]>
Commit | Line | Data |
---|---|---|
da32329d AM |
1 | /////////////////////////////////////////////////////////////////////////// |
2 | // | |
3 | // Copyright 2010 | |
4 | // | |
5 | // This file is part of starlight. | |
6 | // | |
7 | // starlight is free software: you can redistribute it and/or modify | |
8 | // it under the terms of the GNU General Public License as published by | |
9 | // the Free Software Foundation, either version 3 of the License, or | |
10 | // (at your option) any later version. | |
11 | // | |
12 | // starlight is distributed in the hope that it will be useful, | |
13 | // but WITHOUT ANY WARRANTY; without even the implied warranty of | |
14 | // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the | |
15 | // GNU General Public License for more details. | |
16 | // | |
17 | // You should have received a copy of the GNU General Public License | |
18 | // along with starlight. If not, see <http://www.gnu.org/licenses/>. | |
19 | // | |
20 | /////////////////////////////////////////////////////////////////////////// | |
21 | // | |
22 | // File and Version Information: | |
23 | // $Rev:: 28 $: revision of last commit | |
24 | // $Author:: bgrube $: author of last commit | |
25 | // $Date:: 2010-12-10 19:30:01 +0100 #$: date of last commit | |
26 | // | |
27 | // Description: | |
28 | // Bessel functions taken from ROOT | |
29 | // | |
30 | // | |
31 | /////////////////////////////////////////////////////////////////////////// | |
32 | ||
33 | ||
34 | #include <iostream> | |
35 | #include <fstream> | |
36 | #include <cmath> | |
37 | ||
38 | #include "bessel.h" | |
39 | ||
40 | ||
41 | using namespace std; | |
42 | ||
43 | ||
44 | //______________________________________________________________________________ | |
45 | double bessel::besI0(double x) | |
46 | { | |
47 | //FROM ROOT... | |
48 | // Parameters of the polynomial approximation | |
49 | const double p1=1.0, p2=3.5156229, p3=3.0899424, | |
50 | p4=1.2067492, p5=0.2659732, p6=3.60768e-2, p7=4.5813e-3; | |
51 | ||
52 | const double q1= 0.39894228, q2= 1.328592e-2, q3= 2.25319e-3, | |
53 | q4=-1.57565e-3, q5= 9.16281e-3, q6=-2.057706e-2, | |
54 | q7= 2.635537e-2, q8=-1.647633e-2, q9= 3.92377e-3; | |
55 | ||
56 | const double k1 = 3.75; | |
57 | double ax = fabs(x); | |
58 | ||
59 | double y=0., result=0.; | |
60 | ||
61 | if (ax < k1) { | |
62 | double xx = x/k1; | |
63 | y = xx*xx; | |
64 | result = p1+y*(p2+y*(p3+y*(p4+y*(p5+y*(p6+y*p7))))); | |
65 | } else { | |
66 | y = k1/ax; | |
67 | result = (exp(ax)/sqrt(ax))*(q1+y*(q2+y*(q3+y*(q4+y*(q5+y*(q6+y*(q7+y*(q8+y*q9)))))))); | |
68 | } | |
69 | return result; | |
70 | } | |
71 | ||
72 | ||
73 | //______________________________________________________________________________ | |
74 | double bessel::dbesk0(double x) | |
75 | { | |
76 | // Compute the modified Bessel function K_0(x) for positive real x. //should be k0? | |
77 | // | |
78 | // M.Abramowitz and I.A.Stegun, Handbook of Mathematical Functions, | |
79 | // Applied Mathematics Series vol. 55 (1964), Washington. | |
80 | // | |
81 | //--- NvE 12-mar-2000 UU-SAP Utrecht | |
82 | ||
83 | // Parameters of the polynomial approximation | |
84 | const double p1= -0.57721566, p2= 0.42278420, p3=0.23069756, | |
85 | p4=3.488590e-2, p5=2.62698e-3, p6=1.0750e-4, p7=7.4e-6; | |
86 | ||
87 | const double q1= 1.25331414, q2= -7.832358e-2, q3=2.189568e-2, | |
88 | q4= -1.062446e-2, q5=5.87872e-3, q6= -2.51540e-3, q7= 5.3208e-4; | |
89 | ||
90 | if (x <= 0) { | |
91 | cout << "BesselK0 *K0* Invalid argument x = " << x << endl; //Should be k0? | |
92 | return 0; | |
93 | } | |
94 | ||
95 | double y=0.,result=0.; | |
96 | ||
97 | if (x <= 2) { | |
98 | y = x*x/4.; | |
99 | result = (-log(x/2.)*bessel::besI0(x))+(p1+y*(p2+y*(p3+y*(p4+y*(p5+y*(p6+y*p7)))))); | |
100 | } else { | |
101 | y = 2./x; | |
102 | result = (exp(-x)/sqrt(x))*(q1+y*(q2+y*(q3+y*(q4+y*(q5+y*(q6+y*q7)))))); | |
103 | } | |
104 | return result; | |
105 | } | |
106 | ||
107 | ||
108 | //______________________________________________________________________________ | |
109 | double bessel::besI1(double x) | |
110 | { | |
111 | // Compute the modified Bessel function I_1(x) for any real x. | |
112 | // | |
113 | // M.Abramowitz and I.A.Stegun, Handbook of Mathematical Functions, | |
114 | // Applied Mathematics Series vol. 55 (1964), Washington. | |
115 | // | |
116 | //--- NvE 12-mar-2000 UU-SAP Utrecht | |
117 | ||
118 | // Parameters of the polynomial approximation | |
119 | const double p1=0.5, p2=0.87890594, p3=0.51498869, | |
120 | p4=0.15084934, p5=2.658733e-2, p6=3.01532e-3, p7=3.2411e-4; | |
121 | ||
122 | const double q1= 0.39894228, q2=-3.988024e-2, q3=-3.62018e-3, | |
123 | q4= 1.63801e-3, q5=-1.031555e-2, q6= 2.282967e-2, | |
124 | q7=-2.895312e-2, q8= 1.787654e-2, q9=-4.20059e-3; | |
125 | ||
126 | const double k1 = 3.75; | |
127 | double ax = fabs(x); | |
128 | ||
129 | double y=0., result=0.; | |
130 | ||
131 | if (ax < k1) { | |
132 | double xx = x/k1; | |
133 | y = xx*xx; | |
134 | result = x*(p1+y*(p2+y*(p3+y*(p4+y*(p5+y*(p6+y*p7)))))); | |
135 | } else { | |
136 | y = k1/ax; | |
137 | result = (exp(ax)/sqrt(ax))*(q1+y*(q2+y*(q3+y*(q4+y*(q5+y*(q6+y*(q7+y*(q8+y*q9)))))))); | |
138 | if (x < 0) result = -result; | |
139 | } | |
140 | return result; | |
141 | } | |
142 | ||
143 | ||
144 | //______________________________________________________________________________ | |
145 | double bessel::dbesk1(double x) | |
146 | { | |
147 | // Compute the modified Bessel function K_1(x) for positive real x. | |
148 | // | |
149 | // M.Abramowitz and I.A.Stegun, Handbook of Mathematical Functions, | |
150 | // Applied Mathematics Series vol. 55 (1964), Washington. | |
151 | // | |
152 | //--- NvE 12-mar-2000 UU-SAP Utrecht | |
153 | ||
154 | // Parameters of the polynomial approximation | |
155 | const double p1= 1., p2= 0.15443144, p3=-0.67278579, | |
156 | p4=-0.18156897, p5=-1.919402e-2, p6=-1.10404e-3, p7=-4.686e-5; | |
157 | ||
158 | const double q1= 1.25331414, q2= 0.23498619, q3=-3.655620e-2, | |
159 | q4= 1.504268e-2, q5=-7.80353e-3, q6= 3.25614e-3, q7=-6.8245e-4; | |
160 | ||
161 | if (x <= 0) { | |
162 | cout << "bessel:dbesk1 *K1* Invalid argument x = " << x << endl; | |
163 | return 0; | |
164 | } | |
165 | ||
166 | double y=0.,result=0.; | |
167 | ||
168 | if (x <= 2) { | |
169 | y = x*x/4.; | |
170 | result = (log(x/2.)*bessel::besI1(x))+(1./x)*(p1+y*(p2+y*(p3+y*(p4+y*(p5+y*(p6+y*p7)))))); | |
171 | } else { | |
172 | y = 2./x; | |
173 | result = (exp(-x)/sqrt(x))*(q1+y*(q2+y*(q3+y*(q4+y*(q5+y*(q6+y*q7)))))); | |
174 | } | |
175 | return result; | |
176 | } |