multitypeblockmatrix.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_MULTITYPEBLOCKMATRIX_HH
#define DUNE_ISTL_MULTITYPEBLOCKMATRIX_HH

#include <cmath>
#include <iostream>
#include <tuple>

#include <dune/common/hybridutilities.hh>

#include "istlexception.hh"

// forward declaration
namespace Dune
{
  template<typename FirstRow, typename... Args>
  class MultiTypeBlockMatrix;

  template<int I, int crow, int remain_row>
  class MultiTypeBlockMatrix_Solver;
}

#include "gsetc.hh"

namespace Dune {

  template<typename FirstRow, typename... Args>
  class MultiTypeBlockMatrix
  : public std::tuple<FirstRow, Args...>
  {
    using ParentType = std::tuple<FirstRow, Args...>;
  public:

    using ParentType::ParentType;

    typedef MultiTypeBlockMatrix<FirstRow, Args...> type;

    using size_type = std::size_t;

    using field_type = Std::detected_t<std::common_type_t,
      typename FieldTraits<FirstRow>::field_type, typename FieldTraits<Args>::field_type...>;

    using real_type = Std::detected_t<std::common_type_t,
      typename FieldTraits<FirstRow>::real_type, typename FieldTraits<Args>::real_type...>;

    // make sure that we have an std::common_type: using an assertion produces a more readable error message
    // than a compiler template instantiation error
    static_assert ( sizeof...(Args) == 0 or
                    not (std::is_same_v<field_type, Std::nonesuch> or std::is_same_v<real_type, Std::nonesuch>),
        "No std::common_type implemented for the given field_type/real_type of the Args. Please provide an implementation and check that a FieldTraits class is present for your type.");

    static constexpr size_type N()
    {
      return 1+sizeof...(Args);
    }

    static constexpr size_type M()
    {
      return FirstRow::size();
    }

    template< size_type index >
    auto
    operator[] ([[maybe_unused]] const std::integral_constant< size_type, index > indexVariable)
                -> decltype(std::get<index>(*this))
    {
      return std::get<index>(*this);
    }

    template< size_type index >
    auto
    operator[] ([[maybe_unused]] const std::integral_constant< size_type, index > indexVariable) const
                -> decltype(std::get<index>(*this))
    {
      return std::get<index>(*this);
    }

    template<typename T>
    void operator= (const T& newval) {
      using namespace Dune::Hybrid;
      auto size = index_constant<1+sizeof...(Args)>();
      // Since Dune::Hybrid::size(MultiTypeBlockMatrix) is not implemented,
      // we cannot use a plain forEach(*this, ...). This could be achieved,
      // e.g., by implementing a static size() method.
      forEach(integralRange(size), [&](auto&& i) {
        (*this)[i] = newval;
      });
    }

    //===== vector space arithmetic

    MultiTypeBlockMatrix& operator*= (const field_type& k)
    {
      auto size = index_constant<N()>();
      Hybrid::forEach(Hybrid::integralRange(size), [&](auto&& i) {
        (*this)[i] *= k;
      });

      return *this;
    }

    MultiTypeBlockMatrix& operator/= (const field_type& k)
    {
      auto size = index_constant<N()>();
      Hybrid::forEach(Hybrid::integralRange(size), [&](auto&& i) {
        (*this)[i] /= k;
      });

      return *this;
    }


    MultiTypeBlockMatrix& operator+= (const MultiTypeBlockMatrix& b)
    {
      auto size = index_constant<N()>();
      Hybrid::forEach(Hybrid::integralRange(size), [&](auto&& i) {
        (*this)[i] += b[i];
      });

      return *this;
    }

    MultiTypeBlockMatrix& operator-= (const MultiTypeBlockMatrix& b)
    {
      auto size = index_constant<N()>();
      Hybrid::forEach(Hybrid::integralRange(size), [&](auto&& i) {
        (*this)[i] -= b[i];
      });

      return *this;
    }

    template<typename X, typename Y>
    void mv (const X& x, Y& y) const {
      static_assert(X::size() == M(), "length of x does not match row length");
      static_assert(Y::size() == N(), "length of y does not match row count");
      y = 0;                                                                  //reset y (for mv uses umv)
      umv(x,y);
    }

    template<typename X, typename Y>
    void umv (const X& x, Y& y) const {
      static_assert(X::size() == M(), "length of x does not match row length");
      static_assert(Y::size() == N(), "length of y does not match row count");
      using namespace Dune::Hybrid;
      forEach(integralRange(Hybrid::size(y)), [&](auto&& i) {
        using namespace Dune::Hybrid; // needed for icc, see issue #31
        forEach(integralRange(Hybrid::size(x)), [&](auto&& j) {
          (*this)[i][j].umv(x[j], y[i]);
        });
      });
    }

    template<typename X, typename Y>
    void mmv (const X& x, Y& y) const {
      static_assert(X::size() == M(), "length of x does not match row length");
      static_assert(Y::size() == N(), "length of y does not match row count");
      using namespace Dune::Hybrid;
      forEach(integralRange(Hybrid::size(y)), [&](auto&& i) {
        using namespace Dune::Hybrid; // needed for icc, see issue #31
        forEach(integralRange(Hybrid::size(x)), [&](auto&& j) {
          (*this)[i][j].mmv(x[j], y[i]);
        });
      });
    }

    template<typename AlphaType, typename X, typename Y>
    void usmv (const AlphaType& alpha, const X& x, Y& y) const {
      static_assert(X::size() == M(), "length of x does not match row length");
      static_assert(Y::size() == N(), "length of y does not match row count");
      using namespace Dune::Hybrid;
      forEach(integralRange(Hybrid::size(y)), [&](auto&& i) {
        using namespace Dune::Hybrid; // needed for icc, see issue #31
        forEach(integralRange(Hybrid::size(x)), [&](auto&& j) {
          (*this)[i][j].usmv(alpha, x[j], y[i]);
        });
      });
    }

    template<typename X, typename Y>
    void mtv (const X& x, Y& y) const {
      static_assert(X::size() == N(), "length of x does not match number of rows");
      static_assert(Y::size() == M(), "length of y does not match number of columns");
      y = 0;
      umtv(x,y);
    }

    template<typename X, typename Y>
    void umtv (const X& x, Y& y) const {
      static_assert(X::size() == N(), "length of x does not match number of rows");
      static_assert(Y::size() == M(), "length of y does not match number of columns");
      using namespace Dune::Hybrid;
      forEach(integralRange(Hybrid::size(y)), [&](auto&& i) {
        using namespace Dune::Hybrid; // needed for icc, see issue #31
        forEach(integralRange(Hybrid::size(x)), [&](auto&& j) {
          (*this)[j][i].umtv(x[j], y[i]);
        });
      });
    }

    template<typename X, typename Y>
    void mmtv (const X& x, Y& y) const {
      static_assert(X::size() == N(), "length of x does not match number of rows");
      static_assert(Y::size() == M(), "length of y does not match number of columns");
      using namespace Dune::Hybrid;
      forEach(integralRange(Hybrid::size(y)), [&](auto&& i) {
        using namespace Dune::Hybrid; // needed for icc, see issue #31
        forEach(integralRange(Hybrid::size(x)), [&](auto&& j) {
          (*this)[j][i].mmtv(x[j], y[i]);
        });
      });
    }

    template<typename X, typename Y>
    void usmtv (const field_type& alpha, const X& x, Y& y) const {
      static_assert(X::size() == N(), "length of x does not match number of rows");
      static_assert(Y::size() == M(), "length of y does not match number of columns");
      using namespace Dune::Hybrid;
      forEach(integralRange(Hybrid::size(y)), [&](auto&& i) {
        using namespace Dune::Hybrid; // needed for icc, see issue #31
        forEach(integralRange(Hybrid::size(x)), [&](auto&& j) {
          (*this)[j][i].usmtv(alpha, x[j], y[i]);
        });
      });
    }

    template<typename X, typename Y>
    void umhv (const X& x, Y& y) const {
      static_assert(X::size() == N(), "length of x does not match number of rows");
      static_assert(Y::size() == M(), "length of y does not match number of columns");
      using namespace Dune::Hybrid;
      forEach(integralRange(Hybrid::size(y)), [&](auto&& i) {
        using namespace Dune::Hybrid; // needed for icc, see issue #31
        forEach(integralRange(Hybrid::size(x)), [&](auto&& j) {
          (*this)[j][i].umhv(x[j], y[i]);
        });
      });
    }

    template<typename X, typename Y>
    void mmhv (const X& x, Y& y) const {
      static_assert(X::size() == N(), "length of x does not match number of rows");
      static_assert(Y::size() == M(), "length of y does not match number of columns");
      using namespace Dune::Hybrid;
      forEach(integralRange(Hybrid::size(y)), [&](auto&& i) {
        using namespace Dune::Hybrid; // needed for icc, see issue #31
        forEach(integralRange(Hybrid::size(x)), [&](auto&& j) {
          (*this)[j][i].mmhv(x[j], y[i]);
        });
      });
    }

    template<typename X, typename Y>
    void usmhv (const field_type& alpha, const X& x, Y& y) const {
      static_assert(X::size() == N(), "length of x does not match number of rows");
      static_assert(Y::size() == M(), "length of y does not match number of columns");
      using namespace Dune::Hybrid;
      forEach(integralRange(Hybrid::size(y)), [&](auto&& i) {
        using namespace Dune::Hybrid; // needed for icc, see issue #31
        forEach(integralRange(Hybrid::size(x)), [&](auto&& j) {
          (*this)[j][i].usmhv(alpha, x[j], y[i]);
        });
      });
    }


    //===== norms

    real_type frobenius_norm2 () const
    {
      real_type sum=0;

      auto rows = index_constant<N()>();
      Hybrid::forEach(Hybrid::integralRange(rows), [&](auto&& i) {
        auto cols = index_constant<MultiTypeBlockMatrix<FirstRow, Args...>::M()>();
        Hybrid::forEach(Hybrid::integralRange(cols), [&](auto&& j) {
          sum += (*this)[i][j].frobenius_norm2();
        });
      });

      return sum;
    }

    real_type frobenius_norm () const
    {
      return sqrt(frobenius_norm2());
    }

    real_type infinity_norm () const
    {
      using std::max;
      real_type norm=0;

      auto rows = index_constant<N()>();
      Hybrid::forEach(Hybrid::integralRange(rows), [&](auto&& i) {
        real_type sum=0;
        auto cols = index_constant<MultiTypeBlockMatrix<FirstRow, Args...>::M()>();
        Hybrid::forEach(Hybrid::integralRange(cols), [&](auto&& j) {
          sum += (*this)[i][j].infinity_norm();
        });
        norm = max(sum, norm);
      });

      return norm;
    }

    real_type infinity_norm_real () const
    {
      using std::max;
      real_type norm=0;

      auto rows = index_constant<N()>();
      Hybrid::forEach(Hybrid::integralRange(rows), [&](auto&& i) {
        real_type sum=0;
        auto cols = index_constant<MultiTypeBlockMatrix<FirstRow, Args...>::M()>();
        Hybrid::forEach(Hybrid::integralRange(cols), [&](auto&& j) {
          sum += (*this)[i][j].infinity_norm_real();
        });
        norm = max(sum, norm);
      });

      return norm;
    }

  };


  template <typename... Rows>
  struct FieldTraits< MultiTypeBlockMatrix<Rows...> >
  {
    using field_type = typename MultiTypeBlockMatrix<Rows...>::field_type;
    using real_type  = typename MultiTypeBlockMatrix<Rows...>::real_type;
  };


  template<typename T1, typename... Args>
  std::ostream& operator<< (std::ostream& s, const MultiTypeBlockMatrix<T1,Args...>& m) {
    auto N = index_constant<MultiTypeBlockMatrix<T1,Args...>::N()>();
    auto M = index_constant<MultiTypeBlockMatrix<T1,Args...>::M()>();
    using namespace Dune::Hybrid;
    forEach(integralRange(N), [&](auto&& i) {
      using namespace Dune::Hybrid; // needed for icc, see issue #31
      forEach(integralRange(M), [&](auto&& j) {
        s << "\t(" << i << ", " << j << "): \n" << m[i][j];
      });
    });
    s << std::endl;
    return s;
  }

  //make algmeta_itsteps known
  template<int I, typename M>
  struct algmeta_itsteps;

  template<int I, int crow, int ccol, int remain_col>                             //MultiTypeBlockMatrix_Solver_Col: iterating over one row
  class MultiTypeBlockMatrix_Solver_Col {                                                      //calculating b- A[i][j]*x[j]
  public:
    template <typename Trhs, typename TVector, typename TMatrix, typename K>
    static void calc_rhs(const TMatrix& A, TVector& x, TVector& v, Trhs& b, const K& w) {
      std::get<ccol>( std::get<crow>(A) ).mmv( std::get<ccol>(x), b );
      MultiTypeBlockMatrix_Solver_Col<I, crow, ccol+1, remain_col-1>::calc_rhs(A,x,v,b,w); //next column element
    }

  };
  template<int I, int crow, int ccol>                                             //MultiTypeBlockMatrix_Solver_Col recursion end
  class MultiTypeBlockMatrix_Solver_Col<I,crow,ccol,0> {
  public:
    template <typename Trhs, typename TVector, typename TMatrix, typename K>
    static void calc_rhs(const TMatrix&, TVector&, TVector&, Trhs&, const K&) {}
  };



  template<int I, int crow, int remain_row>
  class MultiTypeBlockMatrix_Solver {
  public:

    template <typename TVector, typename TMatrix, typename K>
    static void dbgs(const TMatrix& A, TVector& x, const TVector& b, const K& w) {
      TVector xold(x);
      xold=x;                                                         //store old x values
      MultiTypeBlockMatrix_Solver<I,crow,remain_row>::dbgs(A,x,x,b,w);
      x *= w;
      x.axpy(1-w,xold);                                                       //improve x
    }
    template <typename TVector, typename TMatrix, typename K>
    static void dbgs(const TMatrix& A, TVector& x, TVector& v, const TVector& b, const K& w) {
      auto rhs = std::get<crow> (b);

      MultiTypeBlockMatrix_Solver_Col<I,crow,0, TMatrix::M()>::calc_rhs(A,x,v,rhs,w);  // calculate right side of equation
      //solve on blocklevel I-1
      using M =
        typename std::remove_cv<
          typename std::remove_reference<
            decltype(std::get<crow>( std::get<crow>(A)))
          >::type
        >::type;
      algmeta_itsteps<I-1,M>::dbgs(std::get<crow>( std::get<crow>(A)), std::get<crow>(x),rhs,w);
      MultiTypeBlockMatrix_Solver<I,crow+1,remain_row-1>::dbgs(A,x,v,b,w); //next row
    }



    template <typename TVector, typename TMatrix, typename K>
    static void bsorf(const TMatrix& A, TVector& x, const TVector& b, const K& w) {
      TVector v;
      v=x;                                                            //use latest x values in right side calculation
      MultiTypeBlockMatrix_Solver<I,crow,remain_row>::bsorf(A,x,v,b,w);

    }
    template <typename TVector, typename TMatrix, typename K>               //recursion over all matrix rows (A)
    static void bsorf(const TMatrix& A, TVector& x, TVector& v, const TVector& b, const K& w) {
      auto rhs = std::get<crow> (b);

      MultiTypeBlockMatrix_Solver_Col<I,crow,0,TMatrix::M()>::calc_rhs(A,x,v,rhs,w);  // calculate right side of equation
      //solve on blocklevel I-1
      using M =
        typename std::remove_cv<
          typename std::remove_reference<
            decltype(std::get<crow>( std::get<crow>(A)))
          >::type
        >::type;
      algmeta_itsteps<I-1,M>::bsorf(std::get<crow>( std::get<crow>(A)), std::get<crow>(v),rhs,w);
      std::get<crow>(x).axpy(w,std::get<crow>(v));
      MultiTypeBlockMatrix_Solver<I,crow+1,remain_row-1>::bsorf(A,x,v,b,w);        //next row
    }

    template <typename TVector, typename TMatrix, typename K>
    static void bsorb(const TMatrix& A, TVector& x, const TVector& b, const K& w) {
      TVector v;
      v=x;                                                            //use latest x values in right side calculation
      MultiTypeBlockMatrix_Solver<I,crow,remain_row>::bsorb(A,x,v,b,w);

    }
    template <typename TVector, typename TMatrix, typename K>               //recursion over all matrix rows (A)
    static void bsorb(const TMatrix& A, TVector& x, TVector& v, const TVector& b, const K& w) {
      auto rhs = std::get<crow> (b);

      MultiTypeBlockMatrix_Solver_Col<I,crow,0, TMatrix::M()>::calc_rhs(A,x,v,rhs,w);  // calculate right side of equation
      //solve on blocklevel I-1
      using M =
        typename std::remove_cv<
          typename std::remove_reference<
            decltype(std::get<crow>( std::get<crow>(A)))
          >::type
        >::type;
      algmeta_itsteps<I-1,M>::bsorb(std::get<crow>( std::get<crow>(A)), std::get<crow>(v),rhs,w);
      std::get<crow>(x).axpy(w,std::get<crow>(v));
      MultiTypeBlockMatrix_Solver<I,crow-1,remain_row-1>::bsorb(A,x,v,b,w);        //next row
    }


    template <typename TVector, typename TMatrix, typename K>
    static void dbjac(const TMatrix& A, TVector& x, const TVector& b, const K& w) {
      TVector v(x);
      v=0;                                                            //calc new x in v
      MultiTypeBlockMatrix_Solver<I,crow,remain_row>::dbjac(A,x,v,b,w);
      x.axpy(w,v);                                                    //improve x
    }
    template <typename TVector, typename TMatrix, typename K>
    static void dbjac(const TMatrix& A, TVector& x, TVector& v, const TVector& b, const K& w) {
      auto rhs = std::get<crow> (b);

      MultiTypeBlockMatrix_Solver_Col<I,crow,0, TMatrix::M()>::calc_rhs(A,x,v,rhs,w);  // calculate right side of equation
      //solve on blocklevel I-1
      using M =
        typename std::remove_cv<
          typename std::remove_reference<
            decltype(std::get<crow>( std::get<crow>(A)))
          >::type
        >::type;
      algmeta_itsteps<I-1,M>::dbjac(std::get<crow>( std::get<crow>(A)), std::get<crow>(v),rhs,w);
      MultiTypeBlockMatrix_Solver<I,crow+1,remain_row-1>::dbjac(A,x,v,b,w);        //next row
    }




  };
  template<int I, int crow>                                                       //recursion end for remain_row = 0
  class MultiTypeBlockMatrix_Solver<I,crow,0> {
  public:
    template <typename TVector, typename TMatrix, typename K>
    static void dbgs(const TMatrix&, TVector&, TVector&,
                     const TVector&, const K&) {}

    template <typename TVector, typename TMatrix, typename K>
    static void bsorf(const TMatrix&, TVector&, TVector&,
                      const TVector&, const K&) {}

    template <typename TVector, typename TMatrix, typename K>
    static void bsorb(const TMatrix&, TVector&, TVector&,
                      const TVector&, const K&) {}

    template <typename TVector, typename TMatrix, typename K>
    static void dbjac(const TMatrix&, TVector&, TVector&,
                      const TVector&, const K&) {}
  };

} // end namespace Dune

namespace std
{
  template <size_t i, typename... Args>
  struct tuple_element<i,Dune::MultiTypeBlockMatrix<Args...> >
  {
    using type = typename std::tuple_element<i, std::tuple<Args...> >::type;
  };

  template <typename... Args>
  struct tuple_size<Dune::MultiTypeBlockMatrix<Args...> >
    : std::integral_constant<std::size_t, sizeof...(Args)>
  {};
}
#endif