1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
|
// $Id: gammaUtilities.cpp 962 2006-11-07 15:13:34Z privmane $
#include "gammaUtilities.h"
#include "logFile.h"
#include "errorMsg.h"
#include <cmath>
//gser: returns the incomplete Gamma function evaluated by its series representation
void gser(MDOUBLE *gamser, MDOUBLE a, MDOUBLE x, MDOUBLE *gln)
{
//MDOUBLE gammln(MDOUBLE xx);
int n;
MDOUBLE sum,del,ap;
*gln=gammln(a);
if (x <= 0.0) {
if (x < 0.0) LOG(1,<<"x less than 0 in routine gser");
*gamser=0.0;
return;
} else {
ap=a;
del=sum=1.0/a;
for (n=1;n<=ITMAX;n++) {
++ap;
del *= x/ap;
sum += del;
if (fabs(del) < fabs(sum)*EPS) {
*gamser=sum*exp(-x+a*log(x)-(*gln));
return;
}
}
LOG(1,<<"Too many interations in routine gser");
return;
}
}
//gcf: returns the complement of the incomplete Gamma function evaluated by its continued fraction representation
void gcf(MDOUBLE *gammcf, MDOUBLE a, MDOUBLE x, MDOUBLE *gln)
{
//MDOUBLE gammln(MDOUBLE xx);
int i;
MDOUBLE an,b,c,d,del,h;
*gln=gammln(a);
b=x+1.0-a;
c=1.0/FPMIN;
d=1.0/b;
h=d;
for (i=1;i<=ITMAX;i++) {
an = -i*(i-a);
b += 2.0;
d=an*d+b;
if (fabs(d) < FPMIN) d=FPMIN;
c=b+an/c;
if (fabs(c) < FPMIN) c=FPMIN;
d=1.0/d;
del=d*c;
h *= del;
if (fabs(del-1.0) < EPS) break;
}
if (i > ITMAX) LOG(1,<<"a too large, ITMAX too small in gcf");
*gammcf=exp(-x+a*log(x)-(*gln))*h;
}
//gammp(a, x): computes the incomplete Gamma function which is:
// 1/Gamma(a) * (the integral from 0 to x of (t^(a-1)*e^(-t)) dt)
//gammp can be computed in two different ways: by a series representation (gser(..))
//or by a continued fraction representation (gcf(..))
//gammp chooses to function will be used, according to the values of a and x
MDOUBLE gammp(MDOUBLE a, MDOUBLE x)
{
//void gcf(MDOUBLE *gammcf, MDOUBLE a, MDOUBLE x, MDOUBLE *gln);
//void gser(MDOUBLE *gamser, MDOUBLE a, MDOUBLE x, MDOUBLE *gln);
MDOUBLE gamser,gammcf,gln;
if (x < 0.0 || a <= 0.0) LOG(1,<<"Invalid arguments in routine gammp");
if (x < (a+1.0)) {
gser(&gamser,a,x,&gln);
return gamser;
} else {
gcf(&gammcf,a,x,&gln);
return 1.0-gammcf;
}
}
//I add////////////
MDOUBLE gammq(MDOUBLE a, MDOUBLE x)
{
void gcf(MDOUBLE *gammcf, MDOUBLE a, MDOUBLE x, MDOUBLE *gln);
void gser(MDOUBLE *gamser, MDOUBLE a, MDOUBLE x, MDOUBLE *gln);
MDOUBLE gamser,gammcf,gln;
if (x < 0.0 || a <= 0.0) LOG(1,<<"Invalid arguments in routine gammp");
if (x < (a+1.0)) {
gser(&gamser,a,x,&gln);
return 1.0 - gamser;
} else {
gcf(&gammcf,a,x,&gln);
return gammcf;
}
}
/*************************************************************************
// this function computed the ln of the gamma function
// The Gamma funnction: Gamma(xx) = integral from 0 to infinity of (t^(xx-1)*e^(-t)) dt.
*************************************************************************/
MDOUBLE gammln(MDOUBLE xx)
{
MDOUBLE x,y,tmp,ser;
static MDOUBLE cof[6]={
static_cast<MDOUBLE>(76.18009172947146),
static_cast<MDOUBLE>(-86.50532032941677),
static_cast<MDOUBLE>(24.01409824083091),
static_cast<MDOUBLE>(-1.231739572450155),
static_cast<MDOUBLE>(0.1208650973866179e-2),
static_cast<MDOUBLE>(-0.5395239384953e-5)
};
int j;
y=x=xx;
tmp=x+5.5;
tmp -= (x+0.5)*log(tmp);
ser=1.000000000190015f;
for (j=0;j<6;j++) ser += cof[j]/++y;
return -tmp+log(2.5066282746310005*ser/x);
}
//
MDOUBLE search_for_z_in_dis_with_any_beta(MDOUBLE alpha,MDOUBLE beta, MDOUBLE ahoson)
{
return (search_for_z_in_dis_with_beta_1(alpha,ahoson)/beta);
}
MDOUBLE search_for_z_in_dis_with_beta_1(MDOUBLE alpha, MDOUBLE ahoson)
{
if ( ahoson>1 || ahoson<0 ) errorMsg::reportError("Error in function search_for_z_in_dis_with_beta_1");
MDOUBLE left=0;
MDOUBLE right=99999.0;
MDOUBLE tmp=5000.0;
MDOUBLE results=0.0;
for (int i=0;i<100000000 ; i++)
{
results=gammp(alpha,tmp);
if (fabs(ahoson-results)<ERR_FOR_GAMMA_CALC) {
return tmp;
}
if (results>ahoson) {
right=tmp;
}
else left=tmp;
tmp=(right+left)/2;
}
cout << "ERROR in search_for_z_in_dis_with_beta_1() Alpha is: "<< alpha <<endl;
errorMsg::reportError("Error in function search_for_z_in_dis_with_beta_1 - first bonderi is 0");// also quit the program
return 0;
}
MDOUBLE the_avarage_r_in_category_between_a_and_b(MDOUBLE left, MDOUBLE right, MDOUBLE alpha, MDOUBLE beta, int k)
{// and and b are the border of percentile k)
MDOUBLE tmp;
tmp= gammp(alpha+1,right*beta) - gammp(alpha+1,left*beta);
tmp= (tmp*alpha/beta)*k;
return tmp;
}
|
