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71 lines
2.0 KiB
Python
71 lines
2.0 KiB
Python
# -*- coding: utf-8 -*-
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"""
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Copyright (C) 2020-2024 LiteyukiStudio. All Rights Reserved
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@Time : 2024/8/9 上午11:32
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@Author : snowykami
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@Email : snowykami@outlook.com
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@File : equation.py
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@Software: PyCharm
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"""
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from mbcp.mp_math.mp_math_typing import OneVarFunc, Var, MultiVarFunc, Number
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from mbcp.mp_math.point import Point3
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from mbcp.mp_math.const import EPSILON
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class CurveEquation:
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def __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc):
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"""
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曲线方程。
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:param x_func:
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:param y_func:
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:param z_func:
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"""
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self.x_func = x_func
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self.y_func = y_func
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self.z_func = z_func
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def __call__(self, *t: Var) -> Point3 | tuple[Point3, ...]:
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"""
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计算曲线上的点。
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Args:
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*t:
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Returns:
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"""
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if len(t) == 1:
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return Point3(self.x_func(t[0]), self.y_func(t[0]), self.z_func(t[0]))
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else:
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return tuple([Point3(x, y, z) for x, y, z in zip(self.x_func(t), self.y_func(t), self.z_func(t))])
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def __str__(self):
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return "CurveEquation()"
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def get_partial_derivative_func(func: MultiVarFunc, var: int | tuple[int, ...], epsilon: Number = EPSILON) -> MultiVarFunc:
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"""
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求N元函数偏导函数。
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Args:
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func: 函数
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var: 变量位置，可为整数(一阶偏导)或整数元组(高阶偏导)
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epsilon: 偏移量
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Returns:
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偏导函数
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"""
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if isinstance(var, int):
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def partial_derivative_func(*args: Var) -> Var:
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args_list_plus = list(args)
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args_list_plus[var] += epsilon
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args_list_minus = list(args)
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args_list_minus[var] -= epsilon
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return (func(*args_list_plus) - func(*args_list_minus)) / (2 * epsilon)
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return partial_derivative_func
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elif isinstance(var, tuple):
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for i in var:
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func = get_partial_derivative_func(func, i, epsilon)
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return func
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else:
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raise ValueError("Invalid var type")
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