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@@ -132,32 +132,32 @@ Namespaces</h2></td></tr>
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a id="func-members" name="func-members"></a>
Functions</h2></td></tr>
<tr class="memitem:a7072493d1f0f8a91b2a71d4cc456c09c"><td class="memItemLeft" align="right" valign="top">double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../df/d11/midpoint__integral__method_8cpp.html#a7072493d1f0f8a91b2a71d4cc456c09c">numerical_methods::midpoint_rule::midpoint</a> (const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/types/integer.html">std::int32_t</a> N, const double <a class="el" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>, const double a, const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/functional/function.html">std::function</a>&lt; double(double)&gt; &amp;func)</td></tr>
<tr class="memdesc:a7072493d1f0f8a91b2a71d4cc456c09c"><td class="mdescLeft">&#160;</td><td class="mdescRight">Main function for implementing the Midpoint Integral Method implementation. <a href="../../df/d11/midpoint__integral__method_8cpp.html#a7072493d1f0f8a91b2a71d4cc456c09c">More...</a><br /></td></tr>
<tr class="memdesc:a7072493d1f0f8a91b2a71d4cc456c09c"><td class="mdescLeft">&#160;</td><td class="mdescRight">Main function for implementing the Midpoint Integral Method implementation. <br /></td></tr>
<tr class="separator:a7072493d1f0f8a91b2a71d4cc456c09c"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a7ee8e824ef3e138a9a21883b26d97226"><td class="memItemLeft" align="right" valign="top">double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../df/d11/midpoint__integral__method_8cpp.html#a7ee8e824ef3e138a9a21883b26d97226">numerical_methods::midpoint_rule::f</a> (double x)</td></tr>
<tr class="memdesc:a7ee8e824ef3e138a9a21883b26d97226"><td class="mdescLeft">&#160;</td><td class="mdescRight">A function f(x) that will be used to test the method. <a href="../../df/d11/midpoint__integral__method_8cpp.html#a7ee8e824ef3e138a9a21883b26d97226">More...</a><br /></td></tr>
<tr class="memdesc:a7ee8e824ef3e138a9a21883b26d97226"><td class="mdescLeft">&#160;</td><td class="mdescRight">A function f(x) that will be used to test the method. <br /></td></tr>
<tr class="separator:a7ee8e824ef3e138a9a21883b26d97226"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ae682ee71af44b1e9e884849cc6a6b040"><td class="memItemLeft" align="right" valign="top">double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../df/d11/midpoint__integral__method_8cpp.html#ae682ee71af44b1e9e884849cc6a6b040">numerical_methods::midpoint_rule::g</a> (double x)</td></tr>
<tr class="memdesc:ae682ee71af44b1e9e884849cc6a6b040"><td class="mdescLeft">&#160;</td><td class="mdescRight">A function g(x) that will be used to test the method. <a href="../../df/d11/midpoint__integral__method_8cpp.html#ae682ee71af44b1e9e884849cc6a6b040">More...</a><br /></td></tr>
<tr class="memdesc:ae682ee71af44b1e9e884849cc6a6b040"><td class="mdescLeft">&#160;</td><td class="mdescRight">A function g(x) that will be used to test the method. <br /></td></tr>
<tr class="separator:ae682ee71af44b1e9e884849cc6a6b040"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ae9f66040f8e0ba73c1c741261c22a52a"><td class="memItemLeft" align="right" valign="top">double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../df/d11/midpoint__integral__method_8cpp.html#ae9f66040f8e0ba73c1c741261c22a52a">numerical_methods::midpoint_rule::k</a> (double x)</td></tr>
<tr class="memdesc:ae9f66040f8e0ba73c1c741261c22a52a"><td class="mdescLeft">&#160;</td><td class="mdescRight">A function k(x) that will be used to test the method. <a href="../../df/d11/midpoint__integral__method_8cpp.html#ae9f66040f8e0ba73c1c741261c22a52a">More...</a><br /></td></tr>
<tr class="memdesc:ae9f66040f8e0ba73c1c741261c22a52a"><td class="mdescLeft">&#160;</td><td class="mdescRight">A function k(x) that will be used to test the method. <br /></td></tr>
<tr class="separator:ae9f66040f8e0ba73c1c741261c22a52a"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ad53616fb4fa6880ae876bcba53365c51"><td class="memItemLeft" align="right" valign="top">double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../df/d11/midpoint__integral__method_8cpp.html#ad53616fb4fa6880ae876bcba53365c51">numerical_methods::midpoint_rule::l</a> (double x)</td></tr>
<tr class="memdesc:ad53616fb4fa6880ae876bcba53365c51"><td class="mdescLeft">&#160;</td><td class="mdescRight">A function l(x) that will be used to test the method. <a href="../../df/d11/midpoint__integral__method_8cpp.html#ad53616fb4fa6880ae876bcba53365c51">More...</a><br /></td></tr>
<tr class="memdesc:ad53616fb4fa6880ae876bcba53365c51"><td class="mdescLeft">&#160;</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="memitem:a2ae48a41e43dc6ab11b962742349646e"><td class="memItemLeft" align="right" valign="top">static void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../df/d11/midpoint__integral__method_8cpp.html#a2ae48a41e43dc6ab11b962742349646e">test</a> (<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/types/integer.html">std::int32_t</a> 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>
<tr class="memdesc:a2ae48a41e43dc6ab11b962742349646e"><td class="mdescLeft">&#160;</td><td class="mdescRight">Self-test implementations. <a href="../../df/d11/midpoint__integral__method_8cpp.html#a2ae48a41e43dc6ab11b962742349646e">More...</a><br /></td></tr>
<tr class="memdesc:a2ae48a41e43dc6ab11b962742349646e"><td class="mdescLeft">&#160;</td><td class="mdescRight">Self-test implementations. <br /></td></tr>
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<tr class="memitem:a3c04138a5bfe5d72780bb7e82a18e627"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../df/d11/midpoint__integral__method_8cpp.html#a3c04138a5bfe5d72780bb7e82a18e627">main</a> (int argc, char **argv)</td></tr>
<tr class="memdesc:a3c04138a5bfe5d72780bb7e82a18e627"><td class="mdescLeft">&#160;</td><td class="mdescRight">Main function. <a href="../../df/d11/midpoint__integral__method_8cpp.html#a3c04138a5bfe5d72780bb7e82a18e627">More...</a><br /></td></tr>
<tr class="memdesc:a3c04138a5bfe5d72780bb7e82a18e627"><td class="mdescLeft">&#160;</td><td class="mdescRight">Main function. <br /></td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<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>
<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>
<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>
<p >Arguments can be passed as parameters from the command line argv[1] = N, argv[2] = a, argv[3] = b. In this case if the default values N=16, a=1, b=3 are changed then the tests/assert are disabled.</p>
<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>
<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>
<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>
<p>Arguments can be passed as parameters from the command line argv[1] = N, argv[2] = a, argv[3] = b. In this case if the default values N=16, a=1, b=3 are changed then the tests/assert are disabled.</p>
<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/ggkogkou" target="_blank">ggkogkou</a> </dd></dl>
</div><h2 class="groupheader">Function Documentation</h2>
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</dd>
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<dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
<p >Number of intervals to divide the integration interval.</p>
<p >MUST BE EVEN</p>
<p >Starting and ending point of the integration in</p>
<p >the real axis</p>
<p >Step, calculated by a, b and N</p>
<p>Number of intervals to divide the integration interval.</p>
<p>MUST BE EVEN</p>
<p>Starting and ending point of the integration in</p>
<p>the real axis</p>
<p>Step, calculated by a, b and N</p>
<div class="fragment"><div class="line"><span class="lineno"> 162</span> {</div>
<div class="line"><span class="lineno"> 163</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/types/integer.html">std::int32_t</a> <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a> =</div>
<div class="line"><span class="lineno"> 164</span> 16; <span class="comment">/// Number of intervals to divide the integration interval.</span><span class="comment"></span></div>
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