linear_operator.h

// ---------------------------------------------------------------------
//
// Copyright (C) 2014 - 2017 by the deal.II authors
//
// This file is part of the deal.II library.
//
// The deal.II library is free software; you can use it, 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.
// The full text of the license can be found in the file LICENSE at
// the top level of the deal.II distribution.
//
// ---------------------------------------------------------------------

#ifndef dealii__linear_operator_h
#define dealii__linear_operator_h

#include <deal.II/base/config.h>
#include <deal.II/base/exceptions.h>
#include <deal.II/lac/vector_memory.h>

#ifdef DEAL_II_WITH_CXX11

#include <array>
#include <functional>
#include <type_traits>

DEAL_II_NAMESPACE_OPEN

// Forward declarations:

namespace internal
{
  namespace LinearOperator
  {
    class EmptyPayload;
  }
}

template <typename Number> class Vector;

template <typename Range = Vector<double>,
          typename Domain = Range,
          typename Payload = internal::LinearOperator::EmptyPayload>
class LinearOperator;

template <typename Range = Vector<double>,
          typename Domain = Range,
          typename Payload = internal::LinearOperator::EmptyPayload,
          typename OperatorExemplar,
          typename Matrix>
LinearOperator<Range, Domain, Payload> linear_operator (const OperatorExemplar &,
                                                        const Matrix &);

template <typename Range = Vector<double>,
          typename Domain = Range,
          typename Payload = internal::LinearOperator::EmptyPayload,
          typename Matrix>
LinearOperator<Range, Domain, Payload> linear_operator (const Matrix &);

template <typename Range = Vector<double>,
          typename Domain = Range,
          typename Payload = internal::LinearOperator::EmptyPayload>
LinearOperator<Range, Domain, Payload>
null_operator(const LinearOperator<Range, Domain, Payload> &);


template <typename Range, typename Domain, typename Payload>
class LinearOperator
  : public Payload
{
public:

  LinearOperator(const Payload &payload = Payload())
    :
    Payload (payload),
    is_null_operator(false)
  {

    vmult = [](Range &, const Domain &)
    {
      Assert(false, ExcMessage("Uninitialized LinearOperator<Range, "
                               "Domain>::vmult called"));
    };

    vmult_add = [](Range &, const Domain &)
    {
      Assert(false, ExcMessage("Uninitialized LinearOperator<Range, "
                               "Domain>::vmult_add called"));
    };

    Tvmult = [](Domain &, const Range &)
    {
      Assert(false, ExcMessage("Uninitialized LinearOperator<Range, "
                               "Domain>::Tvmult called"));
    };

    Tvmult_add = [](Domain &, const Range &)
    {
      Assert(false, ExcMessage("Uninitialized LinearOperator<Range, "
                               "Domain>::Tvmult_add called"));
    };

    reinit_range_vector = [](Range &, bool)
    {
      Assert(false, ExcMessage("Uninitialized LinearOperator<Range, "
                               "Domain>::reinit_range_vector method called"));
    };

    reinit_domain_vector = [](Domain &, bool)
    {
      Assert(false, ExcMessage("Uninitialized LinearOperator<Range, "
                               "Domain>::reinit_domain_vector method called"));
    };
  }

  LinearOperator (const LinearOperator<Range, Domain, Payload> &) = default;

  template<typename Op,
           typename = typename std::enable_if<!std::is_base_of<LinearOperator<Range, Domain, Payload>, Op>::value>::type>
  LinearOperator (const Op &op)
  {
    *this = linear_operator<Range, Domain, Payload, Op>(op);
  }

  LinearOperator<Range, Domain, Payload> &
  operator=(const LinearOperator<Range, Domain, Payload> &) = default;

  template <typename Op,
            typename = typename std::enable_if<!std::is_base_of<LinearOperator<Range, Domain, Payload>, Op>::value>::type>
  LinearOperator<Range, Domain, Payload> &operator=(const Op &op)
  {
    *this = linear_operator<Range, Domain, Payload, Op>(op);
    return *this;
  }

  std::function<void(Range &v, const Domain &u)> vmult;

  std::function<void(Range &v, const Domain &u)> vmult_add;

  std::function<void(Domain &v, const Range &u)> Tvmult;

  std::function<void(Domain &v, const Range &u)> Tvmult_add;

  std::function<void(Range &v, bool omit_zeroing_entries)> reinit_range_vector;

  std::function<void(Domain &v, bool omit_zeroing_entries)> reinit_domain_vector;


  LinearOperator<Range, Domain, Payload> &
  operator+=(const LinearOperator<Range, Domain, Payload> &second_op)
  {
    *this = *this + second_op;
    return *this;
  }

  LinearOperator<Range, Domain, Payload> &
  operator-=(const LinearOperator<Range, Domain, Payload> &second_op)
  {
    *this = *this - second_op;
    return *this;
  }

  LinearOperator<Range, Domain, Payload> &
  operator*=(const LinearOperator<Domain, Domain, Payload> &second_op)
  {
    *this = *this * second_op;
    return *this;
  }

  LinearOperator<Range, Domain, Payload>
  operator*=(typename Domain::value_type  number)
  {
    *this = *this * number;
    return *this;
  }

  bool is_null_operator;

};



template <typename Range, typename Domain, typename Payload>
LinearOperator<Range, Domain, Payload>
operator+(const LinearOperator<Range, Domain, Payload> &first_op,
          const LinearOperator<Range, Domain, Payload> &second_op)
{
  if (first_op.is_null_operator)
    {
      return second_op;
    }
  else if (second_op.is_null_operator)
    {
      return first_op;
    }
  else
    {
      LinearOperator<Range, Domain, Payload> return_op (
        static_cast<const Payload &>(first_op) + static_cast<const Payload &>(second_op)
      );

      return_op.reinit_range_vector = first_op.reinit_range_vector;
      return_op.reinit_domain_vector = first_op.reinit_domain_vector;

      // ensure to have valid computation objects by catching first_op and
      // second_op by value

      return_op.vmult = [first_op, second_op](Range &v, const Domain &u)
      {
        first_op.vmult(v, u);
        second_op.vmult_add(v, u);
      };

      return_op.vmult_add = [first_op, second_op](Range &v, const Domain &u)
      {
        first_op.vmult_add(v, u);
        second_op.vmult_add(v, u);
      };

      return_op.Tvmult = [first_op, second_op](Domain &v, const Range &u)
      {
        second_op.Tvmult(v, u);
        first_op.Tvmult_add(v, u);
      };

      return_op.Tvmult_add = [first_op, second_op](Domain &v, const Range &u)
      {
        second_op.Tvmult_add(v, u);
        first_op.Tvmult_add(v, u);
      };

      return return_op;
    }
}


template <typename Range, typename Domain, typename Payload>
LinearOperator<Range, Domain, Payload>
operator-(const LinearOperator<Range, Domain, Payload> &first_op,
          const LinearOperator<Range, Domain, Payload> &second_op)
{
  if (first_op.is_null_operator)
    {
      return -1. * second_op;
    }
  else if (second_op.is_null_operator)
    {
      return first_op;
    }
  else
    {
      // implement with addition and scalar multiplication
      return first_op + (-1. * second_op);
    }
}


template <typename Range, typename Domain, typename Payload>
LinearOperator<Range, Domain, Payload>
operator*(typename Range::value_type  number,
          const LinearOperator<Range, Domain, Payload> &op)
{
  static_assert(
    std::is_convertible<typename Range::value_type, typename Domain::value_type>::value,
    "Range and Domain must have implicitly convertible 'value_type's");

  if (op.is_null_operator)
    {
      return op;
    }
  else if (number == 0.)
    {
      return null_operator(op);
    }
  else
    {
      LinearOperator<Range, Domain, Payload> return_op = op;

      // ensure to have valid computation objects by catching number and op by
      // value

      return_op.vmult = [number, op](Range &v, const Domain &u)
      {
        op.vmult(v,u);
        v *= number;
      };

      return_op.vmult_add = [number, op](Range &v, const Domain &u)
      {
        v /= number;
        op.vmult_add(v,u);
        v *= number;
      };

      return_op.Tvmult = [number, op](Domain &v, const Range &u)
      {
        op.Tvmult(v,u);
        v *= number;
      };

      return_op.Tvmult_add = [number, op](Domain &v, const Range &u)
      {
        v /= number;
        op.Tvmult_add(v,u);
        v *= number;
      };

      return return_op;
    }
}


template <typename Range, typename Domain, typename Payload>
LinearOperator<Range, Domain, Payload>
operator*(const LinearOperator<Range, Domain, Payload> &op,
          typename Domain::value_type  number)
{
  static_assert(
    std::is_convertible<typename Range::value_type, typename Domain::value_type>::value,
    "Range and Domain must have implicitly convertible 'value_type's");

  return number * op;
}




template <typename Range, typename Intermediate, typename Domain, typename Payload>
LinearOperator<Range, Domain, Payload>
operator*(const LinearOperator<Range, Intermediate, Payload> &first_op,
          const LinearOperator<Intermediate, Domain, Payload> &second_op)
{
  if (first_op.is_null_operator || second_op.is_null_operator)
    {
      LinearOperator<Range, Domain, Payload> return_op;
      return_op.reinit_domain_vector = second_op.reinit_domain_vector;
      return_op.reinit_range_vector  = first_op.reinit_range_vector;
      return null_operator(return_op);
    }
  else
    {
      LinearOperator<Range, Domain, Payload> return_op (
        static_cast<const Payload &>(first_op) * static_cast<const Payload &>(second_op)
      );

      return_op.reinit_domain_vector = second_op.reinit_domain_vector;
      return_op.reinit_range_vector  = first_op.reinit_range_vector;

      // ensure to have valid computation objects by catching first_op and
      // second_op by value

      return_op.vmult = [first_op, second_op](Range &v, const Domain &u)
      {
        static GrowingVectorMemory<Intermediate> vector_memory;

        Intermediate *i = vector_memory.alloc();
        second_op.reinit_range_vector(*i, /*bool omit_zeroing_entries =*/ true);
        second_op.vmult(*i, u);
        first_op.vmult(v, *i);
        vector_memory.free(i);
      };

      return_op.vmult_add = [first_op, second_op](Range &v, const Domain &u)
      {
        static GrowingVectorMemory<Intermediate> vector_memory;

        Intermediate *i = vector_memory.alloc();
        second_op.reinit_range_vector(*i, /*bool omit_zeroing_entries =*/ true);
        second_op.vmult(*i, u);
        first_op.vmult_add(v, *i);
        vector_memory.free(i);
      };

      return_op.Tvmult = [first_op, second_op](Domain &v, const Range &u)
      {
        static GrowingVectorMemory<Intermediate> vector_memory;

        Intermediate *i = vector_memory.alloc();
        first_op.reinit_domain_vector(*i, /*bool omit_zeroing_entries =*/ true);
        first_op.Tvmult(*i, u);
        second_op.Tvmult(v, *i);
        vector_memory.free(i);
      };

      return_op.Tvmult_add = [first_op, second_op](Domain &v, const Range &u)
      {
        static GrowingVectorMemory<Intermediate> vector_memory;

        Intermediate *i = vector_memory.alloc();
        first_op.reinit_domain_vector(*i, /*bool omit_zeroing_entries =*/ true);
        first_op.Tvmult(*i, u);
        second_op.Tvmult_add(v, *i);
        vector_memory.free(i);
      };

      return return_op;
    }
}

template <typename Range, typename Domain, typename Payload>
LinearOperator<Domain, Range, Payload>
transpose_operator(const LinearOperator<Range, Domain, Payload> &op)
{
  LinearOperator<Domain, Range, Payload> return_op (
    op.transpose_payload()
  );

  return_op.reinit_range_vector = op.reinit_domain_vector;
  return_op.reinit_domain_vector = op.reinit_range_vector;

  return_op.vmult = op.Tvmult;
  return_op.vmult_add = op.Tvmult_add;
  return_op.Tvmult = op.vmult;
  return_op.Tvmult_add = op.vmult_add;

  return return_op;
}


template <typename Payload,
          typename Solver, typename Preconditioner,
          typename Range = typename Solver::vector_type, typename Domain = Range>
LinearOperator<Domain, Range, Payload>
inverse_operator(const LinearOperator<Range, Domain, Payload> &op,
                 Solver &solver,
                 const Preconditioner &preconditioner)
{
  LinearOperator<Domain, Range, Payload> return_op (
    op.inverse_payload(solver, preconditioner)
  );

  return_op.reinit_range_vector = op.reinit_domain_vector;
  return_op.reinit_domain_vector = op.reinit_range_vector;

  return_op.vmult = [op, &solver, &preconditioner](Range &v, const Domain &u)
  {
    op.reinit_range_vector(v, /*bool omit_zeroing_entries =*/ false);
    solver.solve(op, v, u, preconditioner);
  };

  return_op.vmult_add =
    [op, &solver, &preconditioner](Range &v, const Domain &u)
  {
    static GrowingVectorMemory<Range> vector_memory;

    Range *v2 = vector_memory.alloc();
    op.reinit_range_vector(*v2, /*bool omit_zeroing_entries =*/ false);
    solver.solve(op, *v2, u, preconditioner);
    v += *v2;
    vector_memory.free(v2);
  };

  return_op.Tvmult = [op, &solver, &preconditioner](Range &v, const Domain &u)
  {
    op.reinit_range_vector(v, /*bool omit_zeroing_entries =*/ false);
    solver.solve(transpose_operator(op), v, u, preconditioner);
  };

  return_op.Tvmult_add =
    [op, &solver, &preconditioner](Range &v, const Domain &u)
  {
    static GrowingVectorMemory<Range> vector_memory;

    Range *v2 = vector_memory.alloc();
    op.reinit_range_vector(*v2, /*bool omit_zeroing_entries =*/ false);
    solver.solve(transpose_operator(op), *v2, u, preconditioner);
    v += *v2;
    vector_memory.free(v2);
  };

  return return_op;
}




template <typename Range,
          typename Payload = internal::LinearOperator::EmptyPayload>
LinearOperator<Range, Range, Payload>
identity_operator(const std::function<void(Range &, bool)> &reinit_vector)
{
  LinearOperator<Range, Range, Payload> return_op ((Payload()));

  return_op.reinit_range_vector = reinit_vector;
  return_op.reinit_domain_vector = reinit_vector;

  return_op.vmult = [](Range &v, const Range &u)
  {
    v = u;
  };

  return_op.vmult_add = [](Range &v, const Range &u)
  {
    v += u;
  };

  return_op.Tvmult = [](Range &v, const Range &u)
  {
    v = u;
  };

  return_op.Tvmult_add = [](Range &v, const Range &u)
  {
    v += u;
  };

  return return_op;
}


template <typename Range, typename Domain, typename Payload>
LinearOperator<Range, Domain, Payload>
identity_operator(const LinearOperator<Range, Domain, Payload> &op)
{
  const LinearOperator<Range, Domain, Payload> id_op
    = identity_operator<Range,Payload>(op.reinit_range_vector);
  LinearOperator<Range, Domain, Payload> return_op (
    op.identity_payload()
  );

  return_op.reinit_range_vector = id_op.reinit_range_vector;
  return_op.reinit_domain_vector = id_op.reinit_domain_vector;
  return_op.vmult = id_op.vmult;
  return_op.vmult_add = id_op.vmult_add;
  return_op.Tvmult = id_op.Tvmult;
  return_op.Tvmult_add = id_op.Tvmult_add;

  return return_op;
}


template <typename Range, typename Domain, typename Payload>
LinearOperator<Range, Domain, Payload>
null_operator(const LinearOperator<Range, Domain, Payload> &op)
{
  LinearOperator<Range, Domain, Payload> return_op (
    op.null_payload()
  );

  return_op.is_null_operator = true;

  return_op.reinit_range_vector = op.reinit_range_vector;
  return_op.reinit_domain_vector = op.reinit_domain_vector;

  return_op.vmult = [](Range &v, const Domain &)
  {
    v = 0.;
  };

  return_op.vmult_add = [](Range &, const Domain &)
  {};

  return_op.Tvmult = [](Domain &v, const Range &)
  {
    v = 0.;
  };

  return_op.Tvmult_add = [](Domain &, const Range &)
  {};

  return return_op;
}


namespace internal
{
  namespace LinearOperator
  {
    template<typename Vector>
    class ReinitHelper
    {
    public:
      template <typename Matrix>
      static
      void reinit_range_vector (const Matrix &matrix, Vector &v, bool omit_zeroing_entries)
      {
        v.reinit(matrix.m(), omit_zeroing_entries);
      }

      template <typename Matrix>
      static
      void reinit_domain_vector (const Matrix &matrix, Vector &v, bool omit_zeroing_entries)
      {
        v.reinit(matrix.n(), omit_zeroing_entries);
      }
    };


    class EmptyPayload
    {
    public:

      template <typename... Args>
      EmptyPayload (const Args &...)
      { }


      EmptyPayload
      identity_payload () const
      {
        return *this;
      }


      EmptyPayload
      null_payload () const
      {
        return *this;
      }


      EmptyPayload
      transpose_payload () const
      {
        return *this;
      }


      template <typename Solver, typename Preconditioner>
      EmptyPayload
      inverse_payload (Solver &, const Preconditioner &) const
      {
        return *this;
      }
    };

    inline
    EmptyPayload operator+(const EmptyPayload &,
                           const EmptyPayload &)
    {
      return EmptyPayload();
    }

    inline
    EmptyPayload operator*(const EmptyPayload &,
                           const EmptyPayload &)
    {
      return EmptyPayload();
    }

  } /* namespace LinearOperator */
} /* namespace internal */


namespace
{
  // A trait class that determines whether type T provides public
  // (templated or non-templated) vmult_add member functions
  template <typename Range, typename Domain, typename T>
  class has_vmult_add_and_Tvmult_add
  {
    template <typename C>
    static std::false_type test(...);

    template <typename C>
    static auto test(Range *r, Domain *d)
    -> decltype(std::declval<C>().vmult_add(*r,*d),
                std::declval<C>().Tvmult_add(*d,*r),
                std::true_type());

  public:
    // type is std::true_type if Matrix provides vmult_add and Tvmult_add,
    // otherwise it is std::false_type

    typedef decltype(test<T>(nullptr, nullptr)) type;
  };


  // A helper function to apply a given vmult, or Tvmult to a vector with
  // intermediate storage
  template <typename Function, typename Range, typename Domain>
  void apply_with_intermediate_storage(Function function, Range &v,
                                       const Domain &u, bool add)
  {
    static GrowingVectorMemory<Range> vector_memory;

    Range *i = vector_memory.alloc();
    i->reinit(v, /*bool omit_zeroing_entries =*/true);

    function(*i, u);

    if (add)
      v += *i;
    else
      v = *i;

    vector_memory.free(i);
  }


  // A helper class to add a reduced matrix interface to a LinearOperator
  // (typically provided by Preconditioner classes)
  template <typename Range, typename Domain, typename Payload>
  class MatrixInterfaceWithoutVmultAdd
  {
  public:
    template <typename Matrix>
    void operator()(LinearOperator<Range, Domain, Payload> &op, const Matrix &matrix)
    {
      op.vmult = [&matrix](Range &v, const Domain &u)
      {
        if (PointerComparison::equal(&v, &u))
          {
            // If v and u are the same memory location use intermediate storage
            apply_with_intermediate_storage([&matrix](Range &b, const Domain &a)
            {
              matrix.vmult(b, a);
            },
            v, u, /*bool add =*/ false);
          }
        else
          {
            matrix.vmult(v,u);
          }
      };

      op.vmult_add = [&matrix](Range &v, const Domain &u)
      {
        // use intermediate storage to implement vmult_add with vmult
        apply_with_intermediate_storage([&matrix](Range &b, const Domain &a)
        {
          matrix.vmult(b, a);
        },
        v, u, /*bool add =*/ true);
      };

      op.Tvmult = [&matrix](Domain &v, const Range &u)
      {
        if (PointerComparison::equal(&v, &u))
          {
            // If v and u are the same memory location use intermediate storage
            apply_with_intermediate_storage([&matrix](Domain &b, const Range &a)
            {
              matrix.Tvmult(b, a);
            },
            v, u, /*bool add =*/ false);
          }
        else
          {
            matrix.Tvmult(v,u);
          }

      };

      op.Tvmult_add = [&matrix](Domain &v, const Range &u)
      {
        // use intermediate storage to implement Tvmult_add with Tvmult
        apply_with_intermediate_storage([&matrix](Domain &b, const Range &a)
        {
          matrix.Tvmult(b, a);
        },
        v, u, /*bool add =*/ true);
      };
    }
  };


  // A helper class to add the full matrix interface to a LinearOperator
  template <typename Range, typename Domain, typename Payload>
  class MatrixInterfaceWithVmultAdd
  {
  public:
    template <typename Matrix>
    void operator()(LinearOperator<Range, Domain, Payload> &op, const Matrix &matrix)
    {
      // As above ...

      MatrixInterfaceWithoutVmultAdd<Range, Domain, Payload>().operator()(op, matrix);

      // ... but add native vmult_add and Tvmult_add variants:

      op.vmult_add = [&matrix](Range &v, const Domain &u)
      {
        if (PointerComparison::equal(&v, &u))
          {
            apply_with_intermediate_storage([&matrix](Range &b, const Domain &a)
            {
              matrix.vmult(b, a);
            },
            v, u, /*bool add =*/ false);
          }
        else
          {
            matrix.vmult_add(v,u);
          }
      };

      op.Tvmult_add = [&matrix](Domain &v, const Range &u)
      {
        if (PointerComparison::equal(&v, &u))
          {
            apply_with_intermediate_storage([&matrix](Domain &b, const Range &a)
            {
              matrix.Tvmult(b, a);
            },
            v, u, /*bool add =*/ true);
          }
        else
          {
            matrix.Tvmult_add(v,u);
          }
      };
    }
  };

} /* namespace */


template <typename Range, typename Domain,
          typename Payload, typename Matrix>
LinearOperator<Range, Domain, Payload>
linear_operator(const Matrix &matrix)
{
  // implement with the more generic variant below...
  return linear_operator<Range, Domain, Payload, Matrix, Matrix>(matrix, matrix);
}


template <typename Range,
          typename Domain,
          typename Payload,
          typename OperatorExemplar,
          typename Matrix>
LinearOperator<Range, Domain, Payload>
linear_operator(const OperatorExemplar &operator_exemplar, const Matrix &matrix)
{
  // Initialise the payload based on the input exemplar matrix
  LinearOperator<Range, Domain, Payload> return_op (Payload(operator_exemplar,matrix));

  // Always store a reference to matrix and operator_exemplar in the lambda
  // functions. This ensures that a modification of the matrix after the
  // creation of a LinearOperator wrapper is respected - further a matrix
  // or an operator_exemplar cannot usually be copied...

  return_op.reinit_range_vector = [&operator_exemplar](Range &v, bool omit_zeroing_entries)
  {
    internal::LinearOperator::ReinitHelper<Range>::reinit_range_vector(operator_exemplar, v, omit_zeroing_entries);
  };

  return_op.reinit_domain_vector = [&operator_exemplar](Domain &v, bool omit_zeroing_entries)
  {
    internal::LinearOperator::ReinitHelper<Domain>::reinit_domain_vector(operator_exemplar, v, omit_zeroing_entries);
  };

  typename std::conditional<
  has_vmult_add_and_Tvmult_add<Range, Domain, Matrix>::type::value,
                               MatrixInterfaceWithVmultAdd<Range, Domain, Payload>,
                               MatrixInterfaceWithoutVmultAdd<Range, Domain, Payload>>::type().
                               operator()(return_op, matrix);

  return return_op;
}




DEAL_II_NAMESPACE_CLOSE

#endif // DEAL_II_WITH_CXX11
#endif