505 lines
32 KiB
HTML
505 lines
32 KiB
HTML
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<html lang="zh" dir="ltr" class="client-nojs" xmlns="http://www.w3.org/1999/xhtml" xml:lang="zh">
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<title>std::complex</title>
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<body class="mediawiki ltr sitedir-ltr ns-0 ns-subject page-cpp_numeric_complex skin-cppreference2 action-view cpp-navbar">
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<div id="cpp-content-base">
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<h1 id="firstHeading" class="firstHeading"><span style="font-size:0.7em; line-height:130%">std::</span>complex</h1>
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<div id="contentSub"><span class="subpages">< <a href="cpp.html">cpp</a>‎ | <a href="cpp-numeric.html">numeric</a></span></div>
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<div id="mw-content-text" lang="zh" dir="ltr" class="mw-content-ltr" xml:lang="zh">
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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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<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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<span class="kw1">class</span> complex<span class="sy4">;</span></span></div>
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<td>(1)</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> complex<span class="sy1"><</span><span class="kw4">float</span><span class="sy1">></span><span class="sy4">;</span></span></div>
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<td>(2)</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> complex<span class="sy1"><</span><span class="kw4">double</span><span class="sy1">></span><span class="sy4">;</span></span></div>
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<td>(3)</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> complex<span class="sy1"><</span><span class="kw4">long</span> <span class="kw4">double</span><span class="sy1">></span><span class="sy4">;</span></span></div>
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<td>(4)</td>
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<td class="t-dcl-nopad"></td>
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<td></td>
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<td></td>
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</table>
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<p>模板特化 <span class="t-c"><span class="mw-geshi cpp source-cpp">std<span class="sy4">::</span><span class="me2">complex</span><span class="sy1"><</span><span class="kw4">float</span><span class="sy1">></span></span></span>、 <span class="t-c"><span class="mw-geshi cpp source-cpp">std<span class="sy4">::</span><span class="me2">complex</span><span class="sy1"><</span><span class="kw4">double</span><span class="sy1">></span></span></span> 及 <span class="t-c"><span class="mw-geshi cpp source-cpp">std<span class="sy4">::</span><span class="me2">complex</span><span class="sy1"><</span><span class="kw4">long</span> <span class="kw4">double</span><span class="sy1">></span></span></span> 是表示并计算<a href="https://en.wikipedia.org/wiki/Complex_number" class="extiw" title="enwiki:Complex number">复数</a>的<a href="cpp-named_req-LiteralType.html"><span style="font-style:italic">字面类型</span> <span style="font-family: Georgia, 'DejaVu Serif', serif; font-style:italic">(LiteralType)</span></a> 。</p>
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<p>对任何其他类型，实例化模板 <code>complex</code> 的效果是不确定的。实现可以禁止这种特化的实例化。</p>
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<h3><span class="mw-headline" id=".E6.88.90.E5.91.98.E7.B1.BB.E5.9E.8B">成员类型</span></h3>
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<table class="t-dsc-begin">
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<td>成员类型</td>
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<td>定义</td>
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<tr class="t-dsc">
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<td><code>value_type</code></td>
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<td><code>T</code></td>
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</table>
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<h3><span class="mw-headline" id=".E6.88.90.E5.91.98.E5.87.BD.E6.95.B0">成员函数</span></h3>
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<table class="t-dsc-begin">
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<div class="t-dsc-member-div t-dsc-member-nobold-div">
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<div><a href="cpp-numeric-complex-complex.html"><span class="t-lines"><span>(构造函数)</span></span></a></div>
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</div>
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</td>
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<td>构造一个复数<br />
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<span class="t-mark">(公开成员函数)</span></td>
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<tr class="t-dsc">
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<td>
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<div class="t-dsc-member-div">
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<div><a href="cpp-numeric-complex-operator=.html"><span class="t-lines"><span>operator=</span></span></a></div>
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</div>
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</td>
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<td>赋值内容<br />
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<span class="t-mark">(公开成员函数)</span></td>
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<td>
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<div class="t-dsc-member-div">
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<div><a href="cpp-numeric-complex-real.html"><span class="t-lines"><span>real</span></span></a></div>
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</div>
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</td>
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<td>访问复数的实部<br />
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<span class="t-mark">(公开成员函数)</span></td>
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<tr class="t-dsc">
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<td>
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<div class="t-dsc-member-div">
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<div><a href="cpp-numeric-complex-imag.html"><span class="t-lines"><span>imag</span></span></a></div>
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</div>
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</td>
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<td>访问复数的虚部<br />
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<span class="t-mark">(公开成员函数)</span></td>
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<div><a href="cpp-numeric-complex-operator_arith.html"><span class="t-lines"><span>operator+=</span><span>operator-=</span><span>operator*=</span><span>operator/=</span></span></a></div>
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</div>
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</td>
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<td>两个复数，或一个复数与一个标量的复合赋值<br />
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<span class="t-mark">(公开成员函数)</span></td>
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</table>
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<h3><span class="mw-headline" id=".E9.9D.9E.E6.88.90.E5.91.98.E5.87.BD.E6.95.B0">非成员函数</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-complex-operator_arith2.html"><span class="t-lines"><span>operator+</span><span>operator-</span></span></a></div>
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</div>
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</td>
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<td>对复数运用一元运算符<br />
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<span class="t-mark">(函数模板)</span></td>
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<div><a href="cpp-numeric-complex-operator_arith3.html"><span class="t-lines"><span>operator+</span><span>operator-</span><span>operator*</span><span>operator/</span></span></a></div>
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</div>
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</td>
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<td>在两个复数，或一个复数与一个标量上进行复数算术运算<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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<td>
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<div class="t-dsc-member-div">
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<div><a href="cpp-numeric-complex-operator_cmp.html"><span class="t-lines"><span>operator==</span><span>operator!=</span></span></a></div>
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<div><span class="t-lines"><span></span><span><span class="t-mark-rev t-until-cxx20">(C++20 中移除)</span></span></span></div>
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</div>
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</td>
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<td>比较两个复数，或一个复数与一个标量<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-operator_ltltgtgt.html"><span class="t-lines"><span>operator<<</span><span>operator>></span></span></a></div>
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</div>
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</td>
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<td>复数的序列化和反序列化<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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<td>
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<div class="t-dsc-member-div">
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<div><a href="cpp-numeric-complex-real2.html"><span class="t-lines"><span>real</span></span></a></div>
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</div>
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</td>
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<td>返回实部<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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<td>
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<div class="t-dsc-member-div">
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<div><a href="cpp-numeric-complex-imag2.html"><span class="t-lines"><span>imag</span></span></a></div>
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</div>
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</td>
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<td>返回虚部<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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<td>
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<div class="t-dsc-member-div">
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<div><a href="cpp-numeric-complex-abs.html"><span class="t-lines"><span>abs<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>返回复数的模<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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<td>
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<div class="t-dsc-member-div">
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<div><a href="cpp-numeric-complex-arg.html"><span class="t-lines"><span>arg</span></span></a></div>
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</div>
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</td>
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<td>返回辐角<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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<td>
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<div class="t-dsc-member-div">
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<div><a href="cpp-numeric-complex-norm.html"><span class="t-lines"><span>norm</span></span></a></div>
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</div>
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</td>
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<td>返回模(范数)的平方<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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<td>
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<div class="t-dsc-member-div">
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<div><a href="cpp-numeric-complex-conj.html"><span class="t-lines"><span>conj</span></span></a></div>
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</div>
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</td>
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<td>返回复共轭<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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<td>
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<div class="t-dsc-member-div">
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<div><a href="cpp-numeric-complex-proj.html"><span class="t-lines"><span>proj</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>返回到黎曼球上的投影<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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<td>
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<div class="t-dsc-member-div">
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<div><a href="cpp-numeric-complex-polar.html"><span class="t-lines"><span>polar</span></span></a></div>
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</div>
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</td>
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<td>从模和辐角构造复数<br />
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<span class="t-mark">(函数模板)</span></td>
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<tr>
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<h5><span class="mw-headline" id=".E6.8C.87.E6.95.B0.E5.87.BD.E6.95.B0">指数函数</span></h5>
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</td>
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</tr>
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<tr class="t-dsc">
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<td>
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<div class="t-dsc-member-div">
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<div><a href="cpp-numeric-complex-exp.html"><span class="t-lines"><span>exp<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>以 <i>e</i> 为底复数的指数<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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<td>
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<div class="t-dsc-member-div">
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<div><a href="cpp-numeric-complex-log.html"><span class="t-lines"><span>log<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>沿负实轴切割的复自然对数<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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<td>
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<div class="t-dsc-member-div">
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<div><a href="cpp-numeric-complex-log10.html"><span class="t-lines"><span>log10<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>沿负实轴分割的复常用对数<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>
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<h5><span class="mw-headline" id=".E5.B9.82.E5.87.BD.E6.95.B0">幂函数</span></h5>
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</td>
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</tr>
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<tr class="t-dsc">
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<td>
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<div class="t-dsc-member-div">
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<div><a href="cpp-numeric-complex-pow.html"><span class="t-lines"><span>pow<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>复数幂，一或两个参数可为复数<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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<td>
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<div class="t-dsc-member-div">
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<div><a href="cpp-numeric-complex-sqrt.html"><span class="t-lines"><span>sqrt<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>右半平面范围中的复平方根<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>
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<td colspan="2">
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<h5><span class="mw-headline" id=".E4.B8.89.E8.A7.92.E5.87.BD.E6.95.B0">三角函数</span></h5>
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</td>
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</tr>
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<tr class="t-dsc">
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<td>
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<div class="t-dsc-member-div">
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<div><a href="cpp-numeric-complex-sin.html"><span class="t-lines"><span>sin<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>计算复数的正弦（ <span class="mjax" style="display:none">\({\small\sin{z} }\)</span><span class="mjax-fallback texhtml" style="white-space: nowrap;">sin(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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<td>
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<div class="t-dsc-member-div">
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<div><a href="cpp-numeric-complex-cos.html"><span class="t-lines"><span>cos<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>计算复数的余弦（ <span class="mjax" style="display:none">\({\small\cos{z} }\)</span><span class="mjax-fallback texhtml" style="white-space: nowrap;">cos(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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<td>
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<div><a href="cpp-numeric-complex-tan.html"><span class="t-lines"><span>tan<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>计算复数的正切（ <span class="mjax" style="display:none">\({\small\tan{z} }\)</span><span class="mjax-fallback texhtml" style="white-space: nowrap;">tan(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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<td>
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<div class="t-dsc-member-div">
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<div><a href="cpp-numeric-complex-asin.html"><span class="t-lines"><span>asin<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>计算复数的反正弦（ <span class="mjax" style="display:none">\({\small\arcsin{z} }\)</span><span class="mjax-fallback texhtml" style="white-space: nowrap;">arcsin(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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<td>
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<div class="t-dsc-member-div">
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<div><a href="cpp-numeric-complex-acos.html"><span class="t-lines"><span>acos<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>计算复数的反余弦（ <span class="mjax" style="display:none">\({\small\arccos{z} }\)</span><span class="mjax-fallback texhtml" style="white-space: nowrap;">arccos(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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<td>
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<div class="t-dsc-member-div">
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<div><a href="cpp-numeric-complex-atan.html"><span class="t-lines"><span>atan<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>
|
|
<td>计算复数的反正切（ <span class="mjax" style="display:none">\({\small\arctan{z} }\)</span><span class="mjax-fallback texhtml" style="white-space: nowrap;">arctan(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>
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<td colspan="2">
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<h5><span class="mw-headline" id=".E5.8F.8C.E6.9B.B2.E5.87.BD.E6.95.B0">双曲函数</span></h5>
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</td>
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</tr>
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<tr class="t-dsc">
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<td>
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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>
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<tr class="t-dsc">
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<td>
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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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<td>
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<div class="t-dsc-member-div">
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<div><a href="cpp-numeric-complex-tanh.html"><span class="t-lines"><span>tanh<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>计算复数的双曲正切（ <span class="mjax" style="display:none">\({\small\tanh{z} }\)</span><span class="mjax-fallback texhtml" style="white-space: nowrap;">tanh(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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<td>
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<div class="t-dsc-member-div">
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<div><a href="cpp-numeric-complex-asinh.html"><span class="t-lines"><span>asinh<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弦（ <span class="mjax" style="display:none">\({\small\operatorname{arsinh}{z} }\)</span><span class="mjax-fallback texhtml" style="white-space: nowrap;">arsinh(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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<td>
|
|
<div class="t-dsc-member-div">
|
|
<div><a href="cpp-numeric-complex-acosh.html"><span class="t-lines"><span>acosh<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>
|
|
</div>
|
|
</td>
|
|
<td>计算复数的反双曲余弦（ <span class="mjax" style="display:none">\({\small\operatorname{arcosh}{z} }\)</span><span class="mjax-fallback texhtml" style="white-space: nowrap;">arcosh(z)</span> ）<br />
|
|
<span class="t-mark">(函数模板)</span></td>
|
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</tr>
|
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<tr class="t-dsc">
|
|
<td>
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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>
|
|
</div>
|
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</td>
|
|
<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 />
|
|
<span class="t-mark">(函数模板)</span></td>
|
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</tr>
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</table>
|
|
<h3><span class="mw-headline" id=".E9.80.9A.E8.BF.87.E6.95.B0.E7.BB.84.E8.AE.BF.E9.97.AE">通过数组访问</span></h3>
|
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<table class="t-rev-begin">
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<tr class="t-rev t-since-cxx11">
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<td>
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<p>对于任何 <code>complex<T></code> 类型的对象 <code>z</code> ， <span class="t-c"><span class="mw-geshi cpp source-cpp"><span class="kw1">reinterpret_cast</span><span class="sy1"><</span>T<span class="br0">(</span><span class="sy3">&</span><span class="br0">)</span><span class="br0">[</span><span class="nu0">2</span><span class="br0">]</span><span class="sy1">></span><span class="br0">(</span>z<span class="br0">)</span><span class="br0">[</span><span class="nu0">0</span><span class="br0">]</span></span></span> 为 z 的实部且 <span class="t-c"><span class="mw-geshi cpp source-cpp"><span class="kw1">reinterpret_cast</span><span class="sy1"><</span>T<span class="br0">(</span><span class="sy3">&</span><span class="br0">)</span><span class="br0">[</span><span class="nu0">2</span><span class="br0">]</span><span class="sy1">></span><span class="br0">(</span>z<span class="br0">)</span><span class="br0">[</span><span class="nu0">1</span><span class="br0">]</span></span></span> 为 z 的虚部。</p>
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<p>对于任何名为 <code>p</code> 指向 <code>complex<T></code> 数组元素的指针，及任何合法下标 <span class="t-c"><span class="mw-geshi cpp source-cpp">i</span></span> ， <span class="t-c"><span class="mw-geshi cpp source-cpp"><span class="kw1">reinterpret_cast</span><span class="sy1"><</span>T<span class="sy2">*</span><span class="sy1">></span><span class="br0">(</span>p<span class="br0">)</span><span class="br0">[</span><span class="nu0">2</span><span class="sy2">*</span>i<span class="br0">]</span></span></span> 等于复数 <span class="t-c"><span class="mw-geshi cpp source-cpp">p<span class="br0">[</span>i<span class="br0">]</span></span></span> 的实部，而 <span class="t-c"><span class="mw-geshi cpp source-cpp"><span class="kw1">reinterpret_cast</span><span class="sy1"><</span>T<span class="sy2">*</span><span class="sy1">></span><span class="br0">(</span>p<span class="br0">)</span><span class="br0">[</span><span class="nu0">2</span><span class="sy2">*</span>i <span class="sy2">+</span> <span class="nu0">1</span><span class="br0">]</span></span></span> 等于复数 <span class="t-c"><span class="mw-geshi cpp source-cpp">p<span class="br0">[</span>i<span class="br0">]</span></span></span> 的虚部</p>
|
|
<p>此要求的目的是 C++ 复数类型与 <a href="c-language-arithmetic_types.html#.E5.A4.8D.E6.B5.AE.E7.82.B9.E7.B1.BB.E5.9E.8B">C 语言复数类型</a>（及其数组）的二进制兼容性，其中要求相同的对象表示。</p>
|
|
</td>
|
|
<td><span class="t-mark-rev t-since-cxx11">(C++11 起)</span></td>
|
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</tr>
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</table>
|
|
<h3><span class="mw-headline" id=".E5.AE.9E.E7.8E.B0.E6.B3.A8.E8.A7.A3">实现注解</span></h3>
|
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<table class="t-rev-begin">
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<tr class="t-rev t-since-cxx11">
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<td>
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<p>为满足数组访问的要求，实现需满足在单独且相邻的内存位置存储 <code>std::complex</code> 特化的实部和虚部。其非静态数据成员的可能声明包括：</p>
|
|
<ul>
|
|
<li>数组类型 <span class="t-c"><span class="mw-geshi cpp source-cpp">value_type<span class="br0">[</span><span class="nu0">2</span><span class="br0">]</span></span></span> ，其首元素存有实部而第二元素存有虚部（例如 Microsoft Visual Studio ）；</li>
|
|
<li>单个 <span class="t-c"><span class="mw-geshi cpp source-cpp">value_type _Complex</span></span> 类型成员（封装对应的 <a href="c-language-arithmetic_types.html#.E5.A4.8D.E6.B5.AE.E7.82.B9.E7.B1.BB.E5.9E.8B">C 语言复数类型</a>）（例如 GNU libstdc++ ）；</li>
|
|
<li>两个拥有相同访问权限的 <span class="t-c"><span class="mw-geshi cpp source-cpp">value_type</span></span> 类型成员，分别存有实部和虚部（例如 LLVM libc++ ）。</li>
|
|
</ul>
|
|
<p>实现不能添加会占用与实部和虚部冲突的存储的非静态数据成员，而且必须确保类模板特化不含任何填充。实现也必须确保对数组访问的优化问题，其中要考虑到指向 <span class="t-c"><span class="mw-geshi cpp source-cpp">value_type</span></span> 的指针可能为 <code>std::complex</code> 特化的别名，对应的数组亦然。</p>
|
|
</td>
|
|
<td><span class="t-mark-rev t-since-cxx11">(C++11 起)</span></td>
|
|
</tr>
|
|
</table>
|
|
<h3><span class="mw-headline" id=".E5.AD.97.E9.9D.A2.E9.87.8F">字面量</span></h3>
|
|
<table class="t-dsc-begin">
|
|
<tr class="t-dsc-header">
|
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<td colspan="2">
|
|
<div>定义于内联命名空间 <code>std::literals::complex_literals</code></div>
|
|
</td>
|
|
</tr>
|
|
<tr class="t-dsc">
|
|
<td>
|
|
<div class="t-dsc-member-div">
|
|
<div><a href="cpp-numeric-complex-operator_22_22i.html"><span class="t-lines"><span>operator""if</span><span>operator""i</span><span>operator""il</span></span></a></div>
|
|
<div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx14">(C++14)</span></span></span></div>
|
|
</div>
|
|
</td>
|
|
<td>表示纯虚数的 <span class="t-lc"><strong class="selflink">std::complex</strong></span> 字面量<br />
|
|
<span class="t-mark">(函数)</span></td>
|
|
</tr>
|
|
</table>
|
|
<h3><span class="mw-headline" id=".E7.A4.BA.E4.BE.8B">示例</span></h3>
|
|
<div class="t-example">
|
|
<div class="t-example-live-link"></div>
|
|
<div dir="ltr" class="mw-geshi" style="text-align: left;">
|
|
<div class="cpp source-cpp">
|
|
<pre class="de1"><span class="co2">#include <iostream></span>
|
|
<span class="co2">#include <iomanip></span>
|
|
<span class="co2">#include <complex></span>
|
|
<span class="co2">#include <cmath></span>
|
|
|
|
<span class="kw4">int</span> main<span class="br0">(</span><span class="br0">)</span>
|
|
<span class="br0">{</span>
|
|
<span class="kw1">using</span> <span class="kw1">namespace</span> std<span class="sy4">::</span><span class="me2">complex_literals</span><span class="sy4">;</span>
|
|
<a href="cpp-io-cout.html"><span class="kw1757">std::<span class="me2">cout</span></span></a> <span class="sy1"><<</span> <a href="cpp-io-manip-fixed.html"><span class="kw1783">std::<span class="me2">fixed</span></span></a> <span class="sy1"><<</span> <a href="cpp-io-manip-setprecision.html"><span class="kw1795">std::<span class="me2">setprecision</span></span></a><span class="br0">(</span><span class="nu0">1</span><span class="br0">)</span><span class="sy4">;</span>
|
|
|
|
std<span class="sy4">::</span><span class="me2">complex</span><span class="sy1"><</span><span class="kw4">double</span><span class="sy1">></span> z1 <span class="sy1">=</span> 1i <span class="sy2">*</span> 1i<span class="sy4">;</span> <span class="co1">// 虚数单位平方</span>
|
|
<a href="cpp-io-cout.html"><span class="kw1757">std::<span class="me2">cout</span></span></a> <span class="sy1"><<</span> <span class="st0">"i * i = "</span> <span class="sy1"><<</span> z1 <span class="sy1"><<</span> <span class="st0">'<span class="es1">\n</span>'</span><span class="sy4">;</span>
|
|
|
|
std<span class="sy4">::</span><span class="me2">complex</span><span class="sy1"><</span><span class="kw4">double</span><span class="sy1">></span> z2 <span class="sy1">=</span> <a href="cpp-numeric-math-pow.html"><span class="kw1332">std::<span class="me2">pow</span></span></a><span class="br0">(</span>1i, <span class="nu0">2</span><span class="br0">)</span><span class="sy4">;</span> <span class="co1">// 虚数单位平方</span>
|
|
<a href="cpp-io-cout.html"><span class="kw1757">std::<span class="me2">cout</span></span></a> <span class="sy1"><<</span> <span class="st0">"pow(i, 2) = "</span> <span class="sy1"><<</span> z2 <span class="sy1"><<</span> <span class="st0">'<span class="es1">\n</span>'</span><span class="sy4">;</span>
|
|
|
|
<span class="kw4">double</span> PI <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="sy4">;</span>
|
|
std<span class="sy4">::</span><span class="me2">complex</span><span class="sy1"><</span><span class="kw4">double</span><span class="sy1">></span> z3 <span class="sy1">=</span> <a href="cpp-numeric-math-exp.html"><span class="kw1321">std::<span class="me2">exp</span></span></a><span class="br0">(</span>1i <span class="sy2">*</span> PI<span class="br0">)</span><span class="sy4">;</span> <span class="co1">// 欧拉方程</span>
|
|
<a href="cpp-io-cout.html"><span class="kw1757">std::<span class="me2">cout</span></span></a> <span class="sy1"><<</span> <span class="st0">"exp(i * pi) = "</span> <span class="sy1"><<</span> z3 <span class="sy1"><<</span> <span class="st0">'<span class="es1">\n</span>'</span><span class="sy4">;</span>
|
|
|
|
std<span class="sy4">::</span><span class="me2">complex</span><span class="sy1"><</span><span class="kw4">double</span><span class="sy1">></span> z4 <span class="sy1">=</span> <span class="nu0">1</span>. <span class="sy2">+</span> 2i, z5 <span class="sy1">=</span> <span class="nu0">1</span>. <span class="sy2">-</span> 2i<span class="sy4">;</span> <span class="co1">// 共轭</span>
|
|
<a href="cpp-io-cout.html"><span class="kw1757">std::<span class="me2">cout</span></span></a> <span class="sy1"><<</span> <span class="st0">"(1+2i)*(1-2i) = "</span> <span class="sy1"><<</span> z4 <span class="sy2">*</span> z5 <span class="sy1"><<</span> <span class="st0">'<span class="es1">\n</span>'</span><span class="sy4">;</span>
|
|
<span class="br0">}</span></pre></div>
|
|
</div>
|
|
<p>输出：</p>
|
|
<div dir="ltr" class="mw-geshi" style="text-align: left;">
|
|
<div class="text source-text">
|
|
<pre class="de1">i * i = (-1.0,0.0)
|
|
pow(i, 2) = (-1.0,0.0)
|
|
exp(i * pi) = (-1.0,0.0)
|
|
(1+2i)*(1-2i) = (5.0,0.0)</pre></div>
|
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</div>
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</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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<table class="t-dsc-begin"></table>
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</div>
|
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<div class="visualClear"></div>
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</div>
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</div>
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</div>
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</body>
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</html>
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