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54 lines
1.8 KiB
Python
54 lines
1.8 KiB
Python
"""
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AAA
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"""
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from .mp_math_typing import MultiVarsFunc, OneVarFunc, ThreeSingleVarsFunc, Var
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from .point import Point3
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from .vector import Vector3
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from .const import EPSILON
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def cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float = EPSILON) -> Vector3:
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r"""
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计算三元函数在某点的梯度向量。
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> [!tip]
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> 已知一个函数$f(x, y, z)$，则其在点$(x_0, y_0, z_0)$处的梯度向量为:
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$\nabla f(x_0, y_0, z_0) = \left(\frac{\partial f}{\partial x}, \frac{\partial f}{\partial y}, \frac{\partial f}{\partial z}\right)$
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Args:
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func ([`ThreeSingleVarsFunc`](./mp_math_typing#var-threesinglevarsfunc)): 三元函数
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p ([`Point3`](./point#class-point3)): 点
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epsilon: 偏移量
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Returns:
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梯度
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"""
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dx = (func(p.x + epsilon, p.y, p.z) - func(p.x - epsilon, p.y, p.z)) / (2 * epsilon)
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dy = (func(p.x, p.y + epsilon, p.z) - func(p.x, p.y - epsilon, p.z)) / (2 * epsilon)
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dz = (func(p.x, p.y, p.z + epsilon) - func(p.x, p.y, p.z - epsilon)) / (2 * epsilon)
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return Vector3(dx, dy, dz)
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def curry(func: MultiVarsFunc, *args: Var) -> OneVarFunc:
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r"""
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对多参数函数进行柯里化。
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> [!tip]
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> 有关函数柯里化，可参考[函数式编程--柯理化（Currying）](https://zhuanlan.zhihu.com/p/355859667)
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Args:
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func ([`MultiVarsFunc`](./mp_math_typing#var-multivarsfunc)): 函数
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*args ([`Var`](./mp_math_typing#var-var)): 参数
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Returns:
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柯里化后的函数
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Examples:
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```python
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def add(a: int, b: int, c: int) -> int:
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return a + b + c
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add_curried = curry(add, 1, 2)
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add_curried(3) # 6
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```
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"""
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def curried_func(*args2: Var) -> Var:
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"""@litedoc-hide"""
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return func(*args, *args2)
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return curried_func
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