71 lines
2.6 KiB
Python
71 lines
2.6 KiB
Python
"""Stage 1 - does the SIM formulation repair the failures found in Stage 0?
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Stage 0 showed the raw similarity-proportional step (= regula falsi) beats
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bisection on smooth problems by 2-3x but fails catastrophically when one end
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of the bracket goes stale. Stage 1 asks whether the article's actual
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machinery - prototype memory + softmax aggregation - removes that failure
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WITHOUT introducing a tuning parameter.
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Same 8 problems as Stage 0, plus bisection and Brent for orientation.
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"""
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from __future__ import annotations
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import math
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from simroot.baselines import bisection, brent, regula_falsi
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from simroot.sim import SIMILARITIES, sim_root
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XTOL = 1e-12
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MAXFEV = 200
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PROBLEMS = [
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("x^2 - 2", lambda x: x * x - 2.0, 0.0, 2.0, math.sqrt(2.0)),
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("cos(x) - x", lambda x: math.cos(x) - x, 0.0, 1.0, 0.7390851332151607),
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("exp(x) - 2", lambda x: math.exp(x) - 2.0, 0.0, 2.0, math.log(2.0)),
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("x^3 - x - 2", lambda x: x ** 3 - x - 2.0, 1.0, 2.0, 1.5213797068045676),
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("sin(x) - 0.5", lambda x: math.sin(x) - 0.5, 0.0, 1.5, math.asin(0.5)),
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("x^10 - 1 STALL", lambda x: x ** 10 - 1.0, 0.0, 1.3, 1.0),
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("exp(-x)(x-1) FLAT", lambda x: math.exp(-x) * (x - 1.0), -1.0, 40.0, 1.0),
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("atan(x)", lambda x: math.atan(x), -1.0, 3.0, 0.0),
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]
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METHODS = [
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("bisection", lambda f, a, b: bisection(f, a, b, XTOL, MAXFEV)),
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("regula_falsi", lambda f, a, b: regula_falsi(f, a, b, XTOL, MAXFEV)),
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("brent", lambda f, a, b: brent(f, a, b, XTOL, MAXFEV)),
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]
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for _s in SIMILARITIES:
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for _p in ("point", "pair", "pair2d"):
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for _g in (False, True):
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METHODS.append((
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f"SIM.{_p}.{_s}" + (".guard" if _g else ""),
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(lambda s, p, gu: lambda f, a, b: sim_root(
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f, a, b, XTOL, MAXFEV, similarity=s, prototypes=p,
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guard=gu))(_s, _p, _g),
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))
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def run():
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names = [n for n, _ in METHODS]
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width = max(len(n) for n in names) + 1
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header = f"{'method':{width}s}" + "".join(f"{p[0][:13]:>15s}" for p in PROBLEMS) + f"{'TOTAL':>8s}{'FAIL':>6s}"
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print(header)
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print("-" * len(header))
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for name, fn in METHODS:
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cells, total, fails = [], 0, 0
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for pname, f, a, b, root in PROBLEMS:
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x, n, conv = fn(f, a, b)
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err = abs(x - root)
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ok = conv and err <= 1e-8
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if not ok:
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fails += 1
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cells.append(f"{'FAIL(' + str(n) + ')':>15s}")
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else:
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cells.append(f"{n:>15d}")
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total += n
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print(f"{name:{width}s}" + "".join(cells) + f"{total:>8d}{fails:>6d}")
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if __name__ == "__main__":
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run()
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