internal/ceres/line_search_minimizer.cc - ceres-solver - Git at Google

 // Ceres Solver - A fast non-linear least squares minimizer
 // Copyright 2012 Google Inc. All rights reserved.
 // http://code.google.com/p/ceres-solver/
 //
 // 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)
 //
 // Generic loop for line search based optimization algorithms.
 //
 // This is primarily inpsired by the minFunc packaged written by Mark
 // Schmidt.
 //
 // http://www.di.ens.fr/~mschmidt/Software/minFunc.html
 //
 // For details on the theory and implementation see "Numerical
 // Optimization" by Nocedal & Wright.

 #include "ceres/line_search_minimizer.h"

 #include <algorithm>
 #include <cstdlib>
 #include <cmath>
 #include <string>
 #include <vector>

 #include "Eigen/Dense"
 #include "ceres/array_utils.h"
 #include "ceres/evaluator.h"
 #include "ceres/internal/eigen.h"
 #include "ceres/internal/port.h"
 #include "ceres/internal/scoped_ptr.h"
 #include "ceres/line_search.h"
 #include "ceres/line_search_direction.h"
 #include "ceres/stringprintf.h"
 #include "ceres/types.h"
 #include "ceres/wall_time.h"
 #include "glog/logging.h"

 namespace ceres {
 namespace internal {
 namespace {
 // Small constant for various floating point issues.
 // TODO(sameeragarwal): Change to a better name if this has only one
 // use.
 const double kEpsilon = 1e-12;

 bool Evaluate(Evaluator* evaluator,
               const Vector& x,
               LineSearchMinimizer::State* state) {
   const bool status = evaluator->Evaluate(x.data(),
                                           &(state->cost),
                                           NULL,
                                           state->gradient.data(),
                                           NULL);
   if (status) {
     state->gradient_squared_norm = state->gradient.squaredNorm();
     state->gradient_max_norm = state->gradient.lpNorm<Eigen::Infinity>();
   }

   return status;
 }

 }  // namespace

 void LineSearchMinimizer::Minimize(const Minimizer::Options& options,
                                    double* parameters,
                                    Solver::Summary* summary) {
   double start_time = WallTimeInSeconds();
   double iteration_start_time =  start_time;

   Evaluator* evaluator = CHECK_NOTNULL(options.evaluator);
   const int num_parameters = evaluator->NumParameters();
   const int num_effective_parameters = evaluator->NumEffectiveParameters();

   summary->termination_type = NO_CONVERGENCE;
   summary->num_successful_steps = 0;
   summary->num_unsuccessful_steps = 0;

   VectorRef x(parameters, num_parameters);

   State current_state(num_parameters, num_effective_parameters);
   State previous_state(num_parameters, num_effective_parameters);

   Vector delta(num_effective_parameters);
   Vector x_plus_delta(num_parameters);

   IterationSummary iteration_summary;
   iteration_summary.iteration = 0;
   iteration_summary.step_is_valid = false;
   iteration_summary.step_is_successful = false;
   iteration_summary.cost_change = 0.0;
   iteration_summary.gradient_max_norm = 0.0;
   iteration_summary.step_norm = 0.0;
   iteration_summary.linear_solver_iterations = 0;
   iteration_summary.step_solver_time_in_seconds = 0;

   // Do initial cost and Jacobian evaluation.
   if (!Evaluate(evaluator, x, &current_state)) {
     LOG(WARNING) << "Terminating: Cost and gradient evaluation failed.";
     summary->termination_type = NUMERICAL_FAILURE;
     return;
   }

   summary->initial_cost = current_state.cost + summary->fixed_cost;
   iteration_summary.cost = current_state.cost + summary->fixed_cost;

   iteration_summary.gradient_max_norm = current_state.gradient_max_norm;

   // The initial gradient max_norm is bounded from below so that we do
   // not divide by zero.
   const double initial_gradient_max_norm =
       max(iteration_summary.gradient_max_norm, kEpsilon);
   const double absolute_gradient_tolerance =
       options.gradient_tolerance * initial_gradient_max_norm;

   if (iteration_summary.gradient_max_norm <= absolute_gradient_tolerance) {
     summary->termination_type = GRADIENT_TOLERANCE;
     VLOG(1) << "Terminating: Gradient tolerance reached."
             << "Relative gradient max norm: "
             << iteration_summary.gradient_max_norm / initial_gradient_max_norm
             << " <= " << options.gradient_tolerance;
     return;
   }

   iteration_summary.iteration_time_in_seconds =
       WallTimeInSeconds() - iteration_start_time;
   iteration_summary.cumulative_time_in_seconds =
       WallTimeInSeconds() - start_time
       + summary->preprocessor_time_in_seconds;
   summary->iterations.push_back(iteration_summary);

   LineSearchDirection::Options line_search_direction_options;
   line_search_direction_options.num_parameters = num_effective_parameters;
   line_search_direction_options.type = options.line_search_direction_type;
   line_search_direction_options.nonlinear_conjugate_gradient_type =
       options.nonlinear_conjugate_gradient_type;
   line_search_direction_options.max_lbfgs_rank = options.max_lbfgs_rank;
   scoped_ptr<LineSearchDirection> line_search_direction(
       LineSearchDirection::Create(line_search_direction_options));

   LineSearchFunction line_search_function(evaluator);
   LineSearch::Options line_search_options;
   line_search_options.function = &line_search_function;

   // TODO(sameeragarwal): Make this parameterizable over different
   // line searches.
   ArmijoLineSearch line_search;
   LineSearch::Summary line_search_summary;

   while (true) {
     if (!RunCallbacks(options.callbacks, iteration_summary, summary)) {
       return;
     }

     iteration_start_time = WallTimeInSeconds();
     if (iteration_summary.iteration >= options.max_num_iterations) {
       summary->termination_type = NO_CONVERGENCE;
       VLOG(1) << "Terminating: Maximum number of iterations reached.";
       break;
     }

     const double total_solver_time = iteration_start_time - start_time +
         summary->preprocessor_time_in_seconds;
     if (total_solver_time >= options.max_solver_time_in_seconds) {
       summary->termination_type = NO_CONVERGENCE;
       VLOG(1) << "Terminating: Maximum solver time reached.";
       break;
     }

     iteration_summary = IterationSummary();
     iteration_summary.iteration = summary->iterations.back().iteration + 1;

     bool line_search_status = true;
     if (iteration_summary.iteration == 1) {
       current_state.search_direction = -current_state.gradient;
     } else {
       line_search_status = line_search_direction->NextDirection(
           previous_state,
           current_state,
           &current_state.search_direction);
     }

     if (!line_search_status) {
       LOG(WARNING) << "Line search direction computation failed. "
           "Resorting to steepest descent.";
       current_state.search_direction = -current_state.gradient;
     }

     line_search_function.Init(x, current_state.search_direction);
     current_state.directional_derivative =
         current_state.gradient.dot(current_state.search_direction);

     // TODO(sameeragarwal): Refactor this into its own object and add
     // explanations for the various choices.
     const double initial_step_size = (iteration_summary.iteration == 1)
         ? min(1.0, 1.0 / current_state.gradient_max_norm)
         : min(1.0, 2.0 * (current_state.cost - previous_state.cost) /
               current_state.directional_derivative);

     line_search.Search(line_search_options,
                        initial_step_size,
                        current_state.cost,
                        current_state.directional_derivative,
                        &line_search_summary);

     current_state.step_size = line_search_summary.optimal_step_size;
     delta = current_state.step_size * current_state.search_direction;

     previous_state = current_state;

     // TODO(sameeragarwal): Collect stats.
     if (!evaluator->Plus(x.data(), delta.data(), x_plus_delta.data()) ||
         !Evaluate(evaluator, x_plus_delta, &current_state)) {
       LOG(WARNING) << "Evaluation failed.";
     } else {
       x = x_plus_delta;
     }

     iteration_summary.gradient_max_norm = current_state.gradient_max_norm;
     if (iteration_summary.gradient_max_norm <= absolute_gradient_tolerance) {
       summary->termination_type = GRADIENT_TOLERANCE;
       VLOG(1) << "Terminating: Gradient tolerance reached."
               << "Relative gradient max norm: "
               << iteration_summary.gradient_max_norm / initial_gradient_max_norm
               << " <= " << options.gradient_tolerance;
       break;
     }

     iteration_summary.cost_change = previous_state.cost - current_state.cost;
     const double absolute_function_tolerance =
         options.function_tolerance * previous_state.cost;
     if (fabs(iteration_summary.cost_change) < absolute_function_tolerance) {
       VLOG(1) << "Terminating. Function tolerance reached. "
               << "|cost_change|/cost: "
               << fabs(iteration_summary.cost_change) / previous_state.cost
               << " <= " << options.function_tolerance;
       summary->termination_type = FUNCTION_TOLERANCE;
       return;
     }

     iteration_summary.cost = current_state.cost + summary->fixed_cost;
     iteration_summary.step_norm = delta.norm();
     iteration_summary.step_is_valid = true;
     iteration_summary.step_is_successful = true;
     iteration_summary.step_norm = delta.norm();
     iteration_summary.step_size =  current_state.step_size;
     iteration_summary.line_search_function_evaluations =
         line_search_summary.num_evaluations;
     iteration_summary.iteration_time_in_seconds =
         WallTimeInSeconds() - iteration_start_time;
     iteration_summary.cumulative_time_in_seconds =
         WallTimeInSeconds() - start_time
         + summary->preprocessor_time_in_seconds;

     summary->iterations.push_back(iteration_summary);
   }
 }

 }  // namespace internal
 }  // namespace ceres
	// Ceres Solver - A fast non-linear least squares minimizer
	// Copyright 2012 Google Inc. All rights reserved.
	// http://code.google.com/p/ceres-solver/
	//
	// 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)
	//
	// Generic loop for line search based optimization algorithms.
	//
	// This is primarily inpsired by the minFunc packaged written by Mark
	// Schmidt.
	//
	// http://www.di.ens.fr/~mschmidt/Software/minFunc.html
	//
	// For details on the theory and implementation see "Numerical
	// Optimization" by Nocedal & Wright.

	#include "ceres/line_search_minimizer.h"

	#include <algorithm>
	#include <cstdlib>
	#include <cmath>
	#include <string>
	#include <vector>

	#include "Eigen/Dense"
	#include "ceres/array_utils.h"
	#include "ceres/evaluator.h"
	#include "ceres/internal/eigen.h"
	#include "ceres/internal/port.h"
	#include "ceres/internal/scoped_ptr.h"
	#include "ceres/line_search.h"
	#include "ceres/line_search_direction.h"
	#include "ceres/stringprintf.h"
	#include "ceres/types.h"
	#include "ceres/wall_time.h"
	#include "glog/logging.h"

	namespace ceres {
	namespace internal {
	namespace {
	// Small constant for various floating point issues.
	// TODO(sameeragarwal): Change to a better name if this has only one
	// use.
	const double kEpsilon = 1e-12;

	bool Evaluate(Evaluator* evaluator,
	const Vector& x,
	LineSearchMinimizer::State* state) {
	const bool status = evaluator->Evaluate(x.data(),
	&(state->cost),
	NULL,
	state->gradient.data(),
	NULL);
	if (status) {
	state->gradient_squared_norm = state->gradient.squaredNorm();
	state->gradient_max_norm = state->gradient.lpNorm<Eigen::Infinity>();
	}

	return status;
	}

	} // namespace

	void LineSearchMinimizer::Minimize(const Minimizer::Options& options,
	double* parameters,
	Solver::Summary* summary) {
	double start_time = WallTimeInSeconds();
	double iteration_start_time = start_time;

	Evaluator* evaluator = CHECK_NOTNULL(options.evaluator);
	const int num_parameters = evaluator->NumParameters();
	const int num_effective_parameters = evaluator->NumEffectiveParameters();

	summary->termination_type = NO_CONVERGENCE;
	summary->num_successful_steps = 0;
	summary->num_unsuccessful_steps = 0;

	VectorRef x(parameters, num_parameters);

	State current_state(num_parameters, num_effective_parameters);
	State previous_state(num_parameters, num_effective_parameters);

	Vector delta(num_effective_parameters);
	Vector x_plus_delta(num_parameters);

	IterationSummary iteration_summary;
	iteration_summary.iteration = 0;
	iteration_summary.step_is_valid = false;
	iteration_summary.step_is_successful = false;
	iteration_summary.cost_change = 0.0;
	iteration_summary.gradient_max_norm = 0.0;
	iteration_summary.step_norm = 0.0;
	iteration_summary.linear_solver_iterations = 0;
	iteration_summary.step_solver_time_in_seconds = 0;

	// Do initial cost and Jacobian evaluation.
	if (!Evaluate(evaluator, x, &current_state)) {
	LOG(WARNING) << "Terminating: Cost and gradient evaluation failed.";
	summary->termination_type = NUMERICAL_FAILURE;
	return;
	}

	summary->initial_cost = current_state.cost + summary->fixed_cost;
	iteration_summary.cost = current_state.cost + summary->fixed_cost;

	iteration_summary.gradient_max_norm = current_state.gradient_max_norm;

	// The initial gradient max_norm is bounded from below so that we do
	// not divide by zero.
	const double initial_gradient_max_norm =
	max(iteration_summary.gradient_max_norm, kEpsilon);
	const double absolute_gradient_tolerance =
	options.gradient_tolerance * initial_gradient_max_norm;

	if (iteration_summary.gradient_max_norm <= absolute_gradient_tolerance) {
	summary->termination_type = GRADIENT_TOLERANCE;
	VLOG(1) << "Terminating: Gradient tolerance reached."
	<< "Relative gradient max norm: "
	<< iteration_summary.gradient_max_norm / initial_gradient_max_norm
	<< " <= " << options.gradient_tolerance;
	return;
	}

	iteration_summary.iteration_time_in_seconds =
	WallTimeInSeconds() - iteration_start_time;
	iteration_summary.cumulative_time_in_seconds =
	WallTimeInSeconds() - start_time
	+ summary->preprocessor_time_in_seconds;
	summary->iterations.push_back(iteration_summary);

	LineSearchDirection::Options line_search_direction_options;
	line_search_direction_options.num_parameters = num_effective_parameters;
	line_search_direction_options.type = options.line_search_direction_type;
	line_search_direction_options.nonlinear_conjugate_gradient_type =
	options.nonlinear_conjugate_gradient_type;
	line_search_direction_options.max_lbfgs_rank = options.max_lbfgs_rank;
	scoped_ptr<LineSearchDirection> line_search_direction(
	LineSearchDirection::Create(line_search_direction_options));

	LineSearchFunction line_search_function(evaluator);
	LineSearch::Options line_search_options;
	line_search_options.function = &line_search_function;

	// TODO(sameeragarwal): Make this parameterizable over different
	// line searches.
	ArmijoLineSearch line_search;
	LineSearch::Summary line_search_summary;

	while (true) {
	if (!RunCallbacks(options.callbacks, iteration_summary, summary)) {
	return;
	}

	iteration_start_time = WallTimeInSeconds();
	if (iteration_summary.iteration >= options.max_num_iterations) {
	summary->termination_type = NO_CONVERGENCE;
	VLOG(1) << "Terminating: Maximum number of iterations reached.";
	break;
	}

	const double total_solver_time = iteration_start_time - start_time +
	summary->preprocessor_time_in_seconds;
	if (total_solver_time >= options.max_solver_time_in_seconds) {
	summary->termination_type = NO_CONVERGENCE;
	VLOG(1) << "Terminating: Maximum solver time reached.";
	break;
	}

	iteration_summary = IterationSummary();
	iteration_summary.iteration = summary->iterations.back().iteration + 1;

	bool line_search_status = true;
	if (iteration_summary.iteration == 1) {
	current_state.search_direction = -current_state.gradient;
	} else {
	line_search_status = line_search_direction->NextDirection(
	previous_state,
	current_state,
	&current_state.search_direction);
	}

	if (!line_search_status) {
	LOG(WARNING) << "Line search direction computation failed. "
	"Resorting to steepest descent.";
	current_state.search_direction = -current_state.gradient;
	}

	line_search_function.Init(x, current_state.search_direction);
	current_state.directional_derivative =
	current_state.gradient.dot(current_state.search_direction);

	// TODO(sameeragarwal): Refactor this into its own object and add
	// explanations for the various choices.
	const double initial_step_size = (iteration_summary.iteration == 1)
	? min(1.0, 1.0 / current_state.gradient_max_norm)
	: min(1.0, 2.0 * (current_state.cost - previous_state.cost) /
	current_state.directional_derivative);

	line_search.Search(line_search_options,
	initial_step_size,
	current_state.cost,
	current_state.directional_derivative,
	&line_search_summary);

	current_state.step_size = line_search_summary.optimal_step_size;
	delta = current_state.step_size * current_state.search_direction;

	previous_state = current_state;

	// TODO(sameeragarwal): Collect stats.
	if (!evaluator->Plus(x.data(), delta.data(), x_plus_delta.data()) \|\|
	!Evaluate(evaluator, x_plus_delta, &current_state)) {
	LOG(WARNING) << "Evaluation failed.";
	} else {
	x = x_plus_delta;
	}

	iteration_summary.gradient_max_norm = current_state.gradient_max_norm;
	if (iteration_summary.gradient_max_norm <= absolute_gradient_tolerance) {
	summary->termination_type = GRADIENT_TOLERANCE;
	VLOG(1) << "Terminating: Gradient tolerance reached."
	<< "Relative gradient max norm: "
	<< iteration_summary.gradient_max_norm / initial_gradient_max_norm
	<< " <= " << options.gradient_tolerance;
	break;
	}

	iteration_summary.cost_change = previous_state.cost - current_state.cost;
	const double absolute_function_tolerance =
	options.function_tolerance * previous_state.cost;
	if (fabs(iteration_summary.cost_change) < absolute_function_tolerance) {
	VLOG(1) << "Terminating. Function tolerance reached. "
	<< "\|cost_change\|/cost: "
	<< fabs(iteration_summary.cost_change) / previous_state.cost
	<< " <= " << options.function_tolerance;
	summary->termination_type = FUNCTION_TOLERANCE;
	return;
	}

	iteration_summary.cost = current_state.cost + summary->fixed_cost;
	iteration_summary.step_norm = delta.norm();
	iteration_summary.step_is_valid = true;
	iteration_summary.step_is_successful = true;
	iteration_summary.step_norm = delta.norm();
	iteration_summary.step_size = current_state.step_size;
	iteration_summary.line_search_function_evaluations =
	line_search_summary.num_evaluations;
	iteration_summary.iteration_time_in_seconds =
	WallTimeInSeconds() - iteration_start_time;
	iteration_summary.cumulative_time_in_seconds =
	WallTimeInSeconds() - start_time
	+ summary->preprocessor_time_in_seconds;

	summary->iterations.push_back(iteration_summary);
	}
	}

	} // namespace internal
	} // namespace ceres