//                                               -*- C++ -*-
/**
 *  @brief A class which implements a discrete Markov chain process
 *
 *  Copyright 2005-2023 Airbus-EDF-IMACS-ONERA-Phimeca
 *
 *  This library is free software: you can redistribute it and/or modify
 *  it under the terms of the GNU Lesser General Public License as published by
 *  the Free Software Foundation, either version 3 of the License, or
 *  (at your option) any later version.
 *
 *  This library is distributed in the hope that it will be useful,
 *  but WITHOUT ANY WARRANTY; without even the implied warranty of
 *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 *  GNU Lesser General Public License for more details.
 *
 *  You should have received a copy of the GNU Lesser General Public License
 *  along with this library.  If not, see <http://www.gnu.org/licenses/>.
 *
 */

#include <iostream>
#include "openturns/DiscreteMarkovChain.hxx"
#include "openturns/PersistentObjectFactory.hxx"
#include "openturns/Dirac.hxx"
#include "openturns/ResourceMap.hxx"
#include "openturns/Point.hxx"
#include "openturns/SquareComplexMatrix.hxx"
#include "openturns/DistFunc.hxx"


BEGIN_NAMESPACE_OPENTURNS

CLASSNAMEINIT(DiscreteMarkovChain)

static const Factory<DiscreteMarkovChain> Factory_DiscreteMarkovChain;

/* Default constructor */
DiscreteMarkovChain::DiscreteMarkovChain()
  : ProcessImplementation()
  , origin_(Dirac(0))
  , transitionMatrix_(IdentityMatrix(1))
  , currentState_(0)
{
  // Set the dimension of the process
  setOutputDimension(1);
}

/* Standard constructors */
DiscreteMarkovChain::DiscreteMarkovChain(const Distribution & origin,
    const SquareMatrix & transitionMatrix)
  : ProcessImplementation()
  , origin_(origin)
  , transitionMatrix_(transitionMatrix.transpose())
  , currentState_(0)
{
  // Set the dimension of the process
  setOutputDimension(1);

  // Set the transition matrix of the process
  setTransitionMatrix(transitionMatrix);

  // Set the origin of the process
  setOrigin(origin);

  // Set the currentState of the process
  currentState_ = origin.getRealization()[0];
}

DiscreteMarkovChain::DiscreteMarkovChain(const Distribution & origin,
    const SquareMatrix & transitionMatrix,
    const RegularGrid & timeGrid)
  : ProcessImplementation()
  , origin_(origin)
  , transitionMatrix_(transitionMatrix.transpose())
  , currentState_(0)
{
  // Set the dimension of the process
  setOutputDimension(1);

  // Set the transition matrix of the process
  setTransitionMatrix(transitionMatrix);

  // Set the origin of the process
  setOrigin(origin);

  // Set the currentState of the process
  currentState_ = origin.getRealization()[0];

  // Set the time grid of the process
  setTimeGrid(timeGrid);
}

/* Constructors with fixed origin */
DiscreteMarkovChain::DiscreteMarkovChain(const UnsignedInteger origin,
    const SquareMatrix & transitionMatrix)
  : ProcessImplementation()
  , origin_(Dirac(origin))
  , transitionMatrix_(transitionMatrix.transpose())
  , currentState_(origin)
{
  // Set the dimension of the process
  setOutputDimension(1);

  // Set the transition matrix of the process
  setTransitionMatrix(transitionMatrix);

  // Set the origin of the process
  setOrigin(Dirac(origin));

  // Set the currentState of the process
  currentState_ = origin;
}

DiscreteMarkovChain::DiscreteMarkovChain(const UnsignedInteger origin,
    const SquareMatrix & transitionMatrix,
    const RegularGrid & timeGrid)
  : ProcessImplementation()
  , origin_(Dirac(origin))
  , transitionMatrix_(transitionMatrix.transpose())
  , currentState_(origin)
{
  // Set the dimension of the process
  setOutputDimension(1);

  // Set the transition matrix of the process
  setTransitionMatrix(transitionMatrix);

  // Set the origin of the process
  setOrigin(Dirac(origin));

  // Set the time grid of the process
  setTimeGrid(timeGrid);
}

/* Virtual constructor */
DiscreteMarkovChain * DiscreteMarkovChain::clone() const
{
  return new DiscreteMarkovChain(*this);
}

/* String converters */
String DiscreteMarkovChain::__repr__() const
{
  OSS oss;
  oss << "class=" << DiscreteMarkovChain::GetClassName()
      << ", origin=" << origin_
      << ", transition matrix=" << transitionMatrix_.transpose()
      << ", time grid=" << getTimeGrid();
  return oss;
}

String DiscreteMarkovChain::__str__(const String & offset) const
{
  OSS oss;
  oss << "DiscreteMarkovChain(origin=" << origin_.__str__(offset)
      << ", transition=" << PersistentCollection<Scalar>(*transitionMatrix_.transpose().getImplementation()).__str__(offset)
      << ")";
  return oss;
}

/* Realization accessor */
Field DiscreteMarkovChain::getRealization() const
{
  const UnsignedInteger size = mesh_.getVerticesNumber();
  const UnsignedInteger dimension = transitionMatrix_.getNbColumns();

  /* Loop on mesh points */
  Sample data(size, 1);
  data(0, 0) = origin_.getRealization()[0];
  currentState_ = data(0, 0) ;
  for (UnsignedInteger i = 1; i < size; ++i)
  {
    /* Definition of the weights */
    Point weights(dimension, 0.0);
    std::copy(&transitionMatrix_(0, currentState_), &transitionMatrix_(0, currentState_) + dimension, weights.begin());

    /* Get a realization of the distribution */
    data(i, 0) = DistFunc::rDiscrete(weights);
    currentState_ = data(i, 0);
  }
  return Field(mesh_, data);
}

/* Compute the next steps of a Markov chain */
TimeSeries DiscreteMarkovChain::getFuture(const UnsignedInteger stepNumber) const
{
  // TimeGrid of the process
  RegularGrid timeGrid(getTimeGrid());

  if (stepNumber == 0) throw InvalidArgumentException(HERE) << "Error: the number of future steps must be positive.";

  // TimeGrid associated with the possible future
  const Scalar timeStep = RegularGrid(mesh_).getStep();
  const RegularGrid futurTimeGrid(RegularGrid(mesh_).getEnd(), timeStep, stepNumber);
  const UnsignedInteger size = futurTimeGrid.getVerticesNumber();

  // Loop on mesh points
  const UnsignedInteger dimension = transitionMatrix_.getNbColumns();
  UnsignedInteger previous = currentState_;

  Sample data(size, 1);
  data(0, 0) = previous;
  for (UnsignedInteger i = 1; i < size; ++i)
  {
    // Definition of the distribution
    Point weights(dimension, 0.0);
    std::copy(&transitionMatrix_(0, previous), &transitionMatrix_(0, previous) + dimension, weights.begin());

    /* Get a realization of the distribution */
    data(i, 0) = DistFunc::rDiscrete(weights);
    previous = data(i, 0);
  }
  return TimeSeries(futurTimeGrid, data);
}

/* Transition matrix accessors */
SquareMatrix DiscreteMarkovChain::getTransitionMatrix() const
{
  // For memory access purposes, transition matrix is stored transposed
  return transitionMatrix_.transpose();
}

void DiscreteMarkovChain::setTransitionMatrix(const SquareMatrix & transitionMatrix)
{
  // For memory access purposes, transition matrix is stored transposed
  const SquareMatrix transitionTransposed(transitionMatrix.transpose());

  // Check transition matrix dimension consistency with current state
  if (transitionTransposed.getNbColumns() <= currentState_)
  {
    LOGWARN(OSS() << "Warning: the given transition matrix has a dimension = " << transitionTransposed.getNbColumns() << " incompatible with the current state = " << currentState_ << ". Current state is set to 0.");
    currentState_ = 0;
  }

  // Check transition matrix dimension consistency with origin
  if (transitionTransposed.getNbColumns() <= origin_.getRange().getUpperBound()[0])
  {
    LOGWARN(OSS() << "Warning: the given transition matrix has a dimension = " << transitionTransposed.getNbColumns() << " incompatible with the origin distribution. Origin distribution is set to Dirac(0).");
    setOrigin(0);
  }

  // Check if transition matrix is stochastic
  const Point ones(transitionTransposed.getNbColumns(), 1.0);
  const Point sums(transitionMatrix * ones);
  for (UnsignedInteger i = 0; i < transitionMatrix.getNbRows(); ++i)
  {
    if (!(std::abs(sums[i] - 1.0) < ResourceMap::GetAsScalar("DiscreteMarkovChain-ProbabilitySumPrecision"))) throw InvalidArgumentException(HERE) << "Error: the given transition matrix is not stochastic. Sum of line " << i + 1 << " is equal to " << sums[i];
  }

  // Set transitionMatrix_ attribute
  transitionMatrix_ = transitionTransposed;
}

/* Origin accessors */
Distribution DiscreteMarkovChain::getOrigin() const
{
  return origin_;
}

void DiscreteMarkovChain::setOrigin(const Distribution & origin)
{
  // Check if distribution is 1D
  if (origin.getDimension() != 1) throw InvalidArgumentException(HERE) << "Error: the given origin distribution must be 1D.";

  // Check integral
  if (!origin.isIntegral()) throw InvalidArgumentException(HERE) << "Error: the given origin distribution must be integer-valued.";

  // Check support consistence with transition matrix dimension
  const Interval support(origin.getRange());
  const Bool flb = support.getFiniteLowerBound()[0] > 0;
  const Scalar lb(support.getLowerBound()[0]);
  const Bool fub = support.getFiniteUpperBound()[0] > 0;
  const Scalar ub(support.getUpperBound()[0]);

  if (!flb || lb < 0.0) throw InvalidArgumentException(HERE) << "Error: the given origin distribution support must be positive.";
  if (!fub || ub >= transitionMatrix_.getNbRows()) throw InvalidArgumentException(HERE) << "Error: the given origin distribution support exceeds the number of states of the process = " << transitionMatrix_.getNbRows();

  origin_ = origin;
}


void DiscreteMarkovChain::setOrigin(const UnsignedInteger origin)
{
  if (origin >= transitionMatrix_.getNbRows()) throw InvalidArgumentException(HERE) << "Error: the given origin state exceeds the number of states of the process = " << transitionMatrix_.getNbRows();
  origin_ = Dirac(origin);
}

/* Mesh accessor */
void DiscreteMarkovChain::setMesh(const Mesh & mesh)
{
  if(!mesh.isRegular()) throw InvalidArgumentException(HERE) << "Error: the mesh must be regular.";
  ProcessImplementation::setMesh(mesh);
}

/* Stationary distribution computation */
UserDefined DiscreteMarkovChain::computeStationaryDistribution() const
{
  const UnsignedInteger dimension = transitionMatrix_.getDimension();
  SquareComplexMatrix eigenvectors;
  const SquareMatrix::ComplexCollection eigenvalues(transitionMatrix_.transpose().computeEV(eigenvectors));
  // Find the largest eigenvalue, exactly equal to one in theory
  Scalar largestEV = eigenvalues[0].real();
  UnsignedInteger indexMax = 0;
  for (UnsignedInteger i = 1; i < dimension; ++i)
    if (!(eigenvalues[i].real() < largestEV))
    {
      largestEV = eigenvalues[i].real();
      indexMax = i;
    }
  // Now extract the corresponding eigenvector. We know that it can be chosen with positive components and a L1 norm equal to 1, and it is the probability table of the stationary distribution. There is no need to normalize it as it is done in the UserDefined distribution.
  Sample support(dimension, 1);
  Point probabilities(dimension);
  for (UnsignedInteger i = 0; i < dimension; ++i)
  {
    support(i, 0) = i;
    probabilities[i] = std::abs(eigenvectors(i, indexMax).real());
  }
  return UserDefined(support, probabilities);
}

/* DOT export */
void DiscreteMarkovChain::exportToDOTFile(const FileName & filename) const
{
  std::ofstream dotFile(filename.c_str());
  if (dotFile.fail())
    throw FileOpenException(HERE) << "Could not open file " << filename;
  dotFile.imbue(std::locale("C"));
  dotFile << "digraph " << getName() << " {\n";
  dotFile << "layout=" << ResourceMap::Get("DiscreteMarkovChain-DOTLayout") << "\n";
  dotFile << "node[shape=" << ResourceMap::Get("DiscreteMarkovChain-DOTNodeShape") << ", color=" << ResourceMap::Get("DiscreteMarkovChain-DOTNodeColor") << "]\n";
  const String arcOptions((ResourceMap::Get("DiscreteMarkovChain-DOTArcColor") != "black") ? String(OSS() << ", color=" << ResourceMap::Get("DiscreteMarkovChain-DOTArcColor")) : "");
  for (UnsignedInteger j = 0; j < transitionMatrix_.getNbRows(); ++ j)
    for (UnsignedInteger i = 0; i < transitionMatrix_.getNbRows(); ++ i)
      if (transitionMatrix_(i, j) > 0.0)
        dotFile << j << "->" << i << " [label=" << transitionMatrix_(i, j) << arcOptions << "]\n";
  dotFile << "}\n";
  dotFile.close();
}

/* Method save() stores the object through the StorageManager */
void DiscreteMarkovChain::save(Advocate & adv) const
{
  ProcessImplementation::save(adv);
  adv.saveAttribute( "transitionMatrix", transitionMatrix_ );
  adv.saveAttribute( "origin_", origin_ );
  adv.saveAttribute( "currentState_", currentState_ );
}

/* Method load() reloads the object from the StorageManager */
void DiscreteMarkovChain::load(Advocate & adv)
{
  ProcessImplementation::load(adv);
  adv.loadAttribute( "transitionMatrix_", transitionMatrix_ );
  adv.loadAttribute( "origin_", origin_ );
  adv.loadAttribute( "currentState_", currentState_ );
}

END_NAMESPACE_OPENTURNS
