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<div id="projectname">Templates -- Meow
 <span id="projectnumber">1.2.9</span>
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<div id="projectbrief">A C++ template contains kinds of interesting classes and functions</div>
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<div class="title">utility.h</div> </div>
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<a href="math_2utility_8h.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno"> 1</span> <span class="preprocessor">#ifndef math_utility_H__</span></div>
<div class="line"><a name="l00002"></a><span class="lineno"> 2</span> <span class="preprocessor"></span><span class="preprocessor">#define math_utility_H__</span></div>
<div class="line"><a name="l00003"></a><span class="lineno"> 3</span> <span class="preprocessor"></span></div>
<div class="line"><a name="l00004"></a><span class="lineno"> 4</span> <span class="preprocessor">#include <cstdlib></span></div>
<div class="line"><a name="l00005"></a><span class="lineno"> 5</span> <span class="preprocessor">#include <vector></span></div>
<div class="line"><a name="l00006"></a><span class="lineno"> 6</span> <span class="preprocessor">#include <algorithm></span></div>
<div class="line"><a name="l00007"></a><span class="lineno"> 7</span> <span class="preprocessor">#include <cmath></span></div>
<div class="line"><a name="l00008"></a><span class="lineno"> 8</span> </div>
<div class="line"><a name="l00009"></a><span class="lineno"> 9</span> <span class="keyword">namespace </span>meow {</div>
<div class="line"><a name="l00010"></a><span class="lineno"> 10</span> </div>
<div class="line"><a name="l00012"></a><span class="lineno"><a class="line" href="namespacemeow.html#aa86d5920087a4e73078b759bc3996f76"> 12</a></span> <span class="keyword">static</span> <span class="keyword">const</span> <span class="keywordtype">double</span> <a class="code" href="namespacemeow.html#aa86d5920087a4e73078b759bc3996f76">PI</a> = 3.14159265358979323846264338327950288;</div>
<div class="line"><a name="l00013"></a><span class="lineno"> 13</span> </div>
<div class="line"><a name="l00017"></a><span class="lineno"> 17</span> <span class="keyword">template</span><<span class="keyword">class</span> T></div>
<div class="line"><a name="l00018"></a><span class="lineno"><a class="line" href="namespacemeow.html#ab9456533c0ae85fba812bfb5b017c8d2"> 18</a></span> <span class="keyword">inline</span> T <a class="code" href="namespacemeow.html#ab9456533c0ae85fba812bfb5b017c8d2">noEPS</a>(T value, T eps = 1e-9) {</div>
<div class="line"><a name="l00019"></a><span class="lineno"> 19</span>  T epsp((eps < T(0)) ? -eps : eps);</div>
<div class="line"><a name="l00020"></a><span class="lineno"> 20</span>  <span class="keywordflow">return</span> ((value < -epsp || value > epsp) ? value : T(0));</div>
<div class="line"><a name="l00021"></a><span class="lineno"> 21</span> }</div>
<div class="line"><a name="l00022"></a><span class="lineno"> 22</span> </div>
<div class="line"><a name="l00026"></a><span class="lineno"> 26</span> <span class="keyword">template</span><<span class="keyword">class</span> T></div>
<div class="line"><a name="l00027"></a><span class="lineno"><a class="line" href="namespacemeow.html#aebe1ad335556790c578c4cf7836fd9ca"> 27</a></span> <span class="keyword">inline</span> T <a class="code" href="namespacemeow.html#aebe1ad335556790c578c4cf7836fd9ca">normalize</a>(T lower, T upper, T value) {</div>
<div class="line"><a name="l00028"></a><span class="lineno"> 28</span>  <span class="keywordflow">return</span> (value - lower) / (upper - lower);</div>
<div class="line"><a name="l00029"></a><span class="lineno"> 29</span> }</div>
<div class="line"><a name="l00030"></a><span class="lineno"> 30</span> </div>
<div class="line"><a name="l00034"></a><span class="lineno"> 34</span> <span class="keyword">template</span><<span class="keyword">class</span> T></div>
<div class="line"><a name="l00035"></a><span class="lineno"><a class="line" href="namespacemeow.html#af95cfca15ad7a51ed4d07b06e1296080"> 35</a></span> <span class="keyword">inline</span> T <a class="code" href="namespacemeow.html#af95cfca15ad7a51ed4d07b06e1296080">denormalize</a>(T lower, T upper, T _ratio) {</div>
<div class="line"><a name="l00036"></a><span class="lineno"> 36</span>  <span class="keywordflow">return</span> lower + _ratio * (upper - lower);</div>
<div class="line"><a name="l00037"></a><span class="lineno"> 37</span> }</div>
<div class="line"><a name="l00038"></a><span class="lineno"> 38</span> </div>
<div class="line"><a name="l00042"></a><span class="lineno"> 42</span> <span class="keyword">template</span><<span class="keyword">class</span> T></div>
<div class="line"><a name="l00043"></a><span class="lineno"><a class="line" href="namespacemeow.html#a3b01a91eb4a02909a61a35e406fa5732"> 43</a></span> <span class="keyword">inline</span> T <a class="code" href="namespacemeow.html#a3b01a91eb4a02909a61a35e406fa5732">ratioMapping</a>(T l1, T u1, T m1, T l2, T u2) {</div>
<div class="line"><a name="l00044"></a><span class="lineno"> 44</span>  <span class="keywordflow">return</span> <a class="code" href="namespacemeow.html#af95cfca15ad7a51ed4d07b06e1296080">denormalize</a>(l2, u2, <a class="code" href="namespacemeow.html#aebe1ad335556790c578c4cf7836fd9ca">normalize</a>(l1, u1, m1));</div>
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span> }</div>
<div class="line"><a name="l00046"></a><span class="lineno"> 46</span> </div>
<div class="line"><a name="l00050"></a><span class="lineno"> 50</span> <span class="keyword">template</span><<span class="keyword">class</span> T></div>
<div class="line"><a name="l00051"></a><span class="lineno"><a class="line" href="namespacemeow.html#a98d838d338a3e6f3c57e94562fab3fa7"> 51</a></span> <span class="keyword">inline</span> T <a class="code" href="namespacemeow.html#a98d838d338a3e6f3c57e94562fab3fa7">inRange</a>(T <span class="keyword">const</span>& mn, T <span class="keyword">const</span>& mx, T <span class="keyword">const</span>& v) {</div>
<div class="line"><a name="l00052"></a><span class="lineno"> 52</span>  <span class="keywordflow">return</span> std::min(mx, std::max(mn, v));</div>
<div class="line"><a name="l00053"></a><span class="lineno"> 53</span> }</div>
<div class="line"><a name="l00054"></a><span class="lineno"> 54</span> </div>
<div class="line"><a name="l00058"></a><span class="lineno"> 58</span> <span class="keyword">template</span><<span class="keyword">class</span> T></div>
<div class="line"><a name="l00059"></a><span class="lineno"><a class="line" href="namespacemeow.html#ae8486a6227b6ed69d5ff666fe67ebf4e"> 59</a></span> <span class="keyword">inline</span> T <a class="code" href="namespacemeow.html#ae8486a6227b6ed69d5ff666fe67ebf4e">isInRange</a>(T <span class="keyword">const</span>& mn, T <span class="keyword">const</span>& mx, T <span class="keyword">const</span>& x) {</div>
<div class="line"><a name="l00060"></a><span class="lineno"> 60</span>  <span class="keywordflow">return</span> (mn <= x && x <= mx);</div>
<div class="line"><a name="l00061"></a><span class="lineno"> 61</span> }</div>
<div class="line"><a name="l00062"></a><span class="lineno"> 62</span> </div>
<div class="line"><a name="l00066"></a><span class="lineno"> 66</span> <span class="keyword">template</span><<span class="keyword">class</span> T></div>
<div class="line"><a name="l00067"></a><span class="lineno"><a class="line" href="namespacemeow.html#a1954e235973a2ac79a7a72a4b7d25573"> 67</a></span> <span class="keyword">inline</span> T <a class="code" href="namespacemeow.html#a1954e235973a2ac79a7a72a4b7d25573">squ</a>(T <span class="keyword">const</span>& x) {</div>
<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>  <span class="keywordflow">return</span> x * x;</div>
<div class="line"><a name="l00069"></a><span class="lineno"> 69</span> }</div>
<div class="line"><a name="l00070"></a><span class="lineno"> 70</span> </div>
<div class="line"><a name="l00074"></a><span class="lineno"> 74</span> <span class="keyword">template</span><<span class="keyword">class</span> T></div>
<div class="line"><a name="l00075"></a><span class="lineno"><a class="line" href="namespacemeow.html#a10a8cca705773b7d9f6f91d3fb08c104"> 75</a></span> <span class="keyword">inline</span> T <a class="code" href="namespacemeow.html#a10a8cca705773b7d9f6f91d3fb08c104">cub</a>(T <span class="keyword">const</span>& x) {</div>
<div class="line"><a name="l00076"></a><span class="lineno"> 76</span>  <span class="keywordflow">return</span> x * x * x;</div>
<div class="line"><a name="l00077"></a><span class="lineno"> 77</span> }</div>
<div class="line"><a name="l00078"></a><span class="lineno"> 78</span> </div>
<div class="line"><a name="l00082"></a><span class="lineno"> 82</span> <span class="keyword">template</span><<span class="keyword">class</span> T></div>
<div class="line"><a name="l00083"></a><span class="lineno"><a class="line" href="namespacemeow.html#ad4d1e5fa951e5534204a0ee3eee22777"> 83</a></span> <span class="keyword">inline</span> <span class="keywordtype">double</span> <a class="code" href="namespacemeow.html#ad4d1e5fa951e5534204a0ee3eee22777">average</a>(T <span class="keyword">const</span>& beg, T <span class="keyword">const</span>& end, <span class="keywordtype">double</span> sigs) {</div>
<div class="line"><a name="l00084"></a><span class="lineno"> 84</span>  <span class="keywordtype">int</span> N = 0;</div>
<div class="line"><a name="l00085"></a><span class="lineno"> 85</span>  <span class="keywordtype">double</span> av = 0;</div>
<div class="line"><a name="l00086"></a><span class="lineno"> 86</span>  <span class="keywordflow">for</span> (T it = beg; it != end; ++it, ++N) {</div>
<div class="line"><a name="l00087"></a><span class="lineno"> 87</span>  av += *it;</div>
<div class="line"><a name="l00088"></a><span class="lineno"> 88</span>  }</div>
<div class="line"><a name="l00089"></a><span class="lineno"> 89</span>  av /= N;</div>
<div class="line"><a name="l00090"></a><span class="lineno"> 90</span>  <span class="keywordtype">double</span> sig = 0;</div>
<div class="line"><a name="l00091"></a><span class="lineno"> 91</span>  <span class="keywordflow">for</span> (T it = beg; it != end; ++it) {</div>
<div class="line"><a name="l00092"></a><span class="lineno"> 92</span>  sig += (*it - av) * (*it - av);</div>
<div class="line"><a name="l00093"></a><span class="lineno"> 93</span>  }</div>
<div class="line"><a name="l00094"></a><span class="lineno"> 94</span>  sig = sqrt(sig / N);</div>
<div class="line"><a name="l00095"></a><span class="lineno"> 95</span>  <span class="keywordtype">double</span> lower = av - sig * sigs, upper = av + sig * sigs;</div>
<div class="line"><a name="l00096"></a><span class="lineno"> 96</span>  <span class="keywordtype">double</span> ret = 0, retn = 0;</div>
<div class="line"><a name="l00097"></a><span class="lineno"> 97</span>  <span class="keywordflow">for</span> (T it = beg; it != end; ++it) {</div>
<div class="line"><a name="l00098"></a><span class="lineno"> 98</span>  <span class="keywordflow">if</span> (lower <= *it && *it <= upper) {</div>
<div class="line"><a name="l00099"></a><span class="lineno"> 99</span>  ret += *it;</div>
<div class="line"><a name="l00100"></a><span class="lineno"> 100</span>  retn++;</div>
<div class="line"><a name="l00101"></a><span class="lineno"> 101</span>  }</div>
<div class="line"><a name="l00102"></a><span class="lineno"> 102</span>  }</div>
<div class="line"><a name="l00103"></a><span class="lineno"> 103</span>  <span class="keywordflow">return</span> ret / retn;</div>
<div class="line"><a name="l00104"></a><span class="lineno"> 104</span> }</div>
<div class="line"><a name="l00105"></a><span class="lineno"> 105</span> </div>
<div class="line"><a name="l00109"></a><span class="lineno"> 109</span> <span class="keyword">template</span><<span class="keyword">class</span> T></div>
<div class="line"><a name="l00110"></a><span class="lineno"><a class="line" href="namespacemeow.html#a6ae78e60d507c85de003f8fa8423b650"> 110</a></span> <span class="keyword">inline</span> <span class="keywordtype">double</span> <a class="code" href="namespacemeow.html#ad4d1e5fa951e5534204a0ee3eee22777">average</a>(T <span class="keyword">const</span>& beg, T <span class="keyword">const</span>& end, T <span class="keyword">const</span>& p, <span class="keywordtype">double</span> sigs) {</div>
<div class="line"><a name="l00111"></a><span class="lineno"> 111</span>  <span class="keywordtype">int</span> N = 0;</div>
<div class="line"><a name="l00112"></a><span class="lineno"> 112</span>  <span class="keywordtype">double</span> ps = 0;</div>
<div class="line"><a name="l00113"></a><span class="lineno"> 113</span>  <span class="keywordflow">for</span> (T it = beg, ip = p; it != end; ++it, ++N, ++ip) {</div>
<div class="line"><a name="l00114"></a><span class="lineno"> 114</span>  ps += *ip;</div>
<div class="line"><a name="l00115"></a><span class="lineno"> 115</span>  }</div>
<div class="line"><a name="l00116"></a><span class="lineno"> 116</span>  <span class="keywordtype">double</span> av = 0;</div>
<div class="line"><a name="l00117"></a><span class="lineno"> 117</span>  <span class="keywordflow">for</span> (T it = beg, ip = p; it != end; ++it, ++ip) {</div>
<div class="line"><a name="l00118"></a><span class="lineno"> 118</span>  av += *it * *ip / ps;</div>
<div class="line"><a name="l00119"></a><span class="lineno"> 119</span>  }</div>
<div class="line"><a name="l00120"></a><span class="lineno"> 120</span>  <span class="keywordtype">double</span> sig = 0;</div>
<div class="line"><a name="l00121"></a><span class="lineno"> 121</span>  <span class="keywordflow">for</span> (T it = beg, ip = p; it != end; ++it, ++ip) {</div>
<div class="line"><a name="l00122"></a><span class="lineno"> 122</span>  sig += *ip / ps * (*it - av) * (*it - av);</div>
<div class="line"><a name="l00123"></a><span class="lineno"> 123</span>  }</div>
<div class="line"><a name="l00124"></a><span class="lineno"> 124</span>  sig = sqrt(sig);</div>
<div class="line"><a name="l00125"></a><span class="lineno"> 125</span>  <span class="keywordtype">double</span> lower = av - sig * sigs, upper = av + sig * sigs;</div>
<div class="line"><a name="l00126"></a><span class="lineno"> 126</span>  <span class="keywordtype">double</span> ret = 0, retn = 0;</div>
<div class="line"><a name="l00127"></a><span class="lineno"> 127</span>  <span class="keywordflow">for</span> (T it = beg, ip = p; it != end; ++it, ++ip) {</div>
<div class="line"><a name="l00128"></a><span class="lineno"> 128</span>  <span class="keywordflow">if</span> (lower <= *it && *it <= upper) {</div>
<div class="line"><a name="l00129"></a><span class="lineno"> 129</span>  ret += *it * *ip;</div>
<div class="line"><a name="l00130"></a><span class="lineno"> 130</span>  retn += *ip;</div>
<div class="line"><a name="l00131"></a><span class="lineno"> 131</span>  }</div>
<div class="line"><a name="l00132"></a><span class="lineno"> 132</span>  }</div>
<div class="line"><a name="l00133"></a><span class="lineno"> 133</span>  <span class="keywordflow">if</span> (retn <= 1e-10) <span class="keywordflow">return</span> av;</div>
<div class="line"><a name="l00134"></a><span class="lineno"> 134</span>  <span class="keywordflow">return</span> ret / retn;</div>
<div class="line"><a name="l00135"></a><span class="lineno"> 135</span> }</div>
<div class="line"><a name="l00136"></a><span class="lineno"> 136</span> </div>
<div class="line"><a name="l00140"></a><span class="lineno"> 140</span> <span class="keyword">template</span><<span class="keyword">class</span> T></div>
<div class="line"><a name="l00141"></a><span class="lineno"><a class="line" href="namespacemeow.html#ae880337dfdcc67984a0dccdb50e5c5d0"> 141</a></span> <span class="keyword">inline</span> T <a class="code" href="namespacemeow.html#ae880337dfdcc67984a0dccdb50e5c5d0">tAbs</a>(T <span class="keyword">const</span>& t) {</div>
<div class="line"><a name="l00142"></a><span class="lineno"> 142</span>  <span class="keywordflow">return</span> (t < 0 ? -t : t);</div>
<div class="line"><a name="l00143"></a><span class="lineno"> 143</span> }</div>
<div class="line"><a name="l00144"></a><span class="lineno"> 144</span> </div>
<div class="line"><a name="l00145"></a><span class="lineno"> 145</span> } <span class="comment">// meow</span></div>
<div class="line"><a name="l00146"></a><span class="lineno"> 146</span> </div>
<div class="line"><a name="l00147"></a><span class="lineno"> 147</span> <span class="preprocessor">#endif // math_utility_H__</span></div>
<div class="ttc" id="namespacemeow_html_aebe1ad335556790c578c4cf7836fd9ca"><div class="ttname"><a href="namespacemeow.html#aebe1ad335556790c578c4cf7836fd9ca">meow::normalize</a></div><div class="ttdeci">T normalize(T lower, T upper, T value)</div><div class="ttdoc">(value-lower)/(upper-lower) </div><div class="ttdef"><b>Definition:</b> <a href="math_2utility_8h_source.html#l00027">utility.h:27</a></div></div>
<div class="ttc" id="namespacemeow_html_ae8486a6227b6ed69d5ff666fe67ebf4e"><div class="ttname"><a href="namespacemeow.html#ae8486a6227b6ed69d5ff666fe67ebf4e">meow::isInRange</a></div><div class="ttdeci">T isInRange(T const &mn, T const &mx, T const &x)</div><div class="ttdoc">(mn <= x && x <= mx) </div><div class="ttdef"><b>Definition:</b> <a href="math_2utility_8h_source.html#l00059">utility.h:59</a></div></div>
<div class="ttc" id="namespacemeow_html_a3b01a91eb4a02909a61a35e406fa5732"><div class="ttname"><a href="namespacemeow.html#a3b01a91eb4a02909a61a35e406fa5732">meow::ratioMapping</a></div><div class="ttdeci">T ratioMapping(T l1, T u1, T m1, T l2, T u2)</div><div class="ttdoc">denormalize(l2,u2,normalize(l1,u1,m1)) </div><div class="ttdef"><b>Definition:</b> <a href="math_2utility_8h_source.html#l00043">utility.h:43</a></div></div>
<div class="ttc" id="namespacemeow_html_af95cfca15ad7a51ed4d07b06e1296080"><div class="ttname"><a href="namespacemeow.html#af95cfca15ad7a51ed4d07b06e1296080">meow::denormalize</a></div><div class="ttdeci">T denormalize(T lower, T upper, T _ratio)</div><div class="ttdoc">(lower+_ratio*(upper-lower)) </div><div class="ttdef"><b>Definition:</b> <a href="math_2utility_8h_source.html#l00035">utility.h:35</a></div></div>
<div class="ttc" id="namespacemeow_html_ab9456533c0ae85fba812bfb5b017c8d2"><div class="ttname"><a href="namespacemeow.html#ab9456533c0ae85fba812bfb5b017c8d2">meow::noEPS</a></div><div class="ttdeci">T noEPS(T value, T eps=1e-9)</div><div class="ttdoc">如果abs(輸入的數值) < eps, 則回傳0, 否則回傳輸入的數值 </div><div class="ttdef"><b>Definition:</b> <a href="math_2utility_8h_source.html#l00018">utility.h:18</a></div></div>
<div class="ttc" id="namespacemeow_html_ad4d1e5fa951e5534204a0ee3eee22777"><div class="ttname"><a href="namespacemeow.html#ad4d1e5fa951e5534204a0ee3eee22777">meow::average</a></div><div class="ttdeci">double average(T const &beg, T const &end, double sigs)</div><div class="ttdoc">只將 sigs 個標準差以內的數據拿來取平均 </div><div class="ttdef"><b>Definition:</b> <a href="math_2utility_8h_source.html#l00083">utility.h:83</a></div></div>
<div class="ttc" id="namespacemeow_html_ae880337dfdcc67984a0dccdb50e5c5d0"><div class="ttname"><a href="namespacemeow.html#ae880337dfdcc67984a0dccdb50e5c5d0">meow::tAbs</a></div><div class="ttdeci">T tAbs(T const &t)</div><div class="ttdoc">就只是個取絕對值 </div><div class="ttdef"><b>Definition:</b> <a href="math_2utility_8h_source.html#l00141">utility.h:141</a></div></div>
<div class="ttc" id="namespacemeow_html_a98d838d338a3e6f3c57e94562fab3fa7"><div class="ttname"><a href="namespacemeow.html#a98d838d338a3e6f3c57e94562fab3fa7">meow::inRange</a></div><div class="ttdeci">T inRange(T const &mn, T const &mx, T const &v)</div><div class="ttdoc">std::min(mx,std::max(mn,v)) </div><div class="ttdef"><b>Definition:</b> <a href="math_2utility_8h_source.html#l00051">utility.h:51</a></div></div>
<div class="ttc" id="namespacemeow_html_a10a8cca705773b7d9f6f91d3fb08c104"><div class="ttname"><a href="namespacemeow.html#a10a8cca705773b7d9f6f91d3fb08c104">meow::cub</a></div><div class="ttdeci">T cub(T const &x)</div><div class="ttdoc">x*x*x </div><div class="ttdef"><b>Definition:</b> <a href="math_2utility_8h_source.html#l00075">utility.h:75</a></div></div>
<div class="ttc" id="namespacemeow_html_aa86d5920087a4e73078b759bc3996f76"><div class="ttname"><a href="namespacemeow.html#aa86d5920087a4e73078b759bc3996f76">meow::PI</a></div><div class="ttdeci">static const double PI</div><div class="ttdoc">圓周率... </div><div class="ttdef"><b>Definition:</b> <a href="math_2utility_8h_source.html#l00012">utility.h:12</a></div></div>
<div class="ttc" id="namespacemeow_html_a1954e235973a2ac79a7a72a4b7d25573"><div class="ttname"><a href="namespacemeow.html#a1954e235973a2ac79a7a72a4b7d25573">meow::squ</a></div><div class="ttdeci">T squ(T const &x)</div><div class="ttdoc">x*x </div><div class="ttdef"><b>Definition:</b> <a href="math_2utility_8h_source.html#l00067">utility.h:67</a></div></div>
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