152 lines
11 KiB
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152 lines
11 KiB
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<title>std::atan(std::complex)</title>
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<h1 id="firstHeading" class="firstHeading"><span style="font-size:0.7em; line-height:130%">std::</span>atan<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> atan<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><span class="t-mark-rev t-since-cxx11">(C++11 起)</span></td>
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<p>计算复数值 <code>z</code> 的复弧（反）正切。分支切割存在于虚轴上的 <span class="texhtml" style="white-space: nowrap;">[−i ; +i]</span> 区间之外。</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>若不发生错误，则返回 <code>z</code> 的复弧（反）正切，在沿虚轴无界，沿实轴在区间 <span class="texhtml" style="white-space: nowrap;">[−π/2; +π/2]</span> 内的条状范围中。</p>
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<p>按照如同以 <code>-i * <a href="cpp-numeric-complex-atanh.html">std::atanh</a>(i*z)</code> 实现运算一般处理错误和特殊情况，其中 <code>i</code> 为虚数单位。</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>反正切（或弧正切）是多值函数而要求复平面上的分支切割。约定分支切割置于虚轴的线段 <span class="texhtml" style="white-space: nowrap;">(-∞i,-i)</span> 和 <span class="texhtml" style="white-space: nowrap;">(+i,+∞i)</span> 上。</p>
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反正切主值的数学定义是 <span class="texhtml" style="white-space: nowrap;">atan z = -<span class="t-mfrac"></span></span>
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<td>1</td>
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<td>2</td>
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i [ln(1 - iz) - ln (1 + iz)] 。
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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="co2">#include <cmath></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> z1<span class="br0">(</span><span class="nu0">0</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">"atan"</span> <span class="sy1"><<</span> z1 <span class="sy1"><<</span> <span class="st0">" = "</span> <span class="sy1"><<</span> <a href="cpp-numeric-math-atan.html"><span class="kw1338">std::<span class="me2">atan</span></span></a><span class="br0">(</span>z1<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="sy2">-</span><span class="nu16">0.0</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">"atan"</span> <span class="sy1"><<</span> z2 <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-atan.html"><span class="kw1338">std::<span class="me2">atan</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="nu0">0</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">"2*atan"</span> <span class="sy1"><<</span> z3 <span class="sy1"><<</span> <span class="st0">" = "</span> <span class="sy1"><<</span> <span class="nu16">2.0</span><span class="sy2">*</span><a href="cpp-numeric-math-atan.html"><span class="kw1338">std::<span class="me2">atan</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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<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">atan(0.000000,2.000000) = (1.570796,0.549306)
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atan(-0.000000,2.000000) (the other side of the cut) = (-1.570796,0.549306)
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2*atan(0.000000,inf) = (3.141593,0.000000)</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-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>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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<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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<div class="t-dsc-member-div">
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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>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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<div class="t-dsc-member-div">
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<div><a href="cpp-numeric-math-atan.html"><span class="t-lines"><span>atan</span><span>atanf</span><span>atanl</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>计算反正切（ <span class="mjax" style="display:none">\({\small\arctan{x} }\)</span><span class="mjax-fallback texhtml" style="white-space: nowrap;">arctan(x)</span> ）<br />
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<span class="t-mark">(函数)</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-valarray-atan.html"><span class="t-lines"><span>atan<span class="t-dsc-small">(std::valarray)</span></span></span></a></div>
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</div>
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<td>应用函数 <span class="t-lc"><a href="cpp-numeric-math-atan.html">std::atan</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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</table>
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<div class="visualClear"></div>
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