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<tr class="memitem:a6ccc5eddc537dc0293d0ae3d0480f068"><td class="memItemLeft" align="right" valign="top">double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d4/d18/composite__simpson__rule_8cpp.html#a6ccc5eddc537dc0293d0ae3d0480f068">numerical_methods::simpson_method::evaluate_by_simpson</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, 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>
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<tr class="memitem:a4251b4df4748a0b9c43a48f61bdd2397"><td class="memItemLeft" align="right" valign="top">double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d4/d18/composite__simpson__rule_8cpp.html#a4251b4df4748a0b9c43a48f61bdd2397">numerical_methods::simpson_method::f</a> (double x)</td></tr>
<tr class="memdesc:a4251b4df4748a0b9c43a48f61bdd2397"><td class="mdescLeft">&#160;</td><td class="mdescRight">A function f(x) that will be used to test the method. <a href="../../d4/d18/composite__simpson__rule_8cpp.html#a4251b4df4748a0b9c43a48f61bdd2397">More...</a><br /></td></tr>
<tr class="memdesc:a4251b4df4748a0b9c43a48f61bdd2397"><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:a4251b4df4748a0b9c43a48f61bdd2397"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a2f67508d5f392b0321772169342c98ad"><td class="memItemLeft" align="right" valign="top">double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d4/d18/composite__simpson__rule_8cpp.html#a2f67508d5f392b0321772169342c98ad">numerical_methods::simpson_method::g</a> (double x)</td></tr>
<tr class="memdesc:a2f67508d5f392b0321772169342c98ad"><td class="mdescLeft">&#160;</td><td class="mdescRight">Another test function. <a href="../../d4/d18/composite__simpson__rule_8cpp.html#a2f67508d5f392b0321772169342c98ad">More...</a><br /></td></tr>
<tr class="memdesc:a2f67508d5f392b0321772169342c98ad"><td class="mdescLeft">&#160;</td><td class="mdescRight">Another test function. <br /></td></tr>
<tr class="separator:a2f67508d5f392b0321772169342c98ad"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a1b74d828b33760094906797042b89442"><td class="memItemLeft" align="right" valign="top">double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">numerical_methods::simpson_method::k</a> (double x)</td></tr>
<tr class="memdesc:a1b74d828b33760094906797042b89442"><td class="mdescLeft">&#160;</td><td class="mdescRight">Another test function. <a href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">More...</a><br /></td></tr>
<tr class="memdesc:a1b74d828b33760094906797042b89442"><td class="mdescLeft">&#160;</td><td class="mdescRight">Another test function. <br /></td></tr>
<tr class="separator:a1b74d828b33760094906797042b89442"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a6d8df83a6f26ce24a75d3b358b7f5b8a"><td class="memItemLeft" align="right" valign="top">double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d4/d18/composite__simpson__rule_8cpp.html#a6d8df83a6f26ce24a75d3b358b7f5b8a">numerical_methods::simpson_method::l</a> (double x)</td></tr>
<tr class="memdesc:a6d8df83a6f26ce24a75d3b358b7f5b8a"><td class="mdescLeft">&#160;</td><td class="mdescRight">Another test function. <a href="../../d4/d18/composite__simpson__rule_8cpp.html#a6d8df83a6f26ce24a75d3b358b7f5b8a">More...</a><br /></td></tr>
<tr class="memdesc:a6d8df83a6f26ce24a75d3b358b7f5b8a"><td class="mdescLeft">&#160;</td><td class="mdescRight">Another test function. <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="../../d4/d18/composite__simpson__rule_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="../../d4/d18/composite__simpson__rule_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="../../d4/d18/composite__simpson__rule_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="../../d4/d18/composite__simpson__rule_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 >Implementation of the Composite Simpson Rule for the approximation. </p>
<p >The following is an implementation of the Composite Simpson Rule for the approximation of definite integrals. More info -&gt; wiki: <a href="https://en.wikipedia.org/wiki/Simpson%27s_rule#Composite_Simpson's_rule">https://en.wikipedia.org/wiki/Simpson%27s_rule#Composite_Simpson's_rule</a></p>
<p >The idea is to split the interval in an EVEN number 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/3 * {f(x0) + 4*f(x1) + 2*f(x2) + ... + 2*f(xN-2) + 4*f(xN-1) + f(xN)}</p>
<p >That means that the first and last indexed i f(xi) are multiplied by 1, the odd indexed f(xi) by 4 and the even by 2.</p>
<p >In this program there are 4 sample test functions f, g, k, l that are evaluated in the same interval.</p>
<p >Arguments can be passed as parameters from the command line argv[1] = N, argv[2] = a, argv[3] = b</p>
<p >N must be even number and a&lt;b.</p>
<p >In the end of the <a class="el" href="../../d3/d40/graph__coloring_8cpp.html#gae66f6b31b5ad750f1fe042a706a4e3d4" title="Main function.">main()</a> i compare the program's result with the one from mathematical software with 2 decimal points margin.</p>
<p >Add sample function by replacing one of the f, g, k, l and the assert</p>
<div class="textblock"><p>Implementation of the Composite Simpson Rule for the approximation. </p>
<p>The following is an implementation of the Composite Simpson Rule for the approximation of definite integrals. More info -&gt; wiki: <a href="https://en.wikipedia.org/wiki/Simpson%27s_rule#Composite_Simpson's_rule">https://en.wikipedia.org/wiki/Simpson%27s_rule#Composite_Simpson's_rule</a></p>
<p>The idea is to split the interval in an EVEN number 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/3 * {f(x0) + 4*f(x1) + 2*f(x2) + ... + 2*f(xN-2) + 4*f(xN-1) + f(xN)}</p>
<p>That means that the first and last indexed i f(xi) are multiplied by 1, the odd indexed f(xi) by 4 and the even by 2.</p>
<p>In this program there are 4 sample test functions f, g, k, l that are evaluated in the same interval.</p>
<p>Arguments can be passed as parameters from the command line argv[1] = N, argv[2] = a, argv[3] = b</p>
<p>N must be even number and a&lt;b.</p>
<p>In the end of the <a class="el" href="../../d3/d40/graph__coloring_8cpp.html#gae66f6b31b5ad750f1fe042a706a4e3d4" title="Main function.">main()</a> i compare the program's result with the one from mathematical software with 2 decimal points margin.</p>
<p>Add sample function by replacing one of the f, g, k, l and the assert</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>
<a id="a6ccc5eddc537dc0293d0ae3d0480f068" name="a6ccc5eddc537dc0293d0ae3d0480f068"></a>
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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. MUST BE EVEN</p>
<p >Starting and ending point of the integration in the real axis</p>
<p >Step, calculated by a, b and N</p>
<p>Number of intervals to divide the integration interval. MUST BE EVEN</p>
<p>Starting and ending point of the integration in the real axis</p>
<p>Step, calculated by a, b and N</p>
<div class="fragment"><div class="line"><span class="lineno"> 170</span> {</div>
<div class="line"><span class="lineno"> 171</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> = 16; <span class="comment">/// Number of intervals to divide the integration</span><span class="comment"></span></div>
<div class="line"><span class="lineno"> 172</span><span class="comment"> /// interval. MUST BE EVEN</span></div>
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