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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.
13 // * Neither the name of Google Inc. nor the names of its contributors may be
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
19 // IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
20 // ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
21 // LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
22 // CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
23 // SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
24 // INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
25 // CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
26 // ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
27 // POSSIBILITY OF SUCH DAMAGE.
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