Deniz Donmez
435dfb8ac5
introduced differentiation module built-in l2 norm implementation root finding problems now print #of iteration, new value, error, etc.
52 lines
1.7 KiB
Python
52 lines
1.7 KiB
Python
from __future__ import annotations
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from typing import Callable
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# ----------------------------
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# First derivative approximations
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# ----------------------------
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def ForwardDiff(f: Callable[[float], float], x: float, h: float = 1e-5) -> float:
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"""Forward finite difference approximation of f'(x)."""
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return (f(x + h) - f(x)) / h
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def BackwardDiff(f: Callable[[float], float], x: float, h: float = 1e-5) -> float:
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"""Backward finite difference approximation of f'(x)."""
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return (f(x) - f(x - h)) / h
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def CentralDiff(f: Callable[[float], float], x: float, h: float = 1e-5) -> float:
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"""Central finite difference approximation of f'(x) (2nd-order accurate)."""
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return (f(x + h) - f(x - h)) / (2 * h)
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def CentralDiff4th(f: Callable[[float], float], x: float, h: float = 1e-5) -> float:
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"""Fourth-order accurate central difference approximation of f'(x)."""
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return (-f(x + 2 * h) + 8 * f(x + h) - 8 * f(x - h) + f(x - 2 * h)) / (12 * h)
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# ----------------------------
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# Second derivative
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# ----------------------------
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def SecondDerivative(f: Callable[[float], float], x: float, h: float = 1e-5) -> float:
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"""Central difference approximation of second derivative f''(x)."""
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return (f(x + h) - 2 * f(x) + f(x - h)) / (h**2)
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# ----------------------------
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# Richardson Extrapolation
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# ----------------------------
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def RichardsonExtrap(f: Callable[[float], float], x: float, h: float = 1e-2) -> float:
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"""Richardson extrapolation to improve derivative accuracy.
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Combines estimates with step h and h/2.
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"""
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D_h = CentralDiff(f, x, h)
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D_h2 = CentralDiff(f, x, h / 2)
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return (4 * D_h2 - D_h) / 3
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