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
|
#ifndef math_utility_H__
#define math_utility_H__
#include <cstdlib>
#include <vector>
#include <algorithm>
#include <cmath>
namespace meow {
//! 圓周率...
static const double PI = 3.14159265358979323846264338327950288;
/*!
* @brief 將角度調整於0~2PI
*/
template<class T>
inline T circle(T x) {
while (x < 0) x += 2.0 * PI;
while (2.0 * PI <= x) x -= 2.0 * PI;
return x;
}
/*!
* @brief 如果abs(輸入的數值) < eps, 則回傳0, 否則回傳輸入的數值
*/
template<class T>
inline T noEPS(T value, T eps = 1e-9) {
T epsp((eps < T(0)) ? -eps : eps);
return ((value < -epsp || value > epsp) ? value : T(0));
}
/*!
* @brief \c (value-lower)/(upper-lower)
*/
template<class T>
inline T normalize(T lower, T upper, T value) {
return (value - lower) / (upper - lower);
}
/*!
* @brief \c (lower+_ratio*(upper-lower))
*/
template<class T>
inline T denormalize(T lower, T upper, T _ratio) {
return lower + _ratio * (upper - lower);
}
/*!
* @brief \c denormalize(l2,u2,normalize(l1,u1,m1))
*/
template<class T>
inline T ratioMapping(T l1, T u1, T m1, T l2, T u2) {
return denormalize(l2, u2, normalize(l1, u1, m1));
}
/*!
* @brief \c std::min(mx,std::max(mn,v))
*/
template<class T>
inline T inRange(T const& mn, T const& mx, T const& v) {
return std::min(mx, std::max(mn, v));
}
/*!
* @brief (mn <= x && x <= mx)
*/
template<class T>
inline T isInRange(T const& mn, T const& mx, T const& x) {
return (mn <= x && x <= mx);
}
/*!
* @brief \c x*x
*/
template<class T>
inline T squ(T const& x) {
return x * x;
}
/*!
* @brief \c x*x*x
*/
template<class T>
inline T cub(T const& x) {
return x * x * x;
}
/*!
* @brief 只將 \c sigs 個標準差以內的數據拿來取平均
*/
template<class T>
inline double average(T const& beg, T const& end, double sigs) {
int N = 0;
double av = 0;
for (T it = beg; it != end; ++it, ++N) {
av += *it;
}
av /= N;
double sig = 0;
for (T it = beg; it != end; ++it) {
sig += (*it - av) * (*it - av);
}
sig = sqrt(sig / N);
double lower = av - sig * sigs, upper = av + sig * sigs;
double ret = 0, retn = 0;
for (T it = beg; it != end; ++it) {
if (lower <= *it && *it <= upper) {
ret += *it;
retn++;
}
}
return ret / retn;
}
/*!
* @brief 只將 \c sigs 個標準差以內的數據拿來取平均, 不過這次用 \c p 來加權平均
*/
template<class T>
inline double average(T const& beg, T const& end, T const& p, double sigs) {
int N = 0;
double ps = 0;
for (T it = beg, ip = p; it != end; ++it, ++N, ++ip) {
ps += *ip;
}
double av = 0;
for (T it = beg, ip = p; it != end; ++it, ++ip) {
av += *it * *ip / ps;
}
double sig = 0;
for (T it = beg, ip = p; it != end; ++it, ++ip) {
sig += *ip / ps * (*it - av) * (*it - av);
}
sig = sqrt(sig);
double lower = av - sig * sigs, upper = av + sig * sigs;
double ret = 0, retn = 0;
for (T it = beg, ip = p; it != end; ++it, ++ip) {
if (lower <= *it && *it <= upper) {
ret += *it * *ip;
retn += *ip;
}
}
if (retn <= 1e-10) return av;
return ret / retn;
}
/*!
* @brief 就只是個取絕對值
*/
template<class T>
inline T tAbs(T const& t) {
return (t < 0 ? -t : t);
}
} // meow
#endif // math_utility_H__
|
