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<div class="headertitle"><div class="title">midpoint_integral_method.cpp File Reference</div></div>
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<p><a href="../../df/d11/midpoint__integral__method_8cpp_source.html">Go to the source code of this file.</a></p>
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<table class="memberdecls">
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Namespaces</h2></td></tr>
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<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">namespace  </td><td class="memItemRight" valign="bottom"><a class="el" href="../../d1/de0/namespacenumerical__methods.html">numerical_methods</a></td></tr>
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<tr class="memitem:numerical_5Fmethods" id="r_numerical_5Fmethods"><td class="memItemLeft" align="right" valign="top">namespace  </td><td class="memItemRight" valign="bottom"><a class="el" href="../../d1/de0/namespacenumerical__methods.html">numerical_methods</a></td></tr>
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<tr class="memdesc:d1/de0/namespacenumerical__methods"><td class="mdescLeft"> </td><td class="mdescRight">for assert <br /></td></tr>
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<tr class="separator:"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">namespace  </td><td class="memItemRight" valign="bottom"><a class="el" href="../../d9/daa/namespacemidpoint__rule.html">midpoint_rule</a></td></tr>
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<tr class="memitem:midpoint_5Frule" id="r_midpoint_5Frule"><td class="memItemLeft" align="right" valign="top">namespace  </td><td class="memItemRight" valign="bottom"><a class="el" href="../../d9/daa/namespacemidpoint__rule.html">midpoint_rule</a></td></tr>
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<tr class="memdesc:d9/daa/namespacemidpoint__rule"><td class="mdescLeft"> </td><td class="mdescRight">Functions for the <a href="https://en.wikipedia.org/wiki/Midpoint_method" target="_blank">Midpoint Integral</a> method implementation. <br /></td></tr>
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<tr class="separator:"><td class="memSeparator" colspan="2"> </td></tr>
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</table><table class="memberdecls">
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<tr class="heading"><td colspan="2"><h2 class="groupheader"><a id="func-members" name="func-members"></a>
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<tr class="heading"><td colspan="2"><h2 id="header-func-members" class="groupheader"><a id="func-members" name="func-members"></a>
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Functions</h2></td></tr>
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<tr class="memitem:a7072493d1f0f8a91b2a71d4cc456c09c" id="r_a7072493d1f0f8a91b2a71d4cc456c09c"><td class="memItemLeft" align="right" valign="top">double </td><td class="memItemRight" valign="bottom"><a class="el" href="#a7072493d1f0f8a91b2a71d4cc456c09c">numerical_methods::midpoint_rule::midpoint</a> (const std::int32_t N, const double <a class="el" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>, const double a, const std::function< double(double)> &func)</td></tr>
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<tr class="memdesc:a7072493d1f0f8a91b2a71d4cc456c09c"><td class="mdescLeft"> </td><td class="mdescRight">Main function for implementing the Midpoint Integral Method implementation. <br /></td></tr>
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<tr class="separator:a7072493d1f0f8a91b2a71d4cc456c09c"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a7ee8e824ef3e138a9a21883b26d97226" id="r_a7ee8e824ef3e138a9a21883b26d97226"><td class="memItemLeft" align="right" valign="top">double </td><td class="memItemRight" valign="bottom"><a class="el" href="#a7ee8e824ef3e138a9a21883b26d97226">numerical_methods::midpoint_rule::f</a> (double x)</td></tr>
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<tr class="memdesc:a7ee8e824ef3e138a9a21883b26d97226"><td class="mdescLeft"> </td><td class="mdescRight">A function f(x) that will be used to test the method. <br /></td></tr>
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<tr class="separator:a7ee8e824ef3e138a9a21883b26d97226"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:ae682ee71af44b1e9e884849cc6a6b040" id="r_ae682ee71af44b1e9e884849cc6a6b040"><td class="memItemLeft" align="right" valign="top">double </td><td class="memItemRight" valign="bottom"><a class="el" href="#ae682ee71af44b1e9e884849cc6a6b040">numerical_methods::midpoint_rule::g</a> (double x)</td></tr>
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<tr class="memdesc:ae682ee71af44b1e9e884849cc6a6b040"><td class="mdescLeft"> </td><td class="mdescRight">A function g(x) that will be used to test the method. <br /></td></tr>
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<tr class="separator:ae682ee71af44b1e9e884849cc6a6b040"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:ae9f66040f8e0ba73c1c741261c22a52a" id="r_ae9f66040f8e0ba73c1c741261c22a52a"><td class="memItemLeft" align="right" valign="top">double </td><td class="memItemRight" valign="bottom"><a class="el" href="#ae9f66040f8e0ba73c1c741261c22a52a">numerical_methods::midpoint_rule::k</a> (double x)</td></tr>
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<tr class="memdesc:ae9f66040f8e0ba73c1c741261c22a52a"><td class="mdescLeft"> </td><td class="mdescRight">A function k(x) that will be used to test the method. <br /></td></tr>
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<tr class="separator:ae9f66040f8e0ba73c1c741261c22a52a"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:ad53616fb4fa6880ae876bcba53365c51" id="r_ad53616fb4fa6880ae876bcba53365c51"><td class="memItemLeft" align="right" valign="top">double </td><td class="memItemRight" valign="bottom"><a class="el" href="#ad53616fb4fa6880ae876bcba53365c51">numerical_methods::midpoint_rule::l</a> (double x)</td></tr>
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<tr class="memdesc:ad53616fb4fa6880ae876bcba53365c51"><td class="mdescLeft"> </td><td class="mdescRight">A function l(x) that will be used to test the method. <br /></td></tr>
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<tr class="separator:ad53616fb4fa6880ae876bcba53365c51"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a2ae48a41e43dc6ab11b962742349646e" id="r_a2ae48a41e43dc6ab11b962742349646e"><td class="memItemLeft" align="right" valign="top">static void </td><td class="memItemRight" valign="bottom"><a class="el" href="#a2ae48a41e43dc6ab11b962742349646e">test</a> (std::int32_t N, double <a class="el" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>, double a, double b, bool used_argv_parameters)</td></tr>
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<tr class="memdesc:a2ae48a41e43dc6ab11b962742349646e"><td class="mdescLeft"> </td><td class="mdescRight">Self-test implementations. <br /></td></tr>
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<tr class="memdesc:a3c04138a5bfe5d72780bb7e82a18e627"><td class="mdescLeft"> </td><td class="mdescRight">Main function. <br /></td></tr>
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</table>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
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<a name="details" id="details"></a><h2 id="header-details" class="groupheader">Detailed Description</h2>
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<div class="textblock"><p>A numerical method for easy <a href="https://en.wikipedia.org/wiki/Midpoint_method" target="_blank">approximation of integrals</a> </p>
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<p>The idea is to split the interval into N of intervals and use as interpolation points the xi for which it applies that xi = x0 + i*h, where h is a step defined as h = (b-a)/N where a and b are the first and last points of the interval of the integration [a, b].</p>
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<p>We create a table of the xi and their corresponding f(xi) values and we evaluate the integral by the formula: I = h * {f(x0+h/2) + f(x1+h/2) + ... + f(xN-1+h/2)}</p>
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<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/ggkogkou" target="_blank">ggkogkou</a> </dd></dl>
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<p class="definition">Definition in file <a class="el" href="../../df/d11/midpoint__integral__method_8cpp_source.html">midpoint_integral_method.cpp</a>.</p>
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</div><h2 class="groupheader">Function Documentation</h2>
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</div><a name="doc-func-members" id="doc-func-members"></a><h2 id="header-doc-func-members" class="groupheader">Function Documentation</h2>
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<a id="a7ee8e824ef3e138a9a21883b26d97226" name="a7ee8e824ef3e138a9a21883b26d97226"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#a7ee8e824ef3e138a9a21883b26d97226">◆ </a></span>f()</h2>
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<td class="memname">static void test </td>
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<td class="memname">void test </td>
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<td>(</td>
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<td class="paramtype">std::int32_t</td> <td class="paramname"><span class="paramname"><em>N</em></span>, </td>
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