gtsam/gtsam/nonlinear/NonlinearConjugateGradientOptimizer.h

/* ----------------------------------------------------------------------------

 * GTSAM Copyright 2010, Georgia Tech Research Corporation,
 * Atlanta, Georgia 30332-0415
 * All Rights Reserved
 * Authors: Frank Dellaert, et al. (see THANKS for the full author list)

 * See LICENSE for the license information

 * -------------------------------------------------------------------------- */

/**
 * @file   NonlinearConjugateGradientOptimizer.h
 * @brief  Simple non-linear optimizer that solves using *non-preconditioned* CG
 * @author Yong-Dian Jian
 * @date   June 11, 2012
 */

#pragma once

#include <gtsam/base/Manifold.h>
#include <gtsam/nonlinear/NonlinearOptimizer.h>

namespace gtsam {

/**  An implementation of the nonlinear CG method using the template below */
class GTSAM_EXPORT NonlinearConjugateGradientOptimizer : public NonlinearOptimizer {

  /* a class for the nonlinearConjugateGradient template */
  class System {
  public:
    typedef Values State;
    typedef VectorValues Gradient;
    typedef NonlinearOptimizerParams Parameters;

  protected:
    const NonlinearFactorGraph &graph_;

  public:
    System(const NonlinearFactorGraph &graph) :
        graph_(graph) {
    }
    double error(const State &state) const;
    Gradient gradient(const State &state) const;
    State advance(const State &current, const double alpha,
        const Gradient &g) const;
  };

public:

  typedef NonlinearOptimizer Base;
  typedef NonlinearOptimizerParams Parameters;
  typedef std::shared_ptr<NonlinearConjugateGradientOptimizer> shared_ptr;

protected:
  Parameters params_;

  const NonlinearOptimizerParams& _params() const override {
    return params_;
  }

public:

  /// Constructor
  NonlinearConjugateGradientOptimizer(const NonlinearFactorGraph& graph,
      const Values& initialValues, const Parameters& params = Parameters());

  /// Destructor
  ~NonlinearConjugateGradientOptimizer() override {
  }

  /** 
   * Perform a single iteration, returning GaussianFactorGraph corresponding to 
   * the linearized factor graph.
   */
  GaussianFactorGraph::shared_ptr iterate() override;

  /** 
   * Optimize for the maximum-likelihood estimate, returning a the optimized 
   * variable assignments.
   */
  const Values& optimize() override;
};

/** Implement the golden-section line search algorithm */
template<class S, class V, class W>
double lineSearch(const S &system, const V currentValues, const W &gradient) {

  /* normalize it such that it becomes a unit vector */
  const double g = gradient.norm();

  // perform the golden section search algorithm to decide the the optimal step size
  // detail refer to http://en.wikipedia.org/wiki/Golden_section_search
  const double phi = 0.5 * (1.0 + std::sqrt(5.0)), resphi = 2.0 - phi, tau =
      1e-5;
  double minStep = -1.0 / g, maxStep = 0, newStep = minStep
      + (maxStep - minStep) / (phi + 1.0);

  V newValues = system.advance(currentValues, newStep, gradient);
  double newError = system.error(newValues);

  while (true) {
    const bool flag = (maxStep - newStep > newStep - minStep) ? true : false;
    const double testStep =
        flag ? newStep + resphi * (maxStep - newStep) :
            newStep - resphi * (newStep - minStep);

    if ((maxStep - minStep)
        < tau * (std::abs(testStep) + std::abs(newStep))) {
      return 0.5 * (minStep + maxStep);
    }

    const V testValues = system.advance(currentValues, testStep, gradient);
    const double testError = system.error(testValues);

    // update the working range
    if (testError >= newError) {
      if (flag)
        maxStep = testStep;
      else
        minStep = testStep;
    } else {
      if (flag) {
        minStep = newStep;
        newStep = testStep;
        newError = testError;
      } else {
        maxStep = newStep;
        newStep = testStep;
        newError = testError;
      }
    }
  }
  return 0.0;
}

/**
 * Implement the nonlinear conjugate gradient method using the Polak-Ribiere formula suggested in
 * http://en.wikipedia.org/wiki/Nonlinear_conjugate_gradient_method.
 *
 * The S (system) class requires three member functions: error(state), gradient(state) and
 * advance(state, step-size, direction). The V class denotes the state or the solution.
 *
 * The last parameter is a switch between gradient-descent and conjugate gradient
 */
template<class S, class V>
std::tuple<V, int> nonlinearConjugateGradient(const S &system,
    const V &initial, const NonlinearOptimizerParams &params,
    const bool singleIteration, const bool gradientDescent = false) {

  // GTSAM_CONCEPT_MANIFOLD_TYPE(V)

  size_t iteration = 0;

  // check if we're already close enough
  double currentError = system.error(initial);
  if (currentError <= params.errorTol) {
    if (params.verbosity >= NonlinearOptimizerParams::ERROR) {
      std::cout << "Exiting, as error = " << currentError << " < "
          << params.errorTol << std::endl;
    }
    return {initial, iteration};
  }

  V currentValues = initial;
  typename S::Gradient currentGradient = system.gradient(currentValues),
      prevGradient, direction = currentGradient;

  /* do one step of gradient descent */
  V prevValues = currentValues;
  double prevError = currentError;
  double alpha = lineSearch(system, currentValues, direction);
  currentValues = system.advance(prevValues, alpha, direction);
  currentError = system.error(currentValues);

  // Maybe show output
  if (params.verbosity >= NonlinearOptimizerParams::ERROR)
    std::cout << "Initial error: " << currentError << std::endl;

  // Iterative loop
  do {
    if (gradientDescent == true) {
      direction = system.gradient(currentValues);
    } else {
      prevGradient = currentGradient;
      currentGradient = system.gradient(currentValues);
      // Polak-Ribiere: beta = g'*(g_n-g_n-1)/g_n-1'*g_n-1
      const double beta = std::max(0.0,
          currentGradient.dot(currentGradient - prevGradient)
              / prevGradient.dot(prevGradient));
      direction = currentGradient + (beta * direction);
    }

    alpha = lineSearch(system, currentValues, direction);

    prevValues = currentValues;
    prevError = currentError;

    currentValues = system.advance(prevValues, alpha, direction);
    currentError = system.error(currentValues);

    // User hook:
    if (params.iterationHook)
      params.iterationHook(iteration, prevError, currentError);

    // Maybe show output
    if (params.verbosity >= NonlinearOptimizerParams::ERROR)
      std::cout << "iteration: " << iteration << ", currentError: " << currentError << std::endl;
  } while (++iteration < params.maxIterations && !singleIteration
      && !checkConvergence(params.relativeErrorTol, params.absoluteErrorTol,
          params.errorTol, prevError, currentError, params.verbosity));

  // Printing if verbose
  if (params.verbosity >= NonlinearOptimizerParams::ERROR
      && iteration >= params.maxIterations)
    std::cout
        << "nonlinearConjugateGradient: Terminating because reached maximum iterations"
        << std::endl;

  return {currentValues, iteration};
}

} // \ namespace gtsam