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<div class="title">erf.h</div> </div>
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<a href="erf_8h.shtml">Go to the documentation of this file.</a><div class="fragment"><pre class="fragment"><a name="l00001"></a>00001 <span class="comment">//From http://www.digitalmars.com/archives/cplusplus/3634.html (Jan 2004)</span>
<a name="l00002"></a>00002 <span class="comment">//Author Steve Strand. No intellectual propery rights claimed.</span>
<a name="l00003"></a>00003 <span class="preprocessor">#ifndef OB_ERF_H</span>
<a name="l00004"></a>00004 <span class="preprocessor"></span><span class="preprocessor">#define OB_ERF_H</span>
<a name="l00005"></a>00005 <span class="preprocessor"></span>
<a name="l00006"></a>00006 <span class="preprocessor">#include <math.h></span>
<a name="l00007"></a>00007
<a name="l00009"></a>00009 <span class="comment">// Hide this from doxygen -- internal only code</span>
<a name="l00010"></a>00010 <span class="keyword">namespace </span>temperf
<a name="l00011"></a>00011 {
<a name="l00012"></a>00012 <span class="keywordtype">double</span> erf(<span class="keywordtype">double</span> x);
<a name="l00013"></a>00013 <span class="keywordtype">double</span> erfc(<span class="keywordtype">double</span> x);
<a name="l00014"></a>00014
<a name="l00015"></a>00015 <span class="keyword">static</span> <span class="keyword">const</span> <span class="keywordtype">double</span> rel_error= 1E-12; <span class="comment">//calculate 12 significant figures</span>
<a name="l00016"></a>00016 <span class="comment">//you can adjust rel_error to trade off between accuracy and speed</span>
<a name="l00017"></a>00017 <span class="comment">//but don't ask for > 15 figures (assuming usual 52 bit mantissa in a double)</span>
<a name="l00018"></a>00018
<a name="l00019"></a>00019 <span class="keyword">inline</span> <span class="keywordtype">double</span> erf(<span class="keywordtype">double</span> x)
<a name="l00020"></a>00020 {
<a name="l00021"></a>00021 <span class="comment">//erf(x) = 2/sqrt(pi)*integral(exp(-t^2),t,0,x)</span>
<a name="l00022"></a>00022 <span class="comment">// = 2/sqrt(pi)*[x - x^3/3 + x^5/5*2! - x^7/7*3! + ...]</span>
<a name="l00023"></a>00023 <span class="comment">// = 1-erfc(x)</span>
<a name="l00024"></a>00024 <span class="keyword">static</span> <span class="keyword">const</span> <span class="keywordtype">double</span> two_sqrtpi= 1.128379167095512574; <span class="comment">// 2/sqrt(pi)</span>
<a name="l00025"></a>00025 <span class="keywordflow">if</span> (abs(x) > 2.2)
<a name="l00026"></a>00026 <span class="keywordflow">return</span> 1.0 - erfc(x); <span class="comment">//use continued fraction when fabs(x) > 2.2</span>
<a name="l00027"></a>00027
<a name="l00028"></a>00028 <span class="keywordtype">double</span> sum= x, term= x, xsqr= x*x;
<a name="l00029"></a>00029 <span class="keywordtype">int</span> j= 1;
<a name="l00030"></a>00030 <span class="keywordflow">do</span>
<a name="l00031"></a>00031 {
<a name="l00032"></a>00032 term*= xsqr/j;
<a name="l00033"></a>00033 sum-= term/(2*j+1);
<a name="l00034"></a>00034 ++j;
<a name="l00035"></a>00035 term*= xsqr/j;
<a name="l00036"></a>00036 sum+= term/(2*j+1);
<a name="l00037"></a>00037 ++j;
<a name="l00038"></a>00038 } <span class="keywordflow">while</span> (fabs(term/sum) > rel_error);
<a name="l00039"></a>00039 <span class="keywordflow">return</span> two_sqrtpi*sum;
<a name="l00040"></a>00040 }
<a name="l00041"></a>00041
<a name="l00042"></a>00042 <span class="keyword">inline</span> <span class="keywordtype">double</span> erfc(<span class="keywordtype">double</span> x)
<a name="l00043"></a>00043 {
<a name="l00044"></a>00044 <span class="comment">//erfc(x) = 2/sqrt(pi)*integral(exp(-t^2),t,x,inf)</span>
<a name="l00045"></a>00045 <span class="comment">// = exp(-x^2)/sqrt(pi) * [1/x+ (1/2)/x+ (2/2)/x+ (3/2)/x+ (4/2)/x+ ...]</span>
<a name="l00046"></a>00046 <span class="comment">// = 1-erf(x)</span>
<a name="l00047"></a>00047 <span class="comment">//expression inside [] is a continued fraction so '+' means add to denominator only</span>
<a name="l00048"></a>00048
<a name="l00049"></a>00049 <span class="keyword">static</span> <span class="keyword">const</span> <span class="keywordtype">double</span> one_sqrtpi= 0.564189583547756287; <span class="comment">// 1/sqrt(pi)</span>
<a name="l00050"></a>00050 <span class="keywordflow">if</span> (abs(x) < 2.2)
<a name="l00051"></a>00051 <span class="keywordflow">return</span> 1.0 - erf(x); <span class="comment">//use series when fabs(x) < 2.2</span>
<a name="l00052"></a>00052
<a name="l00053"></a>00053 <span class="keywordflow">if</span> (x<0)<span class="comment">//continued fraction only valid for x>0</span>
<a name="l00054"></a>00054 <span class="keywordflow">return</span> 2.0 - erfc(-x);
<a name="l00055"></a>00055
<a name="l00056"></a>00056 <span class="keywordtype">double</span> a=1, b=x; <span class="comment">//last two convergent numerators</span>
<a name="l00057"></a>00057 <span class="keywordtype">double</span> c=x, d=x*x+0.5; <span class="comment">//last two convergent denominators</span>
<a name="l00058"></a>00058 <span class="keywordtype">double</span> q1, q2= b/d; <span class="comment">//last two convergents (a/c and b/d)</span>
<a name="l00059"></a>00059 <span class="keywordtype">double</span> n= 1.0, t;
<a name="l00060"></a>00060 <span class="keywordflow">do</span>
<a name="l00061"></a>00061 {
<a name="l00062"></a>00062 t= a*n+b*x;
<a name="l00063"></a>00063 a= b;
<a name="l00064"></a>00064 b= t;
<a name="l00065"></a>00065 t= c*n+d*x;
<a name="l00066"></a>00066 c= d;
<a name="l00067"></a>00067 d= t;
<a name="l00068"></a>00068 n+= 0.5;
<a name="l00069"></a>00069 q1= q2;
<a name="l00070"></a>00070 q2= b/d;
<a name="l00071"></a>00071 } <span class="keywordflow">while</span> (fabs(q1-q2)/q2 > rel_error);
<a name="l00072"></a>00072 <span class="keywordflow">return</span> one_sqrtpi*exp(-x*x)*q2;
<a name="l00073"></a>00073 }
<a name="l00075"></a>00075
<a name="l00076"></a>00076 }<span class="comment">//namespace</span>
<a name="l00077"></a>00077 <span class="preprocessor">#endif // OB_ERF_H</span>
<a name="l00078"></a>00078 <span class="preprocessor"></span>
</pre></div></div>
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