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class="content" data-v-01c90815><div class="content-container" data-v-01c90815><!--[--><!--]--><main class="main" data-v-01c90815><div style="position:relative;" class="vp-doc _zht_api_mp_math_equation" data-v-01c90815><div><h1 id="模組-mbcp-mp-math-equation" tabindex="-1"><strong>模組</strong> <code>mbcp.mp_math.equation</code> <a class="header-anchor" href="#模組-mbcp-mp-math-equation" aria-label="Permalink to &quot;**模組** `mbcp.mp_math.equation`&quot;">​</a></h1><p>本模块定义了方程相关的类和函数以及一些常用的数学函数</p><h3 id="class-curveequation" tabindex="-1"><em><strong>class</strong></em> <code>CurveEquation</code> <a class="header-anchor" href="#class-curveequation" aria-label="Permalink to &quot;***class*** `CurveEquation`&quot;">​</a></h3><h4 id="method-init-self-x-func-onevarfunc-y-func-onevarfunc-z-func-onevarfunc" tabindex="-1"><em><strong>method</strong></em> <code>__init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc)</code> <a class="header-anchor" href="#method-init-self-x-func-onevarfunc-y-func-onevarfunc-z-func-onevarfunc" aria-label="Permalink to &quot;***method*** `__init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc)`&quot;">​</a></h4><p><strong>説明</strong>: 曲线方程。</p><p><strong>變數説明</strong>:</p><blockquote><ul><li>x_func (<a href="./mp_math_typing.html#var-onevarfunc"><code>OneVarFunc</code></a>): x函数</li><li>y_func (<a href="./mp_math_typing.html#var-onevarfunc"><code>OneVarFunc</code></a>): y函数</li><li>z_func (<a href="./mp_math_typing.html#var-onevarfunc"><code>OneVarFunc</code></a>): z函数</li></ul></blockquote><details><summary><b>源碼</b> 或 <a href="https://github.com/snowykami/mbcp/tree/main/mbcp/mp_math/equation.py#L12" target="_blank">於GitHub上查看</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;"> __init__</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc):</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>
<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-self-t-var-point3-tuple-point3" tabindex="-1"><em><strong>method</strong></em> <code>self () *t: Var =&gt; Point3 | tuple[Point3, ...]</code> <a class="header-anchor" href="#method-self-t-var-point3-tuple-point3" aria-label="Permalink to &quot;***method*** `self () *t: Var =&gt; Point3 | tuple[Point3, ...]`&quot;">​</a></h4><p><strong>説明</strong>: 计算曲线上的点。</p><p><strong>變數説明</strong>:</p><blockquote><ul><li>*t:</li><li>参数:</li></ul></blockquote><p><strong>返回</strong>: 目标点</p><details><summary><b>源碼</b> 或 <a href="https://github.com/snowykami/mbcp/tree/main/mbcp/mp_math/equation.py#L24" target="_blank">於GitHub上查看</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) -&gt; 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>
<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>
<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) -&gt; 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 &quot;***func*** `get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number = EPSILON) -&gt; MultiVarsFunc`&quot;">​</a></h3><p><strong>説明</strong>: 求N元函数一阶偏导函数。这玩意不太稳定，慎用。</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>變數説明</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>返回</strong>: 偏导函数</p><p><strong>抛出</strong>:</p><blockquote><ul><li>ValueError 无效变量类型</li></ul></blockquote><details><summary><b>源碼</b> 或 <a href="https://github.com/snowykami/mbcp/tree/main/mbcp/mp_math/equation.py#L42" target="_blank">於GitHub上查看</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;">) -&gt; MultiVarsFunc:</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) -&gt; Var:</span></span>
<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) -&gt; 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;"> 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>
<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;">&#39;Invalid var type&#39;</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> 於 GitHub 上編輯這頁<!--]--></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="/zht/api/mp_math/const.html" data-v-28deee4a><!--[--><span class="desc" data-v-28deee4a>上一頁</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="/zht/api/mp_math/function.html" data-v-28deee4a><!--[--><span class="desc" data-v-28deee4a>下一頁</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>文檔由 <a href="https://vitepress.dev/">VitePress</a> 構建 | API引用由 <a href="https://github.com/LiteyukiStudio/litedoc">litedoc</a> 生成</p><p class="copyright" data-v-d69bcf5d>Copyright (C) 2020-2024 SnowyKami. All Rights Reserved</p></div></footer><!--[--><!--]--></div></div>
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