SimplicialCholesky.h

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// Eigen is free software; you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public
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/*

NOTE: the _symbolic, and _numeric functions has been adapted from
      the LDL library:

LDL Copyright (c) 2005 by Timothy A. Davis.  All Rights Reserved.

LDL License:

    Your use or distribution of LDL or any modified version of
    LDL implies that you agree to this License.

    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 2.1 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.

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 */

#ifndef EIGEN_SIMPLICIAL_CHOLESKY_H
#define EIGEN_SIMPLICIAL_CHOLESKY_H

enum SimplicialCholeskyMode {
  SimplicialCholeskyLLt,
  SimplicialCholeskyLDLt
};

template<typename _MatrixType, int _UpLo = Lower>
class SimplicialCholesky
{
  public:
    typedef _MatrixType MatrixType;
    enum { UpLo = _UpLo };
    typedef typename MatrixType::Scalar Scalar;
    typedef typename MatrixType::RealScalar RealScalar;
    typedef typename MatrixType::Index Index;
    typedef SparseMatrix<Scalar,ColMajor,Index> CholMatrixType;
    typedef Matrix<Scalar,MatrixType::ColsAtCompileTime,1> VectorType;

  public:

    SimplicialCholesky()
      : m_info(Success), m_isInitialized(false), m_LDLt(true)
    {}

    SimplicialCholesky(const MatrixType& matrix)
      : m_info(Success), m_isInitialized(false), m_LDLt(true)
    {
      compute(matrix);
    }

    ~SimplicialCholesky()
    {
    }
    
    inline Index cols() const { return m_matrix.cols(); }
    inline Index rows() const { return m_matrix.rows(); }
  
    SimplicialCholesky& setMode(SimplicialCholeskyMode mode)
    {
      switch(mode)
      {
        case SimplicialCholeskyLLt:
          m_LDLt = false;
          break;
        case SimplicialCholeskyLDLt:
          m_LDLt = true;
          break;
        default:
          break;
      }
      
      return *this;
    }
    
    ComputationInfo info() const
    {
      eigen_assert(m_isInitialized && "Decomposition is not initialized.");
      return m_info;
    }

    SimplicialCholesky& compute(const MatrixType& matrix)
    {
      analyzePattern(matrix);
      factorize(matrix);
      return *this;
    }
    
    template<typename Rhs>
    inline const internal::solve_retval<SimplicialCholesky, Rhs>
    solve(const MatrixBase<Rhs>& b) const
    {
      eigen_assert(m_isInitialized && "SimplicialCholesky is not initialized.");
      eigen_assert(rows()==b.rows()
                && "SimplicialCholesky::solve(): invalid number of rows of the right hand side matrix b");
      return internal::solve_retval<SimplicialCholesky, Rhs>(*this, b.derived());
    }
    
//     template<typename Rhs>
//     inline const internal::sparse_solve_retval<CholmodDecomposition, Rhs>
//     solve(const SparseMatrixBase<Rhs>& b) const
//     {
//       eigen_assert(m_isInitialized && "SimplicialCholesky is not initialized.");
//       eigen_assert(rows()==b.rows()
//                 && "SimplicialCholesky::solve(): invalid number of rows of the right hand side matrix b");
//       return internal::sparse_solve_retval<SimplicialCholesky, Rhs>(*this, b.derived());
//     }
    
    void analyzePattern(const MatrixType& a);
    
    
    void factorize(const MatrixType& a);
    
    const PermutationMatrix<Dynamic>& permutationP() const
    { return m_P; }
    
    const PermutationMatrix<Dynamic>& permutationPinv() const
    { return m_Pinv; }
    
    #ifndef EIGEN_PARSED_BY_DOXYGEN

    template<typename Rhs,typename Dest>
    void _solve(const MatrixBase<Rhs> &b, MatrixBase<Dest> &dest) const
    {
      eigen_assert(m_factorizationIsOk && "The decomposition is not in a valid state for solving, you must first call either compute() or symbolic()/numeric()");
      eigen_assert(m_matrix.rows()==b.rows());
      
      if(m_info!=Success)
        return;
    
      if(m_P.size()>0)
        dest = m_Pinv * b;
      else
        dest = b;
      
      if(m_LDLt)
      {
        if(m_matrix.nonZeros()>0) // otherwise L==I
          m_matrix.template triangularView<UnitLower>().solveInPlace(dest);
      
        dest = m_diag.asDiagonal().inverse() * dest;
      
        if (m_matrix.nonZeros()>0) // otherwise L==I
          m_matrix.adjoint().template triangularView<UnitUpper>().solveInPlace(dest);
      }
      else
      {
        if(m_matrix.nonZeros()>0) // otherwise L==I
          m_matrix.template triangularView<Lower>().solveInPlace(dest);
      
        if (m_matrix.nonZeros()>0) // otherwise L==I
          m_matrix.adjoint().template triangularView<Upper>().solveInPlace(dest);
      }
      
      if(m_P.size()>0)
        dest = m_P * dest;
    }
    
    /*
    template<typename RhsScalar, int RhsOptions, typename RhsIndex, typename DestScalar, int DestOptions, typename DestIndex>
    void _solve(const SparseMatrix<RhsScalar,RhsOptions,RhsIndex> &b, SparseMatrix<DestScalar,DestOptions,DestIndex> &dest) const
    {
      // TODO
    }
    */
    #endif // EIGEN_PARSED_BY_DOXYGEN
    
    template<typename Stream>
    void dumpMemory(Stream& s)
    {
      int total = 0;
      s << "  L:        " << ((total+=(m_matrix.cols()+1) * sizeof(int) + m_matrix.nonZeros()*(sizeof(int)+sizeof(Scalar))) >> 20) << "Mb" << "\n";
      s << "  diag:     " << ((total+=m_diag.size() * sizeof(Scalar)) >> 20) << "Mb" << "\n";
      s << "  tree:     " << ((total+=m_parent.size() * sizeof(int)) >> 20) << "Mb" << "\n";
      s << "  nonzeros: " << ((total+=m_nonZerosPerCol.size() * sizeof(int)) >> 20) << "Mb" << "\n";
      s << "  perm:     " << ((total+=m_P.size() * sizeof(int)) >> 20) << "Mb" << "\n";
      s << "  perm^-1:  " << ((total+=m_Pinv.size() * sizeof(int)) >> 20) << "Mb" << "\n";
      s << "  TOTAL:    " << (total>> 20) << "Mb" << "\n";
    }

  protected:
    struct keep_diag {
      inline bool operator() (const Index& row, const Index& col, const Scalar&) const
      {
        return row!=col;
      }
    };

    mutable ComputationInfo m_info;
    bool m_isInitialized;
    bool m_factorizationIsOk;
    bool m_analysisIsOk;
    bool m_LDLt;
    
    CholMatrixType m_matrix;
    VectorType m_diag;                  // the diagonal coefficients in case of a LDLt decomposition
    VectorXi m_parent;                  // elimination tree
    VectorXi m_nonZerosPerCol;
    PermutationMatrix<Dynamic> m_P;     // the permutation
    PermutationMatrix<Dynamic> m_Pinv;  // the inverse permutation
};

template<typename _MatrixType, int _UpLo>
void SimplicialCholesky<_MatrixType,_UpLo>::analyzePattern(const MatrixType& a)
{
  eigen_assert(a.rows()==a.cols());
  const Index size = a.rows();
  m_matrix.resize(size, size);
  m_parent.resize(size);
  m_nonZerosPerCol.resize(size);
  
  ei_declare_aligned_stack_constructed_variable(Index, tags, size, 0);
  
  // TODO allows to configure the permutation
  {
    CholMatrixType C;
    C = a.template selfadjointView<UpLo>();
    // remove diagonal entries:
    C.prune(keep_diag());
    internal::minimum_degree_ordering(C, m_P);
  }
  
  if(m_P.size()>0)
    m_Pinv  = m_P.inverse();
  else
    m_Pinv.resize(0);
  
  SparseMatrix<Scalar,ColMajor,Index> ap(size,size);
  ap.template selfadjointView<Upper>() = a.template selfadjointView<UpLo>().twistedBy(m_Pinv);
  
  for(Index k = 0; k < size; ++k)
  {
    /* L(k,:) pattern: all nodes reachable in etree from nz in A(0:k-1,k) */
    m_parent[k] = -1;             /* parent of k is not yet known */
    tags[k] = k;                  /* mark node k as visited */
    m_nonZerosPerCol[k] = 0;      /* count of nonzeros in column k of L */
    for(typename CholMatrixType::InnerIterator it(ap,k); it; ++it)
    {
      Index i = it.index();
      if(i < k)
      {
        /* follow path from i to root of etree, stop at flagged node */
        for(; tags[i] != k; i = m_parent[i])
        {
          /* find parent of i if not yet determined */
          if (m_parent[i] == -1)
            m_parent[i] = k;
          m_nonZerosPerCol[i]++;        /* L (k,i) is nonzero */
          tags[i] = k;                  /* mark i as visited */
        }
      }
    }
  }
  
  /* construct Lp index array from m_nonZerosPerCol column counts */
  Index* Lp = m_matrix._outerIndexPtr();
  Lp[0] = 0;
  for(Index k = 0; k < size; ++k)
    Lp[k+1] = Lp[k] + m_nonZerosPerCol[k] + (m_LDLt ? 0 : 1);

  m_matrix.resizeNonZeros(Lp[size]);
  
  m_isInitialized     = true;
  m_info              = Success;
  m_analysisIsOk      = true;
  m_factorizationIsOk = false;
}


template<typename _MatrixType, int _UpLo>
void SimplicialCholesky<_MatrixType,_UpLo>::factorize(const MatrixType& a)
{
  eigen_assert(m_analysisIsOk && "You must first call analyzePattern()");
  eigen_assert(a.rows()==a.cols());
  const Index size = a.rows();
  eigen_assert(m_parent.size()==size);
  eigen_assert(m_nonZerosPerCol.size()==size);

  const Index* Lp = m_matrix._outerIndexPtr();
  Index* Li = m_matrix._innerIndexPtr();
  Scalar* Lx = m_matrix._valuePtr();

  ei_declare_aligned_stack_constructed_variable(Scalar, y, size, 0);
  ei_declare_aligned_stack_constructed_variable(Index,  pattern, size, 0);
  ei_declare_aligned_stack_constructed_variable(Index,  tags, size, 0);

  SparseMatrix<Scalar,ColMajor,Index> ap(size,size);
  ap.template selfadjointView<Upper>() = a.template selfadjointView<UpLo>().twistedBy(m_Pinv);
  
  bool ok = true;
  m_diag.resize(m_LDLt ? size : 0);
  
  for(Index k = 0; k < size; ++k)
  {
    // compute nonzero pattern of kth row of L, in topological order
    y[k] = 0.0;                     // Y(0:k) is now all zero
    Index top = size;               // stack for pattern is empty
    tags[k] = k;                    // mark node k as visited
    m_nonZerosPerCol[k] = 0;        // count of nonzeros in column k of L
    for(typename MatrixType::InnerIterator it(ap,k); it; ++it)
    {
      Index i = it.index();
      if(i <= k)
      {
        y[i] += internal::conj(it.value());            /* scatter A(i,k) into Y (sum duplicates) */
        Index len;
        for(len = 0; tags[i] != k; i = m_parent[i])
        {
          pattern[len++] = i;     /* L(k,i) is nonzero */
          tags[i] = k;            /* mark i as visited */
        }
        while(len > 0)
          pattern[--top] = pattern[--len];
      }
    }

    /* compute numerical values kth row of L (a sparse triangular solve) */
    Scalar d = y[k];                  // get D(k,k) and clear Y(k)
    y[k] = 0.0;
    for(; top < size; ++top)
    {
      Index i = pattern[top];       /* pattern[top:n-1] is pattern of L(:,k) */
      Scalar yi = y[i];             /* get and clear Y(i) */
      y[i] = 0.0;
      
      /* the nonzero entry L(k,i) */
      Scalar l_ki;
      if(m_LDLt)
        l_ki = yi / m_diag[i];       
      else
        yi = l_ki = yi / Lx[Lp[i]];
      
      Index p2 = Lp[i] + m_nonZerosPerCol[i];
      Index p;
      for(p = Lp[i] + (m_LDLt ? 0 : 1); p < p2; ++p)
        y[Li[p]] -= internal::conj(Lx[p]) * yi;
      d -= l_ki * internal::conj(yi);
      Li[p] = k;                          /* store L(k,i) in column form of L */
      Lx[p] = l_ki;
      ++m_nonZerosPerCol[i];              /* increment count of nonzeros in col i */
    }
    if(m_LDLt)
      m_diag[k] = d;
    else
    {
      Index p = Lp[k]+m_nonZerosPerCol[k]++;
      Li[p] = k ;                /* store L(k,k) = sqrt (d) in column k */
      Lx[p] = internal::sqrt(d) ;
    }
    if(d == Scalar(0))
    {
      ok = false;                         /* failure, D(k,k) is zero */
      break;
    }
  }

  m_info = ok ? Success : NumericalIssue;
  m_factorizationIsOk = true;
}

namespace internal {
  
template<typename _MatrixType, int _UpLo, typename Rhs>
struct solve_retval<SimplicialCholesky<_MatrixType,_UpLo>, Rhs>
  : solve_retval_base<SimplicialCholesky<_MatrixType,_UpLo>, Rhs>
{
  typedef SimplicialCholesky<_MatrixType,_UpLo> Dec;
  EIGEN_MAKE_SOLVE_HELPERS(Dec,Rhs)

  template<typename Dest> void evalTo(Dest& dst) const
  {
    dec()._solve(rhs(),dst);
  }
};

template<typename _MatrixType, int _UpLo, typename Rhs>
struct sparse_solve_retval<SimplicialCholesky<_MatrixType,_UpLo>, Rhs>
  : sparse_solve_retval_base<SimplicialCholesky<_MatrixType,_UpLo>, Rhs>
{
  typedef SimplicialCholesky<_MatrixType,_UpLo> Dec;
  EIGEN_MAKE_SPARSE_SOLVE_HELPERS(Dec,Rhs)

  template<typename Dest> void evalTo(Dest& dst) const
  {
    dec()._solve(rhs(),dst);
  }
};

}

#endif // EIGEN_SIMPLICIAL_CHOLESKY_H