142 lines
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142 lines
12 KiB
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<title>std::proj(std::complex)</title>
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<h1 id="firstHeading" class="firstHeading"><span style="font-size:0.7em; line-height:130%">std::</span>proj<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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<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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<a href="cpp-numeric-complex.html"><span class="kw1472">std::<span class="me2">complex</span></span></a><span class="sy1"><</span>T<span class="sy1">></span> proj<span class="br0">(</span> <span class="kw4">const</span> <a href="cpp-numeric-complex.html"><span class="kw1472">std::<span class="me2">complex</span></span></a><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>(1)</td>
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<td><span class="t-mark-rev t-since-cxx11">(C++11 起)</span></td>
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<div><span class="mw-geshi cpp source-cpp"><a href="cpp-numeric-complex.html"><span class="kw1472">std::<span class="me2">complex</span></span></a><span class="sy1"><</span><span class="kw4">long</span> <span class="kw4">double</span><span class="sy1">></span> proj<span class="br0">(</span> <span class="kw4">long</span> <span class="kw4">double</span> z <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-cxx11">(C++11 起)</span></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> DoubleOrInteger <span class="sy1">></span><br />
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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> proj<span class="br0">(</span> DoubleOrInteger z <span class="br0">)</span><span class="sy4">;</span></span></div>
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<td>(3)</td>
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<td><span class="t-mark-rev t-since-cxx11">(C++11 起)</span></td>
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<div><span class="mw-geshi cpp source-cpp"><a href="cpp-numeric-complex.html"><span class="kw1472">std::<span class="me2">complex</span></span></a><span class="sy1"><</span><span class="kw4">float</span><span class="sy1">></span> proj<span class="br0">(</span> <span class="kw4">float</span> z <span class="br0">)</span><span class="sy4">;</span></span></div>
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<td>(4)</td>
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<td><span class="t-mark-rev t-since-cxx11">(C++11 起)</span></td>
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<p>返回复数 <code>z</code> 在黎曼球面上的投影。</p>
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<p>对于绝大多数 <code>z</code> ， <span class="t-c"><span class="mw-geshi cpp source-cpp">std<span class="sy4">::</span><span class="me2">proj</span><span class="br0">(</span>z<span class="br0">)</span><span class="sy1">==</span>z</span></span> ，但所有复无穷大，即使是一部为无穷大而另一部为 NaN 者，都变成实正无穷大 <span class="t-c"><span class="mw-geshi cpp source-cpp"><span class="br0">(</span><a href="cpp-numeric-math-INFINITY.html"><span class="kw1377">INFINITY</span></a>, <span class="nu16">0.0</span><span class="br0">)</span></span></span> 或 <span class="t-c"><span class="mw-geshi cpp source-cpp"><span class="br0">(</span><a href="cpp-numeric-math-INFINITY.html"><span class="kw1377">INFINITY</span></a>, <span class="sy2">-</span><span class="nu16">0.0</span><span class="br0">)</span></span></span> 。虚部（零）的符号是 <span class="t-c"><span class="mw-geshi cpp source-cpp">std<span class="sy4">::</span><span class="me2">imag</span><span class="br0">(</span>z<span class="br0">)</span></span></span> 的符号。</p>
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<p>为 <span class="t-c"><span class="mw-geshi cpp source-cpp"><span class="kw4">float</span></span></span> 、 <span class="t-c"><span class="mw-geshi cpp source-cpp"><span class="kw4">double</span></span></span> 、 <span class="t-c"><span class="mw-geshi cpp source-cpp"><span class="kw4">long</span> <span class="kw4">double</span></span></span> 和所有整数类型提供额外重载，将它们当做拥有正零虚部的复数。</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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<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><code>z</code> 在黎曼球面上的投影</p>
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<h3><span class="mw-headline" id=".E6.B3.A8.E6.84.8F">注意</span></h3>
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<p><span class="t-lc">proj</span> 函数以映射所有无穷大到一（给出或接收虚数零的符号），帮助模拟黎曼球面，而且应该在任何操作，特别是比较浅使用，比较可能对任何其他无穷大给出虚假结果。</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="cpp source-cpp">
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<pre class="de1"><span class="co2">#include <iostream></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-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> c1<span class="br0">(</span><span class="nu0">1</span>, <span class="nu0">2</span><span class="br0">)</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">"proj"</span> <span class="sy1"><<</span> c1 <span class="sy1"><<</span> <span class="st0">" = "</span> <span class="sy1"><<</span> std<span class="sy4">::</span><span class="me2">proj</span><span class="br0">(</span>c1<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> c2<span class="br0">(</span><a href="cpp-numeric-math-INFINITY.html"><span class="kw1377">INFINITY</span></a>, <span class="sy2">-</span><span class="nu0">1</span><span class="br0">)</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">"proj"</span> <span class="sy1"><<</span> c2 <span class="sy1"><<</span> <span class="st0">" = "</span> <span class="sy1"><<</span> std<span class="sy4">::</span><span class="me2">proj</span><span class="br0">(</span>c2<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> c3<span class="br0">(</span><span class="nu0">0</span>, <span class="sy2">-</span><a href="cpp-numeric-math-INFINITY.html"><span class="kw1377">INFINITY</span></a><span class="br0">)</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">"proj"</span> <span class="sy1"><<</span> c3 <span class="sy1"><<</span> <span class="st0">" = "</span> <span class="sy1"><<</span> std<span class="sy4">::</span><span class="me2">proj</span><span class="br0">(</span>c3<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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<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">proj(1,2) = (1,2)
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proj(inf,-1) = (inf,-0)
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proj(0,-inf) = (inf,-0)</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-abs.html"><span class="t-lines"><span>abs<span class="t-dsc-small">(std::complex)</span></span></span></a></div>
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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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<div><a href="cpp-numeric-complex-norm.html"><span class="t-lines"><span>norm</span></span></a></div>
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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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<div><a href="cpp-numeric-complex-polar.html"><span class="t-lines"><span>polar</span></span></a></div>
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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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