68 lines
2.6 KiB
Python
68 lines
2.6 KiB
Python
"""How common are near-zero steps - the model promising 'the root is right here' at a point
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that is not the root, so the next evaluation lands almost on the same x and f barely moves?
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Seen on fun9 (diag_fun9_well.py): 0.0002 -> 0.0002, 6.75 -> 6.734, 1.964 -> 1.941, 20.2502 ->
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20.2501. On a steep flank the three-point slope is dominated by a huge value, the scale
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sigma = |slope| D is huge, z = |f|/sigma ~ 0 and S(z) ~ 1.
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DIAGNOSTIC thresholds (reporting only, never in the method): a step is near-zero when
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|x_new - x| < 1% of the bracket, and wasted when after it |f| kept >= 90% of its value.
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Counted on the recorded evaluations of the proposed rule (projection) and of the best
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variant, per group. Nothing in the method changes.
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python -u diag_near_zero_steps.py
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"""
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from __future__ import annotations
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from collections import defaultdict
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from simroot.pure import pure_root
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from sweep_full import MAXFEV, XTOL, load_problems
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FLAT = ("fun3", "fun4", "fun5", "fun6")
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def main():
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for pre in ("none", "defect+flatanalogmempt"):
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agg = defaultdict(lambda: [0, 0, 0, 0]) # problems, evals, near-zero, wasted
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for s, pid, f, a, b, _root in load_problems():
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pts = []
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def g(x, f=f):
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v = f(x)
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pts.append((float(x), float(v)))
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return v
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pure_root(g, a, b, XTOL, MAXFEV, similarity="ratio", scale="derived3",
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guard="project", prestep=pre)
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fam = pid.split(".")[0]
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grp = "APS" if s == "APS" else ("CHA-flat" if fam in FLAT else f"CHA-{fam}")
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lo, hi = min(a, b), max(a, b)
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near = wasted = 0
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for (x0, f0), (x1, f1) in zip(pts[2:], pts[3:]):
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width = hi - lo
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if width > 0 and abs(x1 - x0) < 0.01 * width:
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near += 1
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if f0 != 0.0 and abs(f1) >= 0.9 * abs(f0):
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wasted += 1
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if f1 != 0.0 and lo < x1 < hi:
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# track the bracket as the method does (sign against the left end)
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if (f1 > 0) == (f(lo) > 0):
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lo = x1
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else:
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hi = x1
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ag = agg[grp]
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ag[0] += 1
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ag[1] += len(pts)
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ag[2] += near
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ag[3] += wasted
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print(f"\n== {pre}")
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print(f" {'group':<9} {'problems':>8} {'evals':>6} {'near-zero':>10} {'wasted':>7}")
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for grp in sorted(agg):
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n, e, nz, w = agg[grp]
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print(f" {grp:<9} {n:8d} {e:6d} {nz:10d} {w:7d}")
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print("diag done")
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if __name__ == "__main__":
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main()
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