text: // This file is part of Eigen, a lightweight C++ template library
  // for linear algebra. Eigen itself is part of the KDE project.
  //
  // Copyright (C) 2008-2009 Gael Guennebaud <g.gael@free.fr>
  //
  // Eigen 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.
  //
  // Alternatively, you can redistribute it and/or
  // modify it under the terms of the GNU General Public License as
  // published by the Free Software Foundation; either version 2 of
  // the License, or (at your option) any later version.
  //
  // Eigen 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 or the
  // GNU General Public License for more details.
  //
  // You should have received a copy of the GNU Lesser General Public
  // License and a copy of the GNU General Public License along with
  // Eigen. If not, see <http://www.gnu.org/licenses/>.
  
  #ifndef EIGEN_UMFPACKSUPPORT_H
  #define EIGEN_UMFPACKSUPPORT_H
  
  /* TODO extract L, extract U, compute det, etc... */
  
  // generic double/complex<double> wrapper functions:
  
  inline void umfpack_free_numeric(void **Numeric, double)
  { umfpack_di_free_numeric(Numeric); }
  
  inline void umfpack_free_numeric(void **Numeric, std::complex<double>)
  { umfpack_zi_free_numeric(Numeric); }
  
  inline void umfpack_free_symbolic(void **Symbolic, double)
  { umfpack_di_free_symbolic(Symbolic); }
  
  inline void umfpack_free_symbolic(void **Symbolic, std::complex<double>)
  { umfpack_zi_free_symbolic(Symbolic); }
  
  inline int umfpack_symbolic(int n_row,int n_col,
                              const int Ap[], const int Ai[], const double Ax[], void **Symbolic,
                              const double Control [UMFPACK_CONTROL], double Info [UMFPACK_INFO])
  {
    return umfpack_di_symbolic(n_row,n_col,Ap,Ai,Ax,Symbolic,Control,Info);
  }
  
  inline int umfpack_symbolic(int n_row,int n_col,
                              const int Ap[], const int Ai[], const std::complex<double> Ax[], void **Symbolic,
                              const double Control [UMFPACK_CONTROL], double Info [UMFPACK_INFO])
  {
    return umfpack_zi_symbolic(n_row,n_col,Ap,Ai,&Ax[0].real(),0,Symbolic,Control,Info);
  }
  
  inline int umfpack_numeric( const int Ap[], const int Ai[], const double Ax[],
                              void *Symbolic, void **Numeric,
                              const double Control[UMFPACK_CONTROL],double Info [UMFPACK_INFO])
  {
    return umfpack_di_numeric(Ap,Ai,Ax,Symbolic,Numeric,Control,Info);
  }
  
  inline int umfpack_numeric( const int Ap[], const int Ai[], const std::complex<double> Ax[],
                              void *Symbolic, void **Numeric,
                              const double Control[UMFPACK_CONTROL],double Info [UMFPACK_INFO])
  {
    return umfpack_zi_numeric(Ap,Ai,&Ax[0].real(),0,Symbolic,Numeric,Control,Info);
  }
  
  inline int umfpack_solve( int sys, const int Ap[], const int Ai[], const double Ax[],
                            double X[], const double B[], void *Numeric,
                            const double Control[UMFPACK_CONTROL], double Info[UMFPACK_INFO])
  {
    return umfpack_di_solve(sys,Ap,Ai,Ax,X,B,Numeric,Control,Info);
  }
  
  inline int umfpack_solve( int sys, const int Ap[], const int Ai[], const std::complex<double> Ax[],
                            std::complex<double> X[], const std::complex<double> B[], void *Numeric,
                            const double Control[UMFPACK_CONTROL], double Info[UMFPACK_INFO])
  {
    return umfpack_zi_solve(sys,Ap,Ai,&Ax[0].real(),0,&X[0].real(),0,&B[0].real(),0,Numeric,Control,Info);
  }
  
  inline int umfpack_get_lunz(int *lnz, int *unz, int *n_row, int *n_col, int *nz_udiag, void *Numeric, double)
  {
    return umfpack_di_get_lunz(lnz,unz,n_row,n_col,nz_udiag,Numeric);
  }
  
  inline int umfpack_get_lunz(int *lnz, int *unz, int *n_row, int *n_col, int *nz_udiag, void *Numeric, std::complex<double>)
  {
    return umfpack_zi_get_lunz(lnz,unz,n_row,n_col,nz_udiag,Numeric);
  }
  
  inline int umfpack_get_numeric(int Lp[], int Lj[], double Lx[], int Up[], int Ui[], double Ux[],
                                 int P[], int Q[], double Dx[], int *do_recip, double Rs[], void *Numeric)
  {
    return umfpack_di_get_numeric(Lp,Lj,Lx,Up,Ui,Ux,P,Q,Dx,do_recip,Rs,Numeric);
  }
  
  inline int umfpack_get_numeric(int Lp[], int Lj[], std::complex<double> Lx[], int Up[], int Ui[], std::complex<double> Ux[],
                                 int P[], int Q[], std::complex<double> Dx[], int *do_recip, double Rs[], void *Numeric)
  {
    return umfpack_zi_get_numeric(Lp,Lj,Lx?&Lx[0].real():0,0,Up,Ui,Ux?&Ux[0].real():0,0,P,Q,
                                 Dx?&Dx[0].real():0,0,do_recip,Rs,Numeric);
  }
  
  inline int umfpack_get_determinant(double *Mx, double *Ex, void *NumericHandle, double User_Info [UMFPACK_INFO])
  {
    return umfpack_di_get_determinant(Mx,Ex,NumericHandle,User_Info);
  }
  
  inline int umfpack_get_determinant(std::complex<double> *Mx, double *Ex, void *NumericHandle, double User_Info [UMFPACK_INFO])
  {
    return umfpack_zi_get_determinant(&Mx->real(),0,Ex,NumericHandle,User_Info);
  }
  
  
  template<typename MatrixType>
  class SparseLU<MatrixType,UmfPack> : public SparseLU<MatrixType>
  {
    protected:
      typedef SparseLU<MatrixType> Base;
      typedef typename Base::Scalar Scalar;
      typedef typename Base::RealScalar RealScalar;
      typedef Matrix<Scalar,Dynamic,1> Vector;
      typedef Matrix<int, 1, MatrixType::ColsAtCompileTime> IntRowVectorType;
      typedef Matrix<int, MatrixType::RowsAtCompileTime, 1> IntColVectorType;
      typedef SparseMatrix<Scalar,LowerTriangular|UnitDiagBit> LMatrixType;
      typedef SparseMatrix<Scalar,UpperTriangular> UMatrixType;
      using Base::m_flags;
      using Base::m_status;
  
    public:
  
      SparseLU(int flags = NaturalOrdering)
        : Base(flags), m_numeric(0)
      {
      }
  
      SparseLU(const MatrixType& matrix, int flags = NaturalOrdering)
        : Base(flags), m_numeric(0)
      {
        compute(matrix);
      }
  
      ~SparseLU()
      {
        if (m_numeric)
          umfpack_free_numeric(&m_numeric,Scalar());
      }
  
      inline const LMatrixType& matrixL() const
      {
        if (m_extractedDataAreDirty) extractData();
        return m_l;
      }
  
      inline const UMatrixType& matrixU() const
      {
        if (m_extractedDataAreDirty) extractData();
        return m_u;
      }
  
      inline const IntColVectorType& permutationP() const
      {
        if (m_extractedDataAreDirty) extractData();
        return m_p;
      }
  
      inline const IntRowVectorType& permutationQ() const
      {
        if (m_extractedDataAreDirty) extractData();
        return m_q;
      }
  
      Scalar determinant() const;
  
      template<typename BDerived, typename XDerived>
      bool solve(const MatrixBase<BDerived> &b, MatrixBase<XDerived>* x) const;
  
      void compute(const MatrixType& matrix);
  
    protected:
  
      void extractData() const;
    
    protected:
      // cached data:
      void* m_numeric;
      const MatrixType* m_matrixRef;
      mutable LMatrixType m_l;
      mutable UMatrixType m_u;
      mutable IntColVectorType m_p;
      mutable IntRowVectorType m_q;
      mutable bool m_extractedDataAreDirty;
  };
  
  template<typename MatrixType>
  void SparseLU<MatrixType,UmfPack>::compute(const MatrixType& a)
  {
    const int rows = a.rows();
    const int cols = a.cols();
    ei_assert((MatrixType::Flags&RowMajorBit)==0 && "Row major matrices are not supported yet");
  
    m_matrixRef = &a;
  
    if (m_numeric)
      umfpack_free_numeric(&m_numeric,Scalar());
  
    void* symbolic;
    int errorCode = 0;
    errorCode = umfpack_symbolic(rows, cols, a._outerIndexPtr(), a._innerIndexPtr(), a._valuePtr(),
                                    &symbolic, 0, 0);
    if (errorCode==0)
      errorCode = umfpack_numeric(a._outerIndexPtr(), a._innerIndexPtr(), a._valuePtr(),
                                     symbolic, &m_numeric, 0, 0);
  
    umfpack_free_symbolic(&symbolic,Scalar());
  
    m_extractedDataAreDirty = true;
  
    Base::m_succeeded = (errorCode==0);
  }
  
  template<typename MatrixType>
  void SparseLU<MatrixType,UmfPack>::extractData() const
  {
    if (m_extractedDataAreDirty)
    {
      // get size of the data
      int lnz, unz, rows, cols, nz_udiag;
      umfpack_get_lunz(&lnz, &unz, &rows, &cols, &nz_udiag, m_numeric, Scalar());
  
      // allocate data
      m_l.resize(rows,std::min(rows,cols));
      m_l.resizeNonZeros(lnz);
      
      m_u.resize(std::min(rows,cols),cols);
      m_u.resizeNonZeros(unz);
  
      m_p.resize(rows);
      m_q.resize(cols);
  
      // extract
      umfpack_get_numeric(m_l._outerIndexPtr(), m_l._innerIndexPtr(), m_l._valuePtr(),
                          m_u._outerIndexPtr(), m_u._innerIndexPtr(), m_u._valuePtr(),
                          m_p.data(), m_q.data(), 0, 0, 0, m_numeric);
      
      m_extractedDataAreDirty = false;
    }
  }
  
  template<typename MatrixType>
  typename SparseLU<MatrixType,UmfPack>::Scalar SparseLU<MatrixType,UmfPack>::determinant() const
  {
    Scalar det;
    umfpack_get_determinant(&det, 0, m_numeric, 0);
    return det;
  }
  
  template<typename MatrixType>
  template<typename BDerived,typename XDerived>
  bool SparseLU<MatrixType,UmfPack>::solve(const MatrixBase<BDerived> &b, MatrixBase<XDerived> *x) const
  {
    //const int size = m_matrix.rows();
    const int rhsCols = b.cols();
  //   ei_assert(size==b.rows());
    ei_assert((BDerived::Flags&RowMajorBit)==0 && "UmfPack backend does not support non col-major rhs yet");
    ei_assert((XDerived::Flags&RowMajorBit)==0 && "UmfPack backend does not support non col-major result yet");
  
    int errorCode;
    for (int j=0; j<rhsCols; ++j)
    {
      errorCode = umfpack_solve(UMFPACK_A,
          m_matrixRef->_outerIndexPtr(), m_matrixRef->_innerIndexPtr(), m_matrixRef->_valuePtr(),
          &x->col(j).coeffRef(0), &b.const_cast_derived().col(j).coeffRef(0), m_numeric, 0, 0);
      if (errorCode!=0)
        return false;
    }
  //   errorCode = umfpack_di_solve(UMFPACK_A,
  //       m_matrixRef._outerIndexPtr(), m_matrixRef._innerIndexPtr(), m_matrixRef._valuePtr(),
  //       x->derived().data(), b.derived().data(), m_numeric, 0, 0);
  
    return true;
  }
  
  #endif // EIGEN_UMFPACKSUPPORT_H
  