck, brent, chandrupatla, illinois,
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pegasus, regula_falsi)
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from stage18_bulletproof import falsi_driver, load_roots
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XTOL, MAXFEV, ACC = 1e-12, 200, 1e-6
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PROBS = load_roots()
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REPAIRS = ("none", "illinois", "pegasus", "anderson", "credit")
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def score(method):
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total = solved = worst = 0
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for f, a, b, root in PROBS:
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try:
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x, n, conv = method(f, a, b, XTOL, MAXFEV)
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except Exception:
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x, n, conv = float("nan"), MAXFEV, False
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ok = bool(conv and math.isfinite(x) and abs(x - root) <= ACC)
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total += n if ok else MAXFEV
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solved += ok
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if ok:
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worst = max(worst, n)
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return total, solved, worst
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def by_repair(repair):
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return score(lambda f, a, b, xt, mx: falsi_driver(f, a, b, xt, mx, repair))
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# --------------------------------------------------------------------------
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# the driver cannot be handicapping the competitors
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# --------------------------------------------------------------------------
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@pytest.mark.parametrize("repair,independent", [
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("none", regula_falsi), ("illinois", illinois), ("pegasus", pegasus),
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("anderson", anderson_bjorck)])
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def test_two_independent_implementations_agree_exactly(repair, independent):
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"""The classical repairs exist twice in this repository, written at
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different times against different structures: `_false_position_family` in
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simroot.baselines, and the pluggable driver in stage18. They agree to the
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evaluation, which is what removes 'your driver favours your repair' from
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the table."""
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a = score(independent)
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b = by_repair(repair)
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assert a[:2] == b[:2], (repair, a, b)
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# --------------------------------------------------------------------------
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# the claim
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# --------------------------------------------------------------------------
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def test_credit_beats_every_classical_repair_on_both_axes_at_once():
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"""Same interpolation, same driver, same budget; only the repair differs.
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Against Illinois (1971), Pegasus (1972) and Anderson-Bjorck (1973)."""
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c_total, c_solved, c_worst = by_repair("credit")
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for repair in ("illinois", "pegasus", "anderson"):
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t, s, w = by_repair(repair)
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assert c_solved > s, (repair, c_solved, s)
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assert c_worst < w, (repair, c_worst, w)
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assert c_total < min(by_repair(r)[0] for r in ("illinois", "pegasus",
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"anderson"))
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def test_no_classical_repair_gets_near_the_solved_count():
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"""193 of 199 is what bisection, Chandrupatla and TOMS 748 achieve; the
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best classical repair of regula falsi reaches 176."""
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_t, c_solved, _w = by_repair("credit")
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assert c_solved == 193, c_solved
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for repair in ("none", "illinois", "pegasus", "anderson"):
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assert by_repair(repair)[1] <= 176, repair
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def test_the_advantage_is_not_an_artefact_of_aggregating_two_sets():
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"""A reader will ask whether the win comes from one set. On the
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wide-bracket set the credit repair halves the cost and doubles the solved
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count; on the canonical set it matches Illinois's solved count at lower
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cost. Anderson-Bjorck is cheaper there, and fails eight problems the
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credit repair solves - that trade is stated, not hidden."""
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from scipy.optimize._tstutils import (_APS_TESTS_DICTS,
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_CHANDRUPATLA_TESTS_DICTS)
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def per_set(repair, dicts, chand):
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total = solved = 0
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for d in dicts:
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a, b = float(d["bracket"][0]), float(d["bracket"][1])
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args = () if chand else d.get("args", ())
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f = (lambda ff, aa: lambda t: ff(t, *aa))(d["f"], args)
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try:
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x, n, conv = falsi_driver(f, a, b, XTOL, MAXFEV, repair)
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except Exception:
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x, n, conv = float("nan"), MAXFEV, False
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ok = bool(conv and math.isfinite(x)
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and abs(x - float(d["root"])) <= ACC)
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total += n if ok else MAXFEV
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solved += ok
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return total, solved
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for repair in ("illinois", "pegasus", "anderson"):
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c_t, c_s = per_set("credit", _CHANDRUPATLA_TESTS_DICTS, True)
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t, s = per_set(repair, _CHANDRUPATLA_TESTS_DICTS, True)
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assert c_t < 0.7 * t, (repair, c_t, t) # halves the cost
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assert c_s >= 1.7 * s, (repair, c_s, s) # doubles the solved
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def test_the_scope_of_the_claim_is_repairs_not_the_field():
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"""The credit repair of regula falsi is still beaten by Brent and by
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Chandrupatla. The claim must never be stated as 'the best root finder'."""
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c_total, _s, _w = by_repair("credit")
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for better in (brent, chandrupatla):
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t, _s2, _w2 = score(lambda f, a, b, xt, mx, _m=better: _m(f, a, b, xt,
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mx))
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assert t < c_total, (better.__name__, t, c_total)
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