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<title>Algorithms_in_C++: numerical_methods/ode_semi_implicit_euler.cpp File Reference</title>
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<div id="projectname">Algorithms_in_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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@@ -178,10 +178,10 @@ Functions</h2></td></tr>
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<div class="fragment"><div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span> {</div>
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<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</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"><a id="l00068" name="l00068"></a><span class="lineno"> 68</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"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span>}</div>
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<div class="fragment"><div class="line"><span class="lineno"> 66</span> {</div>
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<div class="line"><span class="lineno"> 67</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"> 68</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"> 69</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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@@ -219,35 +219,35 @@ Here is the call graph for this function:</div>
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</div><div class="memdoc">
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<p >Main Function </p>
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<div class="fragment"><div class="line"><a id="l00189" name="l00189"></a><span class="lineno"> 189</span> {</div>
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<div class="line"><a id="l00190" name="l00190"></a><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"><a id="l00191" name="l00191"></a><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"><a id="l00192" name="l00192"></a><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"><a id="l00193" name="l00193"></a><span class="lineno"> 193</span> <span class="keywordtype">double</span> step_size;</div>
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<div class="line"><a id="l00194" name="l00194"></a><span class="lineno"> 194</span> </div>
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<div class="line"><a id="l00195" name="l00195"></a><span class="lineno"> 195</span> <span class="keywordflow">if</span> (argc == 1) {</div>
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<div class="line"><a id="l00196" name="l00196"></a><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"><a id="l00197" name="l00197"></a><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"><a id="l00198" name="l00198"></a><span class="lineno"> 198</span> } <span class="keywordflow">else</span> {</div>
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<div class="line"><a id="l00199" name="l00199"></a><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"><a id="l00200" name="l00200"></a><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"><a id="l00201" name="l00201"></a><span class="lineno"> 201</span> }</div>
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<div class="line"><a id="l00202" name="l00202"></a><span class="lineno"> 202</span> </div>
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<div class="line"><a id="l00203" name="l00203"></a><span class="lineno"> 203</span> <span class="comment">// get approximate solution</span></div>
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<div class="line"><a id="l00204" name="l00204"></a><span class="lineno"> 204</span> <span class="keywordtype">double</span> total_time = <a class="code hl_function" href="../../d6/d60/group__ode.html#ga3874d294ab00fe9ce8731c5b7991a089">semi_implicit_euler</a>(step_size, X0, X_MAX, &Y0, <span class="keyword">true</span>);</div>
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<div class="line"><a id="l00205" name="l00205"></a><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"><a id="l00206" name="l00206"></a><span class="lineno"> 206</span> </div>
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<div class="line"><a id="l00207" name="l00207"></a><span class="lineno"> 207</span> <span class="comment">/* compute exact solution for comparion */</span></div>
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<div class="line"><a id="l00208" name="l00208"></a><span class="lineno"> 208</span> <a class="code hl_function" href="../../d3/d06/ode__semi__implicit__euler_8cpp.html#aa13517b8e5de1b75592052db7f7e237f">save_exact_solution</a>(X0, X_MAX, step_size, Y0);</div>
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<div class="line"><a id="l00209" name="l00209"></a><span class="lineno"> 209</span> </div>
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<div class="line"><a id="l00210" name="l00210"></a><span class="lineno"> 210</span> <span class="keywordflow">return</span> 0;</div>
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<div class="line"><a id="l00211" name="l00211"></a><span class="lineno"> 211</span>}</div>
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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"> 193</span> <span class="keywordtype">double</span> step_size;</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"> 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"> 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#ga3874d294ab00fe9ce8731c5b7991a089">semi_implicit_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"> 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="../../d3/d06/ode__semi__implicit__euler_8cpp.html#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>
|
||||
<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="agroup__ode_html_ga3874d294ab00fe9ce8731c5b7991a089"><div class="ttname"><a href="../../d6/d60/group__ode.html#ga3874d294ab00fe9ce8731c5b7991a089">semi_implicit_euler</a></div><div class="ttdeci">double semi_implicit_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 semi-implicit-Euler method in the given limits.</div><div class="ttdef"><b>Definition:</b> ode_semi_implicit_euler.cpp:103</div></div>
|
||||
<div class="ttc" id="aode__semi__implicit__euler_8cpp_html_aa13517b8e5de1b75592052db7f7e237f"><div class="ttname"><a href="../../d3/d06/ode__semi__implicit__euler_8cpp.html#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_semi_implicit_euler.cpp:153</div></div>
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||||
<div class="ttc" id="avalarray_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a></div></div>
|
||||
<div class="ttc" id="avalarray_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray< double ></a></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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@@ -299,11 +299,11 @@ Here is the call graph for this function:</div>
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</table>
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</dd>
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</dl>
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<div class="fragment"><div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span> {</div>
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<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</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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||||
<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span> dy[0][0] = y[0][1]; <span class="comment">// x dot</span></div>
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||||
<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span> dy[0][1] = -omega * omega * y[0][0]; <span class="comment">// y dot</span></div>
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||||
<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span>}</div>
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<div class="fragment"><div class="line"><span class="lineno"> 54</span> {</div>
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<div class="line"><span class="lineno"> 55</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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<div class="line"><span class="lineno"> 56</span> dy[0][0] = y[0][1]; <span class="comment">// x dot</span></div>
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<div class="line"><span class="lineno"> 57</span> dy[0][1] = -omega * omega * y[0][0]; <span class="comment">// y dot</span></div>
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<div class="line"><span class="lineno"> 58</span>}</div>
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</div><!-- fragment -->
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@@ -354,36 +354,36 @@ Here is the call graph for this function:</div>
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</table>
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</dd>
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</dl>
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<div class="fragment"><div class="line"><a id="l00155" name="l00155"></a><span class="lineno"> 155</span> {</div>
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<div class="line"><a id="l00156" name="l00156"></a><span class="lineno"> 156</span> <span class="keywordtype">double</span> x = X0;</div>
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<div class="line"><a id="l00157" name="l00157"></a><span class="lineno"> 157</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray<double></a> y = Y0;</div>
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<div class="line"><a id="l00158" name="l00158"></a><span class="lineno"> 158</span> </div>
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<div class="line"><a id="l00159" name="l00159"></a><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"><a id="l00160" name="l00160"></a><span class="lineno"> 160</span> <span class="keywordflow">if</span> (!fp.is_open()) {</div>
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<div class="line"><a id="l00161" name="l00161"></a><span class="lineno"> 161</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/c/perror.html">std::perror</a>(<span class="stringliteral">"Error! "</span>);</div>
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<div class="line"><a id="l00162" name="l00162"></a><span class="lineno"> 162</span> <span class="keywordflow">return</span>;</div>
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<div class="line"><a id="l00163" name="l00163"></a><span class="lineno"> 163</span> }</div>
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<div class="line"><a id="l00164" name="l00164"></a><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"><a id="l00165" name="l00165"></a><span class="lineno"> 165</span> </div>
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<div class="line"><a id="l00166" name="l00166"></a><span class="lineno"> 166</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock_t.html">std::clock_t</a> t1 = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a>();</div>
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<div class="line"><a id="l00167" name="l00167"></a><span class="lineno"> 167</span> <span class="keywordflow">do</span> {</div>
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<div class="line"><a id="l00168" name="l00168"></a><span class="lineno"> 168</span> fp << x << <span class="stringliteral">","</span>;</div>
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<div class="line"><a id="l00169" name="l00169"></a><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"><a id="l00170" name="l00170"></a><span class="lineno"> 170</span> fp << y[i] << <span class="stringliteral">","</span>;</div>
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<div class="line"><a id="l00171" name="l00171"></a><span class="lineno"> 171</span> }</div>
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<div class="line"><a id="l00172" name="l00172"></a><span class="lineno"> 172</span> fp << y[y.size() - 1] << <span class="stringliteral">"\n"</span>;</div>
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<div class="line"><a id="l00173" name="l00173"></a><span class="lineno"> 173</span> </div>
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<div class="line"><a id="l00174" name="l00174"></a><span class="lineno"> 174</span> <a class="code hl_function" href="../../d3/d06/ode__semi__implicit__euler_8cpp.html#af3adf7b092a87868917ee5fb4255192b">exact_solution</a>(x, &y);</div>
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<div class="line"><a id="l00175" name="l00175"></a><span class="lineno"> 175</span> </div>
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<div class="line"><a id="l00176" name="l00176"></a><span class="lineno"> 176</span> x += step_size;</div>
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<div class="line"><a id="l00177" name="l00177"></a><span class="lineno"> 177</span> } <span class="keywordflow">while</span> (x <= X_MAX);</div>
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<div class="line"><a id="l00178" name="l00178"></a><span class="lineno"> 178</span> </div>
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<div class="line"><a id="l00179" name="l00179"></a><span class="lineno"> 179</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock_t.html">std::clock_t</a> t2 = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a>();</div>
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<div class="line"><a id="l00180" name="l00180"></a><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"><a id="l00181" name="l00181"></a><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"><a id="l00182" name="l00182"></a><span class="lineno"> 182</span> </div>
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<div class="line"><a id="l00183" name="l00183"></a><span class="lineno"> 183</span> fp.close();</div>
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<div class="line"><a id="l00184" name="l00184"></a><span class="lineno"> 184</span>}</div>
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<div class="fragment"><div class="line"><span class="lineno"> 155</span> {</div>
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<div class="line"><span class="lineno"> 156</span> <span class="keywordtype">double</span> x = X0;</div>
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<div class="line"><span class="lineno"> 157</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray<double></a> 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"> 160</span> <span class="keywordflow">if</span> (!fp.is_open()) {</div>
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<div class="line"><span class="lineno"> 161</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/c/perror.html">std::perror</a>(<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"> 163</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"> 165</span> </div>
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<div class="line"><span class="lineno"> 166</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock_t.html">std::clock_t</a> t1 = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a>();</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>
|
||||
<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"> 170</span> fp << y[i] << <span class="stringliteral">","</span>;</div>
|
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<div class="line"><span class="lineno"> 171</span> }</div>
|
||||
<div class="line"><span class="lineno"> 172</span> fp << y[y.size() - 1] << <span class="stringliteral">"\n"</span>;</div>
|
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<div class="line"><span class="lineno"> 173</span> </div>
|
||||
<div class="line"><span class="lineno"> 174</span> <a class="code hl_function" href="../../d3/d06/ode__semi__implicit__euler_8cpp.html#af3adf7b092a87868917ee5fb4255192b">exact_solution</a>(x, &y);</div>
|
||||
<div class="line"><span class="lineno"> 175</span> </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>
|
||||
<div class="line"><span class="lineno"> 178</span> </div>
|
||||
<div class="line"><span class="lineno"> 179</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock_t.html">std::clock_t</a> t2 = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a>();</div>
|
||||
<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>
|
||||
<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>
|
||||
<div class="line"><span class="lineno"> 182</span> </div>
|
||||
<div class="line"><span class="lineno"> 183</span> fp.close();</div>
|
||||
<div class="line"><span class="lineno"> 184</span>}</div>
|
||||
<div class="ttc" id="abasic_ofstream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ofstream.html">std::ofstream</a></div></div>
|
||||
<div class="ttc" id="aclock_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a></div><div class="ttdeci">T clock(T... args)</div></div>
|
||||
<div class="ttc" id="aclock_t_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/chrono/c/clock_t.html">std::clock_t</a></div></div>
|
||||
@@ -404,7 +404,7 @@ Here is the call graph for this function:</div>
|
||||
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