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<div class="headertitle"><div class="title">golden_search_extrema.cpp File Reference</div></div>
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<p>Find extrema of a univariate real function in a given interval using <a href="https://en.wikipedia.org/wiki/Golden-section_search" target="_blank">golden section search algorithm</a>.
<a href="#details">More...</a></p>
<div class="textblock"><code>#include &lt;cassert&gt;</code><br />
<code>#include &lt;cmath&gt;</code><br />
<code>#include &lt;functional&gt;</code><br />
<code>#include &lt;iostream&gt;</code><br />
<code>#include &lt;limits&gt;</code><br />
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Include dependency graph for golden_search_extrema.cpp:</div>
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#define&#160;</td><td class="memItemRight" valign="bottom"><b>EPSILON</b>&#160;&#160;&#160;1e-7</td></tr>
<tr class="memdesc:a002b2f4894492820fe708b1b7e7c5e70"><td class="mdescLeft">&#160;</td><td class="mdescRight">solution accuracy limit <br /></td></tr>
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Functions</h2></td></tr>
<tr class="memitem:a1aa76a6d5fd4d333f9072beff1dc486b"><td class="memItemLeft" align="right" valign="top">double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d6/d7a/golden__search__extrema_8cpp.html#a1aa76a6d5fd4d333f9072beff1dc486b">get_minima</a> (const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/functional/function.html">std::function</a>&lt; double(double)&gt; &amp;f, double lim_a, double lim_b)</td></tr>
<tr class="memdesc:a1aa76a6d5fd4d333f9072beff1dc486b"><td class="mdescLeft">&#160;</td><td class="mdescRight">Get the minima of a function in the given interval. To get the maxima, simply negate the function. The golden ratio used here is: <a href="../../d6/d7a/golden__search__extrema_8cpp.html#a1aa76a6d5fd4d333f9072beff1dc486b">More...</a><br /></td></tr>
<tr class="separator:a1aa76a6d5fd4d333f9072beff1dc486b"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a1440a7779ac56f47a3f355ce4a8c7da0"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d6/d7a/golden__search__extrema_8cpp.html#a1440a7779ac56f47a3f355ce4a8c7da0">test1</a> ()</td></tr>
<tr class="memdesc:a1440a7779ac56f47a3f355ce4a8c7da0"><td class="mdescLeft">&#160;</td><td class="mdescRight">Test function to find minima for the function \(f(x)= (x-2)^2\) in the interval \([1,5]\) <br />
Expected result = 2. <a href="../../d6/d7a/golden__search__extrema_8cpp.html#a1440a7779ac56f47a3f355ce4a8c7da0">More...</a><br /></td></tr>
<tr class="separator:a1440a7779ac56f47a3f355ce4a8c7da0"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a0283886819c7c140a023582b7269e2d0"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d6/d7a/golden__search__extrema_8cpp.html#a0283886819c7c140a023582b7269e2d0">test2</a> ()</td></tr>
<tr class="memdesc:a0283886819c7c140a023582b7269e2d0"><td class="mdescLeft">&#160;</td><td class="mdescRight">Test function to find <em>maxima</em> for the function \(f(x)= x^{\frac{1}{x}}\) in the interval \([-2,10]\) <br />
Expected result: \(e\approx 2.71828182845904509\). <a href="../../d6/d7a/golden__search__extrema_8cpp.html#a0283886819c7c140a023582b7269e2d0">More...</a><br /></td></tr>
<tr class="separator:a0283886819c7c140a023582b7269e2d0"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a6d0455dd5c30adda100e95f0423c786e"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d6/d7a/golden__search__extrema_8cpp.html#a6d0455dd5c30adda100e95f0423c786e">test3</a> ()</td></tr>
<tr class="memdesc:a6d0455dd5c30adda100e95f0423c786e"><td class="mdescLeft">&#160;</td><td class="mdescRight">Test function to find <em>maxima</em> for the function \(f(x)= \cos x\) in the interval \([0,12]\) <br />
Expected result: \(\pi\approx 3.14159265358979312\). <a href="../../d6/d7a/golden__search__extrema_8cpp.html#a6d0455dd5c30adda100e95f0423c786e">More...</a><br /></td></tr>
<tr class="separator:a6d0455dd5c30adda100e95f0423c786e"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d6/d7a/golden__search__extrema_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p >Find extrema of a univariate real function in a given interval using <a href="https://en.wikipedia.org/wiki/Golden-section_search" target="_blank">golden section search algorithm</a>. </p>
<dl class="section see"><dt>See also</dt><dd><a class="el" href="../../db/d01/brent__method__extrema_8cpp.html" title="Find real extrema of a univariate real function in a given interval using Brent&#39;s method.">brent_method_extrema.cpp</a> </dd></dl>
<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/kvedala" target="_blank">Krishna Vedala</a> </dd></dl>
</div><h2 class="groupheader">Function Documentation</h2>
<a id="a1aa76a6d5fd4d333f9072beff1dc486b" name="a1aa76a6d5fd4d333f9072beff1dc486b"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a1aa76a6d5fd4d333f9072beff1dc486b">&#9670;&nbsp;</a></span>get_minima()</h2>
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<td class="memname">double get_minima </td>
<td>(</td>
<td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/functional/function.html">std::function</a>&lt; double(double)&gt; &amp;&#160;</td>
<td class="paramname"><em>f</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">double&#160;</td>
<td class="paramname"><em>lim_a</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">double&#160;</td>
<td class="paramname"><em>lim_b</em>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
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</div><div class="memdoc">
<p>Get the minima of a function in the given interval. To get the maxima, simply negate the function. The golden ratio used here is: </p>
<p class="formulaDsp">
\[ k=\frac{3-\sqrt{5}}{2} \approx 0.381966\ldots\]
</p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">f</td><td>function to get minima for </td></tr>
<tr><td class="paramname">lim_a</td><td>lower limit of search window </td></tr>
<tr><td class="paramname">lim_b</td><td>upper limit of search window </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>local minima found in the interval </dd></dl>
<div class="fragment"><div class="line"><a id="l00030" name="l00030"></a><span class="lineno"> 30</span> {</div>
<div class="line"><a id="l00031" name="l00031"></a><span class="lineno"> 31</span> uint32_t iters = 0;</div>
<div class="line"><a id="l00032" name="l00032"></a><span class="lineno"> 32</span> <span class="keywordtype">double</span> c, d;</div>
<div class="line"><a id="l00033" name="l00033"></a><span class="lineno"> 33</span> <span class="keywordtype">double</span> prev_mean, mean = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/types/numeric_limits/infinity.html">std::numeric_limits&lt;double&gt;::infinity</a>();</div>
<div class="line"><a id="l00034" name="l00034"></a><span class="lineno"> 34</span> </div>
<div class="line"><a id="l00035" name="l00035"></a><span class="lineno"> 35</span> <span class="comment">// golden ratio value</span></div>
<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"> 36</span> <span class="keyword">const</span> <span class="keywordtype">double</span> M_GOLDEN_RATIO = (1.f + <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/sqrt.html">std::sqrt</a>(5.f)) / 2.f;</div>
<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span> </div>
<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span> <span class="comment">// ensure that lim_a &lt; lim_b</span></div>
<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span> <span class="keywordflow">if</span> (lim_a &gt; lim_b) {</div>
<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/swap.html">std::swap</a>(lim_a, lim_b);</div>
<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span> } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (std::abs(lim_a - lim_b) &lt;= <a class="code hl_define" href="../../d6/d7a/golden__search__extrema_8cpp.html#a002b2f4894492820fe708b1b7e7c5e70">EPSILON</a>) {</div>
<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;Search range must be greater than &quot;</span> &lt;&lt; <a class="code hl_define" href="../../d6/d7a/golden__search__extrema_8cpp.html#a002b2f4894492820fe708b1b7e7c5e70">EPSILON</a> &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span> <span class="keywordflow">return</span> lim_a;</div>
<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span> }</div>
<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span> </div>
<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span> <span class="keywordflow">do</span> {</div>
<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span> prev_mean = mean;</div>
<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span> </div>
<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span> <span class="comment">// compute the section ratio width</span></div>
<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span> <span class="keywordtype">double</span> ratio = (lim_b - lim_a) / M_GOLDEN_RATIO;</div>
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span> c = lim_b - ratio; <span class="comment">// right-side section start</span></div>
<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span> d = lim_a + ratio; <span class="comment">// left-side section end</span></div>
<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span> </div>
<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span> <span class="keywordflow">if</span> (f(c) &lt; f(d)) {</div>
<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span> <span class="comment">// select left section</span></div>
<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span> lim_b = d;</div>
<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span> } <span class="keywordflow">else</span> {</div>
<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span> <span class="comment">// selct right section</span></div>
<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span> lim_a = c;</div>
<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span> }</div>
<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span> </div>
<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span> mean = (lim_a + lim_b) / 2.f;</div>
<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span> iters++;</div>
<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span> </div>
<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span> <span class="comment">// continue till the interval width is greater than sqrt(system epsilon)</span></div>
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span> } <span class="keywordflow">while</span> (std::abs(lim_a - lim_b) &gt; <a class="code hl_define" href="../../d6/d7a/golden__search__extrema_8cpp.html#a002b2f4894492820fe708b1b7e7c5e70">EPSILON</a>);</div>
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span> </div>
<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot; (iters: &quot;</span> &lt;&lt; iters &lt;&lt; <span class="stringliteral">&quot;) &quot;</span>;</div>
<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span> <span class="keywordflow">return</span> prev_mean;</div>
<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span>}</div>
<div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a></div></div>
<div class="ttc" id="agolden__search__extrema_8cpp_html_a002b2f4894492820fe708b1b7e7c5e70"><div class="ttname"><a href="../../d6/d7a/golden__search__extrema_8cpp.html#a002b2f4894492820fe708b1b7e7c5e70">EPSILON</a></div><div class="ttdeci">#define EPSILON</div><div class="ttdoc">solution accuracy limit</div><div class="ttdef"><b>Definition:</b> golden_search_extrema.cpp:17</div></div>
<div class="ttc" id="ainfinity_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/types/numeric_limits/infinity.html">std::numeric_limits::infinity</a></div><div class="ttdeci">T infinity(T... args)</div></div>
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<div class="ttc" id="aswap_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/algorithm/swap.html">std::swap</a></div><div class="ttdeci">T swap(T... args)</div></div>
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<p >Main function </p>
<div class="fragment"><div class="line"><a id="l00139" name="l00139"></a><span class="lineno"> 139</span> {</div>
<div class="line"><a id="l00140" name="l00140"></a><span class="lineno"> 140</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a>.precision(9);</div>
<div class="line"><a id="l00141" name="l00141"></a><span class="lineno"> 141</span> </div>
<div class="line"><a id="l00142" name="l00142"></a><span class="lineno"> 142</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Computations performed with machine epsilon: &quot;</span> &lt;&lt; <a class="code hl_define" href="../../d6/d7a/golden__search__extrema_8cpp.html#a002b2f4894492820fe708b1b7e7c5e70">EPSILON</a></div>
<div class="line"><a id="l00143" name="l00143"></a><span class="lineno"> 143</span> &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
<div class="line"><a id="l00144" name="l00144"></a><span class="lineno"> 144</span> </div>
<div class="line"><a id="l00145" name="l00145"></a><span class="lineno"> 145</span> <a class="code hl_function" href="../../d6/d7a/golden__search__extrema_8cpp.html#a1440a7779ac56f47a3f355ce4a8c7da0">test1</a>();</div>
<div class="line"><a id="l00146" name="l00146"></a><span class="lineno"> 146</span> <a class="code hl_function" href="../../d6/d7a/golden__search__extrema_8cpp.html#a0283886819c7c140a023582b7269e2d0">test2</a>();</div>
<div class="line"><a id="l00147" name="l00147"></a><span class="lineno"> 147</span> <a class="code hl_function" href="../../d6/d7a/golden__search__extrema_8cpp.html#a6d0455dd5c30adda100e95f0423c786e">test3</a>();</div>
<div class="line"><a id="l00148" name="l00148"></a><span class="lineno"> 148</span> </div>
<div class="line"><a id="l00149" name="l00149"></a><span class="lineno"> 149</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><a id="l00150" name="l00150"></a><span class="lineno"> 150</span>}</div>
<div class="ttc" id="agolden__search__extrema_8cpp_html_a0283886819c7c140a023582b7269e2d0"><div class="ttname"><a href="../../d6/d7a/golden__search__extrema_8cpp.html#a0283886819c7c140a023582b7269e2d0">test2</a></div><div class="ttdeci">void test2()</div><div class="ttdoc">Test function to find maxima for the function in the interval Expected result: .</div><div class="ttdef"><b>Definition:</b> golden_search_extrema.cpp:100</div></div>
<div class="ttc" id="agolden__search__extrema_8cpp_html_a1440a7779ac56f47a3f355ce4a8c7da0"><div class="ttname"><a href="../../d6/d7a/golden__search__extrema_8cpp.html#a1440a7779ac56f47a3f355ce4a8c7da0">test1</a></div><div class="ttdeci">void test1()</div><div class="ttdoc">Test function to find minima for the function in the interval Expected result = 2.</div><div class="ttdef"><b>Definition:</b> golden_search_extrema.cpp:78</div></div>
<div class="ttc" id="agolden__search__extrema_8cpp_html_a6d0455dd5c30adda100e95f0423c786e"><div class="ttname"><a href="../../d6/d7a/golden__search__extrema_8cpp.html#a6d0455dd5c30adda100e95f0423c786e">test3</a></div><div class="ttdeci">void test3()</div><div class="ttdoc">Test function to find maxima for the function in the interval Expected result: .</div><div class="ttdef"><b>Definition:</b> golden_search_extrema.cpp:123</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#a1440a7779ac56f47a3f355ce4a8c7da0">&#9670;&nbsp;</a></span>test1()</h2>
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<p>Test function to find minima for the function \(f(x)= (x-2)^2\) in the interval \([1,5]\) <br />
Expected result = 2. </p>
<div class="fragment"><div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span> {</div>
<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span> <span class="comment">// define the function to minimize as a lambda function</span></div>
<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/functional/function.html">std::function</a>&lt;double(<span class="keywordtype">double</span>)&gt; f1 = [](<span class="keywordtype">double</span> x) {</div>
<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span> <span class="keywordflow">return</span> (x - 2) * (x - 2);</div>
<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span> };</div>
<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"> 83</span> </div>
<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 1.... &quot;</span>;</div>
<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</span> </div>
<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"> 86</span> <span class="keywordtype">double</span> minima = <a class="code hl_function" href="../../d6/d7a/golden__search__extrema_8cpp.html#a1aa76a6d5fd4d333f9072beff1dc486b">get_minima</a>(f1, 1, 5);</div>
<div class="line"><a id="l00087" name="l00087"></a><span class="lineno"> 87</span> </div>
<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"> 88</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; minima &lt;&lt; <span class="stringliteral">&quot;...&quot;</span>;</div>
<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span> </div>
<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"> 90</span> assert(std::abs(minima - 2) &lt; <a class="code hl_define" href="../../d6/d7a/golden__search__extrema_8cpp.html#a002b2f4894492820fe708b1b7e7c5e70">EPSILON</a>);</div>
<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"> 91</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed\n&quot;</span>;</div>
<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"> 92</span>}</div>
<div class="ttc" id="afunction_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/utility/functional/function.html">std::function</a></div></div>
<div class="ttc" id="agolden__search__extrema_8cpp_html_a1aa76a6d5fd4d333f9072beff1dc486b"><div class="ttname"><a href="../../d6/d7a/golden__search__extrema_8cpp.html#a1aa76a6d5fd4d333f9072beff1dc486b">get_minima</a></div><div class="ttdeci">double get_minima(const std::function&lt; double(double)&gt; &amp;f, double lim_a, double lim_b)</div><div class="ttdoc">Get the minima of a function in the given interval. To get the maxima, simply negate the function....</div><div class="ttdef"><b>Definition:</b> golden_search_extrema.cpp:29</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#a0283886819c7c140a023582b7269e2d0">&#9670;&nbsp;</a></span>test2()</h2>
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<td class="memname">void test2 </td>
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<p>Test function to find <em>maxima</em> for the function \(f(x)= x^{\frac{1}{x}}\) in the interval \([-2,10]\) <br />
Expected result: \(e\approx 2.71828182845904509\). </p>
<div class="fragment"><div class="line"><a id="l00100" name="l00100"></a><span class="lineno"> 100</span> {</div>
<div class="line"><a id="l00101" name="l00101"></a><span class="lineno"> 101</span> <span class="comment">// define the function to maximize as a lambda function</span></div>
<div class="line"><a id="l00102" name="l00102"></a><span class="lineno"> 102</span> <span class="comment">// since we are maximixing, we negated the function return value</span></div>
<div class="line"><a id="l00103" name="l00103"></a><span class="lineno"> 103</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/functional/function.html">std::function</a>&lt;double(<span class="keywordtype">double</span>)&gt; func = [](<span class="keywordtype">double</span> x) {</div>
<div class="line"><a id="l00104" name="l00104"></a><span class="lineno"> 104</span> <span class="keywordflow">return</span> -<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">std::pow</a>(x, 1.f / x);</div>
<div class="line"><a id="l00105" name="l00105"></a><span class="lineno"> 105</span> };</div>
<div class="line"><a id="l00106" name="l00106"></a><span class="lineno"> 106</span> </div>
<div class="line"><a id="l00107" name="l00107"></a><span class="lineno"> 107</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 2.... &quot;</span>;</div>
<div class="line"><a id="l00108" name="l00108"></a><span class="lineno"> 108</span> </div>
<div class="line"><a id="l00109" name="l00109"></a><span class="lineno"> 109</span> <span class="keywordtype">double</span> minima = <a class="code hl_function" href="../../d6/d7a/golden__search__extrema_8cpp.html#a1aa76a6d5fd4d333f9072beff1dc486b">get_minima</a>(func, -2, 10);</div>
<div class="line"><a id="l00110" name="l00110"></a><span class="lineno"> 110</span> </div>
<div class="line"><a id="l00111" name="l00111"></a><span class="lineno"> 111</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; minima &lt;&lt; <span class="stringliteral">&quot; (&quot;</span> &lt;&lt; M_E &lt;&lt; <span class="stringliteral">&quot;)...&quot;</span>;</div>
<div class="line"><a id="l00112" name="l00112"></a><span class="lineno"> 112</span> </div>
<div class="line"><a id="l00113" name="l00113"></a><span class="lineno"> 113</span> assert(std::abs(minima - M_E) &lt; <a class="code hl_define" href="../../d6/d7a/golden__search__extrema_8cpp.html#a002b2f4894492820fe708b1b7e7c5e70">EPSILON</a>);</div>
<div class="line"><a id="l00114" name="l00114"></a><span class="lineno"> 114</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed\n&quot;</span>;</div>
<div class="line"><a id="l00115" name="l00115"></a><span class="lineno"> 115</span>}</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a6d0455dd5c30adda100e95f0423c786e">&#9670;&nbsp;</a></span>test3()</h2>
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<p>Test function to find <em>maxima</em> for the function \(f(x)= \cos x\) in the interval \([0,12]\) <br />
Expected result: \(\pi\approx 3.14159265358979312\). </p>
<div class="fragment"><div class="line"><a id="l00123" name="l00123"></a><span class="lineno"> 123</span> {</div>
<div class="line"><a id="l00124" name="l00124"></a><span class="lineno"> 124</span> <span class="comment">// define the function to maximize as a lambda function</span></div>
<div class="line"><a id="l00125" name="l00125"></a><span class="lineno"> 125</span> <span class="comment">// since we are maximixing, we negated the function return value</span></div>
<div class="line"><a id="l00126" name="l00126"></a><span class="lineno"> 126</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/functional/function.html">std::function</a>&lt;double(<span class="keywordtype">double</span>)&gt; func = [](<span class="keywordtype">double</span> x) { <span class="keywordflow">return</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/cos.html">std::cos</a>(x); };</div>
<div class="line"><a id="l00127" name="l00127"></a><span class="lineno"> 127</span> </div>
<div class="line"><a id="l00128" name="l00128"></a><span class="lineno"> 128</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 3.... &quot;</span>;</div>
<div class="line"><a id="l00129" name="l00129"></a><span class="lineno"> 129</span> </div>
<div class="line"><a id="l00130" name="l00130"></a><span class="lineno"> 130</span> <span class="keywordtype">double</span> minima = <a class="code hl_function" href="../../d6/d7a/golden__search__extrema_8cpp.html#a1aa76a6d5fd4d333f9072beff1dc486b">get_minima</a>(func, -4, 12);</div>
<div class="line"><a id="l00131" name="l00131"></a><span class="lineno"> 131</span> </div>
<div class="line"><a id="l00132" name="l00132"></a><span class="lineno"> 132</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; minima &lt;&lt; <span class="stringliteral">&quot; (&quot;</span> &lt;&lt; M_PI &lt;&lt; <span class="stringliteral">&quot;)...&quot;</span>;</div>
<div class="line"><a id="l00133" name="l00133"></a><span class="lineno"> 133</span> </div>
<div class="line"><a id="l00134" name="l00134"></a><span class="lineno"> 134</span> assert(std::abs(minima - M_PI) &lt; <a class="code hl_define" href="../../d6/d7a/golden__search__extrema_8cpp.html#a002b2f4894492820fe708b1b7e7c5e70">EPSILON</a>);</div>
<div class="line"><a id="l00135" name="l00135"></a><span class="lineno"> 135</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed\n&quot;</span>;</div>
<div class="line"><a id="l00136" name="l00136"></a><span class="lineno"> 136</span>}</div>
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