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<title>TheAlgorithms/C++: numerical_methods/brent_method_extrema.cpp File Reference</title>
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/* @license magnet:?xt=urn:btih:d3d9a9a6595521f9666a5e94cc830dab83b65699&dn=expat.txt MIT */
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var searchBox = new SearchBox("searchBox", "../../search/",'.html');
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@@ -176,7 +176,7 @@ Functions</h2></td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
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<div class="textblock"><p>Find real extrema of a univariate real function in a given interval using <a href="https://en.wikipedia.org/wiki/Brent%27s_method" target="_blank">Brent's method</a>. </p>
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<p>Refer the algorithm discoverer's publication <a href="https://maths-people.anu.edu.au/~brent/pd/rpb011i.pdf" target="_blank">online</a> and also associated book: </p><blockquote class="doxtable">
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<p>‍R. P. Brent, Algorithms for Minimization without Derivatives, Prentice-Hall, Englewood Cliffs, New Jersey, 1973 </p>
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<p>R. P. Brent, Algorithms for Minimization without Derivatives, Prentice-Hall, Englewood Cliffs, New Jersey, 1973 </p>
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</blockquote>
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<dl class="section see"><dt>See also</dt><dd><a class="el" href="../../d6/d7a/golden__search__extrema_8cpp.html" title="Find extrema of a univariate real function in a given interval using golden section search algorithm.">golden_search_extrema.cpp</a></dd></dl>
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<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/kvedala" target="_blank">Krishna Vedala</a> </dd></dl>
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@@ -266,8 +266,8 @@ Functions</h2></td></tr>
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<div class="line"><span class="lineno"> 39</span> </div>
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<div class="line"><span class="lineno"> 40</span> <span class="keywordflow">if</span> (lim_a > lim_b) {</div>
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<div class="line"><span class="lineno"> 41</span> std::swap(lim_a, lim_b);</div>
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<div class="line"><span class="lineno"> 42</span> } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (std::abs(lim_a - lim_b) <= <a class="code hl_define" href="#a002b2f4894492820fe708b1b7e7c5e70">EPSILON</a>) {</div>
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<div class="line"><span class="lineno"> 43</span> std::cerr << <span class="stringliteral">"Search range must be greater than "</span> << <a class="code hl_define" href="#a002b2f4894492820fe708b1b7e7c5e70">EPSILON</a> << <span class="stringliteral">"\n"</span>;</div>
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<div class="line"><span class="lineno"> 42</span> } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (std::abs(lim_a - lim_b) <= EPSILON) {</div>
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<div class="line"><span class="lineno"> 43</span> std::cerr << <span class="stringliteral">"Search range must be greater than "</span> << EPSILON << <span class="stringliteral">"\n"</span>;</div>
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<div class="line"><span class="lineno"> 44</span> <span class="keywordflow">return</span> lim_a;</div>
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<div class="line"><span class="lineno"> 45</span> }</div>
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<div class="line"><span class="lineno"> 46</span> </div>
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@@ -287,7 +287,7 @@ Functions</h2></td></tr>
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<div class="line"><span class="lineno"> 60</span> </div>
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<div class="line"><span class="lineno"> 61</span> <span class="keywordflow">do</span> {</div>
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<div class="line"><span class="lineno"> 62</span> mid_point = (lim_a + lim_b) / 2.f;</div>
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<div class="line"><span class="lineno"> 63</span> tolerance = <a class="code hl_define" href="#a002b2f4894492820fe708b1b7e7c5e70">EPSILON</a> * std::abs(x);</div>
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<div class="line"><span class="lineno"> 63</span> tolerance = EPSILON * std::abs(x);</div>
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<div class="line"><span class="lineno"> 64</span> tolerance2 = 2 * tolerance;</div>
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<div class="line"><span class="lineno"> 65</span> </div>
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<div class="line"><span class="lineno"> 66</span> <span class="keywordflow">if</span> (std::abs(e) > tolerance2) {</div>
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@@ -361,7 +361,6 @@ Functions</h2></td></tr>
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<div class="line"><span class="lineno"> 134</span> </div>
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<div class="line"><span class="lineno"> 135</span> <span class="keywordflow">return</span> x;</div>
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<div class="line"><span class="lineno"> 136</span>}</div>
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<div class="ttc" id="abrent__method__extrema_8cpp_html_a002b2f4894492820fe708b1b7e7c5e70"><div class="ttname"><a href="#a002b2f4894492820fe708b1b7e7c5e70">EPSILON</a></div><div class="ttdeci">#define EPSILON</div><div class="ttdoc">system accuracy limit</div><div class="ttdef"><b>Definition</b> <a href="../../db/d01/brent__method__extrema_8cpp_source.html#l00024">brent_method_extrema.cpp:24</a></div></div>
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<div class="ttc" id="acomposite__simpson__rule_8cpp_html_a4251b4df4748a0b9c43a48f61bdd2397"><div class="ttname"><a href="../../d4/d18/composite__simpson__rule_8cpp.html#a4251b4df4748a0b9c43a48f61bdd2397">numerical_methods::simpson_method::f</a></div><div class="ttdeci">double f(double x)</div><div class="ttdoc">A function f(x) that will be used to test the method.</div><div class="ttdef"><b>Definition</b> <a href="../../d4/d18/composite__simpson__rule_8cpp_source.html#l00113">composite_simpson_rule.cpp:113</a></div></div>
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</div><!-- fragment -->
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</div>
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@@ -386,7 +385,7 @@ Functions</h2></td></tr>
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<div class="fragment"><div class="line"><span class="lineno"> 205</span> {</div>
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<div class="line"><span class="lineno"> 206</span> std::cout.precision(18);</div>
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<div class="line"><span class="lineno"> 207</span> </div>
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<div class="line"><span class="lineno"> 208</span> std::cout << <span class="stringliteral">"Computations performed with machine epsilon: "</span> << <a class="code hl_define" href="#a002b2f4894492820fe708b1b7e7c5e70">EPSILON</a></div>
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<div class="line"><span class="lineno"> 208</span> std::cout << <span class="stringliteral">"Computations performed with machine epsilon: "</span> << EPSILON</div>
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<div class="line"><span class="lineno"> 209</span> << <span class="stringliteral">"\n"</span>;</div>
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<div class="line"><span class="lineno"> 210</span> </div>
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<div class="line"><span class="lineno"> 211</span> <a class="code hl_function" href="#a1440a7779ac56f47a3f355ce4a8c7da0">test1</a>();</div>
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<div class="line"><span class="lineno"> 153</span> </div>
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<div class="line"><span class="lineno"> 154</span> std::cout << minima << <span class="stringliteral">"..."</span>;</div>
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<div class="line"><span class="lineno"> 155</span> </div>
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<div class="line"><span class="lineno"> 156</span> assert(std::abs(minima - 2) < <a class="code hl_define" href="#a002b2f4894492820fe708b1b7e7c5e70">EPSILON</a>);</div>
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<div class="line"><span class="lineno"> 156</span> assert(std::abs(minima - 2) < EPSILON);</div>
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<div class="line"><span class="lineno"> 157</span> std::cout << <span class="stringliteral">"passed\n"</span>;</div>
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<div class="line"><span class="lineno"> 158</span>}</div>
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<div class="ttc" id="abrent__method__extrema_8cpp_html_a1aa76a6d5fd4d333f9072beff1dc486b"><div class="ttname"><a href="#a1aa76a6d5fd4d333f9072beff1dc486b">get_minima</a></div><div class="ttdeci">double get_minima(const std::function< double(double)> &f, double lim_a, double lim_b)</div><div class="ttdoc">Get the real root of a function in the given interval.</div><div class="ttdef"><b>Definition</b> <a href="../../db/d01/brent__method__extrema_8cpp_source.html#l00036">brent_method_extrema.cpp:36</a></div></div>
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@@ -471,7 +470,7 @@ Functions</h2></td></tr>
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<div class="line"><span class="lineno"> 176</span> </div>
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<div class="line"><span class="lineno"> 177</span> std::cout << minima << <span class="stringliteral">" ("</span> << M_E << <span class="stringliteral">")..."</span>;</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> assert(std::abs(minima - M_E) < <a class="code hl_define" href="#a002b2f4894492820fe708b1b7e7c5e70">EPSILON</a>);</div>
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<div class="line"><span class="lineno"> 179</span> assert(std::abs(minima - M_E) < EPSILON);</div>
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<div class="line"><span class="lineno"> 180</span> std::cout << <span class="stringliteral">"passed\n"</span>;</div>
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<div class="line"><span class="lineno"> 181</span>}</div>
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</div><!-- fragment -->
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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> std::cout << minima << <span class="stringliteral">" ("</span> << M_PI << <span class="stringliteral">")..."</span>;</div>
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<div class="line"><span class="lineno"> 199</span> </div>
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<div class="line"><span class="lineno"> 200</span> assert(std::abs(minima - M_PI) < <a class="code hl_define" href="#a002b2f4894492820fe708b1b7e7c5e70">EPSILON</a>);</div>
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<div class="line"><span class="lineno"> 200</span> assert(std::abs(minima - M_PI) < EPSILON);</div>
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<div class="line"><span class="lineno"> 201</span> std::cout << <span class="stringliteral">"passed\n"</span>;</div>
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<div class="line"><span class="lineno"> 202</span>}</div>
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</div><!-- fragment -->
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@@ -519,7 +518,7 @@ Functions</h2></td></tr>
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