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

 * 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 Expression.h
 * @date September 18, 2014
 * @author Frank Dellaert
 * @author Paul Furgale
 * @brief Expressions for Block Automatic Differentiation
 */

#pragma once

#include <gtsam/nonlinear/Expression.h>
#include <gtsam/nonlinear/NonlinearFactor.h>
#include <gtsam/base/Testable.h>
#include <numeric>

namespace gtsam {

/**
 * Factor that supports arbitrary expressions via AD
 */
template<class T>
class ExpressionFactor: public NoiseModelFactor {

  T measurement_; ///< the measurement to be compared with the expression
  Expression<T> expression_; ///< the expression that is AD enabled
  FastVector<int> dims_; ///< dimensions of the Jacobian matrices
  size_t augmentedCols_; ///< total number of columns + 1 (for RHS)

  static const int Dim = traits::dimension<T>::value;

public:

  /// Constructor
  ExpressionFactor(const SharedNoiseModel& noiseModel, //
      const T& measurement, const Expression<T>& expression) :
      measurement_(measurement), expression_(expression) {
    if (!noiseModel)
      throw std::invalid_argument("ExpressionFactor: no NoiseModel.");
    if (noiseModel->dim() != Dim)
      throw std::invalid_argument(
          "ExpressionFactor was created with a NoiseModel of incorrect dimension.");
    noiseModel_ = noiseModel;

    // Get keys and dimensions for Jacobian matrices
    // An Expression is assumed unmutable, so we do this now
    boost::tie(keys_, dims_) = expression_.keysAndDims();

    // Add sizes to know how much memory to allocate on stack in linearize
    augmentedCols_ = std::accumulate(dims_.begin(), dims_.end(), 1);

#ifdef DEBUG_ExpressionFactor
    BOOST_FOREACH(size_t d, dims_)
    std::cout << d << " ";
    std::cout << " -> " << Dim << "x" << augmentedCols_ << std::endl;
#endif
  }

  /**
   * Error function *without* the NoiseModel, \f$ h(x)-z \f$.
   * We override this method to provide
   * both the function evaluation and its derivative(s) in H.
   */
  virtual Vector unwhitenedError(const Values& x,
      boost::optional<std::vector<Matrix>&> H = boost::none) const {
    DefaultChart<T> chart;
    if (H) {
      const T value = expression_.value(x, keys_, dims_, *H);
      return chart.local(measurement_, value);
    } else {
      const T value = expression_.value(x);
      return chart.local(measurement_, value);
    }
  }

  virtual boost::shared_ptr<GaussianFactor> linearize(const Values& x) const {
    // Only linearize if the factor is active
    if (!active(x))
      return boost::shared_ptr<JacobianFactor>();

    // Create a writeable JacobianFactor in advance
    // In case noise model is constrained, we need to provide a noise model
    bool constrained = noiseModel_->isConstrained();
    boost::shared_ptr<JacobianFactor> factor(
        constrained ? new JacobianFactor(keys_, dims_, Dim,
            boost::static_pointer_cast<noiseModel::Constrained>(noiseModel_)->unit()) :
            new JacobianFactor(keys_, dims_, Dim));

    // Wrap keys and VerticalBlockMatrix into structure passed to expression_
    VerticalBlockMatrix& Ab = factor->matrixObject();
    JacobianMap jacobianMap(keys_, Ab);

    // Zero out Jacobian so we can simply add to it
    Ab.matrix().setZero();

    // Get value and Jacobians, writing directly into JacobianFactor
    T value = expression_.value(x, jacobianMap); // <<< Reverse AD happens here !

    // Evaluate error and set RHS vector b
    DefaultChart<T> chart;
    Ab(size()).col(0) = -chart.local(measurement_, value);

    // Whiten the corresponding system, Ab already contains RHS
    Vector dummy(Dim);
    noiseModel_->WhitenSystem(Ab.matrix(), dummy);

    return factor;
  }
};
// ExpressionFactor

}