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`cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float = EPSILON) -&gt; Vector3`&quot;">​</a></h3><p><strong>说明</strong>: 计算三元函数在某点的梯度向量。</p>',4),e={class:"tip custom-block github-alert"},h=t("p",{class:"custom-block-title"},"TIP",-1),r={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},d={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"},p=a('<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 683T550 630Q550 594 529 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0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mi",{mathvariant:"normal"},"∇"),t("mi",null,"f"),t("mo",{stretchy:"false"},"("),t("msub",null,[t("mi",null,"x"),t("mn",null,"0")]),t("mo",null,","),t("msub",null,[t("mi",null,"y"),t("mn",null,"0")]),t("mo",null,","),t("msub",null,[t("mi",null,"z"),t("mn",null,"0")]),t("mo",{stretchy:"false"},")"),t("mo",null,"="),t("mrow",{"data-mjx-texclass":"INNER"},[t("mo",{"data-mjx-texclass":"OPEN"},"("),t("mfrac",null,[t("mrow",null,[t("mi",null,"∂"),t("mi",null,"f")]),t("mrow",null,[t("mi",null,"∂"),t("mi",null,"x")])]),t("mo",null,","),t("mfrac",null,[t("mrow",null,[t("mi",null,"∂"),t("mi",null,"f")]),t("mrow",null,[t("mi",null,"∂"),t("mi",null,"y")])]),t("mo",null,","),t("mfrac",null,[t("mrow",null,[t("mi",null,"∂"),t("mi",null,"f")]),t("mrow",null,[t("mi",null,"∂"),t("mi",null,"z")])]),t("mo",{"data-mjx-texclass":"CLOSE"},")")])])],-1),x=a(`<p><strong>参数</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>返回</strong>: 梯度</p><details><summary><b>源代码</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>`,4);function L(C,H,M,Z,b,D){return Q(),s("div",null,[n,t("div",e,[h,t("p",null,[T("已知一个函数"),t("mjx-container",r,[(Q(),s("svg",d,o)),m]),T("，则其在点"),t("mjx-container",k,[(Q(),s("svg",g,y)),u]),T("处的梯度向量为: "),t("mjx-container",f,[(Q(),s("svg",E,_)),w])])]),x])}const V=i(l,[["render",L]]);export{v as __pageData,V as default};
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