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< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > " " " < / span > < / span >
< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > 曲线方程。< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > Args:< / span > < / span >
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< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > x_func ([`OneVarFunc`](./mp_math_typing#var-onevarfunc)): x函数< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > y_func ([`OneVarFunc`](./mp_math_typing#var-onevarfunc)): y函数< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > z_func ([`OneVarFunc`](./mp_math_typing#var-onevarfunc)): z函数< / span > < / span >
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< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > " " " < / span > < / span >
< span class = "line" > < span style = "--shiki-light:#005CC5;--shiki-dark:#79B8FF;" > self< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > .x_func < / span > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > =< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > x_func< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#005CC5;--shiki-dark:#79B8FF;" > self< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > .y_func < / span > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > =< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > y_func< / span > < / span >
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< span class = "line" > < span style = "--shiki-light:#005CC5;--shiki-dark:#79B8FF;" > self< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > .z_func < / span > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > =< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > z_func< / span > < / span > < / code > < / pre > < / div > < / details > < h4 id = "method-call-self-t-var-point3-tuple-point3" tabindex = "-1" > < em > < strong > method< / strong > < / em > < code > __call__(self, *t: Var) -> Point3 | tuple[Point3, ...]< / code > < a class = "header-anchor" href = "#method-call-self-t-var-point3-tuple-point3" aria-label = "Permalink to "***method*** `__call__(self, *t: Var) -> Point3 | tuple[Point3, ...]`"" > < / a > < / h4 > < p > < strong > Description< / strong > : 计算曲线上的点。< / p > < p > < strong > Arguments< / strong > :< / p > < blockquote > < ul > < li > *t:< / li > < li > 参数:< / li > < / ul > < / blockquote > < p > < strong > Return< / strong > : 目标点< / p > < details > < summary > < b > Source code< / b > or < a href = "https://github.com/snowykami/mbcp/tree/main/mbcp/mp_math/equation.py#L24" target = "_blank" > View on GitHub< / a > < / summary > < div class = "language-python vp-adaptive-theme" > < button title = "Copy Code" class = "copy" > < / button > < span class = "lang" > python< / span > < pre class = "shiki shiki-themes github-light github-dark vp-code" tabindex = "0" > < code > < span class = "line" > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > def< / span > < span style = "--shiki-light:#005CC5;--shiki-dark:#79B8FF;" > __call__< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > (self, < / span > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > *< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > t: Var) -> Point3 < / span > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > |< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > tuple[Point3, < / span > < span style = "--shiki-light:#005CC5;--shiki-dark:#79B8FF;" > ...< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > ]:< / span > < / span >
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< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > " " " < / span > < / span >
< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > 计算曲线上的点。< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > Args:< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > *t:< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > 参数< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > Returns:< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > 目标点< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > " " " < / span > < / span >
< span class = "line" > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > if< / span > < span style = "--shiki-light:#005CC5;--shiki-dark:#79B8FF;" > len< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > (t) < / span > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > ==< / span > < span style = "--shiki-light:#005CC5;--shiki-dark:#79B8FF;" > 1< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > :< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > return< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > Point3(< / span > < span style = "--shiki-light:#005CC5;--shiki-dark:#79B8FF;" > self< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > .x_func(t[< / span > < span style = "--shiki-light:#005CC5;--shiki-dark:#79B8FF;" > 0< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > ]), < / span > < span style = "--shiki-light:#005CC5;--shiki-dark:#79B8FF;" > self< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > .y_func(t[< / span > < span style = "--shiki-light:#005CC5;--shiki-dark:#79B8FF;" > 0< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > ]), < / span > < span style = "--shiki-light:#005CC5;--shiki-dark:#79B8FF;" > self< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > .z_func(t[< / span > < span style = "--shiki-light:#005CC5;--shiki-dark:#79B8FF;" > 0< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > ]))< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > else< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > :< / span > < / span >
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< span class = "line" > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > return< / span > < span style = "--shiki-light:#005CC5;--shiki-dark:#79B8FF;" > tuple< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > ([Point3(x, y, z) < / span > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > for< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > x, y, z < / span > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > in< / span > < span style = "--shiki-light:#005CC5;--shiki-dark:#79B8FF;" > zip< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > (< / span > < span style = "--shiki-light:#005CC5;--shiki-dark:#79B8FF;" > self< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > .x_func(t), < / span > < span style = "--shiki-light:#005CC5;--shiki-dark:#79B8FF;" > self< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > .y_func(t), < / span > < span style = "--shiki-light:#005CC5;--shiki-dark:#79B8FF;" > self< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > .z_func(t))])< / span > < / span > < / code > < / pre > < / div > < / details > < h3 id = "func-get-partial-derivative-func-func-multivarsfunc-var-int-tuple-int-epsilon-number-epsilon-multivarsfunc" tabindex = "-1" > < em > < strong > func< / strong > < / em > < code > get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number = EPSILON) -> MultiVarsFunc< / code > < a class = "header-anchor" href = "#func-get-partial-derivative-func-func-multivarsfunc-var-int-tuple-int-epsilon-number-epsilon-multivarsfunc" aria-label = "Permalink to "***func*** `get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number = EPSILON) -> MultiVarsFunc`"" > < / a > < / h3 > < p > < strong > Description< / strong > : 求N元函数一阶偏导函数。这玩意不太稳定， < / p > < div class = "warning custom-block github-alert" > < p class = "custom-block-title" > WARNING< / p > < p > 目前数学界对于一个函数的导函数并没有通解的说法，因此该函数的稳定性有待提升< / p > < / div > < p > < strong > Arguments< / strong > :< / p > < blockquote > < ul > < li > func (< a href = "./mp_math_typing.html#var-multivarsfunc" > < code > MultiVarsFunc< / code > < / a > ): N元函数< / li > < li > var: 变量位置，可为整数(一阶偏导)或整数元组(高阶偏导)< / li > < li > epsilon: 偏移量< / li > < / ul > < / blockquote > < p > < strong > Return< / strong > : 偏导函数< / p > < p > < strong > Raises< / strong > :< / p > < blockquote > < ul > < li > ValueError 无效变量类型< / li > < / ul > < / blockquote > < details > < summary > < b > Source code< / b > or < a href = "https://github.com/snowykami/mbcp/tree/main/mbcp/mp_math/equation.py#L42" target = "_blank" > View on GitHub< / a > < / summary > < div class = "language-python vp-adaptive-theme" > < button title = "Copy Code" class = "copy" > < / button > < span class = "lang" > python< / span > < pre class = "shiki shiki-themes github-light github-dark vp-code" tabindex = "0" > < code > < span class = "line" > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > def< / span > < span style = "--shiki-light:#6F42C1;--shiki-dark:#B392F0;" > get_partial_derivative_func< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > (func: MultiVarsFunc, var: < / span > < span style = "--shiki-light:#005CC5;--shiki-dark:#79B8FF;" > int< / span > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > |< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > tuple[< / span > < span style = "--shiki-light:#005CC5;--shiki-dark:#79B8FF;" > int< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > , < / span > < span style = "--shiki-light:#005CC5;--shiki-dark:#79B8FF;" > ...< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > ], epsilon: Number< / span > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > =< / span > < span style = "--shiki-light:#005CC5;--shiki-dark:#79B8FF;" > EPSILON< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > ) -> MultiVarsFunc:< / span > < / span >
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< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > " " " < / span > < / span >
< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > 求N元函数一阶偏导函数。这玩意不太稳定， < / span > < / span >
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< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > > [!warning]< / span > < / span >
2024-08-29 18:52:57 +08:00
< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > > 目前数学界对于一个函数的导函数并没有通解的说法，因此该函数的稳定性有待提升< / span > < / span >
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< span class = "line" > < / span >
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< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > Args:< / span > < / span >
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< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > func ([`MultiVarsFunc`](./mp_math_typing#var-multivarsfunc)): N元函数< / span > < / span >
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< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > var: 变量位置，可为整数(一阶偏导)或整数元组(高阶偏导)< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > epsilon: 偏移量< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > Returns:< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > 偏导函数< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > Raises:< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > ValueError: 无效变量类型< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > " " " < / span > < / span >
< span class = "line" > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > if< / span > < span style = "--shiki-light:#005CC5;--shiki-dark:#79B8FF;" > isinstance< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > (var, < / span > < span style = "--shiki-light:#005CC5;--shiki-dark:#79B8FF;" > int< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > ):< / span > < / span >
< span class = "line" > < / span >
< span class = "line" > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > def< / span > < span style = "--shiki-light:#6F42C1;--shiki-dark:#B392F0;" > partial_derivative_func< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > (< / span > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > *< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > args: Var) -> Var:< / span > < / span >
2024-08-29 19:00:41 +08:00
< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > " " " @litedoc-hide" " " < / span > < / span >
2024-08-28 20:35:22 +08:00
< span class = "line" > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > args_list_plus < / span > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > =< / span > < span style = "--shiki-light:#005CC5;--shiki-dark:#79B8FF;" > list< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > (args)< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > args_list_plus[var] < / span > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > +=< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > epsilon< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > args_list_minus < / span > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > =< / span > < span style = "--shiki-light:#005CC5;--shiki-dark:#79B8FF;" > list< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > (args)< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > args_list_minus[var] < / span > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > -=< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > epsilon< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > return< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > (func(< / span > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > *< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > args_list_plus) < / span > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > -< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > func(< / span > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > *< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > args_list_minus)) < / span > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > /< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > (< / span > < span style = "--shiki-light:#005CC5;--shiki-dark:#79B8FF;" > 2< / span > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > *< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > epsilon)< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > return< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > partial_derivative_func< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > elif< / span > < span style = "--shiki-light:#005CC5;--shiki-dark:#79B8FF;" > isinstance< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > (var, < / span > < span style = "--shiki-light:#005CC5;--shiki-dark:#79B8FF;" > tuple< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > ):< / span > < / span >
< span class = "line" > < / span >
< span class = "line" > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > def< / span > < span style = "--shiki-light:#6F42C1;--shiki-dark:#B392F0;" > high_order_partial_derivative_func< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > (< / span > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > *< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > args: Var) -> Var:< / span > < / span >
2024-08-29 19:00:41 +08:00
< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > " " " < / span > < / span >
< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > @litedoc-hide< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > 求高阶偏导函数< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > Args:< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > *args: 参数< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > Returns:< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > 高阶偏导数值< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > " " " < / span > < / span >
2024-08-28 20:35:22 +08:00
< span class = "line" > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > result_func < / span > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > =< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > func< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > for< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > v < / span > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > in< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > var:< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > result_func < / span > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > =< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > get_partial_derivative_func(result_func, v, epsilon)< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > return< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > result_func(< / span > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > *< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > args)< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > return< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > high_order_partial_derivative_func< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > else< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > :< / span > < / span >
2024-09-03 22:49:39 +08:00
< span class = "line" > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > raise< / span > < span style = "--shiki-light:#005CC5;--shiki-dark:#79B8FF;" > ValueError< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > (< / span > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > ' Invalid var type' < / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > )< / span > < / span > < / code > < / pre > < / div > < / details > < / div > < / div > < / main > < footer class = "VPDocFooter" data-v-01c90815 data-v-28deee4a > <!-- [ --> <!-- ] --> < div class = "edit-info" data-v-28deee4a > < div class = "edit-link" data-v-28deee4a > < a class = "VPLink link vp-external-link-icon no-icon edit-link-button" href = "https://github.com/snowykami/mbcp/tree/main/mbcp//mp_math/equation.py" target = "_blank" rel = "noreferrer" data-v-28deee4a > <!-- [ --> < span class = "vpi-square-pen edit-link-icon" data-v-28deee4a > < / span > Edit this page on GitHub<!-- ] --> < / a > < / div > <!-- --> < / div > < nav class = "prev-next" aria-labelledby = "doc-footer-aria-label" data-v-28deee4a > < span class = "visually-hidden" id = "doc-footer-aria-label" data-v-28deee4a > Pager< / span > < div class = "pager" data-v-28deee4a > < a class = "VPLink link pager-link prev" href = "/en/api/mp_math/const.html" data-v-28deee4a > <!-- [ --> < span class = "desc" data-v-28deee4a > Prev Page< / span > < span class = "title" data-v-28deee4a > mbcp.mp_math.const< / span > <!-- ] --> < / a > < / div > < div class = "pager" data-v-28deee4a > < a class = "VPLink link pager-link next" href = "/en/api/mp_math/function.html" data-v-28deee4a > <!-- [ --> < span class = "desc" data-v-28deee4a > Next Page< / span > < span class = "title" data-v-28deee4a > mbcp.mp_math.function< / span > <!-- ] --> < / a > < / div > < / nav > < / footer > <!-- [ --> <!-- ] --> < / div > < / div > < / div > <!-- [ --> <!-- ] --> < / div > < / div > < footer class = "VPFooter has-sidebar" data-v-3b4648ff data-v-d69bcf5d > < div class = "container" data-v-d69bcf5d > < p class = "message" data-v-d69bcf5d > Documentation built with < a href = "https://vitepress.dev/" > VitePress< / a > | API references generated by < a href = "https://github.com/LiteyukiStudio/litedoc" > litedoc< / a > < / p > < p class = "copyright" data-v-d69bcf5d > Copyright (C) 2020-2024 SnowyKami. All Rights Reserved< / p > < / div > < / footer > <!-- [ --> <!-- ] --> < / div > < / div >
< script > w i n d o w . _ _ V P _ H A S H _ M A P _ _ = J S O N . p a r s e ( " { \ " a p i _ i n d e x . m d \ " : \ " Y S - z q W w M \ " , \ " a p i _ m p _ m a t h _ a n g l e . m d \ " : \ " C T h Q B 5 n q \ " , \ " a p i _ m p _ m a t h _ c o n s t . m d \ " : \ " D q j Q Q 6 Y m \ " , \ " a p i _ m p _ m a t h _ e q u a t i o n . m d \ " : \ " C 1 Y M G s I R \ " , \ " a p i _ m p _ m a t h _ f u n c t i o n . m d \ " : \ " C 0 P _ - k o l \ " , \ " a p i _ m p _ m a t h _ i n d e x . m d \ " : \ " y E j 9 p z O D \ " , \ " a p i _ m p _ m a t h _ l i n e . m d \ " : \ " O k m n 0 B T W \ " , \ " a p i _ m p _ m a t h _ m p _ m a t h _ t y p i n g . m d \ " : \ " b d i O S v F y \ " , \ " a p i _ m p _ m a t h _ p l a n e . m d \ " : \ " D l - F d X x 3 \ " , \ " a p i _ m p _ m a t h _ p o i n t . m d \ " : \ " x U 6 H j e L 2 \ " , \ " a p i _ m p _ m a t h _ s e g m e n t . m d \ " : \ " B q l o N j d D \ " , \ " a p i _ m p _ m a t h _ u t i l s . m d \ " : \ " C G B Z j r 3 t \ " , \ " a p i _ m p _ m a t h _ v e c t o r . m d \ " : \ " B 4 4 3 f t A V \ " , \ " a p i _ p a r t i c l e _ i n d e x . m d \ " : \ " V x g s H i Z a \ " , \ " a p i _ p r e s e t s _ i n d e x . m d \ " : \ " B E Z B x 6 G j \ " , \ " a p i _ p r e s e t s _ m o d e l _ i n d e x . m d \ " : \ " C z r Z X 1 L i \ " , \ " d e m o _ b e s t - p r a c t i c e . m d \ " : \ " C m Y j f r x d \ " , \ " d e m o _ i n d e x . m d \ " : \ " C V A d l a F I \ " , \ " e n _ a p i _ i n d e x . m d \ " : \ " B r J l a d - k \ " , \ " e n _ a p i _ m p _ m a t h _ a n g l e . m d \ " : \ " B v z e T d t j \ " , \ " e n _ a p i _ m p _ m a t h _ c o n s t . m d \ " : \ " C r U t _ 3 F V \ " , \ " e n _ a p i _ m p _ m a t h _ e q u a t i o n . m d \ " : \ " C H B t H 4 v 6 \ " , \ " e n _ a p i _ m p _ m a t h _ f u n c t i o n . m d \ " : \ " D 6 8 b T y e d \ " , \ " e n _ a p i _ m p _ m a t h _ i n d e x . m d \ " : \ " D 3 3 1 A s 7 i \ " , \ " e n _ a p i _ m p _ m a t h _ l i n e . m d \ " : \ " B 6 9 k H o P c \ " , \ " e n _ a p i _ m p _ m a t h _ m p _ m a t h _ t y p i n g . m d \ " : \ " x R G J G U M m \ " , \ " e n _ a p i _ m p _ m a t h _ p l a n e . m d \ " : \ " B d K g R u m w \ " , \ " e n _ a p i _ m p _ m a t h _ p o i n t . m d \ " : \ " B e T 2 o q I N \ " , \ " e n _ a p i _ m p _ m a t h _ s e g m e n t . m d \ " : \ " D b F v I n H k \ " , \ " e n _ a p i _ m p _ m a t h _ u t i l s . m d \ " : \ " C Y q 8 h n c D \ " , \ " e n _ a p i _ m p _ m a t h _ v e c t o r . m d \ " : \ " C P G k Z z w r \ " , \ " e n _ a p i _ p a r t i c l e _ i n d e x . m d \ " : \ " Z K B y d _ x 0 \ " , \ " e n _ a p i _ p r e s e t s _ i n d e x . m d \ " : \ " B h o Z y G S V \ " , \ " e n _ a p i _ p r e s e t s _ m o d e l _ i n d e x . m d \ " : \ " B M 4 z z W d 9 \ " , \ " e n _ d e m o _ b e s t - p r a c t i c e . m d \ " : \ " C m t Y 1 0 5 n \ " , \ " e n _ g u i d e _ i n d e x . m d \ " : \ " C 3 k I 8 f 8 A \ " , \ " e n _ i n d e x . m d \ " : \ " C c - N t 9 O t \ " , \ " e n _ r e f e r _ i n d e x . m d \ " : \ " C q 6 G W i 0 V \ " , \ " g u i d e _ i n d e x . m d \ " : \ " C J O q v l S E \ " , \ " i n d e x . m d \ " : \ " W V p b C 1 C 1 \ " , \ " j a _ a p i _ i n d e x . m d \ " : \ " 6 u 5 f 7 W 7 q \ " , \ " j a _ a p i _ m p _ m a t h _ a n g l e . m d \ " : \ " C b T F N F p P \ " , \ " j a _ a p i _ m p _ m a t h _ c o n s t . m d \ " : \ " H r V L d L V W \ " , \ " j a _ a p i _ m p _ m a t h _ e q u a t i o n . m d \ " : \ " B R _ c j Y x P \ " , \ " j a _ a p i _ m p _ m a t h _ f u n c t i o n . m d \ " : \ " C e N P n p r i \ " , \ " j a _ a p i _ m p _ m a t h _ i n d e x . m d \ " : \ " B V Y Y B c g X \ " , \ " j a _ a p i _ m p _ m a t h _ l i n e . m d \ " : \ " C m V m q 6 P C \ " , \ " j a _ a p i _ m p _ m a t h _ m p _ m a t h _ t y p i n g . m d \ " : \ " B n S H E E F C \ " , \ " j a _ a p i _ m p _ m a t h _ p l a n e . m d \ " : \ " D 7 v 3 q _ U 8 \ " , \ " j a _ a p i _ m p _ m a t h _ p o i n t . m d \ " : \ " B q C 8 J g j G \ " , \ " j a _ a p i _ m p _ m a t h _ s e g m e n t . m d \ " : \ " v i 1 F H 0 - - \ " , \ " j a _ a p i _ m p _ m a t h _ u t i l s . m d \ " : \ " D h P m c v K - \ " , \ " j a _ a p i _ m p _ m a t h _ v e c t o r . m d \ " : \ " B 7 o D y - S U \ " , \ " j a _ a p i _ p a r t i c l e _ i n d e x . m d \ " : \ " i g h e y 3 J D \ " , \ " j a _ a p i _ p r e s e t s _ i n d e x . m d \ " : \ " B o w 2 2 H N O \ " , \ " j a _ a p i _ p r e s e t s _ m o d e l _ i n d e x . m d \ " : \ " C - u C q j X i \ " , \ " j a _ d e m o _ b e s t - p r a c t i c e . m d \ " : \ " C B H i F 6 e c \ " , \ " j a _ g u i d e _ i n d e x . m d \ " : \ " w 1 T f 2 A d m \ " , \ " j a _ i n d e x . m d \ " : \ " B v j V 8 R I J \ " , \ " j a _ r e f e r _ i n d e x . m d \ " : \ " D a m U s c s 8 \ " , \ " r e f e r _ f u n c t i o n _ c u r r y . m d \ " : \ " D _ o q R D d 3 \ " , \ " r e f e r _ f u n c t i o n _ f u n c t i o n . m d \ " : \ " B i _ 8 2 l I J \ " , \ " r e f e r _ i n d e x . m d \ " : \ " y F Z W 0 k I 4 \ " , \ " z h t _ a p i _ i n d e x . m d \ " : \ " D M j E 1 x B r \ " , \ " z h t _ a p i _ m p _ m a t h _ a n g l e . m d \ " : \ " D 6 i - - 7 z d \ " , \ " z h t _ a p i _ m p _ m a t h _ c o n s t . m d \ " : \ " D I 0 x A y W X \ " , \ " z h t _ a p i _ m p _ m a t h _ e q u a t i o n . m d \ " : \ " B 3 r t 0 P g w \ " , \ " z h t _ a p i _ m p _ m a t h _ f u n c t i o n . m d \ " : \ " C f 9 u t a T V \ " , \ " z h t _ a p i _ m p _ m a t h _ i n d e x . m d \ " : \ " D b g I 3 v D 1 \ " , \ " z h t _ a p i _ m p _ m a t h _ l i n e . m d \ " : \ " - w t K M T M J \ " , \ " z h t _ a p i _ m p _ m a t h _ m p _ m a t h _ t y p i n g . m d \ " : \ " B b O e R s - n \ " , \ " z h t _ a p i _ m p _ m a t h _ p l a n e . m d \ " : \ " o _ V r o q h a \ " , \ " z h t _ a p i _ m p _ m a t h _ p o i n t . m d \ " : \ " C N w x P Y y R \ " , \ " z h t _ a p i _ m p _ m a t h _ s e g m e n t . m d \ " : \ " D r 2 1 f 1 4 B \ " , \ " z h t _ a p i _ m p _ m a t h _ u t i l s . m d \ " : \ " B 5 7 z 4 I w N \ " , \ " z h t _ a p i _ m p _ m a t h _ v e c t o r . m d \ " : \ " D C G 5 C r a B \ " , \ " z h t _ a p i _ p a r t i c l e _ i n d e x . m d \ " : \ " D j Z A B i v I \ " , \ " z h t _ a p i _ p r e s e t s _ i n d e x . m d \ " : \ " B l 7 t n V S 9 \ " , \ " z h t _ a p i _ p r e s e t s _ m o d e l _ i n d e x . m d \ " : \ " B Q a n u b Q 0 \ " , \ " z h t _ d e m o _ b e s t - p r a c t i c e . m d \ " : \ " C P N b D _ L g \ " , \ " z h t _ g u i d e _ i n d e x . m d \ " : \ " B N n M V i C 8 \ " , \ " z h t _ i n d e x . m d \ " : \ " f k O Y k Z Z e \ " , \ " z h t _ r e f e r _ i n d e x . m d \ " : \ " B 7 C Q S 2 U W \ " } " ) ; f u n c t i o n d e s e r i a l i z e F u n c t i o n s ( r ) { r e t u r n A r r a y . i s A r r a y ( r ) ? r . m a p ( d e s e r i a l i z e F u n c t i o n s ) : t y p e o f r = = " o b j e c t " & & r ! = = n u l l ? O b j e c t . k e y s ( r ) . r e d u c e ( ( t , n ) = > ( t [ n ] = d e s e r i a l i z e F u n c t i o n s ( r [ n ] ) , t ) , { } ) : t y p e o f r = = " s t r i n g " & & r . s t a r t s W i t h ( " _ v p - f n _ " ) ? n e w F u n c t i o n ( ` r e t u r n $ { r . s l i c e ( 7 ) } ` ) ( ) : r } ; w i n d o w . _ _ V P _ S I T E _ D A T A _ _ = d e s e r i a l i z e F u n c t i o n s ( J S O N . p a r s e ( " { \ " l a n g \ " : \ " e n - U S \ " , \ " d i r \ " : \ " l t r \ " , \ " t i t l e \ " : \ " V i t e P r e s s \ " , \ " d e s c r i p t i o n \ " : \ " A V i t e P r e s s s i t e \ " , \ " b a s e \ " : \ " / \ " , \ " h e a d \ " : [ ] , \ " r o u t e r \ " : { \ " p r e f e t c h L i n k s \ " : t r u e } , \ " a p p e a r a n c e \ " : t r u e , \ " t h e m e C o n f i g \ " : { \ " l o g o \ " : \ " / m b c p - l o g o . s v g \ " , \ " s i d e b a r \ " : { \ " / a p i / \ " : { \ " b a s e \ " : \ " / a p i / \ " , \ " i t e m s \ " : [ { \ " t e x t \ " : \ " M B C P \ " , \ " i t e m s \ " : [ { \ " t e x t \ " : \ " m p _ m a t h \ " , \ " i t e m s \ " : [ { \ " t e x t \ " : \ " m b c p . m p _ m a t h . a n g l e \ " , \ " l i n k \ " : \ " m p _ m
2024-08-28 20:35:22 +08:00
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