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<div class="headertitle"><div class="title">golden_search_extrema.cpp</div></div>
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<a href="../../d6/d7a/golden__search__extrema_8cpp.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a id="l00001" name="l00001"></a><span class="lineno"> 1</span></div>
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<div class="line"><a id="l00010" name="l00010"></a><span class="lineno"> 10</span><span class="preprocessor">#define _USE_MATH_DEFINES </span><span class="comment">//< required for MS Visual C++</span></div>
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<div class="line"><a id="l00011" name="l00011"></a><span class="lineno"> 11</span><span class="preprocessor">#include <cassert></span></div>
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<div class="line"><a id="l00012" name="l00012"></a><span class="lineno"> 12</span><span class="preprocessor">#include <cmath></span></div>
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<div class="line"><a id="l00013" name="l00013"></a><span class="lineno"> 13</span><span class="preprocessor">#include <cstdint></span></div>
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<div class="line"><a id="l00014" name="l00014"></a><span class="lineno"> 14</span><span class="preprocessor">#include <functional></span></div>
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<div class="line"><a id="l00015" name="l00015"></a><span class="lineno"> 15</span><span class="preprocessor">#include <iostream></span></div>
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<div class="line"><a id="l00016" name="l00016"></a><span class="lineno"> 16</span><span class="preprocessor">#include <limits></span></div>
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<div class="line"><a id="l00017" name="l00017"></a><span class="lineno"> 17</span> </div>
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<div class="line"><a id="l00018" name="l00018"></a><span class="lineno"><a class="line" href="../../d6/d7a/golden__search__extrema_8cpp.html#a002b2f4894492820fe708b1b7e7c5e70"> 18</a></span><span class="preprocessor">#define EPSILON 1e-7 </span></div>
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<div class="line"><a id="l00019" name="l00019"></a><span class="lineno"> 19</span></div>
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<div class="foldopen" id="foldopen00030" data-start="{" data-end="}">
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<div class="line"><a id="l00030" name="l00030"></a><span class="lineno"><a class="line" href="../../d6/d7a/golden__search__extrema_8cpp.html#a1aa76a6d5fd4d333f9072beff1dc486b"> 30</a></span><span class="keywordtype">double</span> <a class="code hl_function" href="../../d6/d7a/golden__search__extrema_8cpp.html#a1aa76a6d5fd4d333f9072beff1dc486b">get_minima</a>(<span class="keyword">const</span> std::function<<span class="keywordtype">double</span>(<span class="keywordtype">double</span>)> &f, <span class="keywordtype">double</span> lim_a,</div>
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<div class="line"><a id="l00031" name="l00031"></a><span class="lineno"> 31</span> <span class="keywordtype">double</span> lim_b) {</div>
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<div class="line"><a id="l00032" name="l00032"></a><span class="lineno"> 32</span> uint32_t iters = 0;</div>
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<div class="line"><a id="l00033" name="l00033"></a><span class="lineno"> 33</span> <span class="keywordtype">double</span> c, d;</div>
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<div class="line"><a id="l00034" name="l00034"></a><span class="lineno"> 34</span> <span class="keywordtype">double</span> prev_mean, mean = std::numeric_limits<double>::infinity();</div>
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<div class="line"><a id="l00035" name="l00035"></a><span class="lineno"> 35</span> </div>
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<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"> 36</span> <span class="comment">// golden ratio value</span></div>
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<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span> <span class="keyword">const</span> <span class="keywordtype">double</span> M_GOLDEN_RATIO = (1.f + std::sqrt(5.f)) / 2.f;</div>
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<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span> </div>
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<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span> <span class="comment">// ensure that lim_a < lim_b</span></div>
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<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span> <span class="keywordflow">if</span> (lim_a > lim_b) {</div>
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<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span> std::swap(lim_a, lim_b);</div>
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<div class="line"><a id="l00042" name="l00042"></a><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"><a id="l00043" name="l00043"></a><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"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span> <span class="keywordflow">return</span> lim_a;</div>
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<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span> }</div>
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<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span> </div>
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<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span> <span class="keywordflow">do</span> {</div>
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<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span> prev_mean = mean;</div>
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<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span> </div>
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<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span> <span class="comment">// compute the section ratio width</span></div>
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<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span> <span class="keywordtype">double</span> ratio = (lim_b - lim_a) / M_GOLDEN_RATIO;</div>
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<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span> c = lim_b - ratio; <span class="comment">// right-side section start</span></div>
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<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span> d = lim_a + ratio; <span class="comment">// left-side section end</span></div>
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<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="keywordflow">if</span> (f(c) < f(d)) {</div>
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<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span> <span class="comment">// select left section</span></div>
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<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span> lim_b = d;</div>
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<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span> } <span class="keywordflow">else</span> {</div>
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<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span> <span class="comment">// selct right section</span></div>
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<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span> lim_a = c;</div>
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<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span> }</div>
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<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span> </div>
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<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span> mean = (lim_a + lim_b) / 2.f;</div>
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<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span> iters++;</div>
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<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span> </div>
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<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span> <span class="comment">// continue till the interval width is greater than sqrt(system epsilon)</span></div>
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<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span> } <span class="keywordflow">while</span> (std::abs(lim_a - lim_b) > EPSILON);</div>
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<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span> </div>
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<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span> std::cout << <span class="stringliteral">" (iters: "</span> << iters << <span class="stringliteral">") "</span>;</div>
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<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span> <span class="keywordflow">return</span> prev_mean;</div>
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<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span>}</div>
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</div>
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<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span></div>
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<div class="foldopen" id="foldopen00079" data-start="{" data-end="}">
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<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"><a class="line" href="../../d6/d7a/golden__search__extrema_8cpp.html#a1440a7779ac56f47a3f355ce4a8c7da0"> 79</a></span><span class="keywordtype">void</span> <a class="code hl_function" href="../../d6/d7a/golden__search__extrema_8cpp.html#a1440a7779ac56f47a3f355ce4a8c7da0">test1</a>() {</div>
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<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span> <span class="comment">// define the function to minimize as a lambda function</span></div>
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<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span> std::function<double(<span class="keywordtype">double</span>)> f1 = [](<span class="keywordtype">double</span> x) {</div>
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<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span> <span class="keywordflow">return</span> (x - 2) * (x - 2);</div>
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<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"> 83</span> };</div>
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<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span> </div>
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<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</span> std::cout << <span class="stringliteral">"Test 1.... "</span>;</div>
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<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"> 86</span> </div>
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<div class="line"><a id="l00087" name="l00087"></a><span class="lineno"> 87</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>
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<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"> 88</span> </div>
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<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span> std::cout << minima << <span class="stringliteral">"..."</span>;</div>
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<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"> 90</span> </div>
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<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"> 91</span> assert(std::abs(minima - 2) < EPSILON);</div>
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<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"> 92</span> std::cout << <span class="stringliteral">"passed\n"</span>;</div>
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<div class="line"><a id="l00093" name="l00093"></a><span class="lineno"> 93</span>}</div>
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</div>
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<div class="line"><a id="l00094" name="l00094"></a><span class="lineno"> 94</span></div>
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<div class="foldopen" id="foldopen00101" data-start="{" data-end="}">
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<div class="line"><a id="l00101" name="l00101"></a><span class="lineno"><a class="line" href="../../d6/d7a/golden__search__extrema_8cpp.html#a0283886819c7c140a023582b7269e2d0"> 101</a></span><span class="keywordtype">void</span> <a class="code hl_function" href="../../d6/d7a/golden__search__extrema_8cpp.html#a0283886819c7c140a023582b7269e2d0">test2</a>() {</div>
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<div class="line"><a id="l00102" name="l00102"></a><span class="lineno"> 102</span> <span class="comment">// define the function to maximize as a lambda function</span></div>
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<div class="line"><a id="l00103" name="l00103"></a><span class="lineno"> 103</span> <span class="comment">// since we are maximixing, we negated the function return value</span></div>
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<div class="line"><a id="l00104" name="l00104"></a><span class="lineno"> 104</span> std::function<double(<span class="keywordtype">double</span>)> func = [](<span class="keywordtype">double</span> x) {</div>
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<div class="line"><a id="l00105" name="l00105"></a><span class="lineno"> 105</span> <span class="keywordflow">return</span> -std::pow(x, 1.f / x);</div>
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<div class="line"><a id="l00106" name="l00106"></a><span class="lineno"> 106</span> };</div>
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<div class="line"><a id="l00107" name="l00107"></a><span class="lineno"> 107</span> </div>
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<div class="line"><a id="l00108" name="l00108"></a><span class="lineno"> 108</span> std::cout << <span class="stringliteral">"Test 2.... "</span>;</div>
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<div class="line"><a id="l00109" name="l00109"></a><span class="lineno"> 109</span> </div>
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<div class="line"><a id="l00110" name="l00110"></a><span class="lineno"> 110</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>
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<div class="line"><a id="l00111" name="l00111"></a><span class="lineno"> 111</span> </div>
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<div class="line"><a id="l00112" name="l00112"></a><span class="lineno"> 112</span> std::cout << minima << <span class="stringliteral">" ("</span> << M_E << <span class="stringliteral">")..."</span>;</div>
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<div class="line"><a id="l00113" name="l00113"></a><span class="lineno"> 113</span> </div>
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<div class="line"><a id="l00114" name="l00114"></a><span class="lineno"> 114</span> assert(std::abs(minima - M_E) < EPSILON);</div>
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<div class="line"><a id="l00115" name="l00115"></a><span class="lineno"> 115</span> std::cout << <span class="stringliteral">"passed\n"</span>;</div>
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<div class="line"><a id="l00116" name="l00116"></a><span class="lineno"> 116</span>}</div>
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</div>
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<div class="line"><a id="l00117" name="l00117"></a><span class="lineno"> 117</span></div>
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<div class="foldopen" id="foldopen00124" data-start="{" data-end="}">
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<div class="line"><a id="l00124" name="l00124"></a><span class="lineno"><a class="line" href="../../d6/d7a/golden__search__extrema_8cpp.html#a6d0455dd5c30adda100e95f0423c786e"> 124</a></span><span class="keywordtype">void</span> <a class="code hl_function" href="../../d6/d7a/golden__search__extrema_8cpp.html#a6d0455dd5c30adda100e95f0423c786e">test3</a>() {</div>
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<div class="line"><a id="l00125" name="l00125"></a><span class="lineno"> 125</span> <span class="comment">// define the function to maximize as a lambda function</span></div>
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<div class="line"><a id="l00126" name="l00126"></a><span class="lineno"> 126</span> <span class="comment">// since we are maximixing, we negated the function return value</span></div>
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<div class="line"><a id="l00127" name="l00127"></a><span class="lineno"> 127</span> std::function<double(<span class="keywordtype">double</span>)> func = [](<span class="keywordtype">double</span> x) { <span class="keywordflow">return</span> std::cos(x); };</div>
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<div class="line"><a id="l00128" name="l00128"></a><span class="lineno"> 128</span> </div>
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<div class="line"><a id="l00129" name="l00129"></a><span class="lineno"> 129</span> std::cout << <span class="stringliteral">"Test 3.... "</span>;</div>
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<div class="line"><a id="l00130" name="l00130"></a><span class="lineno"> 130</span> </div>
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<div class="line"><a id="l00131" name="l00131"></a><span class="lineno"> 131</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>
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<div class="line"><a id="l00132" name="l00132"></a><span class="lineno"> 132</span> </div>
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<div class="line"><a id="l00133" name="l00133"></a><span class="lineno"> 133</span> std::cout << minima << <span class="stringliteral">" ("</span> << M_PI << <span class="stringliteral">")..."</span>;</div>
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<div class="line"><a id="l00134" name="l00134"></a><span class="lineno"> 134</span> </div>
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<div class="line"><a id="l00135" name="l00135"></a><span class="lineno"> 135</span> assert(std::abs(minima - M_PI) < EPSILON);</div>
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<div class="line"><a id="l00136" name="l00136"></a><span class="lineno"> 136</span> std::cout << <span class="stringliteral">"passed\n"</span>;</div>
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<div class="line"><a id="l00137" name="l00137"></a><span class="lineno"> 137</span>}</div>
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</div>
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<div class="line"><a id="l00138" name="l00138"></a><span class="lineno"> 138</span></div>
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<div class="foldopen" id="foldopen00140" data-start="{" data-end="}">
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<div class="line"><a id="l00140" name="l00140"></a><span class="lineno"><a class="line" href="../../d6/d7a/golden__search__extrema_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4"> 140</a></span><span class="keywordtype">int</span> <a class="code hl_function" href="../../d6/d7a/golden__search__extrema_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a>() {</div>
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<div class="line"><a id="l00141" name="l00141"></a><span class="lineno"> 141</span> std::cout.precision(9);</div>
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<div class="line"><a id="l00142" name="l00142"></a><span class="lineno"> 142</span> </div>
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<div class="line"><a id="l00143" name="l00143"></a><span class="lineno"> 143</span> std::cout << <span class="stringliteral">"Computations performed with machine epsilon: "</span> << EPSILON</div>
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<div class="line"><a id="l00144" name="l00144"></a><span class="lineno"> 144</span> << <span class="stringliteral">"\n"</span>;</div>
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<div class="line"><a id="l00145" name="l00145"></a><span class="lineno"> 145</span> </div>
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<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#a1440a7779ac56f47a3f355ce4a8c7da0">test1</a>();</div>
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<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#a0283886819c7c140a023582b7269e2d0">test2</a>();</div>
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<div class="line"><a id="l00148" name="l00148"></a><span class="lineno"> 148</span> <a class="code hl_function" href="../../d6/d7a/golden__search__extrema_8cpp.html#a6d0455dd5c30adda100e95f0423c786e">test3</a>();</div>
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<div class="line"><a id="l00149" name="l00149"></a><span class="lineno"> 149</span> </div>
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<div class="line"><a id="l00150" name="l00150"></a><span class="lineno"> 150</span> <span class="keywordflow">return</span> 0;</div>
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<div class="line"><a id="l00151" name="l00151"></a><span class="lineno"> 151</span>}</div>
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</div>
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<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> <a href="#l00101">golden_search_extrema.cpp:101</a></div></div>
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<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> <a href="#l00079">golden_search_extrema.cpp:79</a></div></div>
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<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< double(double)> &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> <a href="#l00030">golden_search_extrema.cpp:30</a></div></div>
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<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> <a href="#l00124">golden_search_extrema.cpp:124</a></div></div>
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<div class="ttc" id="agolden__search__extrema_8cpp_html_ae66f6b31b5ad750f1fe042a706a4e3d4"><div class="ttname"><a href="../../d6/d7a/golden__search__extrema_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a></div><div class="ttdeci">int main()</div><div class="ttdef"><b>Definition</b> <a href="#l00140">golden_search_extrema.cpp:140</a></div></div>
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