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
|
/* Copyright (c) 2008-2022 the MRtrix3 contributors.
*
* This Source Code Form is subject to the terms of the Mozilla Public
* License, v. 2.0. If a copy of the MPL was not distributed with this
* file, You can obtain one at http://mozilla.org/MPL/2.0/.
*
* Covered Software is provided under this License on an "as is"
* basis, without warranty of any kind, either expressed, implied, or
* statutory, including, without limitation, warranties that the
* Covered Software is free of defects, merchantable, fit for a
* particular purpose or non-infringing.
* See the Mozilla Public License v. 2.0 for more details.
*
* For more details, see http://www.mrtrix.org/.
*/
#ifndef __math_one_over_cosh_h__
#define __math_one_over_cosh_h__
#include "math/math.h"
#include "math/vector.h"
namespace MR {
namespace Math {
namespace Sech {
template <typename T> inline T lnP (const T measured, const T actual, const T one_over_noise_squared)
{
T n = sqrt (one_over_noise_squared);
T e = n * (actual - measured);
if (e < -20.0) e = -e;
else if (e <= 20.0) { e = exp(e); e = log (e + 1.0/e); }
return (e - 0.5*log (one_over_noise_squared));
}
template <typename T> inline T lnP (const T measured, const T actual, const T one_over_noise_squared, T& dP_dactual, T& dP_dN)
{
assert (one_over_noise_squared > 0.0);
T n = sqrt(one_over_noise_squared);
T e = n * (actual - measured);
T lnP;
if (e < -20.0) { lnP = -e; e = -1.0; }
else if (e <= 20.0) { e = exp (e); lnP = e + 1.0/e; e = (e - 1.0/e) / lnP; lnP = log (lnP); }
else { lnP = e; e = 1.0; }
dP_dactual = n * e;
dP_dN = 0.5 * ((actual - measured) * e / n - 1.0/one_over_noise_squared);
return (lnP - 0.5*log (one_over_noise_squared));
}
template <typename T> inline T lnP (const int N, const T* measured, const T* actual, const T one_over_noise_squared)
{
assert (one_over_noise_squared > 0.0);
T n = sqrt (one_over_noise_squared);
T lnP = 0.0;
for (int i = 0; i < N; i++) {
T e = n * (actual[i] - measured[i]);
if (e < -20.0) e = -e;
else if (e <= 20.0) { e = exp (e); e = log (e + 1.0/e); }
lnP += e;
}
return (lnP - 0.5*N*log (one_over_noise_squared));
}
template <typename T> inline T lnP (const Math::Vector<T>& measured, const Math::Vector<T>& actual, const T one_over_noise_squared)
{
assert (one_over_noise_squared > 0.0);
assert (measured.size() == actual.size());
T n = sqrt (one_over_noise_squared);
T lnP = 0.0;
for (size_t i = 0; i < actual.size(); i++) {
T e = n * (actual[i] - measured[i]);
if (e < -20.0) e = -e;
else if (e <= 20.0) { e = exp (e); e = log (e + 1.0/e); }
lnP += e;
}
return (lnP - 0.5*actual.size()*log (one_over_noise_squared));
}
template <typename T> inline T lnP (const int N, const T* measured, const T* actual, const T one_over_noise_squared, T* dP_dactual, T& dP_dN)
{
assert (one_over_noise_squared > 0.0);
T n = sqrt (one_over_noise_squared);
T lnP = 0.0;
dP_dN = 0.0;
for (int i = 0; i < N; i++) {
T e = n * (actual[i] - measured[i]);
T t;
if (e < -20.0) { t = -e; e = -1.0; }
else if (e <= 20.0) { e = exp (e); t = e + 1.0/e; e = (e - 1.0/e) / t; t = log (t); }
else { t = e; e = 1.0; }
lnP += t;
dP_dactual[i] = n * e;
dP_dN += (actual[i] - measured[i]) * e;
}
dP_dN = 0.5 * (dP_dN / n - N / one_over_noise_squared);
return (lnP - 0.5*N*log (one_over_noise_squared));
}
template <typename T> inline T lnP (const Math::Vector<T>& measured, const Math::Vector<T>& actual, const T one_over_noise_squared, Math::Vector<T>& dP_dactual, T& dP_dN)
{
assert (one_over_noise_squared > 0.0);
assert (measured.size() == actual.size());
T n = sqrt (one_over_noise_squared);
T lnP = 0.0;
dP_dN = 0.0;
for (size_t i = 0; i < actual.size(); i++) {
T e = n * (actual[i] - measured[i]);
T t;
if (e < -20.0) { t = -e; e = -1.0; }
else if (e <= 20.0) { e = exp (e); t = e + 1.0/e; e = (e - 1.0/e) / t; t = log (t); }
else { t = e; e = 1.0; }
lnP += t;
dP_dactual[i] = n * e;
dP_dN += (actual[i] - measured[i]) * e;
}
dP_dN = 0.5 * (dP_dN / n - actual.size() / one_over_noise_squared);
return (lnP - 0.5*actual.size()*log (one_over_noise_squared));
}
}
}
}
#endif
|
