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<div id="projectname">TheAlgorithms/C++<span id="projectnumber"> 1.0.0</span>
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<div class="dyncontent">
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<div class="center"><iframe scrolling="no" frameborder="0" src="../../de/d1c/midpoint__integral__method_8cpp__incl.svg" width="592" height="126"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe></div>
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<table class="memberdecls">
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<tr class="heading"><td colspan="2"><h2 class="groupheader"><a id="namespaces" name="namespaces"></a>
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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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@@ -137,7 +156,7 @@ Namespaces</h2></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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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 <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>< double(double)> &func)</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="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> (<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>
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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="memitem:a3c04138a5bfe5d72780bb7e82a18e627" id="r_a3c04138a5bfe5d72780bb7e82a18e627"><td class="memItemLeft" align="right" valign="top">int </td><td class="memItemRight" valign="bottom"><a class="el" href="#a3c04138a5bfe5d72780bb7e82a18e627">main</a> (int argc, char **argv)</td></tr>
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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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<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>
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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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<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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<dl class="section return"><dt>Returns</dt><dd>the value of the dependent variable yi = f(xi) = sqrt(xi) + ln(xi) </dd></dl>
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<div class="fragment"><div class="line"><span class="lineno"> 90</span>{ <span class="keywordflow">return</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/sqrt.html">std::sqrt</a>(x) + <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/log.html">std::log</a>(x); }</div>
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<div class="ttc" id="alog_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/math/log.html">std::log</a></div><div class="ttdeci">T log(T... args)</div></div>
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<div class="ttc" id="asqrt_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/math/sqrt.html">std::sqrt</a></div><div class="ttdeci">T sqrt(T... args)</div></div>
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<div class="center"><iframe scrolling="no" frameborder="0" src="../../df/d11/midpoint__integral__method_8cpp_a7ee8e824ef3e138a9a21883b26d97226_cgraph.svg" width="271" height="86"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe></div>
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<p class="definition">Definition at line <a class="el" href="../../df/d11/midpoint__integral__method_8cpp_source.html#l00090">90</a> of file <a class="el" href="../../df/d11/midpoint__integral__method_8cpp_source.html">midpoint_integral_method.cpp</a>.</p>
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<div class="fragment"><div class="line"><span class="lineno"> 90</span>{ <span class="keywordflow">return</span> std::sqrt(x) + std::log(x); }</div>
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</dd>
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<dl class="section return"><dt>Returns</dt><dd>the value of the dependent variable yi = g(xi) = e^(-xi) * (4 - xi^2) </dd></dl>
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<div class="fragment"><div class="line"><span class="lineno"> 97</span>{ <span class="keywordflow">return</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/exp.html">std::exp</a>(-x) * (4 - <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">std::pow</a>(x, 2)); }</div>
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<div class="ttc" id="aexp_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/math/exp.html">std::exp</a></div><div class="ttdeci">T exp(T... args)</div></div>
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<div class="ttc" id="apow_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">std::pow</a></div><div class="ttdeci">T pow(T... args)</div></div>
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<div class="center"><iframe scrolling="no" frameborder="0" src="../../df/d11/midpoint__integral__method_8cpp_ae682ee71af44b1e9e884849cc6a6b040_cgraph.svg" width="272" height="86"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe></div>
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<p class="definition">Definition at line <a class="el" href="../../df/d11/midpoint__integral__method_8cpp_source.html#l00097">97</a> of file <a class="el" href="../../df/d11/midpoint__integral__method_8cpp_source.html">midpoint_integral_method.cpp</a>.</p>
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<div class="fragment"><div class="line"><span class="lineno"> 97</span>{ <span class="keywordflow">return</span> std::exp(-x) * (4 - std::pow(x, 2)); }</div>
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<dl class="section return"><dt>Returns</dt><dd>the value of the dependent variable yi = k(xi) = sqrt(2*xi^3 + 3) </dd></dl>
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<div class="fragment"><div class="line"><span class="lineno"> 103</span>{ <span class="keywordflow">return</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/sqrt.html">std::sqrt</a>(2 * <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">std::pow</a>(x, 3) + 3); }</div>
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<p class="definition">Definition at line <a class="el" href="../../df/d11/midpoint__integral__method_8cpp_source.html#l00103">103</a> of file <a class="el" href="../../df/d11/midpoint__integral__method_8cpp_source.html">midpoint_integral_method.cpp</a>.</p>
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<div class="fragment"><div class="line"><span class="lineno"> 103</span>{ <span class="keywordflow">return</span> std::sqrt(2 * std::pow(x, 3) + 3); }</div>
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</dd>
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<dl class="section return"><dt>Returns</dt><dd>the value of the dependent variable yi = l(xi) = xi + ln(2*xi + 1) </dd></dl>
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<div class="fragment"><div class="line"><span class="lineno"> 109</span>{ <span class="keywordflow">return</span> x + <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/log.html">std::log</a>(2 * x + 1); }</div>
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<p class="definition">Definition at line <a class="el" href="../../df/d11/midpoint__integral__method_8cpp_source.html#l00109">109</a> of file <a class="el" href="../../df/d11/midpoint__integral__method_8cpp_source.html">midpoint_integral_method.cpp</a>.</p>
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<div class="fragment"><div class="line"><span class="lineno"> 109</span>{ <span class="keywordflow">return</span> x + std::log(2 * x + 1); }</div>
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<p>Starting and ending point of the integration in</p>
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<p>the real axis</p>
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<p>Step, calculated by a, b and N</p>
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<p class="definition">Definition at line <a class="el" href="../../df/d11/midpoint__integral__method_8cpp_source.html#l00162">162</a> of file <a class="el" href="../../df/d11/midpoint__integral__method_8cpp_source.html">midpoint_integral_method.cpp</a>.</p>
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<div class="fragment"><div class="line"><span class="lineno"> 162</span> {</div>
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<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="../../d8/dab/sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a> =</div>
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<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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<div class="line"><span class="lineno"> 165</span><span class="comment"> /// MUST BE EVEN</span></div>
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<div class="line"><span class="lineno"> 166</span><span class="comment"></span> <span class="keywordtype">double</span> a = 1, b = 3; <span class="comment">/// Starting and ending point of the integration in</span><span class="comment"></span></div>
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<div class="line"><span class="lineno"> 167</span><span class="comment"> /// the real axis</span></div>
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<div class="line"><span class="lineno"> 168</span><span class="comment"></span> <span class="keywordtype">double</span> <a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a> = NAN; <span class="comment">/// Step, calculated by a, b and N</span></div>
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<div class="line"><span class="lineno"> 163</span> std::int32_t <a class="code hl_variable" href="../../d8/dab/sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a> =</div>
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<div class="line"><span class="lineno"> 164</span> 16; </div>
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<div class="line"><span class="lineno"> 166</span> <span class="keywordtype">double</span> a = 1, b = 3; </div>
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<div class="line"><span class="lineno"> 168</span> <span class="keywordtype">double</span> <a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a> = NAN; </div>
|
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<div class="line"><span class="lineno"> 169</span> </div>
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<div class="line"><span class="lineno"> 170</span> <span class="keywordtype">bool</span> used_argv_parameters =</div>
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<div class="line"><span class="lineno"> 171</span> <span class="keyword">false</span>; <span class="comment">// If argv parameters are used then the assert must be omitted</span></div>
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<div class="line"><span class="lineno"> 174</span> <span class="comment">// Get user input (by the command line parameters or the console after</span></div>
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<div class="line"><span class="lineno"> 175</span> <span class="comment">// displaying messages)</span></div>
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<div class="line"><span class="lineno"> 176</span> <span class="keywordflow">if</span> (argc == 4) {</div>
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<div class="line"><span class="lineno"> 177</span> <a class="code hl_variable" href="../../d8/dab/sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a> = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/byte/atoi.html">std::atoi</a>(argv[1]);</div>
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<div class="line"><span class="lineno"> 178</span> a = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/byte/atof.html">std::atof</a>(argv[2]);</div>
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<div class="line"><span class="lineno"> 179</span> b = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/byte/atof.html">std::atof</a>(argv[3]);</div>
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<div class="line"><span class="lineno"> 177</span> <a class="code hl_variable" href="../../d8/dab/sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a> = std::atoi(argv[1]);</div>
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<div class="line"><span class="lineno"> 178</span> a = std::atof(argv[2]);</div>
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<div class="line"><span class="lineno"> 179</span> b = std::atof(argv[3]);</div>
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<div class="line"><span class="lineno"> 180</span> <span class="comment">// Check if a<b else abort</span></div>
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<div class="line"><span class="lineno"> 181</span> assert(a < b && <span class="stringliteral">"a has to be less than b"</span>);</div>
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<div class="line"><span class="lineno"> 182</span> assert(N > 0 && <span class="stringliteral">"N has to be > 0"</span>);</div>
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<div class="line"><span class="lineno"> 183</span> <span class="keywordflow">if</span> (N < 4 || a != 1 || b != 3) {</div>
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<div class="line"><span class="lineno"> 184</span> used_argv_parameters = <span class="keyword">true</span>;</div>
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<div class="line"><span class="lineno"> 185</span> }</div>
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<div class="line"><span class="lineno"> 186</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"You selected N="</span> << <a class="code hl_variable" href="../../d8/dab/sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a> << <span class="stringliteral">", a="</span> << a << <span class="stringliteral">", b="</span> << b</div>
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<div class="line"><span class="lineno"> 187</span> << <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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<div class="line"><span class="lineno"> 186</span> std::cout << <span class="stringliteral">"You selected N="</span> << <a class="code hl_variable" href="../../d8/dab/sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a> << <span class="stringliteral">", a="</span> << a << <span class="stringliteral">", b="</span> << b</div>
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<div class="line"><span class="lineno"> 187</span> << std::endl;</div>
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<div class="line"><span class="lineno"> 188</span> } <span class="keywordflow">else</span> {</div>
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<div class="line"><span class="lineno"> 189</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"Default N="</span> << <a class="code hl_variable" href="../../d8/dab/sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a> << <span class="stringliteral">", a="</span> << a << <span class="stringliteral">", b="</span> << b</div>
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<div class="line"><span class="lineno"> 190</span> << <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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<div class="line"><span class="lineno"> 189</span> std::cout << <span class="stringliteral">"Default N="</span> << <a class="code hl_variable" href="../../d8/dab/sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a> << <span class="stringliteral">", a="</span> << a << <span class="stringliteral">", b="</span> << b</div>
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<div class="line"><span class="lineno"> 190</span> << std::endl;</div>
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<div class="line"><span class="lineno"> 191</span> }</div>
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<div class="line"><span class="lineno"> 192</span> </div>
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<div class="line"><span class="lineno"> 193</span> <span class="comment">// Find the step</span></div>
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<div class="line"><span class="lineno"> 197</span> </div>
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<div class="line"><span class="lineno"> 198</span> <span class="keywordflow">return</span> 0;</div>
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<div class="line"><span class="lineno"> 199</span>}</div>
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<div class="ttc" id="aatof_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/string/byte/atof.html">std::atof</a></div><div class="ttdeci">T atof(T... args)</div></div>
|
||||
<div class="ttc" id="aatoi_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/string/byte/atoi.html">std::atoi</a></div><div class="ttdeci">T atoi(T... args)</div></div>
|
||||
<div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
|
||||
<div class="ttc" id="aendl_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a></div><div class="ttdeci">T endl(T... args)</div></div>
|
||||
<div class="ttc" id="agenerate__parentheses_8cpp_html_aa8dca7b867074164d5f45b0f3851269d"><div class="ttname"><a href="../../dd/d1e/generate__parentheses_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a></div><div class="ttdeci">static void test()</div><div class="ttdoc">Self-test implementations.</div><div class="ttdef"><b>Definition</b> generate_parentheses.cpp:82</div></div>
|
||||
<div class="ttc" id="ahash__search_8cpp_html_a566eaf0ffafd50bc61e644561fd27001"><div class="ttname"><a href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a></div><div class="ttdeci">int h(int key)</div><div class="ttdef"><b>Definition</b> hash_search.cpp:45</div></div>
|
||||
<div class="ttc" id="ainteger_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/types/integer.html">std::int32_t</a></div></div>
|
||||
<div class="ttc" id="asparse__table_8cpp_html_a10f3ffb3f6f7e1b83d556b9c8de89a5d"><div class="ttname"><a href="../../d8/dab/sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">data_structures::sparse_table::N</a></div><div class="ttdeci">constexpr uint32_t N</div><div class="ttdoc">A struct to represent sparse table for min() as their invariant function, for the given array A....</div><div class="ttdef"><b>Definition</b> sparse_table.cpp:48</div></div>
|
||||
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||||
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<div class="center"><div class="zoom"><iframe scrolling="no" frameborder="0" src="../../df/d11/midpoint__integral__method_8cpp_a3c04138a5bfe5d72780bb7e82a18e627_cgraph.svg" width="100%" height="523"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe></div></div>
|
||||
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|
||||
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<div class="ttc" id="agenerate__parentheses_8cpp_html_aa8dca7b867074164d5f45b0f3851269d"><div class="ttname"><a href="../../dd/d1e/generate__parentheses_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a></div><div class="ttdeci">static void test()</div><div class="ttdoc">Self-test implementations.</div><div class="ttdef"><b>Definition</b> <a href="../../dd/d1e/generate__parentheses_8cpp_source.html#l00082">generate_parentheses.cpp:82</a></div></div>
|
||||
<div class="ttc" id="ahash__search_8cpp_html_a566eaf0ffafd50bc61e644561fd27001"><div class="ttname"><a href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a></div><div class="ttdeci">int h(int key)</div><div class="ttdef"><b>Definition</b> <a href="../../d1/df3/hash__search_8cpp_source.html#l00045">hash_search.cpp:45</a></div></div>
|
||||
<div class="ttc" id="asparse__table_8cpp_html_a10f3ffb3f6f7e1b83d556b9c8de89a5d"><div class="ttname"><a href="../../d8/dab/sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">data_structures::sparse_table::N</a></div><div class="ttdeci">constexpr uint32_t N</div><div class="ttdoc">A struct to represent sparse table for min() as their invariant function, for the given array A....</div><div class="ttdef"><b>Definition</b> <a href="../../d8/dab/sparse__table_8cpp_source.html#l00048">sparse_table.cpp:48</a></div></div>
|
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||||
@@ -394,7 +389,7 @@ Here is the call graph for this function:</div>
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||||
<tr>
|
||||
<td class="memname">double numerical_methods::midpoint_rule::midpoint </td>
|
||||
<td>(</td>
|
||||
<td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/types/integer.html">std::int32_t</a></td> <td class="paramname"><span class="paramname"><em>N</em></span>, </td>
|
||||
<td class="paramtype">const std::int32_t</td> <td class="paramname"><span class="paramname"><em>N</em></span>, </td>
|
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<td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/functional/function.html">std::function</a>< double(double)> &</td> <td class="paramname"><span class="paramname"><em>func</em></span> )</td>
|
||||
<td class="paramtype">const std::function< double(double)> &</td> <td class="paramname"><span class="paramname"><em>func</em></span> )</td>
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||||
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||||
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||||
<dl class="section return"><dt>Returns</dt><dd>the result of the integration </dd></dl>
|
||||
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||||
<p class="definition">Definition at line <a class="el" href="../../df/d11/midpoint__integral__method_8cpp_source.html#l00052">52</a> of file <a class="el" href="../../df/d11/midpoint__integral__method_8cpp_source.html">midpoint_integral_method.cpp</a>.</p>
|
||||
<div class="fragment"><div class="line"><span class="lineno"> 53</span> {</div>
|
||||
<div class="line"><span class="lineno"> 54</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/map.html">std::map<int, double></a></div>
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||||
<div class="line"><span class="lineno"> 54</span> std::map<int, double></div>
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||||
<div class="line"><span class="lineno"> 55</span> data_table; <span class="comment">// Contains the data points, key: i, value: f(xi)</span></div>
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||||
<div class="line"><span class="lineno"> 56</span> <span class="keywordtype">double</span> xi = a; <span class="comment">// Initialize xi to the starting point x0 = a</span></div>
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||||
<div class="line"><span class="lineno"> 57</span> </div>
|
||||
<div class="line"><span class="lineno"> 58</span> <span class="comment">// Create the data table</span></div>
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||||
<div class="line"><span class="lineno"> 59</span> <span class="comment">// Loop from x0 to xN-1</span></div>
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||||
<div class="line"><span class="lineno"> 60</span> <span class="keywordtype">double</span> temp = NAN;</div>
|
||||
<div class="line"><span class="lineno"> 61</span> <span class="keywordflow">for</span> (<a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/types/integer.html">std::int32_t</a> i = 0; i < <a class="code hl_variable" href="../../d8/dab/sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; i++) {</div>
|
||||
<div class="line"><span class="lineno"> 61</span> <span class="keywordflow">for</span> (std::int32_t i = 0; i < <a class="code hl_variable" href="../../d8/dab/sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; i++) {</div>
|
||||
<div class="line"><span class="lineno"> 62</span> temp = func(xi + <a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a> / 2); <span class="comment">// find f(xi+h/2)</span></div>
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||||
<div class="line"><span class="lineno"> 63</span> data_table.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/map/insert.html">insert</a>(</div>
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||||
<div class="line"><span class="lineno"> 64</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair.html">std::pair<std::int32_t, double></a>(i, temp)); <span class="comment">// add i and f(xi)</span></div>
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||||
<div class="line"><span class="lineno"> 63</span> data_table.insert(</div>
|
||||
<div class="line"><span class="lineno"> 64</span> std::pair<std::int32_t, double>(i, temp)); <span class="comment">// add i and f(xi)</span></div>
|
||||
<div class="line"><span class="lineno"> 65</span> xi += <a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>; <span class="comment">// Get the next point xi for the next iteration</span></div>
|
||||
<div class="line"><span class="lineno"> 66</span> }</div>
|
||||
<div class="line"><span class="lineno"> 67</span> </div>
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||||
<div class="line"><span class="lineno"> 68</span> <span class="comment">// Evaluate the integral.</span></div>
|
||||
<div class="line"><span class="lineno"> 69</span> <span class="comment">// Remember: {f(x0+h/2) + f(x1+h/2) + ... + f(xN-1+h/2)}</span></div>
|
||||
<div class="line"><span class="lineno"> 70</span> <span class="keywordtype">double</span> evaluate_integral = 0;</div>
|
||||
<div class="line"><span class="lineno"> 71</span> <span class="keywordflow">for</span> (<a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/types/integer.html">std::int32_t</a> i = 0; i < <a class="code hl_variable" href="../../d8/dab/sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; i++) evaluate_integral += data_table.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/map/at.html">at</a>(i);</div>
|
||||
<div class="line"><span class="lineno"> 71</span> <span class="keywordflow">for</span> (std::int32_t i = 0; i < <a class="code hl_variable" href="../../d8/dab/sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; i++) evaluate_integral += data_table.at(i);</div>
|
||||
<div class="line"><span class="lineno"> 72</span> </div>
|
||||
<div class="line"><span class="lineno"> 73</span> <span class="comment">// Multiply by the coefficient h</span></div>
|
||||
<div class="line"><span class="lineno"> 74</span> evaluate_integral *= <a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>;</div>
|
||||
<div class="line"><span class="lineno"> 75</span> </div>
|
||||
<div class="line"><span class="lineno"> 76</span> <span class="comment">// If the result calculated is nan, then the user has given wrong input</span></div>
|
||||
<div class="line"><span class="lineno"> 77</span> <span class="comment">// interval.</span></div>
|
||||
<div class="line"><span class="lineno"> 78</span> assert(!<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/isnan.html">std::isnan</a>(evaluate_integral) &&</div>
|
||||
<div class="line"><span class="lineno"> 78</span> assert(!std::isnan(evaluate_integral) &&</div>
|
||||
<div class="line"><span class="lineno"> 79</span> <span class="stringliteral">"The definite integral can't be evaluated. Check the validity of "</span></div>
|
||||
<div class="line"><span class="lineno"> 80</span> <span class="stringliteral">"your input.\n"</span>);</div>
|
||||
<div class="line"><span class="lineno"> 81</span> <span class="comment">// Else return</span></div>
|
||||
<div class="line"><span class="lineno"> 82</span> <span class="keywordflow">return</span> evaluate_integral;</div>
|
||||
<div class="line"><span class="lineno"> 83</span>}</div>
|
||||
<div class="ttc" id="aat_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/map/at.html">std::map::at</a></div><div class="ttdeci">T at(T... args)</div></div>
|
||||
<div class="ttc" id="ainsert_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/map/insert.html">std::map::insert</a></div><div class="ttdeci">T insert(T... args)</div></div>
|
||||
<div class="ttc" id="aisnan_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/math/isnan.html">std::isnan</a></div><div class="ttdeci">T isnan(T... args)</div></div>
|
||||
<div class="ttc" id="amap_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/map.html">std::map</a></div></div>
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||||
<div class="ttc" id="apair_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/utility/pair.html">std::pair</a></div></div>
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<td>(</td>
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<td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/types/integer.html">std::int32_t</a></td> <td class="paramname"><span class="paramname"><em>N</em></span>, </td>
|
||||
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<p class="definition">Definition at line <a class="el" href="../../df/d11/midpoint__integral__method_8cpp_source.html#l00123">123</a> of file <a class="el" href="../../df/d11/midpoint__integral__method_8cpp_source.html">midpoint_integral_method.cpp</a>.</p>
|
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<div class="fragment"><div class="line"><span class="lineno"> 124</span> {</div>
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<div class="line"><span class="lineno"> 125</span> <span class="comment">// Call midpoint() for each of the test functions f, g, k, l</span></div>
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<div class="line"><span class="lineno"> 126</span> <span class="comment">// Assert with two decimal point precision</span></div>
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@@ -529,37 +518,32 @@ Here is the call graph for this function:</div>
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<div class="line"><span class="lineno"> 128</span> N, <a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>, a, numerical_methods::midpoint_rule::f);</div>
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<div class="line"><span class="lineno"> 129</span> assert((used_argv_parameters || (result_f >= 4.09 && result_f <= 4.10)) &&</div>
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<div class="line"><span class="lineno"> 130</span> <span class="stringliteral">"The result of f(x) is wrong"</span>);</div>
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<div class="line"><span class="lineno"> 131</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"The result of integral f(x) on interval ["</span> << a << <span class="stringliteral">", "</span> << b</div>
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<div class="line"><span class="lineno"> 132</span> << <span class="stringliteral">"] is equal to: "</span> << result_f << <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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<div class="line"><span class="lineno"> 131</span> std::cout << <span class="stringliteral">"The result of integral f(x) on interval ["</span> << a << <span class="stringliteral">", "</span> << b</div>
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<div class="line"><span class="lineno"> 132</span> << <span class="stringliteral">"] is equal to: "</span> << result_f << std::endl;</div>
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<div class="line"><span class="lineno"> 133</span> </div>
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<div class="line"><span class="lineno"> 134</span> <span class="keywordtype">double</span> result_g = <a class="code hl_function" href="#a7072493d1f0f8a91b2a71d4cc456c09c">numerical_methods::midpoint_rule::midpoint</a>(</div>
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<div class="line"><span class="lineno"> 135</span> N, <a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>, a, numerical_methods::midpoint_rule::g);</div>
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<div class="line"><span class="lineno"> 136</span> assert((used_argv_parameters || (result_g >= 0.27 && result_g <= 0.28)) &&</div>
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<div class="line"><span class="lineno"> 137</span> <span class="stringliteral">"The result of g(x) is wrong"</span>);</div>
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<div class="line"><span class="lineno"> 138</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"The result of integral g(x) on interval ["</span> << a << <span class="stringliteral">", "</span> << b</div>
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<div class="line"><span class="lineno"> 139</span> << <span class="stringliteral">"] is equal to: "</span> << result_g << <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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<div class="line"><span class="lineno"> 138</span> std::cout << <span class="stringliteral">"The result of integral g(x) on interval ["</span> << a << <span class="stringliteral">", "</span> << b</div>
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<div class="line"><span class="lineno"> 139</span> << <span class="stringliteral">"] is equal to: "</span> << result_g << std::endl;</div>
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<div class="line"><span class="lineno"> 140</span> </div>
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<div class="line"><span class="lineno"> 141</span> <span class="keywordtype">double</span> result_k = <a class="code hl_function" href="#a7072493d1f0f8a91b2a71d4cc456c09c">numerical_methods::midpoint_rule::midpoint</a>(</div>
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<div class="line"><span class="lineno"> 142</span> N, <a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>, a, numerical_methods::midpoint_rule::k);</div>
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<div class="line"><span class="lineno"> 143</span> assert((used_argv_parameters || (result_k >= 9.06 && result_k <= 9.07)) &&</div>
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<div class="line"><span class="lineno"> 144</span> <span class="stringliteral">"The result of k(x) is wrong"</span>);</div>
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<div class="line"><span class="lineno"> 145</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"The result of integral k(x) on interval ["</span> << a << <span class="stringliteral">", "</span> << b</div>
|
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<div class="line"><span class="lineno"> 146</span> << <span class="stringliteral">"] is equal to: "</span> << result_k << <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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<div class="line"><span class="lineno"> 145</span> std::cout << <span class="stringliteral">"The result of integral k(x) on interval ["</span> << a << <span class="stringliteral">", "</span> << b</div>
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||||
<div class="line"><span class="lineno"> 146</span> << <span class="stringliteral">"] is equal to: "</span> << result_k << std::endl;</div>
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||||
<div class="line"><span class="lineno"> 147</span> </div>
|
||||
<div class="line"><span class="lineno"> 148</span> <span class="keywordtype">double</span> result_l = <a class="code hl_function" href="#a7072493d1f0f8a91b2a71d4cc456c09c">numerical_methods::midpoint_rule::midpoint</a>(</div>
|
||||
<div class="line"><span class="lineno"> 149</span> N, <a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>, a, numerical_methods::midpoint_rule::l);</div>
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<div class="line"><span class="lineno"> 150</span> assert((used_argv_parameters || (result_l >= 7.16 && result_l <= 7.17)) &&</div>
|
||||
<div class="line"><span class="lineno"> 151</span> <span class="stringliteral">"The result of l(x) is wrong"</span>);</div>
|
||||
<div class="line"><span class="lineno"> 152</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"The result of integral l(x) on interval ["</span> << a << <span class="stringliteral">", "</span> << b</div>
|
||||
<div class="line"><span class="lineno"> 153</span> << <span class="stringliteral">"] is equal to: "</span> << result_l << <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
|
||||
<div class="line"><span class="lineno"> 152</span> std::cout << <span class="stringliteral">"The result of integral l(x) on interval ["</span> << a << <span class="stringliteral">", "</span> << b</div>
|
||||
<div class="line"><span class="lineno"> 153</span> << <span class="stringliteral">"] is equal to: "</span> << result_l << std::endl;</div>
|
||||
<div class="line"><span class="lineno"> 154</span>}</div>
|
||||
<div class="ttc" id="amidpoint__integral__method_8cpp_html_a7072493d1f0f8a91b2a71d4cc456c09c"><div class="ttname"><a href="#a7072493d1f0f8a91b2a71d4cc456c09c">numerical_methods::midpoint_rule::midpoint</a></div><div class="ttdeci">double midpoint(const std::int32_t N, const double h, const double a, const std::function< double(double)> &func)</div><div class="ttdoc">Main function for implementing the Midpoint Integral Method implementation.</div><div class="ttdef"><b>Definition</b> midpoint_integral_method.cpp:52</div></div>
|
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</div><!-- fragment --><div class="dynheader">
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Here is the call graph for this function:</div>
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<div class="center"><iframe scrolling="no" frameborder="0" src="../../df/d11/midpoint__integral__method_8cpp_a2ae48a41e43dc6ab11b962742349646e_cgraph.svg" width="174" height="86"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe></div>
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</div>
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<div class="ttc" id="amidpoint__integral__method_8cpp_html_a7072493d1f0f8a91b2a71d4cc456c09c"><div class="ttname"><a href="#a7072493d1f0f8a91b2a71d4cc456c09c">numerical_methods::midpoint_rule::midpoint</a></div><div class="ttdeci">double midpoint(const std::int32_t N, const double h, const double a, const std::function< double(double)> &func)</div><div class="ttdoc">Main function for implementing the Midpoint Integral Method implementation.</div><div class="ttdef"><b>Definition</b> <a href="../../df/d11/midpoint__integral__method_8cpp_source.html#l00052">midpoint_integral_method.cpp:52</a></div></div>
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</div><!-- fragment -->
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</div>
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</div>
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</div><!-- contents -->
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