168 lines
15 KiB
HTML
168 lines
15 KiB
HTML
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<title>std::tanh(std::complex)</title>
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<body class="mediawiki ltr sitedir-ltr ns-0 ns-subject page-cpp_numeric_complex_tanh skin-cppreference2 action-view cpp-navbar">
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<h1 id="firstHeading" class="firstHeading"><span style="font-size:0.7em; line-height:130%">std::</span>tanh<span style="font-size:0.7em; line-height:130%">(std::complex)</span></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-complex.html">complex</a></span></div>
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<div>定义于头文件 <code><a href="cpp-header-complex.html"><complex></a></code></div>
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<td></td>
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<div><span class="mw-geshi cpp source-cpp"><span class="kw1">template</span><span class="sy1"><</span> <span class="kw1">class</span> T <span class="sy1">></span><br />
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complex<span class="sy1"><</span>T<span class="sy1">></span> tanh<span class="br0">(</span> <span class="kw4">const</span> complex<span class="sy1"><</span>T<span class="sy1">></span><span class="sy3">&</span> z <span class="br0">)</span><span class="sy4">;</span></span></div>
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</td>
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<td class="t-dcl-nopad"></td>
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<td><span class="t-mark-rev t-since-cxx11">(C++11 起)</span></td>
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<tr class="t-dcl-sep">
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<td></td>
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<td></td>
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<td></td>
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</table>
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<p>计算复数值 <code>z</code> 的复双曲正切。</p>
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<h3><span class="mw-headline" id=".E5.8F.82.E6.95.B0">参数</span></h3>
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<table class="t-par-begin">
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<td>z</td>
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<td>-</td>
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<td>复数值</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>若不发生错误，则返回 <code>z</code> 的复双曲正切。</p>
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<h3><span class="mw-headline" id=".E9.94.99.E8.AF.AF.E5.A4.84.E7.90.86.E5.8F.8A.E7.89.B9.E6.AE.8A.E5.80.BC">错误处理及特殊值</span></h3>
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<p>报告的错误与 <a href="cpp-numeric-math-math_errhandling.html"><tt>math_errhandling</tt></a> 一致。</p>
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<p>若实现支持 IEEE 浮点算术，则</p>
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<ul>
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<li><span class="t-c"><span class="mw-geshi cpp source-cpp"><a href="cpp-numeric-math-tanh.html"><span class="kw1342">std::<span class="me2">tanh</span></span></a><span class="br0">(</span>std<span class="sy4">::</span><span class="me2">conj</span><span class="br0">(</span>z<span class="br0">)</span><span class="br0">)</span> <span class="sy1">==</span> std<span class="sy4">::</span><span class="me2">conj</span><span class="br0">(</span><a href="cpp-numeric-math-tanh.html"><span class="kw1342">std::<span class="me2">tanh</span></span></a><span class="br0">(</span>z<span class="br0">)</span><span class="br0">)</span></span></span></li>
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<li><span class="t-c"><span class="mw-geshi cpp source-cpp"><a href="cpp-numeric-math-tanh.html"><span class="kw1342">std::<span class="me2">tanh</span></span></a><span class="br0">(</span><span class="sy2">-</span>z<span class="br0">)</span> <span class="sy1">==</span> <span class="sy2">-</span><a href="cpp-numeric-math-tanh.html"><span class="kw1342">std::<span class="me2">tanh</span></span></a><span class="br0">(</span>z<span class="br0">)</span></span></span></li>
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<li>若 <code>z</code> 为 <code>(+0,+0)</code> ，则结果为 <code>(+0,+0)</code> 。</li>
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<li>若 <code>z</code> 为 <code>(x,+∞)</code> （对于任何<sup id="cite_ref-1" class="reference"><a href="cpp-numeric-complex-tanh.html#cite_note-1">[1]</a></sup>有限 x ），结果为 <code>(NaN,NaN)</code> 并引发 <span class="t-lc"><a href="cpp-numeric-fenv-FE_exceptions.html">FE_INVALID</a></span> 。</li>
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<li>若 <code>z</code> 为 <code>(x,NaN)</code> （对于任何<sup id="cite_ref-2" class="reference"><a href="cpp-numeric-complex-tanh.html#cite_note-2">[2]</a></sup>有限 x ），结果为 <code>(NaN,NaN)</code> 并可能引发 <span class="t-lc"><a href="cpp-numeric-fenv-FE_exceptions.html">FE_INVALID</a></span> 。</li>
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<li>若 <code>z</code> 为 <code>(+∞,y)</code> （对于任何有限正 y ），结果为 <code>(1,+0)</code> 。</li>
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<li>若 <code>z</code> 为 <code>(+∞,+∞)</code> ，则结果为 <code>(1,±0)</code> （虚部符号未指定）。</li>
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<li>若 <code>z</code> 为 <code>(+∞,NaN)</code> ，则结果为 <code>(1,±0)</code> （虚部符号未指定）。</li>
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<li>若 <code>z</code> 为 <code>(NaN,+0)</code> ，则结果为 <code>(NaN,+0)</code> 。</li>
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<li>若 <code>z</code> 为 <code>(NaN,y)</code> （对于任何非零 y ），则结果为 <code>(NaN,NaN)</code> 并可能引发 <span class="t-lc"><a href="cpp-numeric-fenv-FE_exceptions.html">FE_INVALID</a></span> 。</li>
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<li>若 <code>z</code> 为 <code>(NaN,NaN)</code> ，则结果为 <code>(NaN,NaN)</code> 。</li>
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</ul>
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<ol class="references">
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<li id="cite_note-1"><span class="mw-cite-backlink"><a href="cpp-numeric-complex-tanh.html#cite_ref-1">↑</a></span> <span class="reference-text">由 <a rel="nofollow" class="external text" href="http://www.open-std.org/jtc1/sc22/wg14/www/docs/n1892.htm#dr_471">C11 DR471</a> ，这只对非零 x 成立。若 <code>z</code> 为 <code>(0,∞)</code> ，则结果应为 <code>(0,NaN)</code> 。</span></li>
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<li id="cite_note-2"><span class="mw-cite-backlink"><a href="cpp-numeric-complex-tanh.html#cite_ref-2">↑</a></span> <span class="reference-text">由 <a rel="nofollow" class="external text" href="http://www.open-std.org/jtc1/sc22/wg14/www/docs/n1892.htm#dr_471">C11 DR471</a> ，这只对非零 x 成立。若 <code>z</code> 为 <code>(0,NaN)</code> ，则结果应为 <code>(0,NaN)</code> 。</span></li>
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</ol>
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<h3><span class="mw-headline" id=".E6.B3.A8.E6.84.8F">注意</span></h3>
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双曲正切的数学定义是 <span class="texhtml" style="white-space: nowrap;">tanh z = <span class="t-mfrac"></span></span>
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<td>e<span class="t-su">z<br /></span>-e<span class="t-su">-z<br /></span></td>
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<td>e<span class="t-su">z<br /></span>+e<span class="t-su">-z<br /></span></td>
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。
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<p>双曲正切是复平面上的解析函数且无分支切割。它对于虚部是周期的，周期为 πi ，而且沿虚轴有一阶极点，位于坐标 <span class="texhtml" style="white-space: nowrap;">(0, π(1/2 + n))</span> 。然而无常用浮点表示能准确表示 π/2 ，故没有参数值能导致极点错误。</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="t-example-live-link"></div>
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<div class="cpp source-cpp">
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<pre class="de1"><span class="co2">#include <iostream></span>
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<span class="co2">#include <cmath></span>
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<span class="co2">#include <complex></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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<a href="cpp-io-cout.html"><span class="kw1758">std::<span class="me2">cout</span></span></a> <span class="sy1"><<</span> <a href="cpp-io-manip-fixed.html"><span class="kw1784">std::<span class="me2">fixed</span></span></a><span class="sy4">;</span>
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<a href="cpp-numeric-complex.html"><span class="kw1472">std::<span class="me2">complex</span></span></a><span class="sy1"><</span><span class="kw4">double</span><span class="sy1">></span> z<span class="br0">(</span><span class="nu0">1</span>, <span class="nu0">0</span><span class="br0">)</span><span class="sy4">;</span> <span class="co1">// 表现类似沿实轴的 tanh</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">"tanh"</span> <span class="sy1"><<</span> z <span class="sy1"><<</span> <span class="st0">" = "</span> <span class="sy1"><<</span> <a href="cpp-numeric-math-tanh.html"><span class="kw1342">std::<span class="me2">tanh</span></span></a><span class="br0">(</span>z<span class="br0">)</span>
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<span class="sy1"><<</span> <span class="st0">" (tanh(1) = "</span> <span class="sy1"><<</span> <a href="cpp-numeric-math-tanh.html"><span class="kw1342">std::<span class="me2">tanh</span></span></a><span class="br0">(</span><span class="nu0">1</span><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-numeric-complex.html"><span class="kw1472">std::<span class="me2">complex</span></span></a><span class="sy1"><</span><span class="kw4">double</span><span class="sy1">></span> z2<span class="br0">(</span><span class="nu0">0</span>, <span class="nu0">1</span><span class="br0">)</span><span class="sy4">;</span> <span class="co1">// 表现类似沿虚轴的正切</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">"tanh"</span> <span class="sy1"><<</span> z2 <span class="sy1"><<</span> <span class="st0">" = "</span> <span class="sy1"><<</span> <a href="cpp-numeric-math-tanh.html"><span class="kw1342">std::<span class="me2">tanh</span></span></a><span class="br0">(</span>z2<span class="br0">)</span>
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<span class="sy1"><<</span> <span class="st0">" ( tan(1) = "</span> <span class="sy1"><<</span> <a href="cpp-numeric-math-tan.html"><span class="kw1335">std::<span class="me2">tan</span></span></a><span class="br0">(</span><span class="nu0">1</span><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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<span class="br0">}</span></pre></div>
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</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">tanh(1.000000,0.000000) = (0.761594,0.000000) (tanh(1) = 0.761594)
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tanh(0.000000,1.000000) = (0.000000,1.557408) ( tan(1) = 1.557408)</pre></div>
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<h3><span class="mw-headline" id=".E5.8F.82.E9.98.85">参阅</span></h3>
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<div class="t-dsc-member-div">
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<div><a href="cpp-numeric-complex-sinh.html"><span class="t-lines"><span>sinh<span class="t-dsc-small">(std::complex)</span></span></span></a></div>
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</div>
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</td>
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<td>计算复数的双曲正弦（ <span class="mjax" style="display:none">\({\small\sinh{z} }\)</span><span class="mjax-fallback texhtml" style="white-space: nowrap;">sinh(z)</span> ）<br />
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<span class="t-mark">(函数模板)</span></td>
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<tr class="t-dsc">
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<div class="t-dsc-member-div">
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<div><a href="cpp-numeric-complex-cosh.html"><span class="t-lines"><span>cosh<span class="t-dsc-small">(std::complex)</span></span></span></a></div>
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</div>
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</td>
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<td>计算复数的双曲余弦（ <span class="mjax" style="display:none">\({\small\cosh{z} }\)</span><span class="mjax-fallback texhtml" style="white-space: nowrap;">cosh(z)</span> ）<br />
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<span class="t-mark">(函数模板)</span></td>
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</tr>
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<tr class="t-dsc">
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<div class="t-dsc-member-div">
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<div><a href="cpp-numeric-complex-atanh.html"><span class="t-lines"><span>atanh<span class="t-dsc-small">(std::complex)</span></span></span></a></div>
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<div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx11">(C++11)</span></span></span></div>
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</div>
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</td>
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<td>计算复数的反双曲正切（ <span class="mjax" style="display:none">\({\small\operatorname{artanh}{z} }\)</span><span class="mjax-fallback texhtml" style="white-space: nowrap;">artanh(z)</span> ）<br />
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<span class="t-mark">(函数模板)</span></td>
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</tr>
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<tr class="t-dsc">
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<div class="t-dsc-member-div">
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<div><a href="cpp-numeric-math-tanh.html"><span class="t-lines"><span>tanh</span><span>tanhf</span><span>tanhl</span></span></a></div>
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<div><span class="t-lines"><span></span><span><span class="t-mark-rev t-since-cxx11">(C++11)</span></span><span><span class="t-mark-rev t-since-cxx11">(C++11)</span></span></span></div>
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</div>
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</td>
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<td>计算双曲正切（ <span class="mjax" style="display:none">\({\small\tanh{x} }\)</span><span class="mjax-fallback texhtml" style="white-space: nowrap;">tanh(x)</span> ）<br />
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<span class="t-mark">(函数)</span></td>
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</tr>
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<tr class="t-dsc">
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<div class="t-dsc-member-div">
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<div><a href="cpp-numeric-valarray-tanh.html"><span class="t-lines"><span>tanh<span class="t-dsc-small">(std::valarray)</span></span></span></a></div>
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</div>
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</td>
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<td>在 valarray 的每个元素上调用 <span class="t-lc"><a href="cpp-numeric-math-tanh.html">std::tanh</a></span> 函数<br />
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<span class="t-mark">(函数模板)</span></td>
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</table>
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