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<div id="projectname">TheAlgorithms/C++<span id="projectnumber"> 1.0.0</span>
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<div id="projectbrief">Set of algorithms implemented in C++.</div>
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<div id="projectbrief">All the algorithms implemented in C++</div>
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@@ -122,22 +139,24 @@ Include dependency graph for ode_forward_euler.cpp:</div>
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<div class="dyncontent">
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<div class="center"><iframe scrolling="no" frameborder="0" src="../../dc/dc5/ode__forward__euler_8cpp__incl.svg" width="423" 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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<p><a href="../../db/dd3/ode__forward__euler_8cpp_source.html">Go to the source code of this file.</a></p>
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<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:abaeae8f62a018d197f0187a1c80a90fe" id="r_abaeae8f62a018d197f0187a1c80a90fe"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="#abaeae8f62a018d197f0187a1c80a90fe">problem</a> (const double &x, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>< double > *y, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>< double > *dy)</td></tr>
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||||
<tr class="memitem:abaeae8f62a018d197f0187a1c80a90fe" id="r_abaeae8f62a018d197f0187a1c80a90fe"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="#abaeae8f62a018d197f0187a1c80a90fe">problem</a> (const double &x, std::valarray< double > *y, std::valarray< double > *dy)</td></tr>
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<tr class="memdesc:abaeae8f62a018d197f0187a1c80a90fe"><td class="mdescLeft"> </td><td class="mdescRight">Problem statement for a system with first-order differential equations. Updates the system differential variables. <br /></td></tr>
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<tr class="separator:abaeae8f62a018d197f0187a1c80a90fe"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:af3adf7b092a87868917ee5fb4255192b" id="r_af3adf7b092a87868917ee5fb4255192b"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="#af3adf7b092a87868917ee5fb4255192b">exact_solution</a> (const double &x, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>< double > *y)</td></tr>
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<tr class="memitem:af3adf7b092a87868917ee5fb4255192b" id="r_af3adf7b092a87868917ee5fb4255192b"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="#af3adf7b092a87868917ee5fb4255192b">exact_solution</a> (const double &x, std::valarray< double > *y)</td></tr>
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<tr class="memdesc:af3adf7b092a87868917ee5fb4255192b"><td class="mdescLeft"> </td><td class="mdescRight">Exact solution of the problem. Used for solution comparison. <br /></td></tr>
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<tr class="separator:af3adf7b092a87868917ee5fb4255192b"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:ga195d23bbdfcb80e83c9cda45c9ad5723" id="r_ga195d23bbdfcb80e83c9cda45c9ad5723"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="../../d6/d60/group__ode.html#ga195d23bbdfcb80e83c9cda45c9ad5723">forward_euler_step</a> (const double dx, const double x, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>< double > *y, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>< double > *dy)</td></tr>
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||||
<tr class="memitem:ga195d23bbdfcb80e83c9cda45c9ad5723" id="r_ga195d23bbdfcb80e83c9cda45c9ad5723"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="../../d6/d60/group__ode.html#ga195d23bbdfcb80e83c9cda45c9ad5723">forward_euler_step</a> (const double dx, const double x, std::valarray< double > *y, std::valarray< double > *dy)</td></tr>
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<tr class="memdesc:ga195d23bbdfcb80e83c9cda45c9ad5723"><td class="mdescLeft"> </td><td class="mdescRight">Compute next step approximation using the forward-Euler method. <br /></td></tr>
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<tr class="separator:ga195d23bbdfcb80e83c9cda45c9ad5723"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:gae0509f8843e2bc42de2abbd00a14b7b9" id="r_gae0509f8843e2bc42de2abbd00a14b7b9"><td class="memItemLeft" align="right" valign="top">double </td><td class="memItemRight" valign="bottom"><a class="el" href="../../d6/d60/group__ode.html#gae0509f8843e2bc42de2abbd00a14b7b9">forward_euler</a> (double dx, double x0, double x_max, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>< double > *y, bool save_to_file=false)</td></tr>
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<tr class="memitem:gae0509f8843e2bc42de2abbd00a14b7b9" id="r_gae0509f8843e2bc42de2abbd00a14b7b9"><td class="memItemLeft" align="right" valign="top">double </td><td class="memItemRight" valign="bottom"><a class="el" href="../../d6/d60/group__ode.html#gae0509f8843e2bc42de2abbd00a14b7b9">forward_euler</a> (double dx, double x0, double x_max, std::valarray< double > *y, bool save_to_file=false)</td></tr>
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<tr class="memdesc:gae0509f8843e2bc42de2abbd00a14b7b9"><td class="mdescLeft"> </td><td class="mdescRight">Compute approximation using the forward-Euler method in the given limits. <br /></td></tr>
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<tr class="separator:gae0509f8843e2bc42de2abbd00a14b7b9"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:aa13517b8e5de1b75592052db7f7e237f" id="r_aa13517b8e5de1b75592052db7f7e237f"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="#aa13517b8e5de1b75592052db7f7e237f">save_exact_solution</a> (const double &X0, const double &X_MAX, const double &step_size, const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>< double > &Y0)</td></tr>
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<tr class="memitem:aa13517b8e5de1b75592052db7f7e237f" id="r_aa13517b8e5de1b75592052db7f7e237f"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="#aa13517b8e5de1b75592052db7f7e237f">save_exact_solution</a> (const double &X0, const double &X_MAX, const double &step_size, const std::valarray< double > &Y0)</td></tr>
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<tr class="separator:aa13517b8e5de1b75592052db7f7e237f"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a0ddf1224851353fc92bfbff6f499fa97" id="r_a0ddf1224851353fc92bfbff6f499fa97"><td class="memItemLeft" align="right" valign="top">int </td><td class="memItemRight" valign="bottom"><a class="el" href="#a0ddf1224851353fc92bfbff6f499fa97">main</a> (int argc, char *argv[])</td></tr>
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@@ -164,6 +183,8 @@ Functions</h2></td></tr>
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<div class="line">dy[0] = y[1];</div>
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<div class="line">dy[1] = mu * (1.f - y[0] * y[0]) * y[1] - y[0];</div>
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</div><!-- fragment --> <dl class="section see"><dt>See also</dt><dd><a class="el" href="../../d6/dd3/ode__midpoint__euler_8cpp.html" title="Solve a multivariable first order ordinary differential equation (ODEs) using midpoint Euler method">ode_midpoint_euler.cpp</a>, <a class="el" href="../../d3/d06/ode__semi__implicit__euler_8cpp.html" title="Solve a multivariable first order ordinary differential equation (ODEs) using semi implicit Euler met...">ode_semi_implicit_euler.cpp</a> </dd></dl>
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<p class="definition">Definition in file <a class="el" href="../../db/dd3/ode__forward__euler_8cpp_source.html">ode_forward_euler.cpp</a>.</p>
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||||
</div><h2 class="groupheader">Function Documentation</h2>
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<a id="af3adf7b092a87868917ee5fb4255192b" name="af3adf7b092a87868917ee5fb4255192b"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#af3adf7b092a87868917ee5fb4255192b">◆ </a></span>exact_solution()</h2>
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@@ -179,7 +200,7 @@ Functions</h2></td></tr>
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<td class="paramkey"></td>
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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/numeric/valarray.html">std::valarray</a>< double > *</td> <td class="paramname"><span class="paramname"><em>y</em></span> )</td>
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<td class="paramtype">std::valarray< double > *</td> <td class="paramname"><span class="paramname"><em>y</em></span> )</td>
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<div class="fragment"><div class="line"><span class="lineno"> 67</span> {</div>
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<div class="line"><span class="lineno"> 68</span> y[0][0] = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/cos.html">std::cos</a>(x);</div>
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<div class="line"><span class="lineno"> 69</span> y[0][1] = -<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/sin.html">std::sin</a>(x);</div>
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<div class="line"><span class="lineno"> 70</span>}</div>
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<div class="ttc" id="acos_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/math/cos.html">std::cos</a></div><div class="ttdeci">T cos(T... args)</div></div>
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<div class="ttc" id="asin_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/math/sin.html">std::sin</a></div><div class="ttdeci">T sin(T... args)</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="dyncontent">
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||||
<div class="center"><iframe scrolling="no" frameborder="0" src="../../db/dd3/ode__forward__euler_8cpp_af3adf7b092a87868917ee5fb4255192b_cgraph.svg" width="232" 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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<p class="definition">Definition at line <a class="el" href="../../db/dd3/ode__forward__euler_8cpp_source.html#l00067">67</a> of file <a class="el" href="../../db/dd3/ode__forward__euler_8cpp_source.html">ode_forward_euler.cpp</a>.</p>
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<div class="fragment"><div class="line"><span class="lineno"> 67</span> {</div>
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<div class="line"><span class="lineno"> 68</span> y[0][0] = std::cos(x);</div>
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<div class="line"><span class="lineno"> 69</span> y[0][1] = -std::sin(x);</div>
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<div class="line"><span class="lineno"> 70</span>}</div>
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</div><!-- fragment -->
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</div>
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</div>
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<a id="a0ddf1224851353fc92bfbff6f499fa97" name="a0ddf1224851353fc92bfbff6f499fa97"></a>
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@@ -225,41 +241,34 @@ Here is the call graph for this function:</div>
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</table>
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</div><div class="memdoc">
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<p>Main Function </p>
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<p class="definition">Definition at line <a class="el" href="../../db/dd3/ode__forward__euler_8cpp_source.html#l00189">189</a> of file <a class="el" href="../../db/dd3/ode__forward__euler_8cpp_source.html">ode_forward_euler.cpp</a>.</p>
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<div class="fragment"><div class="line"><span class="lineno"> 189</span> {</div>
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<div class="line"><span class="lineno"> 190</span> <span class="keywordtype">double</span> X0 = 0.f; <span class="comment">/* initial value of x0 */</span></div>
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<div class="line"><span class="lineno"> 191</span> <span class="keywordtype">double</span> X_MAX = 10.F; <span class="comment">/* upper limit of integration */</span></div>
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<div class="line"><span class="lineno"> 192</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray<double></a> Y0{1.f, 0.f}; <span class="comment">/* initial value Y = y(x = x_0) */</span></div>
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<div class="line"><span class="lineno"> 192</span> std::valarray<double> Y0{1.f, 0.f}; <span class="comment">/* initial value Y = y(x = x_0) */</span></div>
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<div class="line"><span class="lineno"> 193</span> <span class="keywordtype">double</span> step_size = NAN;</div>
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<div class="line"><span class="lineno"> 194</span> </div>
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<div class="line"><span class="lineno"> 195</span> <span class="keywordflow">if</span> (argc == 1) {</div>
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<div class="line"><span class="lineno"> 196</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">"\nEnter the step size: "</span>;</div>
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<div class="line"><span class="lineno"> 197</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> >> step_size;</div>
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<div class="line"><span class="lineno"> 196</span> std::cout << <span class="stringliteral">"\nEnter the step size: "</span>;</div>
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<div class="line"><span class="lineno"> 197</span> std::cin >> step_size;</div>
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<div class="line"><span class="lineno"> 198</span> } <span class="keywordflow">else</span> {</div>
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<div class="line"><span class="lineno"> 199</span> <span class="comment">// use commandline argument as independent variable step size</span></div>
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<div class="line"><span class="lineno"> 200</span> step_size = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/byte/atof.html">std::atof</a>(argv[1]);</div>
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<div class="line"><span class="lineno"> 200</span> step_size = std::atof(argv[1]);</div>
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<div class="line"><span class="lineno"> 201</span> }</div>
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<div class="line"><span class="lineno"> 202</span> </div>
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<div class="line"><span class="lineno"> 203</span> <span class="comment">// get approximate solution</span></div>
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<div class="line"><span class="lineno"> 204</span> <span class="keywordtype">double</span> total_time = <a class="code hl_function" href="../../d6/d60/group__ode.html#gae0509f8843e2bc42de2abbd00a14b7b9">forward_euler</a>(step_size, X0, X_MAX, &Y0, <span class="keyword">true</span>);</div>
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<div class="line"><span class="lineno"> 205</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">"\tTime = "</span> << total_time << <span class="stringliteral">" ms\n"</span>;</div>
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<div class="line"><span class="lineno"> 205</span> std::cout << <span class="stringliteral">"\tTime = "</span> << total_time << <span class="stringliteral">" ms\n"</span>;</div>
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<div class="line"><span class="lineno"> 206</span> </div>
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<div class="line"><span class="lineno"> 207</span> <span class="comment">/* compute exact solution for comparion */</span></div>
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<div class="line"><span class="lineno"> 208</span> <a class="code hl_function" href="#aa13517b8e5de1b75592052db7f7e237f">save_exact_solution</a>(X0, X_MAX, step_size, Y0);</div>
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<div class="line"><span class="lineno"> 209</span> </div>
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<div class="line"><span class="lineno"> 210</span> <span class="keywordflow">return</span> 0;</div>
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<div class="line"><span class="lineno"> 211</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>
|
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<div class="ttc" id="abasic_istream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a></div></div>
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<div class="ttc" id="agroup__ode_html_gae0509f8843e2bc42de2abbd00a14b7b9"><div class="ttname"><a href="../../d6/d60/group__ode.html#gae0509f8843e2bc42de2abbd00a14b7b9">forward_euler</a></div><div class="ttdeci">double forward_euler(double dx, double x0, double x_max, std::valarray< double > *y, bool save_to_file=false)</div><div class="ttdoc">Compute approximation using the forward-Euler method in the given limits.</div><div class="ttdef"><b>Definition</b> ode_forward_euler.cpp:102</div></div>
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<div class="ttc" id="aode__forward__euler_8cpp_html_aa13517b8e5de1b75592052db7f7e237f"><div class="ttname"><a href="#aa13517b8e5de1b75592052db7f7e237f">save_exact_solution</a></div><div class="ttdeci">void save_exact_solution(const double &X0, const double &X_MAX, const double &step_size, const std::valarray< double > &Y0)</div><div class="ttdef"><b>Definition</b> ode_forward_euler.cpp:153</div></div>
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<div class="ttc" id="agroup__ode_html_gae0509f8843e2bc42de2abbd00a14b7b9"><div class="ttname"><a href="../../d6/d60/group__ode.html#gae0509f8843e2bc42de2abbd00a14b7b9">forward_euler</a></div><div class="ttdeci">double forward_euler(double dx, double x0, double x_max, std::valarray< double > *y, bool save_to_file=false)</div><div class="ttdoc">Compute approximation using the forward-Euler method in the given limits.</div><div class="ttdef"><b>Definition</b> <a href="../../db/dd3/ode__forward__euler_8cpp_source.html#l00102">ode_forward_euler.cpp:102</a></div></div>
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<div class="ttc" id="aode__forward__euler_8cpp_html_aa13517b8e5de1b75592052db7f7e237f"><div class="ttname"><a href="#aa13517b8e5de1b75592052db7f7e237f">save_exact_solution</a></div><div class="ttdeci">void save_exact_solution(const double &X0, const double &X_MAX, const double &step_size, const std::valarray< double > &Y0)</div><div class="ttdef"><b>Definition</b> <a href="../../db/dd3/ode__forward__euler_8cpp_source.html#l00153">ode_forward_euler.cpp:153</a></div></div>
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<p class="definition">Definition at line <a class="el" href="../../db/dd3/ode__forward__euler_8cpp_source.html#l00054">54</a> of file <a class="el" href="../../db/dd3/ode__forward__euler_8cpp_source.html">ode_forward_euler.cpp</a>.</p>
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<div class="fragment"><div class="line"><span class="lineno"> 55</span> {</div>
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<div class="line"><span class="lineno"> 56</span> <span class="keyword">const</span> <span class="keywordtype">double</span> omega = 1.F; <span class="comment">// some const for the problem</span></div>
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<p class="definition">Definition at line <a class="el" href="../../db/dd3/ode__forward__euler_8cpp_source.html#l00153">153</a> of file <a class="el" href="../../db/dd3/ode__forward__euler_8cpp_source.html">ode_forward_euler.cpp</a>.</p>
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<div class="line"><span class="lineno"> 157</span> std::valarray<double> y(Y0);</div>
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<div class="line"><span class="lineno"> 158</span> </div>
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<div class="line"><span class="lineno"> 159</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ofstream.html">std::ofstream</a> fp(<span class="stringliteral">"exact.csv"</span>, std::ostream::out);</div>
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<div class="line"><span class="lineno"> 159</span> std::ofstream fp(<span class="stringliteral">"exact.csv"</span>, std::ostream::out);</div>
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<div class="line"><span class="lineno"> 160</span> <span class="keywordflow">if</span> (!fp.is_open()) {</div>
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<div class="line"><span class="lineno"> 161</span> std::perror(<span class="stringliteral">"Error! "</span>);</div>
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<div class="line"><span class="lineno"> 162</span> <span class="keywordflow">return</span>;</div>
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<div class="line"><span class="lineno"> 164</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">"Finding exact solution\n"</span>;</div>
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<div class="line"><span class="lineno"> 164</span> std::cout << <span class="stringliteral">"Finding exact solution\n"</span>;</div>
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<div class="line"><span class="lineno"> 165</span> </div>
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<div class="line"><span class="lineno"> 166</span> std::clock_t t1 = std::clock();</div>
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<div class="line"><span class="lineno"> 167</span> <span class="keywordflow">do</span> {</div>
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<div class="line"><span class="lineno"> 168</span> fp << x << <span class="stringliteral">","</span>;</div>
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||||
<div class="line"><span class="lineno"> 169</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < y.size() - 1; i++) {</div>
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<div class="line"><span class="lineno"> 176</span> x += step_size;</div>
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<div class="line"><span class="lineno"> 177</span> } <span class="keywordflow">while</span> (x <= X_MAX);</div>
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<div class="line"><span class="lineno"> 178</span> </div>
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<div class="line"><span class="lineno"> 179</span> std::clock_t t2 = std::clock();</div>
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<div class="line"><span class="lineno"> 180</span> <span class="keywordtype">double</span> total_time = <span class="keyword">static_cast<</span><span class="keywordtype">double</span><span class="keyword">></span>(t2 - t1) / CLOCKS_PER_SEC;</div>
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<div class="line"><span class="lineno"> 181</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">"\tTime = "</span> << total_time << <span class="stringliteral">" ms\n"</span>;</div>
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<div class="line"><span class="lineno"> 181</span> std::cout << <span class="stringliteral">"\tTime = "</span> << total_time << <span class="stringliteral">" ms\n"</span>;</div>
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|
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<div class="ttc" id="aperror_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/c/perror.html">std::perror</a></div><div class="ttdeci">T perror(T... args)</div></div>
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