// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2011-2014 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.

#ifndef EIGEN_ITERATIVE_SOLVER_BASE_H
#define EIGEN_ITERATIVE_SOLVER_BASE_H

namespace Eigen { 

/** \ingroup IterativeLinearSolvers_Module
  * \brief Base class for linear iterative solvers
  *
  * \sa class SimplicialCholesky, DiagonalPreconditioner, IdentityPreconditioner
  */
template< typename Derived>
class IterativeSolverBase : public SparseSolverBase<Derived>
{
protected:
  typedef SparseSolverBase<Derived> Base;
  using Base::m_isInitialized;
  
public:
  typedef typename internal::traits<Derived>::MatrixType MatrixType;
  typedef typename internal::traits<Derived>::Preconditioner Preconditioner;
  typedef typename MatrixType::Scalar Scalar;
  typedef typename MatrixType::StorageIndex StorageIndex;
  typedef typename MatrixType::RealScalar RealScalar;

  enum {
    ColsAtCompileTime = MatrixType::ColsAtCompileTime,
    MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime
  };

public:

  using Base::derived;

  /** Default constructor. */
  IterativeSolverBase()
    : m_dummy(0,0), mp_matrix(m_dummy)
  {
    init();
  }

  /** Initialize the solver with matrix \a A for further \c Ax=b solving.
    * 
    * This constructor is a shortcut for the default constructor followed
    * by a call to compute().
    * 
    * \warning this class stores a reference to the matrix A as well as some
    * precomputed values that depend on it. Therefore, if \a A is changed
    * this class becomes invalid. Call compute() to update it with the new
    * matrix A, or modify a copy of A.
    */
  template<typename MatrixDerived>
  explicit IterativeSolverBase(const EigenBase<MatrixDerived>& A)
    : mp_matrix(A.derived())
  {
    init();
    compute(mp_matrix);
  }

  ~IterativeSolverBase() {}
  
  /** Initializes the iterative solver for the sparsity pattern of the matrix \a A for further solving \c Ax=b problems.
    *
    * Currently, this function mostly calls analyzePattern on the preconditioner. In the future
    * we might, for instance, implement column reordering for faster matrix vector products.
    */
  template<typename MatrixDerived>
  Derived& analyzePattern(const EigenBase<MatrixDerived>& A)
  {
    grab(A.derived());
    m_preconditioner.analyzePattern(mp_matrix);
    m_isInitialized = true;
    m_analysisIsOk = true;
    m_info = m_preconditioner.info();
    return derived();
  }
  
  /** Initializes the iterative solver with the numerical values of the matrix \a A for further solving \c Ax=b problems.
    *
    * Currently, this function mostly calls factorize on the preconditioner.
    *
    * \warning this class stores a reference to the matrix A as well as some
    * precomputed values that depend on it. Therefore, if \a A is changed
    * this class becomes invalid. Call compute() to update it with the new
    * matrix A, or modify a copy of A.
    */
  template<typename MatrixDerived>
  Derived& factorize(const EigenBase<MatrixDerived>& A)
  {
    eigen_assert(m_analysisIsOk && "You must first call analyzePattern()"); 
    grab(A.derived());
    m_preconditioner.factorize(mp_matrix);
    m_factorizationIsOk = true;
    m_info = m_preconditioner.info();
    return derived();
  }

  /** Initializes the iterative solver with the matrix \a A for further solving \c Ax=b problems.
    *
    * Currently, this function mostly initializes/computes the preconditioner. In the future
    * we might, for instance, implement column reordering for faster matrix vector products.
    *
    * \warning this class stores a reference to the matrix A as well as some
    * precomputed values that depend on it. Therefore, if \a A is changed
    * this class becomes invalid. Call compute() to update it with the new
    * matrix A, or modify a copy of A.
    */
  template<typename MatrixDerived>
  Derived& compute(const EigenBase<MatrixDerived>& A)
  {
    grab(A.derived());
    m_preconditioner.compute(mp_matrix);
    m_isInitialized = true;
    m_analysisIsOk = true;
    m_factorizationIsOk = true;
    m_info = m_preconditioner.info();
    return derived();
  }

  /** \internal */
  Index rows() const { return mp_matrix.rows(); }

  /** \internal */
  Index cols() const { return mp_matrix.cols(); }

  /** \returns the tolerance threshold used by the stopping criteria.
    * \sa setTolerance()
    */
  RealScalar tolerance() const { return m_tolerance; }
  
  /** Sets the tolerance threshold used by the stopping criteria.
    *
    * This value is used as an upper bound to the relative residual error: |Ax-b|/|b|.
    * The default value is the machine precision given by NumTraits<Scalar>::epsilon()
    */
  Derived& setTolerance(const RealScalar& tolerance)
  {
    m_tolerance = tolerance;
    return derived();
  }

  /** \returns a read-write reference to the preconditioner for custom configuration. */
  Preconditioner& preconditioner() { return m_preconditioner; }
  
  /** \returns a read-only reference to the preconditioner. */
  const Preconditioner& preconditioner() const { return m_preconditioner; }

  /** \returns the max number of iterations.
    * It is either the value setted by setMaxIterations or, by default,
    * twice the number of columns of the matrix.
    */
  Index maxIterations() const
  {
    return (m_maxIterations<0) ? 2*mp_matrix.cols() : m_maxIterations;
  }
  
  /** Sets the max number of iterations.
    * Default is twice the number of columns of the matrix.
    */
  Derived& setMaxIterations(Index maxIters)
  {
    m_maxIterations = maxIters;
    return derived();
  }

  /** \returns the number of iterations performed during the last solve */
  Index iterations() const
  {
    eigen_assert(m_isInitialized && "ConjugateGradient is not initialized.");
    return m_iterations;
  }

  /** \returns the tolerance error reached during the last solve.
    * It is a close approximation of the true relative residual error |Ax-b|/|b|.
    */
  RealScalar error() const
  {
    eigen_assert(m_isInitialized && "ConjugateGradient is not initialized.");
    return m_error;
  }

  /** \returns the solution x of \f$ A x = b \f$ using the current decomposition of A
    * and \a x0 as an initial solution.
    *
    * \sa solve(), compute()
    */
  template<typename Rhs,typename Guess>
  inline const SolveWithGuess<Derived, Rhs, Guess>
  solveWithGuess(const MatrixBase<Rhs>& b, const Guess& x0) const
  {
    eigen_assert(m_isInitialized && "Solver is not initialized.");
    eigen_assert(derived().rows()==b.rows() && "solve(): invalid number of rows of the right hand side matrix b");
    return SolveWithGuess<Derived, Rhs, Guess>(derived(), b.derived(), x0);
  }

  /** \returns Success if the iterations converged, and NoConvergence otherwise. */
  ComputationInfo info() const
  {
    eigen_assert(m_isInitialized && "IterativeSolverBase is not initialized.");
    return m_info;
  }
  
  /** \internal */
  template<typename Rhs, typename DestScalar, int DestOptions, typename DestIndex>
  void _solve_impl(const Rhs& b, SparseMatrix<DestScalar,DestOptions,DestIndex> &dest) const
  {
    eigen_assert(rows()==b.rows());
    
    Index rhsCols = b.cols();
    Index size = b.rows();
    Eigen::Matrix<DestScalar,Dynamic,1> tb(size);
    Eigen::Matrix<DestScalar,Dynamic,1> tx(cols());
    // We do not directly fill dest because sparse expressions have to be free of aliasing issue.
    // For non square least-square problems, b and dest might not have the same size whereas they might alias each-other.
    SparseMatrix<DestScalar,DestOptions,DestIndex> tmp(cols(),rhsCols);
    for(Index k=0; k<rhsCols; ++k)
    {
      tb = b.col(k);
      tx = derived().solve(tb);
      tmp.col(k) = tx.sparseView(0);
    }
    tmp.swap(dest);
  }

protected:
  void init()
  {
    m_isInitialized = false;
    m_analysisIsOk = false;
    m_factorizationIsOk = false;
    m_maxIterations = -1;
    m_tolerance = NumTraits<Scalar>::epsilon();
  }
  
  template<typename MatrixDerived>
  void grab(const EigenBase<MatrixDerived> &A)
  {
    mp_matrix.~Ref<const MatrixType>();
    ::new (&mp_matrix) Ref<const MatrixType>(A.derived());
  }
  
  void grab(const Ref<const MatrixType> &A)
  {
    if(&(A.derived()) != &mp_matrix)
    {
      mp_matrix.~Ref<const MatrixType>();
      ::new (&mp_matrix) Ref<const MatrixType>(A);
    }
  }
  
  MatrixType m_dummy;
  Ref<const MatrixType> mp_matrix;
  Preconditioner m_preconditioner;

  Index m_maxIterations;
  RealScalar m_tolerance;
  
  mutable RealScalar m_error;
  mutable Index m_iterations;
  mutable ComputationInfo m_info;
  mutable bool m_analysisIsOk, m_factorizationIsOk;
};

} // end namespace Eigen

#endif // EIGEN_ITERATIVE_SOLVER_BASE_H