125 lines
10 KiB
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125 lines
10 KiB
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<title>std::log10(std::complex)</title>
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<h1 id="firstHeading" class="firstHeading"><span style="font-size:0.7em; line-height:130%">std::</span>log10<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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complex<span class="sy1"><</span>T<span class="sy1">></span> log10<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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<p>计算复数值 <code>z</code> 的复常用（底 <span class="t-c"><span class="mw-geshi cpp source-cpp"><span class="nu0">10</span></span></span> ）对数，分支切割沿负实轴。</p>
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<p>此函数的行为等价于 <code><a href="cpp-numeric-complex-log.html">std::log</a>(z)/<a href="cpp-numeric-math-log.html">std::log</a>(T(10))</code> 。</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><code>z</code> 的复常用对数</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 <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-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">0</span>, <span class="nu0">1</span><span class="br0">)</span><span class="sy4">;</span> <span class="co1">// // r = 0, θ = pi/2</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">"2*log10"</span> <span class="sy1"><<</span> z <span class="sy1"><<</span> <span class="st0">" = "</span> <span class="sy1"><<</span> <span class="nu0">2</span>.<span class="sy2">*</span><a href="cpp-numeric-math-log10.html"><span class="kw1325">std::<span class="me2">log10</span></span></a><span class="br0">(</span>z<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>sqrt<span class="br0">(</span><span class="nu0">2</span><span class="br0">)</span><span class="sy2">/</span><span class="nu0">2</span>, sqrt<span class="br0">(</span><span class="nu0">2</span><span class="br0">)</span><span class="sy2">/</span><span class="nu0">2</span><span class="br0">)</span><span class="sy4">;</span> <span class="co1">// r = 1, θ = pi/4</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">"4*log10"</span> <span class="sy1"><<</span> z2 <span class="sy1"><<</span> <span class="st0">" = "</span> <span class="sy1"><<</span> <span class="nu0">4</span>.<span class="sy2">*</span><a href="cpp-numeric-math-log10.html"><span class="kw1325">std::<span class="me2">log10</span></span></a><span class="br0">(</span>z2<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> z3<span class="br0">(</span><span class="sy2">-</span><span class="nu0">100</span>, <span class="nu0">0</span><span class="br0">)</span><span class="sy4">;</span> <span class="co1">// r = 100, θ = pi</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">"log10"</span> <span class="sy1"><<</span> z3 <span class="sy1"><<</span> <span class="st0">" = "</span> <span class="sy1"><<</span> <a href="cpp-numeric-math-log10.html"><span class="kw1325">std::<span class="me2">log10</span></span></a><span class="br0">(</span>z3<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> z4<span class="br0">(</span><span class="sy2">-</span><span class="nu0">100</span>, <span class="sy2">-</span><span class="nu16">0.0</span><span class="br0">)</span><span class="sy4">;</span> <span class="co1">// 切割的另一侧</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">"log10"</span> <span class="sy1"><<</span> z4 <span class="sy1"><<</span> <span class="st0">" (the other side of the cut) = "</span>
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<span class="sy1"><<</span> <a href="cpp-numeric-math-log10.html"><span class="kw1325">std::<span class="me2">log10</span></span></a><span class="br0">(</span>z4<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">"(note: pi/log(10) = "</span> <span class="sy1"><<</span> acos<span class="br0">(</span><span class="sy2">-</span><span class="nu0">1</span><span class="br0">)</span><span class="sy2">/</span>log<span class="br0">(</span><span class="nu0">10</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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<p>输出：</p>
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<div class="text source-text">
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<pre class="de1">2*log10(0,1) = (0,1.36438)
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4*log10(0.707107,0.707107) = (0,1.36438)
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log10(-100,0) = (2,1.36438)
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log10(-100,-0) (the other side of the cut) = (2,-1.36438)
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(note: pi/log(10) = 1.36438)</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-log.html"><span class="t-lines"><span>log<span class="t-dsc-small">(std::complex)</span></span></span></a></div>
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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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<div class="t-dsc-member-div">
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<div><a href="cpp-numeric-math-log10.html"><span class="t-lines"><span>log10</span><span>log10f</span><span>log10l</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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<td>计算常用（以 <i>10</i> 为底）对数（ <span class="mjax" style="display:none">\({\small \log_{10}{x} }\)</span><span class="mjax-fallback texhtml" style="white-space: nowrap;">log<sub>10</sub>(x)</span> ）<br />
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<span class="t-mark">(函数)</span></td>
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<div class="t-dsc-member-div">
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<div><a href="cpp-numeric-valarray-log10.html"><span class="t-lines"><span>log10<span class="t-dsc-small">(std::valarray)</span></span></span></a></div>
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<td>应用函数 <span class="t-lc"><a href="cpp-numeric-math-log10.html">std::log10</a></span> 到 valarray 的每个元素<br />
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<span class="t-mark">(函数模板)</span></td>
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