Squashed 'third_party/ceres/' content from commit e51e9b4
Change-Id: I763587619d57e594d3fa158dc3a7fe0b89a1743b
git-subtree-dir: third_party/ceres
git-subtree-split: e51e9b46f6ca88ab8b2266d0e362771db6d98067
diff --git a/internal/ceres/loss_function.cc b/internal/ceres/loss_function.cc
new file mode 100644
index 0000000..bf41b9e
--- /dev/null
+++ b/internal/ceres/loss_function.cc
@@ -0,0 +1,177 @@
+// Ceres Solver - A fast non-linear least squares minimizer
+// Copyright 2015 Google Inc. All rights reserved.
+// http://ceres-solver.org/
+//
+// Redistribution and use in source and binary forms, with or without
+// modification, are permitted provided that the following conditions are met:
+//
+// * Redistributions of source code must retain the above copyright notice,
+// this list of conditions and the following disclaimer.
+// * Redistributions in binary form must reproduce the above copyright notice,
+// this list of conditions and the following disclaimer in the documentation
+// and/or other materials provided with the distribution.
+// * Neither the name of Google Inc. nor the names of its contributors may be
+// used to endorse or promote products derived from this software without
+// specific prior written permission.
+//
+// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
+// AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+// ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
+// LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
+// CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
+// SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
+// INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
+// CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
+// ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+// POSSIBILITY OF SUCH DAMAGE.
+//
+// Author: sameeragarwal@google.com (Sameer Agarwal)
+//
+// Purpose: See .h file.
+
+#include "ceres/loss_function.h"
+
+#include <algorithm>
+#include <cmath>
+#include <cstddef>
+#include <limits>
+
+namespace ceres {
+
+void TrivialLoss::Evaluate(double s, double rho[3]) const {
+ rho[0] = s;
+ rho[1] = 1.0;
+ rho[2] = 0.0;
+}
+
+void HuberLoss::Evaluate(double s, double rho[3]) const {
+ if (s > b_) {
+ // Outlier region.
+ // 'r' is always positive.
+ const double r = sqrt(s);
+ rho[0] = 2.0 * a_ * r - b_;
+ rho[1] = std::max(std::numeric_limits<double>::min(), a_ / r);
+ rho[2] = - rho[1] / (2.0 * s);
+ } else {
+ // Inlier region.
+ rho[0] = s;
+ rho[1] = 1.0;
+ rho[2] = 0.0;
+ }
+}
+
+void SoftLOneLoss::Evaluate(double s, double rho[3]) const {
+ const double sum = 1.0 + s * c_;
+ const double tmp = sqrt(sum);
+ // 'sum' and 'tmp' are always positive, assuming that 's' is.
+ rho[0] = 2.0 * b_ * (tmp - 1.0);
+ rho[1] = std::max(std::numeric_limits<double>::min(), 1.0 / tmp);
+ rho[2] = - (c_ * rho[1]) / (2.0 * sum);
+}
+
+void CauchyLoss::Evaluate(double s, double rho[3]) const {
+ const double sum = 1.0 + s * c_;
+ const double inv = 1.0 / sum;
+ // 'sum' and 'inv' are always positive, assuming that 's' is.
+ rho[0] = b_ * log(sum);
+ rho[1] = std::max(std::numeric_limits<double>::min(), inv);
+ rho[2] = - c_ * (inv * inv);
+}
+
+void ArctanLoss::Evaluate(double s, double rho[3]) const {
+ const double sum = 1 + s * s * b_;
+ const double inv = 1 / sum;
+ // 'sum' and 'inv' are always positive.
+ rho[0] = a_ * atan2(s, a_);
+ rho[1] = std::max(std::numeric_limits<double>::min(), inv);
+ rho[2] = -2.0 * s * b_ * (inv * inv);
+}
+
+TolerantLoss::TolerantLoss(double a, double b)
+ : a_(a),
+ b_(b),
+ c_(b * log(1.0 + exp(-a / b))) {
+ CHECK_GE(a, 0.0);
+ CHECK_GT(b, 0.0);
+}
+
+void TolerantLoss::Evaluate(double s, double rho[3]) const {
+ const double x = (s - a_) / b_;
+ // The basic equation is rho[0] = b ln(1 + e^x). However, if e^x is too
+ // large, it will overflow. Since numerically 1 + e^x == e^x when the
+ // x is greater than about ln(2^53) for doubles, beyond this threshold
+ // we substitute x for ln(1 + e^x) as a numerically equivalent approximation.
+ static const double kLog2Pow53 = 36.7; // ln(MathLimits<double>::kEpsilon).
+ if (x > kLog2Pow53) {
+ rho[0] = s - a_ - c_;
+ rho[1] = 1.0;
+ rho[2] = 0.0;
+ } else {
+ const double e_x = exp(x);
+ rho[0] = b_ * log(1.0 + e_x) - c_;
+ rho[1] = std::max(std::numeric_limits<double>::min(), e_x / (1.0 + e_x));
+ rho[2] = 0.5 / (b_ * (1.0 + cosh(x)));
+ }
+}
+
+void TukeyLoss::Evaluate(double s, double* rho) const {
+ if (s <= a_squared_) {
+ // Inlier region.
+ const double value = 1.0 - s / a_squared_;
+ const double value_sq = value * value;
+ rho[0] = a_squared_ / 6.0 * (1.0 - value_sq * value);
+ rho[1] = 0.5 * value_sq;
+ rho[2] = -1.0 / a_squared_ * value;
+ } else {
+ // Outlier region.
+ rho[0] = a_squared_ / 6.0;
+ rho[1] = 0.0;
+ rho[2] = 0.0;
+ }
+}
+
+ComposedLoss::ComposedLoss(const LossFunction* f, Ownership ownership_f,
+ const LossFunction* g, Ownership ownership_g)
+ : f_(f),
+ g_(g),
+ ownership_f_(ownership_f),
+ ownership_g_(ownership_g) {
+ CHECK(f_ != nullptr);
+ CHECK(g_ != nullptr);
+}
+
+ComposedLoss::~ComposedLoss() {
+ if (ownership_f_ == DO_NOT_TAKE_OWNERSHIP) {
+ f_.release();
+ }
+ if (ownership_g_ == DO_NOT_TAKE_OWNERSHIP) {
+ g_.release();
+ }
+}
+
+void ComposedLoss::Evaluate(double s, double rho[3]) const {
+ double rho_f[3], rho_g[3];
+ g_->Evaluate(s, rho_g);
+ f_->Evaluate(rho_g[0], rho_f);
+ rho[0] = rho_f[0];
+ // f'(g(s)) * g'(s).
+ rho[1] = rho_f[1] * rho_g[1];
+ // f''(g(s)) * g'(s) * g'(s) + f'(g(s)) * g''(s).
+ rho[2] = rho_f[2] * rho_g[1] * rho_g[1] + rho_f[1] * rho_g[2];
+}
+
+void ScaledLoss::Evaluate(double s, double rho[3]) const {
+ if (rho_.get() == NULL) {
+ rho[0] = a_ * s;
+ rho[1] = a_;
+ rho[2] = 0.0;
+ } else {
+ rho_->Evaluate(s, rho);
+ rho[0] *= a_;
+ rho[1] *= a_;
+ rho[2] *= a_;
+ }
+}
+
+} // namespace ceres