// 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 <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_(CHECK_NOTNULL(f)),

      g_(CHECK_NOTNULL(g)),

      ownership_f_(ownership_f),

      ownership_g_(ownership_g) {

}

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