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<h1>Erfc.cxx</h1><a href="Erfc_8cxx.html">Go to the documentation of this file.</a><div class="fragment"><pre class="fragment"><a name="l00001"></a>00001
<a name="l00013"></a>00013 <span class="preprocessor">#ifdef _MSC_VER</span>
<a name="l00014"></a>00014 <span class="preprocessor"></span><span class="preprocessor">#include "msdevstudio/MSconfig.h"</span>
<a name="l00015"></a>00015 <span class="preprocessor">#endif</span>
<a name="l00016"></a>00016 <span class="preprocessor"></span>
<a name="l00017"></a>00017 <span class="preprocessor">#include "<a class="code" href="Erfc_8h.html" title="Complementary Error function class interface (hippodraw::Erfc).">Erfc.h</a>"</span>
<a name="l00018"></a>00018 <span class="preprocessor">#include "<a class="code" href="FunctionHelper_8h.html" title="FunctionHelper class interface.">FunctionHelper.h</a>"</span>
<a name="l00019"></a>00019
<a name="l00020"></a>00020 <span class="preprocessor">#include <cmath></span>
<a name="l00021"></a>00021
<a name="l00022"></a>00022 <span class="preprocessor">#include <cassert></span>
<a name="l00023"></a>00023
<a name="l00024"></a>00024 <span class="preprocessor">#ifdef ITERATOR_MEMBER_DEFECT</span>
<a name="l00025"></a>00025 <span class="preprocessor"></span><span class="keyword">using namespace </span>std;
<a name="l00026"></a>00026 <span class="preprocessor">#else</span>
<a name="l00027"></a>00027 <span class="preprocessor"></span><span class="keyword">using</span> std::exp;
<a name="l00028"></a>00028 <span class="keyword">using</span> std::vector;
<a name="l00029"></a>00029 <span class="preprocessor">#endif</span>
<a name="l00030"></a>00030 <span class="preprocessor"></span>
<a name="l00031"></a>00031 <span class="keyword">namespace </span>hippodraw {
<a name="l00032"></a>00032
<a name="l00033"></a><a class="code" href="classhippodraw_1_1Erfc.html#a9874bc6728d450243a5aa6415aea6094">00033</a> <a class="code" href="classhippodraw_1_1Erfc.html#a9874bc6728d450243a5aa6415aea6094" title="The default constructor.">Erfc::Erfc</a> ( )
<a name="l00034"></a>00034 {
<a name="l00035"></a>00035 <a class="code" href="classhippodraw_1_1Erfc.html#a25a40b6614565f755233080a384c35f1" title="Initializes the function and parameter names.">initialize</a> ();
<a name="l00036"></a>00036 }
<a name="l00037"></a>00037
<a name="l00038"></a><a class="code" href="classhippodraw_1_1Erfc.html#a9cd618279a0ba2e0f1828a662d6a38dd">00038</a> <a class="code" href="classhippodraw_1_1Erfc.html#a9874bc6728d450243a5aa6415aea6094" title="The default constructor.">Erfc::Erfc</a>(<span class="keywordtype">double</span> m, <span class="keywordtype">double</span> s, <span class="keywordtype">double</span> n)
<a name="l00039"></a>00039 {
<a name="l00040"></a>00040 <a class="code" href="classhippodraw_1_1Erfc.html#a25a40b6614565f755233080a384c35f1" title="Initializes the function and parameter names.">initialize</a>();
<a name="l00041"></a>00041
<a name="l00042"></a>00042 <a class="code" href="classhippodraw_1_1FunctionBase.html#aa892dcf9755ccd651b666f353b723c34" title="The parameter values.">m_parms</a>[<a class="code" href="classhippodraw_1_1Erfc.html#a06fc87d81c62e9abb8790b6e5713c55bab8037c675dad16b9139e24e000143c78">MEAN</a>] = m;
<a name="l00043"></a>00043 <a class="code" href="classhippodraw_1_1FunctionBase.html#aa892dcf9755ccd651b666f353b723c34" title="The parameter values.">m_parms</a>[<a class="code" href="classhippodraw_1_1Erfc.html#a06fc87d81c62e9abb8790b6e5713c55bad3071ccb5d54bbadcd61b726d215b10f">SIGMA</a>] = s;
<a name="l00044"></a>00044 <a class="code" href="classhippodraw_1_1FunctionBase.html#aa892dcf9755ccd651b666f353b723c34" title="The parameter values.">m_parms</a>[<a class="code" href="classhippodraw_1_1Erfc.html#a06fc87d81c62e9abb8790b6e5713c55bae003ec1158e3a4e295616ced12af154e">NORM</a>] = n;
<a name="l00045"></a>00045 }
<a name="l00046"></a>00046
<a name="l00047"></a><a class="code" href="classhippodraw_1_1Erfc.html#a25a40b6614565f755233080a384c35f1">00047</a> <span class="keywordtype">void</span> <a class="code" href="classhippodraw_1_1Erfc.html#a25a40b6614565f755233080a384c35f1" title="Initializes the function and parameter names.">Erfc::initialize</a> ()
<a name="l00048"></a>00048 {
<a name="l00049"></a>00049 <a class="code" href="classhippodraw_1_1FunctionBase.html#adb41893ba19e889e56c559f25fc1a68a" title="The name of the function.">m_name</a> = <span class="stringliteral">"Erfc"</span>;
<a name="l00050"></a>00050
<a name="l00051"></a>00051 <a class="code" href="classhippodraw_1_1FunctionBase.html#a96bf64e362e48f2ad4ecd76c32e4bc54" title="The names of the function parameters.">m_parm_names</a>.push_back ( <span class="stringliteral">"Mean"</span> );
<a name="l00052"></a>00052 <a class="code" href="classhippodraw_1_1FunctionBase.html#a96bf64e362e48f2ad4ecd76c32e4bc54" title="The names of the function parameters.">m_parm_names</a>.push_back ( <span class="stringliteral">"Sigma"</span> );
<a name="l00053"></a>00053 <a class="code" href="classhippodraw_1_1FunctionBase.html#a96bf64e362e48f2ad4ecd76c32e4bc54" title="The names of the function parameters.">m_parm_names</a>.push_back ( <span class="stringliteral">"Normalization"</span> );
<a name="l00054"></a>00054
<a name="l00055"></a>00055 <a class="code" href="classhippodraw_1_1FunctionBase.html#a0fc3d585aa53859602ac79c9c421f2a9" title="Re-sizes the appropriate vectors maintained in this base class.">resize</a> ();
<a name="l00056"></a>00056 }
<a name="l00057"></a>00057
<a name="l00058"></a><a class="code" href="classhippodraw_1_1Erfc.html#a5e4b003c4faa8b7729e762445c7578d8">00058</a> <a class="code" href="classhippodraw_1_1FunctionBase.html" title="A function that can be added to a DataRep and used in a fitter.">FunctionBase</a> * <a class="code" href="classhippodraw_1_1Erfc.html#a5e4b003c4faa8b7729e762445c7578d8" title="Creates a new function object by copying an existing one.">Erfc::clone</a> ()<span class="keyword"> const</span>
<a name="l00059"></a>00059 <span class="keyword"></span>{
<a name="l00060"></a>00060 <span class="keywordflow">return</span> <span class="keyword">new</span> <a class="code" href="classhippodraw_1_1Erfc.html#a9874bc6728d450243a5aa6415aea6094" title="The default constructor.">Erfc</a> ( *<span class="keyword">this</span> );
<a name="l00061"></a>00061 }
<a name="l00062"></a>00062
<a name="l00065"></a>00065 <span class="keywordtype">double</span> <a class="code" href="classhippodraw_1_1Erfc.html#a35b6d3300fa7025c7a1f54d1c7fe6013" title="The function call operator.">Erfc::operator () </a>(<span class="keywordtype">double</span> value)<span class="keyword"> const</span>
<a name="l00066"></a>00066 <span class="keyword"></span>{
<a name="l00067"></a>00067 <span class="keywordtype">double</span> result = 1; <span class="comment">// The return value</span>
<a name="l00068"></a>00068
<a name="l00069"></a>00069 <span class="keywordtype">double</span> x = <a class="code" href="classhippodraw_1_1Erfc.html#a5610f1b8c5396e3b3a5216896d6a28e4" title="compute the reduced variable: ">calcRed</a>(value); <span class="comment">//reduced variable</span>
<a name="l00070"></a>00070
<a name="l00071"></a>00071 result = <a class="code" href="classhippodraw_1_1Erfc.html#a672080a40f7ea4f7eb92bbc053e69711">calcErfc</a>(x); <span class="comment">//this method is a copy of ROOT method in TMath.cxx</span>
<a name="l00072"></a>00072
<a name="l00073"></a>00073 result *= <a class="code" href="classhippodraw_1_1FunctionBase.html#aa892dcf9755ccd651b666f353b723c34" title="The parameter values.">m_parms</a>[<a class="code" href="classhippodraw_1_1Erfc.html#a06fc87d81c62e9abb8790b6e5713c55bae003ec1158e3a4e295616ced12af154e">NORM</a>];
<a name="l00074"></a>00074
<a name="l00075"></a>00075 <span class="keywordflow">return</span> result;
<a name="l00076"></a>00076 }
<a name="l00077"></a>00077
<a name="l00078"></a>00078
<a name="l00079"></a>00079 <span class="comment">/* virtual */</span>
<a name="l00080"></a><a class="code" href="classhippodraw_1_1Erfc.html#ac89ece7f0010b352e8d897f0a352f811">00080</a> <span class="keywordtype">void</span> <a class="code" href="classhippodraw_1_1Erfc.html#ac89ece7f0010b352e8d897f0a352f811" title="returns Erfc computed at the reduced variable double Erfc::operator () (double value)...">Erfc::initialParameters</a> ( <span class="keyword">const</span> <a class="code" href="classhippodraw_1_1FunctionHelper.html" title="An abstract base class to help FunctionBase objects perform some operations.">FunctionHelper</a> * helper )
<a name="l00081"></a>00081 {
<a name="l00082"></a>00082 <a class="code" href="classhippodraw_1_1FunctionBase.html#aa892dcf9755ccd651b666f353b723c34" title="The parameter values.">m_parms</a>[<a class="code" href="classhippodraw_1_1Erfc.html#a06fc87d81c62e9abb8790b6e5713c55bab8037c675dad16b9139e24e000143c78">MEAN</a>] = helper-><a class="code" href="classhippodraw_1_1FunctionHelper.html#a1402e98aa11796bfa8a52d5b8f4fc37b" title="Returns the mean of the coordinates along a X axis in the data set.">meanCoord</a>();
<a name="l00083"></a>00083 <a class="code" href="classhippodraw_1_1FunctionBase.html#aa892dcf9755ccd651b666f353b723c34" title="The parameter values.">m_parms</a>[<a class="code" href="classhippodraw_1_1Erfc.html#a06fc87d81c62e9abb8790b6e5713c55bad3071ccb5d54bbadcd61b726d215b10f">SIGMA</a>] = 1;
<a name="l00084"></a>00084 <a class="code" href="classhippodraw_1_1FunctionBase.html#aa892dcf9755ccd651b666f353b723c34" title="The parameter values.">m_parms</a>[<a class="code" href="classhippodraw_1_1Erfc.html#a06fc87d81c62e9abb8790b6e5713c55bae003ec1158e3a4e295616ced12af154e">NORM</a>] = helper-><a class="code" href="classhippodraw_1_1FunctionHelper.html#a2be3e090b19415ac06d8388b5fc91fe2" title="Returns the largest value in the data set.">maxValue</a> () / 2;
<a name="l00085"></a>00085 }
<a name="l00086"></a>00086
<a name="l00087"></a>00087
<a name="l00088"></a><a class="code" href="classhippodraw_1_1Erfc.html#a8617a1aa7536e4cb61f2a4ec29a39f36">00088</a> <span class="keywordtype">double</span> <a class="code" href="classhippodraw_1_1Erfc.html#a8617a1aa7536e4cb61f2a4ec29a39f36" title="Returns the function&#39;s derivative at the coordinate value x with respect to the...">Erfc::derivByParm</a> ( <span class="keywordtype">int</span> i, <span class="keywordtype">double</span> value )<span class="keyword"> const</span>
<a name="l00089"></a>00089 <span class="keyword"></span>{
<a name="l00090"></a>00090 <span class="keywordtype">double</span> result = 0;
<a name="l00091"></a>00091
<a name="l00092"></a>00092 <span class="keywordflow">switch</span> ( i ) {
<a name="l00093"></a>00093 <span class="keywordflow">case</span> <a class="code" href="classhippodraw_1_1Erfc.html#a06fc87d81c62e9abb8790b6e5713c55bab8037c675dad16b9139e24e000143c78">MEAN</a> :
<a name="l00094"></a>00094 result = -1.0/<a class="code" href="classhippodraw_1_1FunctionBase.html#aa892dcf9755ccd651b666f353b723c34" title="The parameter values.">m_parms</a>[<a class="code" href="classhippodraw_1_1Erfc.html#a06fc87d81c62e9abb8790b6e5713c55bad3071ccb5d54bbadcd61b726d215b10f">SIGMA</a>] * <a class="code" href="classhippodraw_1_1FunctionBase.html#aa892dcf9755ccd651b666f353b723c34" title="The parameter values.">m_parms</a>[<a class="code" href="classhippodraw_1_1Erfc.html#a06fc87d81c62e9abb8790b6e5713c55bae003ec1158e3a4e295616ced12af154e">NORM</a>] * <a class="code" href="classhippodraw_1_1Erfc.html#accdd20961098ca1dbef1e36ab56d9853">derivByRed</a> ( <a class="code" href="classhippodraw_1_1Erfc.html#a5610f1b8c5396e3b3a5216896d6a28e4" title="compute the reduced variable: ">calcRed</a>(value) );
<a name="l00095"></a>00095 <span class="keywordflow">return</span> result;
<a name="l00096"></a>00096 <span class="keywordflow">break</span>;
<a name="l00097"></a>00097
<a name="l00098"></a>00098 <span class="keywordflow">case</span> <a class="code" href="classhippodraw_1_1Erfc.html#a06fc87d81c62e9abb8790b6e5713c55bad3071ccb5d54bbadcd61b726d215b10f">SIGMA</a> :
<a name="l00099"></a>00099 result = - <a class="code" href="classhippodraw_1_1Erfc.html#a5610f1b8c5396e3b3a5216896d6a28e4" title="compute the reduced variable: ">calcRed</a>(value)/<a class="code" href="classhippodraw_1_1FunctionBase.html#aa892dcf9755ccd651b666f353b723c34" title="The parameter values.">m_parms</a>[<a class="code" href="classhippodraw_1_1Erfc.html#a06fc87d81c62e9abb8790b6e5713c55bad3071ccb5d54bbadcd61b726d215b10f">SIGMA</a>] * <a class="code" href="classhippodraw_1_1FunctionBase.html#aa892dcf9755ccd651b666f353b723c34" title="The parameter values.">m_parms</a>[<a class="code" href="classhippodraw_1_1Erfc.html#a06fc87d81c62e9abb8790b6e5713c55bae003ec1158e3a4e295616ced12af154e">NORM</a>] * <a class="code" href="classhippodraw_1_1Erfc.html#accdd20961098ca1dbef1e36ab56d9853">derivByRed</a> ( <a class="code" href="classhippodraw_1_1Erfc.html#a5610f1b8c5396e3b3a5216896d6a28e4" title="compute the reduced variable: ">calcRed</a>(value) );
<a name="l00100"></a>00100 <span class="keywordflow">return</span> result;
<a name="l00101"></a>00101 <span class="keywordflow">break</span>;
<a name="l00102"></a>00102
<a name="l00103"></a>00103 <span class="keywordflow">case</span> <a class="code" href="classhippodraw_1_1Erfc.html#a06fc87d81c62e9abb8790b6e5713c55bae003ec1158e3a4e295616ced12af154e">NORM</a> :
<a name="l00104"></a>00104 result = <a class="code" href="classhippodraw_1_1Erfc.html#a35b6d3300fa7025c7a1f54d1c7fe6013" title="The function call operator.">operator () </a>( value ) / <a class="code" href="classhippodraw_1_1FunctionBase.html#aa892dcf9755ccd651b666f353b723c34" title="The parameter values.">m_parms</a>[<a class="code" href="classhippodraw_1_1Erfc.html#a06fc87d81c62e9abb8790b6e5713c55bae003ec1158e3a4e295616ced12af154e">NORM</a>];
<a name="l00105"></a>00105 <span class="keywordflow">return</span> result;
<a name="l00106"></a>00106 <span class="keywordflow">break</span>;
<a name="l00107"></a>00107
<a name="l00108"></a>00108 <span class="keywordflow">default</span> :
<a name="l00109"></a>00109 assert ( <span class="keyword">false</span> );
<a name="l00110"></a>00110 <span class="keywordflow">break</span>;
<a name="l00111"></a>00111 }
<a name="l00112"></a>00112
<a name="l00113"></a>00113 <span class="keywordflow">return</span> 0.0;
<a name="l00114"></a>00114 }
<a name="l00115"></a>00115
<a name="l00116"></a>00116
<a name="l00117"></a>00117 <span class="comment">//Derivative wrt reduced is gaussian!</span>
<a name="l00118"></a><a class="code" href="classhippodraw_1_1Erfc.html#accdd20961098ca1dbef1e36ab56d9853">00118</a> <span class="keywordtype">double</span> <a class="code" href="classhippodraw_1_1Erfc.html#accdd20961098ca1dbef1e36ab56d9853">Erfc::derivByRed</a>( <span class="keyword">const</span> <span class="keywordtype">double</span> x )<span class="keyword"> const</span>
<a name="l00119"></a>00119 <span class="keyword"></span>{
<a name="l00120"></a>00120 <span class="comment">//I don't know if this is platform independant: std::M_2_SQRTPI from math.h</span>
<a name="l00121"></a>00121 <span class="keyword">static</span> <span class="keyword">const</span> <span class="keywordtype">double</span> m_2_sqrtpi = 1.12837916709551257390; <span class="comment">// 2/sqrt(pi)</span>
<a name="l00122"></a>00122
<a name="l00123"></a>00123 <span class="keywordtype">double</span> result = - m_2_sqrtpi; <span class="comment">// minus sign comes from the fact that x is lower</span>
<a name="l00124"></a>00124 <span class="comment">// bound of Erfc definition</span>
<a name="l00125"></a>00125 result *= exp(-x*x);
<a name="l00126"></a>00126 <span class="keywordflow">return</span> result;
<a name="l00127"></a>00127 }
<a name="l00128"></a>00128
<a name="l00129"></a>00129
<a name="l00130"></a>00130 <span class="comment">//this is the copy from ROOT TMath.cxx</span>
<a name="l00131"></a><a class="code" href="classhippodraw_1_1Erfc.html#a672080a40f7ea4f7eb92bbc053e69711">00131</a> <span class="keywordtype">double</span> <a class="code" href="classhippodraw_1_1Erfc.html#a672080a40f7ea4f7eb92bbc053e69711">Erfc::calcErfc</a>(<span class="keywordtype">double</span> x)<span class="keyword"> const</span>
<a name="l00132"></a>00132 <span class="keyword"></span>{
<a name="l00133"></a>00133 <span class="comment">// Compute the complementary error function erfc(x).</span>
<a name="l00134"></a>00134 <span class="comment">// Erfc(x) = (2/sqrt(pi)) Integral(exp(-t^2))dt between x and infinity</span>
<a name="l00135"></a>00135 <span class="comment">//</span>
<a name="l00136"></a>00136 <span class="comment">//--- Nve 14-nov-1998 UU-SAP Utrecht</span>
<a name="l00137"></a>00137
<a name="l00138"></a>00138 <span class="comment">// The parameters of the Chebyshev fit</span>
<a name="l00139"></a>00139 <span class="keyword">const</span> <span class="keywordtype">double</span>
<a name="l00140"></a>00140 a1 = -1.26551223, a2 = 1.00002368,
<a name="l00141"></a>00141 a3 = 0.37409196, a4 = 0.09678418,
<a name="l00142"></a>00142 a5 = -0.18628806, a6 = 0.27886807,
<a name="l00143"></a>00143 a7 = -1.13520398, a8 = 1.48851587,
<a name="l00144"></a>00144 a9 = -0.82215223, a10 = 0.17087277;
<a name="l00145"></a>00145
<a name="l00146"></a>00146 <span class="keywordtype">double</span> v = 1; <span class="comment">// The return value</span>
<a name="l00147"></a>00147
<a name="l00148"></a>00148 <span class="keywordtype">double</span> z = x>=0 ? x : -x; <span class="comment">//absolute value</span>
<a name="l00149"></a>00149
<a name="l00150"></a>00150 <span class="keywordflow">if</span> (z <= 0) <span class="keywordflow">return</span> v; <span class="comment">// erfc(0)=1</span>
<a name="l00151"></a>00151
<a name="l00152"></a>00152 <span class="keywordtype">double</span> t = 1/(1+0.5*z);
<a name="l00153"></a>00153
<a name="l00154"></a>00154 v = t*exp((-z*z) +a1+t*(a2+t*(a3+t*(a4+t*(a5+t*(a6+t*(a7+t*(a8+t*(a9+t*a10)))))))));
<a name="l00155"></a>00155
<a name="l00156"></a>00156 <span class="keywordflow">if</span> (x < 0) v = 2-v; <span class="comment">// erfc(-x)=2-erfc(x)</span>
<a name="l00157"></a>00157
<a name="l00158"></a>00158 <span class="keywordflow">return</span> v;
<a name="l00159"></a>00159 }
<a name="l00160"></a>00160
<a name="l00161"></a>00161 } <span class="comment">// namespace hippodraw</span>
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