124 lines
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124 lines
12 KiB
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<title>std::comp_ellint_1, std::comp_ellint_1f, std::comp_ellint_1l</title>
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<h1 id="firstHeading" class="firstHeading"><span style="font-size:0.7em; line-height:130%">std::</span>comp_ellint_1, <span style="font-size:0.7em; line-height:130%">std::</span>comp_ellint_1f, <span style="font-size:0.7em; line-height:130%">std::</span>comp_ellint_1l</h1>
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<div id="contentSub"><span class="subpages">< <a href="cpp.html">cpp</a>‎ | <a href="cpp-numeric.html">numeric</a>‎ | <a href="cpp-numeric-special_functions.html">special functions</a></span></div>
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<div>定义于头文件 <code><a href="cpp-header-cmath.html"><cmath></a></code></div>
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<td></td>
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<div><span class="mw-geshi cpp source-cpp"><span class="kw4">double</span> comp_ellint_1<span class="br0">(</span> <span class="kw4">double</span> k <span class="br0">)</span><span class="sy4">;</span><br /></span>
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<p><span class="kw4">float</span> comp_ellint_1<span class="br0">(</span> <span class="kw4">float</span> k <span class="br0">)</span><span class="sy4">;</span><br />
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<span class="kw4">long</span> <span class="kw4">double</span> comp_ellint_1<span class="br0">(</span> <span class="kw4">long</span> <span class="kw4">double</span> k <span class="br0">)</span><span class="sy4">;</span><br />
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<span class="kw4">float</span> comp_ellint_1f<span class="br0">(</span> <span class="kw4">float</span> k <span class="br0">)</span><span class="sy4">;</span><br /></p>
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<span class="kw4">long</span> <span class="kw4">double</span> comp_ellint_1l<span class="br0">(</span> <span class="kw4">long</span> <span class="kw4">double</span> k <span class="br0">)</span><span class="sy4">;</span></div>
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<td>(1)</td>
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<td><span class="t-mark-rev t-since-cxx17">(C++17 起)</span></td>
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<div><span class="mw-geshi cpp source-cpp"><span class="kw4">double</span> comp_ellint_1<span class="br0">(</span> IntegralType k <span class="br0">)</span><span class="sy4">;</span></span></div>
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<td>(2)</td>
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<td><span class="t-mark-rev t-since-cxx17">(C++17 起)</span></td>
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<div class="t-li1"><span class="t-li">1)</span> 计算 <code>k</code> 的<a href="https://en.wikipedia.org/wiki/Elliptic_integral#Complete_elliptic_integral_of_the_first_kind" class="extiw" title="enwiki:Elliptic integral">第一类完全椭圆积分</a>。</div>
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<div class="t-li1"><span class="t-li">2)</span> 接受任意<a href="cpp-types-is_integral.html">整数类型</a>参数的重载集或函数模板。等价于将参数转型到 <span class="t-c"><span class="mw-geshi cpp source-cpp"><span class="kw4">double</span></span></span> 后的 <span class="t-v">(1)</span> 。</div>
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<h3><span class="mw-headline" id=".E5.8F.82.E6.95.B0">参数</span></h3>
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<td>k</td>
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<td>-</td>
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<td>椭圆模或离心率（浮点或整数类型值）</td>
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<h3><span class="mw-headline" id=".E8.BF.94.E5.9B.9E.E5.80.BC">返回值</span></h3>
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<p>若无错误发生，则返回 <code>k</code> 的第一类完全椭圆积的值，即 <span class="t-lc">ellint_1(k,π/2)</span> 。</p>
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<h3><span class="mw-headline" id=".E9.94.99.E8.AF.AF.E5.A4.84.E7.90.86">错误处理</span></h3>
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<p>可能报告 <a href="cpp-numeric-math-math_errhandling.html"><tt>math_errhandling</tt></a> 中指定的错误。</p>
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<ul>
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<li>若参数是 NaN ，则返回 NaN 且不报告定义域错误</li>
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<li>若 <span class="texhtml" style="white-space: nowrap;">|k|>1</span> ，则可能发生定义域错误</li>
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</ul>
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<h3><span class="mw-headline" id=".E6.B3.A8.E8.A7.A3">注解</span></h3>
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<p>不支持 C++17 ，但支持 <a href="cpp-experimental-special_functions.html">ISO 29124:2010</a> 的实现会提供此函数，若实现定义了 <code>__STDCPP_MATH_SPEC_FUNCS__</code> 为至少 201003L 的值，且用户在包含任何标准库头文件前定义了 <code>__STDCPP_WANT_MATH_SPEC_FUNCS__</code> 。</p>
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<p>不支持 ISO 29124:2010 但支持 TR 19768:2007 (TR1) 的实现，在头文件 <code>tr1/cmath</code> 及命名空间 <code>std::tr1</code> 中提供此函数。</p>
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<p>此函数的一种实现亦<a rel="nofollow" class="external text" href="http://www.boost.org/doc/libs/1_60_0/libs/math/doc/html/math_toolkit/ellint/ellint_1.html">可用于 boost.math</a></p>
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<p>给定重力加速度 <span class="texhtml" style="white-space: nowrap;">g</span> ，及初始角 θ ，则长度为 <span class="texhtml" style="white-space: nowrap;">l</span> 的<a href="https://en.wikipedia.org/wiki/Pendulum_(mathematics)" class="extiw" title="enwiki:Pendulum (mathematics)">钟摆周期</a>等于 <span class="texhtml" style="white-space: nowrap;">4<span class="t-mrad"><span>√</span><span>l/g</span></span>K(sin<span class="t-su">2<br /></span>(θ/2))</span> ，其中 <span class="texhtml" style="white-space: nowrap;">K</span> 是 <code>std::comp_ellint_1</code> 。</p>
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<h3><span class="mw-headline" id=".E7.A4.BA.E4.BE.8B">示例</span></h3>
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<div class="t-example">
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<div class="cpp source-cpp">
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<pre class="de1"><span class="co2">#include <cmath></span>
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<span class="co2">#include <iostream></span>
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<span class="kw4">int</span> main<span class="br0">(</span><span class="br0">)</span>
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<span class="br0">{</span>
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<span class="kw4">double</span> hpi <span class="sy1">=</span> <a href="cpp-numeric-math-acos.html"><span class="kw1337">std::<span class="me2">acos</span></span></a><span class="br0">(</span><span class="sy2">-</span><span class="nu0">1</span><span class="br0">)</span><span class="sy2">/</span><span class="nu0">2</span><span class="sy4">;</span>
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<a href="cpp-io-cout.html"><span class="kw1758">std::<span class="me2">cout</span></span></a> <span class="sy1"><<</span> <span class="st0">"K(0) = "</span> <span class="sy1"><<</span> <a href="cpp-numeric-special_math-comp_ellint_1.html"><span class="kw1396">std::<span class="me2">comp_ellint_1</span></span></a><span class="br0">(</span><span class="nu0">0</span><span class="br0">)</span> <span class="sy1"><<</span> <span class="st0">'<span class="es1">\n</span>'</span>
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<span class="sy1"><<</span> <span class="st0">"π/2 = "</span> <span class="sy1"><<</span> hpi <span class="sy1"><<</span> <span class="st0">'<span class="es1">\n</span>'</span>
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<span class="sy1"><<</span> <span class="st0">"K(0.5) = "</span> <span class="sy1"><<</span> <a href="cpp-numeric-special_math-comp_ellint_1.html"><span class="kw1396">std::<span class="me2">comp_ellint_1</span></span></a><span class="br0">(</span><span class="nu16">0.5</span><span class="br0">)</span> <span class="sy1"><<</span> <span class="st0">'<span class="es1">\n</span>'</span>
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<span class="sy1"><<</span> <span class="st0">"F(0.5, π/2) = "</span> <span class="sy1"><<</span> <a href="cpp-numeric-special_math-ellint_1.html"><span class="kw1417">std::<span class="me2">ellint_1</span></span></a><span class="br0">(</span><span class="nu16">0.5</span>, hpi<span class="br0">)</span> <span class="sy1"><<</span> <span class="st0">'<span class="es1">\n</span>'</span><span class="sy4">;</span>
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<a href="cpp-io-cout.html"><span class="kw1758">std::<span class="me2">cout</span></span></a> <span class="sy1"><<</span> <span class="st0">"Period of a pendulum length 1 m at 90 degree initial angle is "</span>
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<span class="sy1"><<</span> <span class="nu0">4</span><span class="sy2">*</span><a href="cpp-numeric-math-sqrt.html"><span class="kw1329">std::<span class="me2">sqrt</span></span></a><span class="br0">(</span><span class="nu0">1</span><span class="sy2">/</span><span class="nu16">9.80665</span><span class="br0">)</span><span class="sy2">*</span>
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<a href="cpp-numeric-special_math-comp_ellint_1.html"><span class="kw1396">std::<span class="me2">comp_ellint_1</span></span></a><span class="br0">(</span><a href="cpp-numeric-math-pow.html"><span class="kw1332">std::<span class="me2">pow</span></span></a><span class="br0">(</span><a href="cpp-numeric-math-sin.html"><span class="kw1333">std::<span class="me2">sin</span></span></a><span class="br0">(</span>hpi<span class="sy2">/</span><span class="nu0">2</span><span class="br0">)</span>,<span class="nu0">2</span><span class="br0">)</span><span class="br0">)</span> <span class="sy1"><<</span> <span class="st0">" s<span class="es1">\n</span>"</span><span class="sy4">;</span>
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<span class="br0">}</span></pre></div>
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<p>输出：</p>
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<div dir="ltr" class="mw-geshi" style="text-align: left;">
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<div class="text source-text">
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<pre class="de1">K(0) = 1.5708
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π/2 = 1.5708
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K(0.5) = 1.68575
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F(0.5, π/2) = 1.68575
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Period of a pendulum length 1 m at 90 degree initial angle is 2.15324 s</pre></div>
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<h3><span class="mw-headline" id=".E5.A4.96.E9.83.A8.E9.93.BE.E6.8E.A5">外部链接</span></h3>
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<p><a rel="nofollow" class="external text" href="http://mathworld.wolfram.com/CompleteEllipticIntegraloftheFirstKind.html">Weisstein, Eric W. “第一类完全椭圆积分”</a>来自 MathWorld--A Wolfram Web Resource 。</p>
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<h3><span class="mw-headline" id=".E5.8F.82.E9.98.85">参阅</span></h3>
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<table class="t-dsc-begin">
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<div class="t-dsc-member-div">
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<div><a href="cpp-numeric-special_functions-ellint_1.html"><span class="t-lines"><span>ellint_1</span><span>ellint_1f</span><span>ellint_1l</span></span></a></div>
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<div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx17">(C++17)</span></span><span><span class="t-mark-rev t-since-cxx17">(C++17)</span></span><span><span class="t-mark-rev t-since-cxx17">(C++17)</span></span></span></div>
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</div>
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</td>
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<td>第一类（不完全）椭圆积分<br />
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<span class="t-mark">(函数)</span></td>
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<div class="visualClear"></div>
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