// Ceres Solver - A fast non-linear least squares minimizer

// Copyright 2015 Google Inc. All rights reserved.

// http://ceres-solver.org/

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// Author: sameeragarwal@google.com (Sameer Agarwal)

#include "ceres/levenberg_marquardt_strategy.h"

#include <cmath>

#include "Eigen/Core"

#include "ceres/array_utils.h"

#include "ceres/internal/eigen.h"

#include "ceres/linear_least_squares_problems.h"

#include "ceres/linear_solver.h"

#include "ceres/sparse_matrix.h"

#include "ceres/trust_region_strategy.h"

#include "ceres/types.h"

#include "glog/logging.h"

namespace ceres {

namespace internal {

LevenbergMarquardtStrategy::LevenbergMarquardtStrategy(

    const TrustRegionStrategy::Options& options)

    : linear_solver_(options.linear_solver),

      radius_(options.initial_radius),

      max_radius_(options.max_radius),

      min_diagonal_(options.min_lm_diagonal),

      max_diagonal_(options.max_lm_diagonal),

      decrease_factor_(2.0),

      reuse_diagonal_(false) {

  CHECK_NOTNULL(linear_solver_);

  CHECK_GT(min_diagonal_, 0.0);

  CHECK_LE(min_diagonal_, max_diagonal_);

  CHECK_GT(max_radius_, 0.0);

}

LevenbergMarquardtStrategy::~LevenbergMarquardtStrategy() {

}

TrustRegionStrategy::Summary LevenbergMarquardtStrategy::ComputeStep(

    const TrustRegionStrategy::PerSolveOptions& per_solve_options,

    SparseMatrix* jacobian,

    const double* residuals,

    double* step) {

  CHECK_NOTNULL(jacobian);

  CHECK_NOTNULL(residuals);

  CHECK_NOTNULL(step);

  const int num_parameters = jacobian->num_cols();

  if (!reuse_diagonal_) {

    if (diagonal_.rows() != num_parameters) {

      diagonal_.resize(num_parameters, 1);

    }

    jacobian->SquaredColumnNorm(diagonal_.data());

    for (int i = 0; i < num_parameters; ++i) {

      diagonal_[i] = std::min(std::max(diagonal_[i], min_diagonal_),

                              max_diagonal_);

    }

  }

  lm_diagonal_ = (diagonal_ / radius_).array().sqrt();

  LinearSolver::PerSolveOptions solve_options;

  solve_options.D = lm_diagonal_.data();

  solve_options.q_tolerance = per_solve_options.eta;

  // Disable r_tolerance checking. Since we only care about

  // termination via the q_tolerance. As Nash and Sofer show,

  // r_tolerance based termination is essentially useless in

  // Truncated Newton methods.

  solve_options.r_tolerance = -1.0;

  // Invalidate the output array lm_step, so that we can detect if

  // the linear solver generated numerical garbage.  This is known

  // to happen for the DENSE_QR and then DENSE_SCHUR solver when

  // the Jacobin is severly rank deficient and mu is too small.

  InvalidateArray(num_parameters, step);

  // Instead of solving Jx = -r, solve Jy = r.

  // Then x can be found as x = -y, but the inputs jacobian and residuals

  // do not need to be modified.

  LinearSolver::Summary linear_solver_summary =

      linear_solver_->Solve(jacobian, residuals, solve_options, step);

  if (linear_solver_summary.termination_type == LINEAR_SOLVER_FATAL_ERROR) {

    LOG(WARNING) << "Linear solver fatal error: "

                 << linear_solver_summary.message;

  } else if (linear_solver_summary.termination_type == LINEAR_SOLVER_FAILURE)  {

    LOG(WARNING) << "Linear solver failure. Failed to compute a step: "

                 << linear_solver_summary.message;

  } else if (!IsArrayValid(num_parameters, step)) {

    LOG(WARNING) << "Linear solver failure. Failed to compute a finite step.";

    linear_solver_summary.termination_type = LINEAR_SOLVER_FAILURE;

  } else {

    VectorRef(step, num_parameters) *= -1.0;

  }

  reuse_diagonal_ = true;

  if (per_solve_options.dump_format_type == CONSOLE ||

      (per_solve_options.dump_format_type != CONSOLE &&

       !per_solve_options.dump_filename_base.empty())) {

    if (!DumpLinearLeastSquaresProblem(per_solve_options.dump_filename_base,

                                       per_solve_options.dump_format_type,

                                       jacobian,

                                       solve_options.D,

                                       residuals,

                                       step,

                                       0)) {

      LOG(ERROR) << "Unable to dump trust region problem."

                 << " Filename base: " << per_solve_options.dump_filename_base;

    }

  }

  TrustRegionStrategy::Summary summary;

  summary.residual_norm = linear_solver_summary.residual_norm;

  summary.num_iterations = linear_solver_summary.num_iterations;

  summary.termination_type = linear_solver_summary.termination_type;

  return summary;

}

void LevenbergMarquardtStrategy::StepAccepted(double step_quality) {

  CHECK_GT(step_quality, 0.0);

  radius_ = radius_ / std::max(1.0 / 3.0,

                               1.0 - pow(2.0 * step_quality - 1.0, 3));

  radius_ = std::min(max_radius_, radius_);

  decrease_factor_ = 2.0;

  reuse_diagonal_ = false;

}

void LevenbergMarquardtStrategy::StepRejected(double step_quality) {

  radius_ = radius_ / decrease_factor_;

  decrease_factor_ *= 2.0;

  reuse_diagonal_ = true;

}

double LevenbergMarquardtStrategy::Radius() const {

  return radius_;

}

}  // namespace internal

}  // namespace ceres