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cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float = EPSILON) -> Vector3 Description: 计算三元函数在某点的梯度向量。
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- func (
ThreeSingleVarsFunc): 三元函数- p (
Point3): 点- epsilon: 偏移量
Return: 梯度
def cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float=EPSILON) -> Vector3:
"""
计算三元函数在某点的梯度向量。
> [!tip]
> 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:
$\\\\nabla f(x_0, y_0, z_0) = \\\\left(\\\\frac{\\\\partial f}{\\\\partial x}, \\\\frac{\\\\partial f}{\\\\partial y}, \\\\frac{\\\\partial f}{\\\\partial z}\\\\right)$
Args:
func ([\`ThreeSingleVarsFunc\`](./mp_math_typing#var-threesinglevarsfunc)): 三元函数
p ([\`Point3\`](./point#class-point3)): 点
epsilon: 偏移量
Returns:
梯度
"""
dx = (func(p.x + epsilon, p.y, p.z) - func(p.x - epsilon, p.y, p.z)) / (2 * epsilon)
dy = (func(p.x, p.y + epsilon, p.z) - func(p.x, p.y - epsilon, p.z)) / (2 * epsilon)
dz = (func(p.x, p.y, p.z + epsilon) - func(p.x, p.y, p.z - epsilon)) / (2 * epsilon)
return Vector3(dx, dy, dz)curry(func: MultiVarsFunc, *args: Var) -> OneVarFunc Description: 对多参数函数进行柯里化。
TIP
有关函数柯里化，可参考函数式编程--柯理化（Currying）
Arguments:
- func (
MultiVarsFunc): 函数- *args (
Var): 参数
Return: 柯里化后的函数
Examples:
def add(a: int, b: int, c: int) -> int:
return a + b + c
add_curried = curry(add, 1, 2)
add_curried(3) # 6def curry(func: MultiVarsFunc, *args: Var) -> OneVarFunc:
"""
对多参数函数进行柯里化。
> [!tip]
> 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)
Args:
func ([\`MultiVarsFunc\`](./mp_math_typing#var-multivarsfunc)): 函数
*args ([\`Var\`](./mp_math_typing#var-var)): 参数
Returns:
柯里化后的函数
Examples:
\`\`\`python
def add(a: int, b: int, c: int) -> int:
return a + b + c
add_curried = curry(add, 1, 2)
add_curried(3) # 6
\`\`\`
"""
def curried_func(*args2: Var) -> Var:
"""@litedoc-hide"""
return func(*args, *args2)
return curried_func