umfpack.hh

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// SPDX-FileCopyrightText: Copyright © DUNE Project contributors, see file LICENSE.md in module root
// SPDX-License-Identifier: LicenseRef-GPL-2.0-only-with-DUNE-exception
// -*- tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 2 -*-
// vi: set et ts=4 sw=2 sts=2:
#ifndef DUNE_ISTL_UMFPACK_HH
#define DUNE_ISTL_UMFPACK_HH
 
#if HAVE_SUITESPARSE_UMFPACK || defined DOXYGEN
 
#include<complex>
#include<type_traits>
 
#include<umfpack.h>
 
#include<dune/common/exceptions.hh>
#include<dune/common/fmatrix.hh>
#include<dune/common/fvector.hh>
#include<dune/istl/bccsmatrixinitializer.hh>
#include<dune/istl/bcrsmatrix.hh>
#include<dune/istl/matrix.hh>
#include<dune/istl/foreach.hh>
#include<dune/istl/multitypeblockmatrix.hh>
#include<dune/istl/multitypeblockvector.hh>
#include<dune/istl/solvers.hh>
#include<dune/istl/solvertype.hh>
#include<dune/istl/solverfactory.hh>
 
 
 
namespace Dune {
  // FORWARD DECLARATIONS
  template<class M, class T, class TM, class TD, class TA>
  class SeqOverlappingSchwarz;
 
  template<class T, bool tag>
  struct SeqOverlappingSchwarzAssemblerHelper;
 
  // wrapper class for C-Function Calls in the backend. Choose the right function namespace
  // depending on the template parameter used.
  template<typename T>
  struct UMFPackMethodChooser
  {
    static constexpr bool valid = false ;
  };
 
  template<>
  struct UMFPackMethodChooser<double>
  {
    static constexpr bool valid = true ;
 
    template<typename... A>
    static void defaults(A... args)
    {
      umfpack_dl_defaults(args...);
    }
    template<typename... A>
    static void free_numeric(A... args)
    {
      umfpack_dl_free_numeric(args...);
    }
    template<typename... A>
    static void free_symbolic(A... args)
    {
      umfpack_dl_free_symbolic(args...);
    }
    template<typename... A>
    static int load_numeric(A... args)
    {
      return umfpack_dl_load_numeric(args...);
    }
    template<typename... A>
    static void numeric(A... args)
    {
      umfpack_dl_numeric(args...);
    }
    template<typename... A>
    static void report_info(A... args)
    {
      umfpack_dl_report_info(args...);
    }
    template<typename... A>
    static void report_status(A... args)
    {
      umfpack_dl_report_status(args...);
    }
    template<typename... A>
    static int save_numeric(A... args)
    {
      return umfpack_dl_save_numeric(args...);
    }
    template<typename... A>
    static void solve(A... args)
    {
      umfpack_dl_solve(args...);
    }
    template<typename... A>
    static void symbolic(A... args)
    {
      umfpack_dl_symbolic(args...);
    }
  };
 
  template<>
  struct UMFPackMethodChooser<std::complex<double> >
  {
    static constexpr bool valid = true ;
    using size_type = SuiteSparse_long;
 
    template<typename... A>
    static void defaults(A... args)
    {
      umfpack_zl_defaults(args...);
    }
    template<typename... A>
    static void free_numeric(A... args)
    {
      umfpack_zl_free_numeric(args...);
    }
    template<typename... A>
    static void free_symbolic(A... args)
    {
      umfpack_zl_free_symbolic(args...);
    }
    template<typename... A>
    static int load_numeric(A... args)
    {
      return umfpack_zl_load_numeric(args...);
    }
    template<typename... A>
    static void numeric(const size_type* cs, const size_type* ri, const double* val, A... args)
    {
      umfpack_zl_numeric(cs,ri,val,NULL,args...);
    }
    template<typename... A>
    static void report_info(A... args)
    {
      umfpack_zl_report_info(args...);
    }
    template<typename... A>
    static void report_status(A... args)
    {
      umfpack_zl_report_status(args...);
    }
    template<typename... A>
    static int save_numeric(A... args)
    {
      return umfpack_zl_save_numeric(args...);
    }
    template<typename... A>
    static void solve(size_type m, const size_type* cs, const size_type* ri, std::complex<double>* val, double* x, const double* b,A... args)
    {
      const double* cval = reinterpret_cast<const double*>(val);
      umfpack_zl_solve(m,cs,ri,cval,NULL,x,NULL,b,NULL,args...);
    }
    template<typename... A>
    static void symbolic(size_type m, size_type n, const size_type* cs, const size_type* ri, const double* val, A... args)
    {
      umfpack_zl_symbolic(m,n,cs,ri,val,NULL,args...);
    }
  };
 
  namespace Impl
  {
    template<class M, class = void>
    struct UMFPackVectorChooser;
 
    template<class M> using UMFPackDomainType = typename UMFPackVectorChooser<M>::domain_type;
 
    template<class M> using UMFPackRangeType = typename UMFPackVectorChooser<M>::range_type;
 
    template<class M>
    struct UMFPackVectorChooser<M,
      std::enable_if_t<(std::is_same<M,double>::value) || (std::is_same<M,std::complex<double> >::value)>>
    {
      using domain_type = M;
      using range_type  = M;
    };
 
    template<typename T, int n, int m>
    struct UMFPackVectorChooser<FieldMatrix<T,n,m>,
      std::enable_if_t<(std::is_same<T,double>::value) || (std::is_same<T,std::complex<double> >::value)>>
    {
      using domain_type = FieldVector<T,m>;
      using range_type  = FieldVector<T,n>;
    };
 
    template<typename T, typename A>
    struct UMFPackVectorChooser<BCRSMatrix<T,A>,
      std::void_t<UMFPackDomainType<T>, UMFPackRangeType<T>>>
    {
      // In case of recursive deduction (e.g., BCRSMatrix<FieldMatrix<...>, Allocator<FieldMatrix<...>>>)
      // the allocator needs to be converted to the sub-block allocator type too (e.g., Allocator<FieldVector<...>>).
      // Note that matrix allocator is assumed to be the same as the domain/range type of allocators
      using domain_type = BlockVector<UMFPackDomainType<T>, typename std::allocator_traits<A>::template rebind_alloc<UMFPackDomainType<T>>>;
      using range_type  = BlockVector<UMFPackRangeType<T>, typename std::allocator_traits<A>::template rebind_alloc<UMFPackRangeType<T>>>;
    };
 
    template<typename T, typename A>
    struct UMFPackVectorChooser<Matrix<T,A>,
      std::void_t<UMFPackDomainType<T>, UMFPackRangeType<T>>>
    : public UMFPackVectorChooser<BCRSMatrix<T,A>, std::void_t<UMFPackDomainType<T>, UMFPackRangeType<T>>>
    {};
 
    // to make the `UMFPackVectorChooser` work with `MultiTypeBlockMatrix`, we need to add an intermediate step for the rows, which are typically `MultiTypeBlockVector`
    template<typename FirstBlock, typename... Blocks>
    struct UMFPackVectorChooser<MultiTypeBlockVector<FirstBlock, Blocks...>,
      std::void_t<UMFPackDomainType<FirstBlock>, UMFPackRangeType<FirstBlock>, UMFPackDomainType<Blocks>...>>
    {
      using domain_type = MultiTypeBlockVector<UMFPackDomainType<FirstBlock>, UMFPackDomainType<Blocks>...>;
      using range_type  = UMFPackRangeType<FirstBlock>;
    };
 
    // specialization for `MultiTypeBlockMatrix` with `MultiTypeBlockVector` rows
    template<typename FirstRow, typename... Rows>
    struct UMFPackVectorChooser<MultiTypeBlockMatrix<FirstRow, Rows...>,
      std::void_t<UMFPackDomainType<FirstRow>, UMFPackRangeType<FirstRow>, UMFPackRangeType<Rows>...>>
    {
      using domain_type = UMFPackDomainType<FirstRow>;
      using range_type  = MultiTypeBlockVector< UMFPackRangeType<FirstRow>, UMFPackRangeType<Rows>... >;
    };
 
    // dummy class to represent no BitVector
    struct NoBitVector
    {};
 
 
  }
 
  template<typename M>
  class UMFPack : public InverseOperator<Impl::UMFPackDomainType<M>,Impl::UMFPackRangeType<M>>
  {
    using T = typename M::field_type;
 
    public:
    using size_type = SuiteSparse_long;
 
    using Matrix = M;
    using matrix_type = M;
    using UMFPackMatrix = ISTL::Impl::BCCSMatrix<typename Matrix::field_type, size_type>;
    using MatrixInitializer = ISTL::Impl::BCCSMatrixInitializer<M, size_type>;
    using domain_type = Impl::UMFPackDomainType<M>;
    using range_type = Impl::UMFPackRangeType<M>;
 
    SolverCategory::Category category() const override
    {
      return SolverCategory::Category::sequential;
    }
 
    UMFPack(const Matrix& matrix, int verbose=0) : matrixIsLoaded_(false)
    {
      //check whether T is a supported type
      static_assert((std::is_same<T,double>::value) || (std::is_same<T,std::complex<double> >::value),
                    "Unsupported Type in UMFPack (only double and std::complex<double> supported)");
      Caller::defaults(UMF_Control);
      setVerbosity(verbose);
      setMatrix(matrix);
    }
 
    UMFPack(const Matrix& matrix, int verbose, bool) : matrixIsLoaded_(false)
    {
      //check whether T is a supported type
      static_assert((std::is_same<T,double>::value) || (std::is_same<T,std::complex<double> >::value),
                    "Unsupported Type in UMFPack (only double and std::complex<double> supported)");
      Caller::defaults(UMF_Control);
      setVerbosity(verbose);
      setMatrix(matrix);
    }
 
    UMFPack(const Matrix& mat_, const ParameterTree& config) : matrixIsLoaded_(false)
    {
      //check whether T is a supported type
      static_assert((std::is_same<T,double>::value) || (std::is_same<T,std::complex<double> >::value),
                    "Unsupported Type in UMFPack (only double and std::complex<double> supported)");
      Caller::defaults(UMF_Control);
      setVerbosity(config.get<int>("verbose", 0));
      if (config.hasKey("ordering")) {
        const auto &ordering = config["ordering"];
        if (ordering == "cholmod") setOption(UMFPACK_ORDERING, UMFPACK_ORDERING_CHOLMOD);
        else if (ordering == "default") setOption(UMFPACK_ORDERING, UMFPACK_DEFAULT_ORDERING);
        else if (ordering == "amd") setOption(UMFPACK_ORDERING, UMFPACK_ORDERING_AMD);
        else if (ordering == "metis") setOption(UMFPACK_ORDERING, UMFPACK_ORDERING_METIS);
        else if (ordering == "best") setOption(UMFPACK_ORDERING, UMFPACK_ORDERING_BEST);
        else if (ordering == "none") setOption(UMFPACK_ORDERING, UMFPACK_ORDERING_NONE);
        #if defined(UMFPACK_VER) && (UMFPACK_VER >= UMFPACK_VER_CODE(6, 0))
        else if (ordering == "metis_guard") setOption(UMFPACK_ORDERING, UMFPACK_ORDERING_METIS_GUARD);
        #endif
        else DUNE_THROW(Dune::NotImplemented, "The UMFPACK ordering '" << ordering << "' is not implemented");
      }
      setMatrix(mat_);
    }
 
    UMFPack() : matrixIsLoaded_(false), verbosity_(0)
    {
      //check whether T is a supported type
      static_assert((std::is_same<T,double>::value) || (std::is_same<T,std::complex<double> >::value),
                    "Unsupported Type in UMFPack (only double and std::complex<double> supported)");
      Caller::defaults(UMF_Control);
    }
 
    UMFPack(const Matrix& mat_, const char* file, int verbose=0)
    {
      //check whether T is a supported type
      static_assert((std::is_same<T,double>::value) || (std::is_same<T,std::complex<double> >::value),
                    "Unsupported Type in UMFPack (only double and std::complex<double> supported)");
      Caller::defaults(UMF_Control);
      setVerbosity(verbose);
      int errcode = Caller::load_numeric(&UMF_Numeric, const_cast<char*>(file));
      if ((errcode == UMFPACK_ERROR_out_of_memory) || (errcode == UMFPACK_ERROR_file_IO))
      {
        matrixIsLoaded_ = false;
        setMatrix(mat_);
        saveDecomposition(file);
      }
      else
      {
        matrixIsLoaded_ = true;
        std::cout << "UMFPack decomposition successfully loaded from " << file << std::endl;
      }
    }
 
    UMFPack(const char* file, int verbose=0)
    {
      //check whether T is a supported type
      static_assert((std::is_same<T,double>::value) || (std::is_same<T,std::complex<double> >::value),
                    "Unsupported Type in UMFPack (only double and std::complex<double> supported)");
      Caller::defaults(UMF_Control);
      int errcode = Caller::load_numeric(&UMF_Numeric, const_cast<char*>(file));
      if (errcode == UMFPACK_ERROR_out_of_memory)
        DUNE_THROW(Dune::Exception, "ran out of memory while loading UMFPack decomposition");
      if (errcode == UMFPACK_ERROR_file_IO)
        DUNE_THROW(Dune::Exception, "IO error while loading UMFPack decomposition");
      matrixIsLoaded_ = true;
      std::cout << "UMFPack decomposition successfully loaded from " << file << std::endl;
      setVerbosity(verbose);
    }
 
    virtual ~UMFPack()
    {
      if ((umfpackMatrix_.N() + umfpackMatrix_.M() > 0) || matrixIsLoaded_)
        free();
    }
 
    void apply(domain_type& x, range_type& b, InverseOperatorResult& res) override
    {
      if (umfpackMatrix_.N() != b.dim())
        DUNE_THROW(Dune::ISTLError, "Size of right-hand-side vector b does not match the number of matrix rows!");
      if (umfpackMatrix_.M() != x.dim())
        DUNE_THROW(Dune::ISTLError, "Size of solution vector x does not match the number of matrix columns!");
      if (b.size() == 0)
        return;
 
      // we have to convert x and b into flat structures
      // however, this is linear in time
      std::vector<T> xFlat(x.dim()), bFlat(b.dim());
 
      flatVectorForEach(x, [&](auto&& entry, auto&& offset)
      {
        xFlat[ offset ] = entry;
      });
 
      flatVectorForEach(b, [&](auto&& entry, auto&& offset)
      {
        bFlat[ offset ] = entry;
      });
 
      double UMF_Apply_Info[UMFPACK_INFO];
      Caller::solve(UMFPACK_A,
                    umfpackMatrix_.getColStart(),
                    umfpackMatrix_.getRowIndex(),
                    umfpackMatrix_.getValues(),
                    reinterpret_cast<double*>(&xFlat[0]),
                    reinterpret_cast<double*>(&bFlat[0]),
                    UMF_Numeric,
                    UMF_Control,
                    UMF_Apply_Info);
 
      // copy back to blocked vector
      flatVectorForEach(x, [&](auto&& entry, auto offset)
      {
        entry = xFlat[offset];
      });
 
      //this is a direct solver
      res.iterations = 1;
      res.converged = true;
      res.elapsed = UMF_Apply_Info[UMFPACK_SOLVE_WALLTIME];
 
      printOnApply(UMF_Apply_Info);
    }
 
    void apply (domain_type& x, range_type& b, [[maybe_unused]] double reduction, InverseOperatorResult& res) override
    {
      apply(x,b,res);
    }
 
    void apply(T* x, T* b)
    {
      double UMF_Apply_Info[UMFPACK_INFO];
      Caller::solve(UMFPACK_A,
                    umfpackMatrix_.getColStart(),
                    umfpackMatrix_.getRowIndex(),
                    umfpackMatrix_.getValues(),
                    x,
                    b,
                    UMF_Numeric,
                    UMF_Control,
                    UMF_Apply_Info);
      printOnApply(UMF_Apply_Info);
    }
 
    void setOption(unsigned int option, double value)
    {
      if (option >= UMFPACK_CONTROL)
        DUNE_THROW(RangeError, "Requested non-existing UMFPack option");
 
      UMF_Control[option] = value;
    }
 
    void saveDecomposition(const char* file)
    {
      int errcode = Caller::save_numeric(UMF_Numeric, const_cast<char*>(file));
      if (errcode != UMFPACK_OK)
        DUNE_THROW(Dune::Exception,"IO ERROR while trying to save UMFPack decomposition");
    }
 
    template<class BitVector = Impl::NoBitVector>
    void setMatrix(const Matrix& matrix, const BitVector& bitVector = {})
    {
      if ((umfpackMatrix_.N() + umfpackMatrix_.M() > 0) || matrixIsLoaded_)
        free();
      if (matrix.N() == 0 or matrix.M() == 0)
        return;
 
      if (umfpackMatrix_.N() + umfpackMatrix_.M() + umfpackMatrix_.nonzeroes() != 0)
        umfpackMatrix_.free();
 
      constexpr bool useBitVector = not std::is_same_v<BitVector,Impl::NoBitVector>;
 
      // use a dynamic flat vector for the bitset
      std::vector<bool> flatBitVector;
      // and a mapping from the compressed indices
      std::vector<size_type> subIndices;
 
      [[maybe_unused]] int numberOfIgnoredDofs = 0;
      int nonZeros = 0;
 
      if constexpr ( useBitVector )
      {
        auto flatSize = flatVectorForEach(bitVector, [](auto&&, auto&&){});
        flatBitVector.resize(flatSize);
 
        flatVectorForEach(bitVector, [&](auto&& entry, auto&& offset)
        {
          flatBitVector[ offset ] = entry;
          if ( entry )
          {
            numberOfIgnoredDofs++;
          }
        });
      }
 
      // compute the flat dimension and the number of nonzeros of the matrix
      auto [flatRows,flatCols] = flatMatrixForEach( matrix, [&](auto&& /*entry*/, auto&& row, auto&& col){
        // do not count ignored entries
        if constexpr ( useBitVector )
          if ( flatBitVector[row] or flatBitVector[col] )
            return;
 
        nonZeros++;
      });
 
      if constexpr ( useBitVector )
      {
        // use the original flatRows!
        subIndices.resize(flatRows,std::numeric_limits<std::size_t>::max());
 
        size_type subIndexCounter = 0;
        for ( size_type i=0; i<size_type(flatRows); i++ )
          if ( not  flatBitVector[ i ] )
            subIndices[ i ] = subIndexCounter++;
 
        // update the original matrix size
        flatRows -= numberOfIgnoredDofs;
        flatCols -= numberOfIgnoredDofs;
      }
 
 
      umfpackMatrix_.setSize(flatRows,flatCols);
      umfpackMatrix_.Nnz_ = nonZeros;
 
      // prepare the arrays
      umfpackMatrix_.colstart = new size_type[flatCols+1];
      umfpackMatrix_.rowindex = new size_type[nonZeros];
      umfpackMatrix_.values   = new T[nonZeros];
 
      for ( size_type i=0; i<size_type(flatCols+1); i++ )
      {
        umfpackMatrix_.colstart[i] = 0;
      }
 
      // at first, we need to compute the column start indices
      // therefore, we count all entries in each column and in the end we accumulate everything
      flatMatrixForEach(matrix, [&](auto&& /*entry*/, auto&& flatRowIndex, auto&& flatColIndex)
      {
        // do nothing if entry is excluded
        if constexpr ( useBitVector )
          if ( flatBitVector[flatRowIndex] or flatBitVector[flatColIndex] )
            return;
 
        // pick compressed or uncompressed index
        // compiler will hopefully do some constexpr optimization here
        auto colIdx = useBitVector ? subIndices[flatColIndex] : flatColIndex;
 
        umfpackMatrix_.colstart[colIdx+1]++;
      });
 
      // now accumulate
      for ( size_type i=0; i<(size_type)flatCols; i++ )
      {
        umfpackMatrix_.colstart[i+1] += umfpackMatrix_.colstart[i];
      }
 
      // we need a compressed position counter in each column
      std::vector<size_type> colPosition(flatCols,0);
 
      // now we can set the entries: the procedure below works with both row- or column major index ordering
      flatMatrixForEach(matrix, [&](auto&& entry, auto&& flatRowIndex, auto&& flatColIndex)
      {
        // do nothing if entry is excluded
        if constexpr ( useBitVector )
          if ( flatBitVector[flatRowIndex] or flatBitVector[flatColIndex] )
            return;
 
        // pick compressed or uncompressed index
        // compiler will hopefully do some constexpr optimization here
        auto rowIdx = useBitVector ? subIndices[flatRowIndex] : flatRowIndex;
        auto colIdx = useBitVector ? subIndices[flatColIndex] : flatColIndex;
 
        // the start index of each column is already fixed
        auto colStart = umfpackMatrix_.colstart[colIdx];
        // get the current number of picked elements in this column
        auto colPos   = colPosition[colIdx];
        // assign the corresponding row index and the value of this element
        umfpackMatrix_.rowindex[ colStart + colPos ] = rowIdx;
        umfpackMatrix_.values[ colStart + colPos ] = entry;
        // increase the number of picked elements in this column
        colPosition[colIdx]++;
      });
 
      decompose();
    }
 
    // Keep legacy version using a set of scalar indices
    // The new version using a bitVector type for marking the active matrix indices is
    // directly given in `setMatrix` with an additional BitVector argument.
    // The new version is more flexible and allows, e.g., marking single components of a matrix block.
    void setSubMatrix(const Matrix& _mat, const std::set<typename Matrix::size_type>& rowIndexSet)
    {
      if ((umfpackMatrix_.N() + umfpackMatrix_.M() > 0) || matrixIsLoaded_)
        free();
 
      if (umfpackMatrix_.N() + umfpackMatrix_.M() + umfpackMatrix_.nonzeroes() != 0)
        umfpackMatrix_.free();
 
      umfpackMatrix_.setSize(rowIndexSet.size()*MatrixDimension<Matrix>::rowdim(_mat) / _mat.N(),
                             rowIndexSet.size()*MatrixDimension<Matrix>::coldim(_mat) / _mat.M());
      ISTL::Impl::BCCSMatrixInitializer<Matrix, SuiteSparse_long> initializer(umfpackMatrix_);
 
      copyToBCCSMatrix(initializer, ISTL::Impl::MatrixRowSubset<Matrix,std::set<typename Matrix::size_type> >(_mat,rowIndexSet));
 
      decompose();
    }
 
    void setVerbosity(int v)
    {
      verbosity_ = v;
      // set the verbosity level in UMFPack
      if (verbosity_ == 0)
        UMF_Control[UMFPACK_PRL] = 1;
      if (verbosity_ == 1)
        UMF_Control[UMFPACK_PRL] = 2;
      if (verbosity_ == 2)
        UMF_Control[UMFPACK_PRL] = 4;
    }
 
    void* getFactorization()
    {
      return UMF_Numeric;
    }
 
    UMFPackMatrix& getInternalMatrix()
    {
      return umfpackMatrix_;
    }
 
    void free()
    {
      if (!matrixIsLoaded_)
      {
        Caller::free_symbolic(&UMF_Symbolic);
        umfpackMatrix_.free();
      }
      Caller::free_numeric(&UMF_Numeric);
      matrixIsLoaded_ = false;
    }
 
    const char* name() { return "UMFPACK"; }
 
    private:
    typedef typename Dune::UMFPackMethodChooser<T> Caller;
 
    template<class Mat,class X, class TM, class TD, class T1>
    friend class SeqOverlappingSchwarz;
    friend struct SeqOverlappingSchwarzAssemblerHelper<UMFPack<Matrix>,true>;
 
    void decompose()
    {
      double UMF_Decomposition_Info[UMFPACK_INFO];
      Caller::symbolic(static_cast<SuiteSparse_long>(umfpackMatrix_.N()),
                       static_cast<SuiteSparse_long>(umfpackMatrix_.N()),
                       umfpackMatrix_.getColStart(),
                       umfpackMatrix_.getRowIndex(),
                       reinterpret_cast<double*>(umfpackMatrix_.getValues()),
                       &UMF_Symbolic,
                       UMF_Control,
                       UMF_Decomposition_Info);
      Caller::numeric(umfpackMatrix_.getColStart(),
                      umfpackMatrix_.getRowIndex(),
                      reinterpret_cast<double*>(umfpackMatrix_.getValues()),
                      UMF_Symbolic,
                      &UMF_Numeric,
                      UMF_Control,
                      UMF_Decomposition_Info);
      Caller::report_status(UMF_Control,UMF_Decomposition_Info[UMFPACK_STATUS]);
      if (verbosity_ == 1)
      {
        std::cout << "[UMFPack Decomposition]" << std::endl;
        std::cout << "Wallclock Time taken: " << UMF_Decomposition_Info[UMFPACK_NUMERIC_WALLTIME] << " (CPU Time: " << UMF_Decomposition_Info[UMFPACK_NUMERIC_TIME] << ")" << std::endl;
        std::cout << "Flops taken: " << UMF_Decomposition_Info[UMFPACK_FLOPS] << std::endl;
        std::cout << "Peak Memory Usage: " << UMF_Decomposition_Info[UMFPACK_PEAK_MEMORY]*UMF_Decomposition_Info[UMFPACK_SIZE_OF_UNIT] << " bytes" << std::endl;
        std::cout << "Condition number estimate: " << 1./UMF_Decomposition_Info[UMFPACK_RCOND] << std::endl;
        std::cout << "Numbers of non-zeroes in decomposition: L: " << UMF_Decomposition_Info[UMFPACK_LNZ] << " U: " << UMF_Decomposition_Info[UMFPACK_UNZ] << std::endl;
      }
      if (verbosity_ == 2)
      {
        Caller::report_info(UMF_Control,UMF_Decomposition_Info);
      }
    }
 
    void printOnApply(double* UMF_Info)
    {
      Caller::report_status(UMF_Control,UMF_Info[UMFPACK_STATUS]);
      if (verbosity_ > 0)
      {
        std::cout << "[UMFPack Solve]" << std::endl;
        std::cout << "Wallclock Time: " << UMF_Info[UMFPACK_SOLVE_WALLTIME] << " (CPU Time: " << UMF_Info[UMFPACK_SOLVE_TIME] << ")" << std::endl;
        std::cout << "Flops Taken: " << UMF_Info[UMFPACK_SOLVE_FLOPS] << std::endl;
        std::cout << "Iterative Refinement steps taken: " << UMF_Info[UMFPACK_IR_TAKEN] << std::endl;
        std::cout << "Error Estimate: " << UMF_Info[UMFPACK_OMEGA1] << " resp. " << UMF_Info[UMFPACK_OMEGA2] << std::endl;
      }
    }
 
    UMFPackMatrix umfpackMatrix_;
    bool matrixIsLoaded_;
    int verbosity_;
    void *UMF_Symbolic;
    void *UMF_Numeric;
    double UMF_Control[UMFPACK_CONTROL];
  };
 
  template<typename M>
  struct IsDirectSolver<UMFPack<M>>
  {
    enum { value=true};
  };
 
  template<typename T, typename A>
  struct StoresColumnCompressed<UMFPack<BCRSMatrix<T,A> > >
  {
    enum { value = true };
  };
 
  namespace UMFPackImpl {
    template<class OpTraits, class=void> struct isValidBlock : std::false_type{};
    template<class OpTraits> struct isValidBlock<OpTraits,
      std::enable_if_t<
           std::is_same_v<Impl::UMFPackDomainType<typename OpTraits::matrix_type>, typename OpTraits::domain_type>
        && std::is_same_v<Impl::UMFPackRangeType<typename OpTraits::matrix_type>, typename OpTraits::range_type>
        && std::is_same_v<typename FieldTraits<typename OpTraits::domain_type::field_type>::real_type, double>
        && std::is_same_v<typename FieldTraits<typename OpTraits::range_type::field_type>::real_type, double>
      >> : std::true_type {};
  }
  DUNE_REGISTER_SOLVER("umfpack",
                       [](auto opTraits, const auto& op, const Dune::ParameterTree& config)
                       -> std::shared_ptr<typename decltype(opTraits)::solver_type>
                       {
                         using OpTraits = decltype(opTraits);
                         // works only for sequential operators
                         if constexpr (OpTraits::isParallel){
                           if(opTraits.getCommOrThrow(op).communicator().size() > 1)
                             DUNE_THROW(Dune::InvalidStateException, "UMFPack works only for sequential operators.");
                         }
                         if constexpr (OpTraits::isAssembled){
                           using M = typename OpTraits::matrix_type;
                           // check if UMFPack<M>* is convertible to
                           // InverseOperator*. This checks compatibility of the
                           // domain and range types
                           if constexpr (UMFPackImpl::isValidBlock<OpTraits>::value) {
                             const auto& A = opTraits.getAssembledOpOrThrow(op);
                             const M& mat = A->getmat();
                             return std::make_shared<Dune::UMFPack<M>>(mat, config);
                           }
                         }
                         DUNE_THROW(UnsupportedType,
                                    "Unsupported Type in UMFPack (only double and std::complex<double> supported)");
                         return nullptr;
                       });
} // end namespace Dune
 
#endif // HAVE_SUITESPARSE_UMFPACK
 
#endif //DUNE_ISTL_UMFPACK_HH