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<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;"> &quot;&quot;&quot;</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;"> 计算三元函数在某点的梯度向量。</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;"> &gt; [!tip]</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;"> &gt; 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:</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;"> $</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">\\</span><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">nabla f(x_0, y_0, z_0) = </span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">\\</span><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">left(</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">\\</span><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">frac{</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">\\</span><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">partial f}{</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">\\</span><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">partial x}, </span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">\\</span><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">frac{</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">\\</span><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">partial f}{</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">\\</span><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">partial y}, </span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">\\</span><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">frac{</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">\\</span><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">partial f}{</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">\\</span><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">partial z}</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">\\</span><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">right)$</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;"> func ([`ThreeSingleVarsFunc`](./mp_math_typing#var-threesinglevarsfunc)): 三元函数</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;"> p ([`Point3`](./point#class-point3)): 点</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;"> 梯度</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;"> &quot;&quot;&quot;</span></span>
<span class="line"><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> dx </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">=</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> (func(p.x </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">+</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> epsilon, p.y, p.z) </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">-</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> func(p.x </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">-</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> epsilon, p.y, p.z)) </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:#24292E;--shiki-dark:#E1E4E8;"> dy </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">=</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> (func(p.x, p.y </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">+</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> epsilon, p.z) </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">-</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> func(p.x, p.y </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">-</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> epsilon, p.z)) </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:#24292E;--shiki-dark:#E1E4E8;"> dz </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">=</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> (func(p.x, p.y, p.z </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">+</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> epsilon) </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">-</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> func(p.x, p.y, p.z </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">-</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> epsilon)) </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;"> Vector3(dx, dy, dz)</span></span></code></pre></div></details><h3 id="func-curry-func-multivarsfunc-args-var-onevarfunc" tabindex="-1"><em><strong>func</strong></em> <code>curry(func: MultiVarsFunc, *args: Var) -&gt; OneVarFunc</code> <a class="header-anchor" href="#func-curry-func-multivarsfunc-args-var-onevarfunc" aria-label="Permalink to &quot;***func*** `curry(func: MultiVarsFunc, *args: Var) -&gt; OneVarFunc`&quot;"></a></h3><p><strong>説明</strong>: 对多参数函数进行柯里化。</p><div class="tip custom-block github-alert"><p class="custom-block-title">TIP</p><p>有关函数柯里化,可参考<a href="https://zhuanlan.zhihu.com/p/355859667" target="_blank" rel="noreferrer">函数式编程--柯理化Currying</a></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>): 函数</li><li>*args (<a href="./mp_math_typing.html#var-var"><code>Var</code></a>): 参数</li></ul></blockquote><p><strong>返回</strong>: 柯里化后的函数</p><p><strong>範例</strong>:</p><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;"> add</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">(a: </span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">int</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">, b: </span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">int</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">, c: </span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">int</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">) -&gt; </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 style="--shiki-light:#D73A49;--shiki-dark:#F97583;"> return</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> a </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">+</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> b </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">+</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> c</span></span>
<span class="line"><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">add_curried </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">=</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> curry(add, </span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">1</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">, </span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">2</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">)</span></span>
<span class="line"><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">add_curried(</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">3</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">) </span><span style="--shiki-light:#6A737D;--shiki-dark:#6A737D;"># 6</span></span></code></pre></div><details><summary><b>源碼</b><a href="https://github.com/snowykami/mbcp/tree/main/mbcp/mp_math/function.py#L30" 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;"> curry</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">(func: MultiVarsFunc, </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">*</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">args: Var) -&gt; OneVarFunc:</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;"> &quot;&quot;&quot;</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;"> 对多参数函数进行柯里化。</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;"> &gt; [!tip]</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;"> &gt; 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)</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;"> func ([`MultiVarsFunc`](./mp_math_typing#var-multivarsfunc)): 函数</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;"> *args ([`Var`](./mp_math_typing#var-var)): 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;"> 柯里化后的函数</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;"> Examples:</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;"> ```python</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;"> def add(a: int, b: int, c: int) -&gt; int:</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;"> return a + b + c</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;"> add_curried = curry(add, 1, 2)</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;"> add_curried(3) # 6</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;"> ```</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;"> &quot;&quot;&quot;</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;"> curried_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;">args2: Var) -&gt; Var:</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;"> &quot;&quot;&quot;@litedoc-hide&quot;&quot;&quot;</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, </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">*</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">args2)</span></span>
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;"> return</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> curried_func</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/function.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/equation.html" data-v-28deee4a><!--[--><span class="desc" data-v-28deee4a>上一頁</span><span class="title" data-v-28deee4a>mbcp.mp_math.equation</span><!--]--></a></div><div class="pager" data-v-28deee4a><a class="VPLink link pager-link next" href="/zht/api/mp_math/" data-v-28deee4a><!--[--><span class="desc" data-v-28deee4a>下一頁</span><span class="title" data-v-28deee4a>mbcp.mp_math</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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