1 // Ceres Solver - A fast non-linear least squares minimizer
2 // Copyright 2010, 2011, 2012 Google Inc. All rights reserved.
3 // http://code.google.com/p/ceres-solver/
4 //
5 // Redistribution and use in source and binary forms, with or without
6 // modification, are permitted provided that the following conditions are met:
7 //
8 // * Redistributions of source code must retain the above copyright notice,
9 // this list of conditions and the following disclaimer.
10 // * Redistributions in binary form must reproduce the above copyright notice,
11 // this list of conditions and the following disclaimer in the documentation
12 // and/or other materials provided with the distribution.
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14 // used to endorse or promote products derived from this software without
15 // specific prior written permission.
16 //
17 // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
18 // AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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20 // ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
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24 // INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
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26 // ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
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28 //
29 // Author: sameeragarwal@google.com (Sameer Agarwal)
30 //
31 // Purpose: See .h file.
32
33 #include "ceres/loss_function.h"
34
35 #include <cmath>
36 #include <cstddef>
37
38 namespace ceres {
39
Evaluate(double s,double rho[3]) const40 void TrivialLoss::Evaluate(double s, double rho[3]) const {
41 rho[0] = s;
42 rho[1] = 1.0;
43 rho[2] = 0.0;
44 }
45
Evaluate(double s,double rho[3]) const46 void HuberLoss::Evaluate(double s, double rho[3]) const {
47 if (s > b_) {
48 // Outlier region.
49 // 'r' is always positive.
50 const double r = sqrt(s);
51 rho[0] = 2.0 * a_ * r - b_;
52 rho[1] = std::max(std::numeric_limits<double>::min(), a_ / r);
53 rho[2] = - rho[1] / (2.0 * s);
54 } else {
55 // Inlier region.
56 rho[0] = s;
57 rho[1] = 1.0;
58 rho[2] = 0.0;
59 }
60 }
61
Evaluate(double s,double rho[3]) const62 void SoftLOneLoss::Evaluate(double s, double rho[3]) const {
63 const double sum = 1.0 + s * c_;
64 const double tmp = sqrt(sum);
65 // 'sum' and 'tmp' are always positive, assuming that 's' is.
66 rho[0] = 2.0 * b_ * (tmp - 1.0);
67 rho[1] = std::max(std::numeric_limits<double>::min(), 1.0 / tmp);
68 rho[2] = - (c_ * rho[1]) / (2.0 * sum);
69 }
70
Evaluate(double s,double rho[3]) const71 void CauchyLoss::Evaluate(double s, double rho[3]) const {
72 const double sum = 1.0 + s * c_;
73 const double inv = 1.0 / sum;
74 // 'sum' and 'inv' are always positive, assuming that 's' is.
75 rho[0] = b_ * log(sum);
76 rho[1] = std::max(std::numeric_limits<double>::min(), inv);
77 rho[2] = - c_ * (inv * inv);
78 }
79
Evaluate(double s,double rho[3]) const80 void ArctanLoss::Evaluate(double s, double rho[3]) const {
81 const double sum = 1 + s * s * b_;
82 const double inv = 1 / sum;
83 // 'sum' and 'inv' are always positive.
84 rho[0] = a_ * atan2(s, a_);
85 rho[1] = std::max(std::numeric_limits<double>::min(), inv);
86 rho[2] = -2.0 * s * b_ * (inv * inv);
87 }
88
TolerantLoss(double a,double b)89 TolerantLoss::TolerantLoss(double a, double b)
90 : a_(a),
91 b_(b),
92 c_(b * log(1.0 + exp(-a / b))) {
93 CHECK_GE(a, 0.0);
94 CHECK_GT(b, 0.0);
95 }
96
Evaluate(double s,double rho[3]) const97 void TolerantLoss::Evaluate(double s, double rho[3]) const {
98 const double x = (s - a_) / b_;
99 // The basic equation is rho[0] = b ln(1 + e^x). However, if e^x is too
100 // large, it will overflow. Since numerically 1 + e^x == e^x when the
101 // x is greater than about ln(2^53) for doubles, beyond this threshold
102 // we substitute x for ln(1 + e^x) as a numerically equivalent approximation.
103 static const double kLog2Pow53 = 36.7; // ln(MathLimits<double>::kEpsilon).
104 if (x > kLog2Pow53) {
105 rho[0] = s - a_ - c_;
106 rho[1] = 1.0;
107 rho[2] = 0.0;
108 } else {
109 const double e_x = exp(x);
110 rho[0] = b_ * log(1.0 + e_x) - c_;
111 rho[1] = std::max(std::numeric_limits<double>::min(), e_x / (1.0 + e_x));
112 rho[2] = 0.5 / (b_ * (1.0 + cosh(x)));
113 }
114 }
115
ComposedLoss(const LossFunction * f,Ownership ownership_f,const LossFunction * g,Ownership ownership_g)116 ComposedLoss::ComposedLoss(const LossFunction* f, Ownership ownership_f,
117 const LossFunction* g, Ownership ownership_g)
118 : f_(CHECK_NOTNULL(f)),
119 g_(CHECK_NOTNULL(g)),
120 ownership_f_(ownership_f),
121 ownership_g_(ownership_g) {
122 }
123
~ComposedLoss()124 ComposedLoss::~ComposedLoss() {
125 if (ownership_f_ == DO_NOT_TAKE_OWNERSHIP) {
126 f_.release();
127 }
128 if (ownership_g_ == DO_NOT_TAKE_OWNERSHIP) {
129 g_.release();
130 }
131 }
132
Evaluate(double s,double rho[3]) const133 void ComposedLoss::Evaluate(double s, double rho[3]) const {
134 double rho_f[3], rho_g[3];
135 g_->Evaluate(s, rho_g);
136 f_->Evaluate(rho_g[0], rho_f);
137 rho[0] = rho_f[0];
138 // f'(g(s)) * g'(s).
139 rho[1] = rho_f[1] * rho_g[1];
140 // f''(g(s)) * g'(s) * g'(s) + f'(g(s)) * g''(s).
141 rho[2] = rho_f[2] * rho_g[1] * rho_g[1] + rho_f[1] * rho_g[2];
142 }
143
Evaluate(double s,double rho[3]) const144 void ScaledLoss::Evaluate(double s, double rho[3]) const {
145 if (rho_.get() == NULL) {
146 rho[0] = a_ * s;
147 rho[1] = a_;
148 rho[2] = 0.0;
149 } else {
150 rho_->Evaluate(s, rho);
151 rho[0] *= a_;
152 rho[1] *= a_;
153 rho[2] *= a_;
154 }
155 }
156
157 } // namespace ceres
158