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PdfFuncMathCore.cxx
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1// @(#)root/mathcore:$Id$
2// Authors: Andras Zsenei & Lorenzo Moneta 06/2005
3
4/**********************************************************************
5 * *
6 * Copyright (c) 2005 , LCG ROOT MathLib Team *
7 * *
8 * *
9 **********************************************************************/
10
11
12
13#include "Math/Math.h"
15#include <limits>
16
17
18namespace ROOT {
19namespace Math {
20
21 double landau_pdf(double x, double xi, double x0) {
22 // LANDAU pdf : algorithm from CERNLIB G110 denlan
23 // same algorithm is used in GSL
24
25 static double p1[5] = {0.4259894875,-0.1249762550, 0.03984243700, -0.006298287635, 0.001511162253};
26 static double q1[5] = {1.0 ,-0.3388260629, 0.09594393323, -0.01608042283, 0.003778942063};
27
28 static double p2[5] = {0.1788541609, 0.1173957403, 0.01488850518, -0.001394989411, 0.0001283617211};
29 static double q2[5] = {1.0 , 0.7428795082, 0.3153932961, 0.06694219548, 0.008790609714};
30
31 static double p3[5] = {0.1788544503, 0.09359161662,0.006325387654, 0.00006611667319,-0.000002031049101};
32 static double q3[5] = {1.0 , 0.6097809921, 0.2560616665, 0.04746722384, 0.006957301675};
33
34 static double p4[5] = {0.9874054407, 118.6723273, 849.2794360, -743.7792444, 427.0262186};
35 static double q4[5] = {1.0 , 106.8615961, 337.6496214, 2016.712389, 1597.063511};
36
37 static double p5[5] = {1.003675074, 167.5702434, 4789.711289, 21217.86767, -22324.94910};
38 static double q5[5] = {1.0 , 156.9424537, 3745.310488, 9834.698876, 66924.28357};
39
40 static double p6[5] = {1.000827619, 664.9143136, 62972.92665, 475554.6998, -5743609.109};
41 static double q6[5] = {1.0 , 651.4101098, 56974.73333, 165917.4725, -2815759.939};
42
43 static double a1[3] = {0.04166666667,-0.01996527778, 0.02709538966};
44
45 static double a2[2] = {-1.845568670,-4.284640743};
46
47 if (xi <= 0) return 0;
48 double v = (x - x0)/xi;
49 double u, ue, us, denlan;
50 if (v < -5.5) {
51 u = std::exp(v+1.0);
52 if (u < 1e-10) return 0.0;
53 ue = std::exp(-1/u);
54 us = std::sqrt(u);
55 denlan = 0.3989422803*(ue/us)*(1+(a1[0]+(a1[1]+a1[2]*u)*u)*u);
56 } else if(v < -1) {
57 u = std::exp(-v-1);
58 denlan = std::exp(-u)*std::sqrt(u)*
59 (p1[0]+(p1[1]+(p1[2]+(p1[3]+p1[4]*v)*v)*v)*v)/
60 (q1[0]+(q1[1]+(q1[2]+(q1[3]+q1[4]*v)*v)*v)*v);
61 } else if(v < 1) {
62 denlan = (p2[0]+(p2[1]+(p2[2]+(p2[3]+p2[4]*v)*v)*v)*v)/
63 (q2[0]+(q2[1]+(q2[2]+(q2[3]+q2[4]*v)*v)*v)*v);
64 } else if(v < 5) {
65 denlan = (p3[0]+(p3[1]+(p3[2]+(p3[3]+p3[4]*v)*v)*v)*v)/
66 (q3[0]+(q3[1]+(q3[2]+(q3[3]+q3[4]*v)*v)*v)*v);
67 } else if(v < 12) {
68 u = 1/v;
69 denlan = u*u*(p4[0]+(p4[1]+(p4[2]+(p4[3]+p4[4]*u)*u)*u)*u)/
70 (q4[0]+(q4[1]+(q4[2]+(q4[3]+q4[4]*u)*u)*u)*u);
71 } else if(v < 50) {
72 u = 1/v;
73 denlan = u*u*(p5[0]+(p5[1]+(p5[2]+(p5[3]+p5[4]*u)*u)*u)*u)/
74 (q5[0]+(q5[1]+(q5[2]+(q5[3]+q5[4]*u)*u)*u)*u);
75 } else if(v < 300) {
76 u = 1/v;
77 denlan = u*u*(p6[0]+(p6[1]+(p6[2]+(p6[3]+p6[4]*u)*u)*u)*u)/
78 (q6[0]+(q6[1]+(q6[2]+(q6[3]+q6[4]*u)*u)*u)*u);
79 } else {
80 u = 1/(v-v*std::log(v)/(v+1));
81 denlan = u*u*(1+(a2[0]+a2[1]*u)*u);
82 }
83 return denlan/xi;
84
85 }
86
87
88} // namespace Math
89} // namespace ROOT
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#define e(i)
Definition: RSha256.hxx:103
double sqrt(double)
double exp(double)
double log(double)
double landau_pdf(double x, double xi=1, double x0=0)
Probability density function of the Landau distribution:
Double_t x[n]
Definition: legend1.C:17
Namespace for new Math classes and functions.
tbb::task_arena is an alias of tbb::interface7::task_arena, which doesn't allow to forward declare tb...
Definition: RNumpyDS.hxx:30
static constexpr double us