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data-v-51c2c770><!--[--><!--]--></ul></div></nav><!--[--><!--]--><div class="spacer" data-v-0ff3c77f></div><!--[--><!--]--><!----><!--[--><!--]--><!--[--><!--]--></div></div></div></div><div class="content" data-v-40342069><div class="content-container" data-v-40342069><!--[--><!--]--><main class="main" data-v-40342069><div style="position:relative;" class="vp-doc _ja_api_mp_math_function" data-v-40342069><div><h1 id="mbcp-mp-math-function" tabindex="-1">mbcp.mp_math.function <a class="header-anchor" href="#mbcp-mp-math-function" aria-label="Permalink to &quot;mbcp.mp_math.function&quot;"></a></h1><p><strong>説明</strong>: AAA</p><h3 id="def-cal-gradient-3vf-func-threesinglevarsfunc-p-point3-epsilon-float-epsilon-vector3" tabindex="-1"><em><strong>def</strong></em> <code>cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float = EPSILON) -&gt; Vector3</code> <a class="header-anchor" href="#def-cal-gradient-3vf-func-threesinglevarsfunc-p-point3-epsilon-float-epsilon-vector3" aria-label="Permalink to &quot;***def*** `cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float = EPSILON) -&gt; Vector3`&quot;"></a></h3><p><strong>説明</strong>: 计算三元函数在某点的梯度向量。</p><div class="tip custom-block github-alert"><p class="custom-block-title">TIP</p><p>已知一个函数<mjx-container class="MathJax" jax="SVG" style="direction:ltr;position:relative;"><svg style="overflow:visible;min-height:1px;min-width:1px;vertical-align:-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="8.471ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 3744.3 1000" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D453" d="M118 -162Q120 -162 124 -164T135 -167T147 -168Q160 -168 171 -155T187 -126Q197 -99 221 27T267 267T289 382V385H242Q195 385 192 387Q188 390 188 397L195 425Q197 430 203 430T250 431Q298 431 298 432Q298 434 307 482T319 540Q356 705 465 705Q502 703 526 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data-mjx-texclass="OPEN">(</mo><mfrac><mrow><mi>∂</mi><mi>f</mi></mrow><mrow><mi>∂</mi><mi>x</mi></mrow></mfrac><mo>,</mo><mfrac><mrow><mi>∂</mi><mi>f</mi></mrow><mrow><mi>∂</mi><mi>y</mi></mrow></mfrac><mo>,</mo><mfrac><mrow><mi>∂</mi><mi>f</mi></mrow><mrow><mi>∂</mi><mi>z</mi></mrow></mfrac><mo data-mjx-texclass="CLOSE">)</mo></mrow></math></mjx-assistive-mml></mjx-container></p></div><p><strong>引数</strong>:</p><blockquote><ul><li>func: 三元函数</li><li>p: 点</li><li>epsilon: 偏移量</li></ul></blockquote><p><strong>戻り値</strong>: 梯度</p><details><summary><b>ソースコード</b></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;"> cal_gradient_3vf</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">(func: ThreeSingleVarsFunc, p: Point3, epsilon: </span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">float</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; Vector3:</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;">    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: 三元函数</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">        p: 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></div></div></main><footer class="VPDocFooter" data-v-40342069 data-v-a4b38bd6><!--[--><!--]--><!----><nav class="prev-next" aria-labelledby="doc-footer-aria-label" data-v-a4b38bd6><span class="visually-hidden" id="doc-footer-aria-label" data-v-a4b38bd6>Pager</span><div class="pager" data-v-a4b38bd6><a class="VPLink link pager-link prev" href="/ja/api/mp_math/equation.html" data-v-a4b38bd6><!--[--><span class="desc" data-v-a4b38bd6>Previous page</span><span class="title" data-v-a4b38bd6>mbcp.mp_math.equation</span><!--]--></a></div><div class="pager" data-v-a4b38bd6><a class="VPLink link pager-link next" href="/ja/api/mp_math/" data-v-a4b38bd6><!--[--><span class="desc" data-v-a4b38bd6>Next page</span><span class="title" data-v-a4b38bd6>mbcp.mp_math</span><!--]--></a></div></nav></footer><!--[--><!--]--></div></div></div><!--[--><!--]--></div></div><footer class="VPFooter has-sidebar" data-v-22f859ac data-v-e3ca6860><div class="container" data-v-e3ca6860><p class="message" data-v-e3ca6860><a href="https://vitepress.dev/">VitePress</a> で構築されたドキュメント | <a href="https://github.com/LiteyukiStudio/litedoc">litedoc</a> によって生成されたAPIリファレンス</p><p class="copyright" data-v-e3ca6860>Copyright (C) 2020-2024 SnowyKami. All Rights Reserved</p></div></footer><!--[--><!--]--></div></div>
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