/* -----------------------------------------------------------------
 * Programmer(s): Slaven Peles @ LLNL
 * -----------------------------------------------------------------
 * SUNDIALS Copyright Start
 * Copyright (c) 2002-2020, Lawrence Livermore National Security
 * and Southern Methodist University.
 * All rights reserved.
 *
 * See the top-level LICENSE and NOTICE files for details.
 *
 * SPDX-License-Identifier: BSD-3-Clause
 * SUNDIALS Copyright End
 * -----------------------------------------------------------------*/

#ifndef _TPETRA_SUNDIALS_VECTOR_KERNELS_HPP_
#define _TPETRA_SUNDIALS_VECTOR_KERNELS_HPP_

#include <Tpetra_Vector.hpp>
#include <Kokkos_Core.hpp>
#include <nvector/trilinos/SundialsTpetraVectorInterface.hpp>

namespace Sundials
{

  /**
   * The namespace contains custom Kokkos-based kernels needed by SUNDIALS
   *
   * Kernels are inlined in case this file is included in more than one
   * translation unit.
   */
  namespace TpetraVector
  {
    using Teuchos::outArg;
    using Teuchos::REDUCE_SUM;
    using Teuchos::REDUCE_MIN;
    using Teuchos::REDUCE_MAX;
    using Teuchos::reduceAll;

    typedef Sundials::TpetraVectorInterface::vector_type vector_type;
    typedef vector_type::scalar_type scalar_type;
    typedef vector_type::mag_type mag_type;
    typedef vector_type::global_ordinal_type global_ordinal_type;
    typedef vector_type::local_ordinal_type local_ordinal_type;
    typedef vector_type::node_type::memory_space memory_space;
    typedef vector_type::execution_space execution_space;

    static constexpr scalar_type zero   = 0;
    static constexpr scalar_type half   = 0.5;
    static constexpr scalar_type one    = 1.0;
    static constexpr scalar_type onept5 = 1.5;

    /*----------------------------------------------------------------
     *  Streaming vector kernels
     *---------------------------------------------------------------*/

    /// Divide: z(i) = x(i)/y(i) forall i
    inline void elementWiseDivide(const vector_type& x,
                                  const vector_type& y,
                                  vector_type& z)
    {
      const local_ordinal_type N =
        static_cast<local_ordinal_type>(x.getLocalLength());

      if (x.need_sync<memory_space>())
        const_cast<vector_type&>(x).sync<memory_space>();
      if (y.need_sync<memory_space>())
        const_cast<vector_type&>(y).sync<memory_space>();

      auto x_2d = x.getLocalView<memory_space>();
      auto x_1d = Kokkos::subview (x_2d, Kokkos::ALL(), 0);
      auto y_2d = y.getLocalView<memory_space>();
      auto y_1d = Kokkos::subview (y_2d, Kokkos::ALL(), 0);
      auto z_2d = z.getLocalView<memory_space>();
      auto z_1d = Kokkos::subview (z_2d, Kokkos::ALL(), 0);

      z.modify<memory_space>();

      Kokkos::parallel_for ("elementWiseDivide", Kokkos::RangePolicy<execution_space>(0, N),
        KOKKOS_LAMBDA (const local_ordinal_type &i)
        {
          z_1d(i) = x_1d(i)/y_1d(i);
        }
      );
    }


    /// Add constant to all vector elements: z(i) = x(i) + b
    inline void addConst(const vector_type& x,
                         scalar_type b,
                         vector_type& z)
    {
      const local_ordinal_type N =
        static_cast<local_ordinal_type>(x.getLocalLength());

      if (x.need_sync<memory_space>())
        const_cast<vector_type&>(x).sync<memory_space>();
      if (z.need_sync<memory_space>())
        const_cast<vector_type&>(z).sync<memory_space>();

      auto x_2d = x.getLocalView<memory_space>();
      auto x_1d = Kokkos::subview (x_2d, Kokkos::ALL(), 0);
      auto z_2d = z.getLocalView<memory_space>();
      auto z_1d = Kokkos::subview (z_2d, Kokkos::ALL(), 0);

      z.modify<memory_space>();

      Kokkos::parallel_for ("addConst", Kokkos::RangePolicy<execution_space>(0, N),
        KOKKOS_LAMBDA (const local_ordinal_type &i)
        {
          z_1d(i) = x_1d(i) + b;
        }
      );
    }


    /// Compare vector elements to c: z(i) = |x(i)| >= c ? 1 : 0
    inline void compare(scalar_type c,
                        const vector_type& x,
                        vector_type& z)
    {
      const local_ordinal_type N =
        static_cast<local_ordinal_type>(x.getLocalLength());

      if (x.need_sync<memory_space>())
        const_cast<vector_type&>(x).sync<memory_space>();
      if (z.need_sync<memory_space>())
        const_cast<vector_type&>(z).sync<memory_space>();

      auto x_2d = x.getLocalView<memory_space>();
      auto x_1d = Kokkos::subview (x_2d, Kokkos::ALL(), 0);
      auto z_2d = z.getLocalView<memory_space>();
      auto z_1d = Kokkos::subview (z_2d, Kokkos::ALL(), 0);

      z.modify<memory_space>();

      Kokkos::parallel_for ("compare", Kokkos::RangePolicy<execution_space>(0, N),
        KOKKOS_LAMBDA (const local_ordinal_type &i)
        {
          z_1d(i) = std::abs(x_1d(i)) >= c ? one : zero;
        }
      );
    }


    /*----------------------------------------------------------------
     *  Reduction vector kernels
     *---------------------------------------------------------------*/

    /// Weighted root-mean-square norm
    inline mag_type normWrms(const vector_type& x,
                             const vector_type& w)
    {
      const Teuchos::RCP<const Teuchos::Comm<int> >& comm = x.getMap()->getComm();
      const local_ordinal_type  N =
        static_cast<local_ordinal_type>(x.getLocalLength());
      const global_ordinal_type Nglob =
        static_cast<global_ordinal_type>(x.getGlobalLength());

      if (x.need_sync<memory_space>())
        const_cast<vector_type&>(x).sync<memory_space>();
      if (w.need_sync<memory_space>())
        const_cast<vector_type&>(w).sync<memory_space>();

      auto x_2d = x.getLocalView<memory_space>();
      auto x_1d = Kokkos::subview (x_2d, Kokkos::ALL(), 0);
      auto w_2d = w.getLocalView<memory_space>();
      auto w_1d = Kokkos::subview (w_2d, Kokkos::ALL(), 0);

      mag_type sum = zero;
      Kokkos::parallel_reduce ("normWrms", Kokkos::RangePolicy<execution_space>(0, N),
        KOKKOS_LAMBDA (const local_ordinal_type &i, mag_type &local_sum)
        {
          local_sum += x_1d(i)*w_1d(i)*(x_1d(i)*w_1d(i));
        }, sum);

      mag_type globalSum = zero;
      reduceAll<int, mag_type>(*comm, REDUCE_SUM, sum, outArg(globalSum));
      return std::sqrt(globalSum/static_cast<mag_type>(Nglob));
    }


    /// Weighted root-mean-square norm with mask
    inline mag_type normWrmsMask(const vector_type& x,
                                 const vector_type& w,
                                 const vector_type& id)
    {
      const Teuchos::RCP<const Teuchos::Comm<int> >& comm = x.getMap()->getComm();
      const local_ordinal_type  N =
        static_cast<local_ordinal_type>(x.getLocalLength());
      const global_ordinal_type Nglob =
        static_cast<global_ordinal_type>(x.getGlobalLength());

      if (x.need_sync<memory_space>())
        const_cast<vector_type&>(x).sync<memory_space>();
      if (w.need_sync<memory_space>())
        const_cast<vector_type&>(w).sync<memory_space>();
      if (id.need_sync<memory_space>())
        const_cast<vector_type&>(id).sync<memory_space>();

      auto x_2d = x.getLocalView<memory_space>();
      auto x_1d = Kokkos::subview (x_2d, Kokkos::ALL(), 0);
      auto w_2d = w.getLocalView<memory_space>();
      auto w_1d = Kokkos::subview (w_2d, Kokkos::ALL(), 0);
      auto id_2d = id.getLocalView<memory_space>();
      auto id_1d = Kokkos::subview (id_2d, Kokkos::ALL(), 0);

      mag_type sum = zero;
      Kokkos::parallel_reduce ("normWrmsMask", Kokkos::RangePolicy<execution_space>(0, N),
        KOKKOS_LAMBDA (const local_ordinal_type &i, mag_type &local_sum)
        {
          if (id_1d(i) > zero)
            local_sum += x_1d(i)*w_1d(i)*(x_1d(i)*w_1d(i));
        }, sum);

      mag_type globalSum = zero;
      reduceAll<int, mag_type>(*comm, REDUCE_SUM, sum, outArg(globalSum));
      return std::sqrt(globalSum/static_cast<mag_type>(Nglob));
    }


    /// Find minimum element value in the vector
    inline scalar_type minElement(const vector_type& x)
    {
      using namespace Kokkos;

      const Teuchos::RCP<const Teuchos::Comm<int> >& comm = x.getMap()->getComm();
      const local_ordinal_type  N =
        static_cast<local_ordinal_type>(x.getLocalLength());

      if (x.need_sync<memory_space>())
        const_cast<vector_type&>(x).sync<memory_space>();

      auto x_2d = x.getLocalView<memory_space>();
      auto x_1d = Kokkos::subview (x_2d, Kokkos::ALL(), 0);

      scalar_type minimum;
      Min<scalar_type> min_reducer(minimum);

      Kokkos::parallel_reduce ("minElement", Kokkos::RangePolicy<execution_space>(0, N),
        KOKKOS_LAMBDA (const local_ordinal_type &i, scalar_type &local_min)
        {
          min_reducer.join(local_min, x_1d(i));
        }, min_reducer);

      scalar_type globalMin;
      reduceAll<int, scalar_type>(*comm, REDUCE_MIN, minimum, outArg(globalMin));
      return globalMin;
    }


    /// Weighted L2 norm
    inline mag_type normWL2(const vector_type& x,
                            const vector_type& w)
    {
      const Teuchos::RCP<const Teuchos::Comm<int> >& comm = x.getMap()->getComm();
      const local_ordinal_type  N =
        static_cast<local_ordinal_type>(x.getLocalLength());

      if (x.need_sync<memory_space>())
        const_cast<vector_type&>(x).sync<memory_space>();
      if (w.need_sync<memory_space>())
        const_cast<vector_type&>(w).sync<memory_space>();

      auto x_2d = x.getLocalView<memory_space>();
      auto x_1d = Kokkos::subview (x_2d, Kokkos::ALL(), 0);
      auto w_2d = w.getLocalView<memory_space>();
      auto w_1d = Kokkos::subview (w_2d, Kokkos::ALL(), 0);

      mag_type sum = zero;
      Kokkos::parallel_reduce ("normWL2", Kokkos::RangePolicy<execution_space>(0, N),
        KOKKOS_LAMBDA (const local_ordinal_type &i, mag_type &local_sum)
        {
          local_sum += x_1d(i)*w_1d(i)*(x_1d(i)*w_1d(i));
        }, sum);

      mag_type globalSum = zero;
      reduceAll<int, mag_type>(*comm, REDUCE_SUM, sum, outArg(globalSum));
      return std::sqrt(globalSum);
    }


    /// Elementwise inverse, return false if any denominator is zero.
    inline bool invTest(const vector_type& x,
                        vector_type& z)
    {
      using namespace Kokkos;

      const Teuchos::RCP<const Teuchos::Comm<int> >& comm = x.getMap()->getComm();
      const local_ordinal_type  N =
        static_cast<local_ordinal_type>(x.getLocalLength());

      if (x.need_sync<memory_space>())
        const_cast<vector_type&>(x).sync<memory_space>();

      auto x_2d = x.getLocalView<memory_space>();
      auto x_1d = Kokkos::subview (x_2d, Kokkos::ALL(), 0);
      auto z_2d = z.getLocalView<memory_space>();
      auto z_1d = Kokkos::subview (z_2d, Kokkos::ALL(), 0);

      scalar_type minimum;
      Min<scalar_type> min_reducer(minimum);

      z.modify<memory_space>();

      Kokkos::parallel_reduce ("invTest", Kokkos::RangePolicy<execution_space>(0, N),
        KOKKOS_LAMBDA (const local_ordinal_type &i, scalar_type &local_min)
        {
          static constexpr scalar_type zero   = 0;
          static constexpr scalar_type one    = 1.0;
          if (x_1d(i) == zero)
          {
            min_reducer.join(local_min, zero);
          }
          else
          {
            z_1d(i) = one/x_1d(i);
          }
        }, min_reducer);

      scalar_type globalMin;
      reduceAll<int, scalar_type>(*comm, REDUCE_MIN, minimum, outArg(globalMin));
      return (globalMin > half);
    }


    /// Find constraint violations
    inline bool constraintMask(const vector_type& c,
                               const vector_type& x,
                               vector_type& m)
    {
      const Teuchos::RCP<const Teuchos::Comm<int> >& comm = x.getMap()->getComm();
      const local_ordinal_type  N =
        static_cast<local_ordinal_type>(x.getLocalLength());

      if (c.need_sync<memory_space>())
        const_cast<vector_type&>(c).sync<memory_space>();
      if (x.need_sync<memory_space>())
        const_cast<vector_type&>(x).sync<memory_space>();

      auto c_2d = c.getLocalView<memory_space>();
      auto c_1d = Kokkos::subview (c_2d, Kokkos::ALL(), 0);
      auto x_2d = x.getLocalView<memory_space>();
      auto x_1d = Kokkos::subview (x_2d, Kokkos::ALL(), 0);
      auto m_2d = m.getLocalView<memory_space>();
      auto m_1d = Kokkos::subview (m_2d, Kokkos::ALL(), 0);

      m.modify<memory_space>();

      mag_type sum = zero;
      Kokkos::parallel_reduce ("constraintMask", Kokkos::RangePolicy<execution_space>(0, N),
        KOKKOS_LAMBDA (const local_ordinal_type &i, mag_type &local_sum)
        {
          const bool test = (std::abs(c_1d(i)) > onept5 && c_1d(i)*x_1d(i) <= zero) ||
                            (std::abs(c_1d(i)) > half   && c_1d(i)*x_1d(i) <  zero);
          m_1d(i) = test ? one : zero;
          local_sum += m_1d(i);
        }, sum);

      mag_type globalSum = zero;
      reduceAll<int, mag_type>(*comm, REDUCE_SUM, sum, outArg(globalSum));
      return (globalSum < half);
    }


    /// Minimum quotient: min_i(num(i)/den(i))
    inline scalar_type minQuotient(const vector_type& num,
                                   const vector_type& den)
    {
      using namespace Kokkos;

      const Teuchos::RCP<const Teuchos::Comm<int> >& comm = num.getMap()->getComm();
      const local_ordinal_type  N =
        static_cast<local_ordinal_type>(num.getLocalLength());

      if (num.need_sync<memory_space>())
        const_cast<vector_type&>(num).sync<memory_space>();
      if (den.need_sync<memory_space>())
        const_cast<vector_type&>(den).sync<memory_space>();

      auto num_2d = num.getLocalView<memory_space>();
      auto num_1d = Kokkos::subview (num_2d, Kokkos::ALL(), 0);
      auto den_2d = den.getLocalView<memory_space>();
      auto den_1d = Kokkos::subview (den_2d, Kokkos::ALL(), 0);

      scalar_type minimum;
      Min<scalar_type> min_reducer(minimum);

      Kokkos::parallel_reduce ("minQuotient", Kokkos::RangePolicy<execution_space>(0, N),
        KOKKOS_LAMBDA (const local_ordinal_type &i, scalar_type &local_min)
        {
          if (den_1d(i) != zero)
            min_reducer.join(local_min, num_1d(i)/den_1d(i));
        }, min_reducer);

      scalar_type globalMin;
      reduceAll<int, scalar_type>(*comm, REDUCE_MIN, minimum, outArg(globalMin));
      return globalMin;
    }


    /// MPI task-local dot-product
    inline scalar_type dotProdLocal(const vector_type& x,
                                    const vector_type& y)
    {
      const local_ordinal_type  N =
        static_cast<local_ordinal_type>(x.getLocalLength());
      if (x.need_sync<memory_space>())
        const_cast<vector_type&>(x).sync<memory_space>();
      if (y.need_sync<memory_space>())
        const_cast<vector_type&>(y).sync<memory_space>();

      auto x_2d = x.getLocalView<memory_space>();
      auto x_1d = Kokkos::subview (x_2d, Kokkos::ALL(), 0);
      auto y_2d = y.getLocalView<memory_space>();
      auto y_1d = Kokkos::subview (y_2d, Kokkos::ALL(), 0);

      scalar_type sum = zero;
      Kokkos::parallel_reduce ("dotProdLocal", Kokkos::RangePolicy<execution_space>(0, N),
        KOKKOS_LAMBDA (const local_ordinal_type &i, scalar_type &local_sum)
        {
          local_sum += x_1d(i)*y_1d(i);
        }, sum);

      return sum;
    }


    /// MPI task-local maximum norm of a vector
    inline mag_type maxNormLocal(const vector_type& x)
    {
      using namespace Kokkos;

      const local_ordinal_type  N =
        static_cast<local_ordinal_type>(x.getLocalLength());
      if (x.need_sync<memory_space>())
        const_cast<vector_type&>(x).sync<memory_space>();

      auto x_2d = x.getLocalView<memory_space>();
      auto x_1d = Kokkos::subview (x_2d, Kokkos::ALL(), 0);

      mag_type maximum;
      Max<mag_type> max_reducer(maximum);

      Kokkos::parallel_reduce ("maxNormLocal", Kokkos::RangePolicy<execution_space>(0, N),
        KOKKOS_LAMBDA (const local_ordinal_type &i, mag_type &local_max)
        {
          max_reducer.join(local_max, std::abs(x_1d(i)));
        }, max_reducer);

      return maximum;
    }


    /// MPI task-local minimum element in the vector
    inline scalar_type minLocal(const vector_type& x)
    {
      using namespace Kokkos;

      const local_ordinal_type  N =
        static_cast<local_ordinal_type>(x.getLocalLength());
      if (x.need_sync<memory_space>())
        const_cast<vector_type&>(x).sync<memory_space>();

      auto x_2d = x.getLocalView<memory_space>();
      auto x_1d = Kokkos::subview (x_2d, Kokkos::ALL(), 0);

      scalar_type minimum;
      Min<scalar_type> min_reducer(minimum);

      Kokkos::parallel_reduce ("minElement", Kokkos::RangePolicy<execution_space>(0, N),
        KOKKOS_LAMBDA (const local_ordinal_type &i, scalar_type &local_min)
        {
          min_reducer.join(local_min, x_1d(i));
        }, min_reducer);

      return minimum;
    }


    /// MPI task-local L1 norm of a vector
    inline mag_type L1NormLocal(const vector_type& x)
    {
      using namespace Kokkos;

      const local_ordinal_type  N =
        static_cast<local_ordinal_type>(x.getLocalLength());
      if (x.need_sync<memory_space>())
        const_cast<vector_type&>(x).sync<memory_space>();

      auto x_2d = x.getLocalView<memory_space>();
      auto x_1d = Kokkos::subview (x_2d, Kokkos::ALL(), 0);

      mag_type sum = zero;
      Kokkos::parallel_reduce ("L1NormLocal", Kokkos::RangePolicy<execution_space>(0, N),
        KOKKOS_LAMBDA (const local_ordinal_type &i, mag_type &local_sum)
        {
          local_sum += std::abs(x_1d(i));
        }, sum);

      return sum;
    }


    /// MPI task-local weighted squared sum
    inline mag_type WSqrSumLocal(const vector_type& x,
                                 const vector_type& w)
    {
      const local_ordinal_type  N =
        static_cast<local_ordinal_type>(x.getLocalLength());
      if (x.need_sync<memory_space>())
        const_cast<vector_type&>(x).sync<memory_space>();
      if (w.need_sync<memory_space>())
        const_cast<vector_type&>(w).sync<memory_space>();

      auto x_2d = x.getLocalView<memory_space>();
      auto x_1d = Kokkos::subview (x_2d, Kokkos::ALL(), 0);
      auto w_2d = w.getLocalView<memory_space>();
      auto w_1d = Kokkos::subview (w_2d, Kokkos::ALL(), 0);

      mag_type sum = zero;
      Kokkos::parallel_reduce ("WSqrSumLocal", Kokkos::RangePolicy<execution_space>(0, N),
        KOKKOS_LAMBDA (const local_ordinal_type &i, mag_type &local_sum)
        {
          local_sum += x_1d(i)*w_1d(i)*(x_1d(i)*w_1d(i));
        }, sum);

      return sum;
    }


    /// MPI task-local weighted squared masked sum
    inline mag_type WSqrSumMaskLocal(const vector_type& x,
                                     const vector_type& w,
                                     const vector_type& id)
    {
      const local_ordinal_type  N =
        static_cast<local_ordinal_type>(x.getLocalLength());
      if (x.need_sync<memory_space>())
        const_cast<vector_type&>(x).sync<memory_space>();
      if (w.need_sync<memory_space>())
        const_cast<vector_type&>(w).sync<memory_space>();
      if (id.need_sync<memory_space>())
        const_cast<vector_type&>(id).sync<memory_space>();

      auto x_2d = x.getLocalView<memory_space>();
      auto x_1d = Kokkos::subview (x_2d, Kokkos::ALL(), 0);
      auto w_2d = w.getLocalView<memory_space>();
      auto w_1d = Kokkos::subview (w_2d, Kokkos::ALL(), 0);
      auto id_2d = id.getLocalView<memory_space>();
      auto id_1d = Kokkos::subview (id_2d, Kokkos::ALL(), 0);

      mag_type sum = zero;
      Kokkos::parallel_reduce ("WSqrSumMaskLocal", Kokkos::RangePolicy<execution_space>(0, N),
        KOKKOS_LAMBDA (const local_ordinal_type &i, mag_type &local_sum)
        {
          if (id_1d(i) > zero)
            local_sum += x_1d(i)*w_1d(i)*(x_1d(i)*w_1d(i));
        }, sum);

      return sum;
    }


    /// MPI task-local elementwise inverse, return false if any denominator is zero.
    inline bool invTestLocal(const vector_type& x,
                             vector_type& z)
    {
      using namespace Kokkos;

      const local_ordinal_type  N =
        static_cast<local_ordinal_type>(x.getLocalLength());
      if (x.need_sync<memory_space>())
        const_cast<vector_type&>(x).sync<memory_space>();

      auto x_2d = x.getLocalView<memory_space>();
      auto x_1d = Kokkos::subview (x_2d, Kokkos::ALL(), 0);
      auto z_2d = z.getLocalView<memory_space>();
      auto z_1d = Kokkos::subview (z_2d, Kokkos::ALL(), 0);

      scalar_type minimum;
      Min<scalar_type> min_reducer(minimum);

      z.modify<memory_space>();

      Kokkos::parallel_reduce ("invTestLocal", Kokkos::RangePolicy<execution_space>(0, N),
        KOKKOS_LAMBDA (const local_ordinal_type &i, scalar_type &local_min)
        {
          static constexpr scalar_type zero   = 0;
          static constexpr scalar_type one    = 1.0;
          if (x_1d(i) == zero)
          {
            min_reducer.join(local_min, zero);
          }
          else
          {
            z_1d(i) = one/x_1d(i);
          }
        }, min_reducer);

      return (minimum > half);
    }


    /// MPI task-local constraint violation check
    inline bool constraintMaskLocal(const vector_type& c,
                                    const vector_type& x,
                                    vector_type& m)
    {
      const local_ordinal_type  N =
        static_cast<local_ordinal_type>(x.getLocalLength());
      if (c.need_sync<memory_space>())
        const_cast<vector_type&>(c).sync<memory_space>();
      if (x.need_sync<memory_space>())
        const_cast<vector_type&>(x).sync<memory_space>();

      auto c_2d = c.getLocalView<memory_space>();
      auto c_1d = Kokkos::subview (c_2d, Kokkos::ALL(), 0);
      auto x_2d = x.getLocalView<memory_space>();
      auto x_1d = Kokkos::subview (x_2d, Kokkos::ALL(), 0);
      auto m_2d = m.getLocalView<memory_space>();
      auto m_1d = Kokkos::subview (m_2d, Kokkos::ALL(), 0);

      m.modify<memory_space>();

      mag_type sum = zero;
      Kokkos::parallel_reduce ("constraintMaskLocal", Kokkos::RangePolicy<execution_space>(0, N),
        KOKKOS_LAMBDA (const local_ordinal_type &i, mag_type &local_sum)
        {
          const bool test = (std::abs(c_1d(i)) > onept5 && c_1d(i)*x_1d(i) <= zero) ||
                            (std::abs(c_1d(i)) > half   && c_1d(i)*x_1d(i) <  zero);
          m_1d(i) = test ? one : zero;
          local_sum += m_1d(i);
        }, sum);

      return (sum < half);
    }


    /// MPI task-local minimum quotient: min_i(num(i)/den(i))
    inline scalar_type minQuotientLocal(const vector_type& num,
                                        const vector_type& den)
    {
      using namespace Kokkos;

      const local_ordinal_type  N =
        static_cast<local_ordinal_type>(num.getLocalLength());
      if (num.need_sync<memory_space>())
        const_cast<vector_type&>(num).sync<memory_space>();
      if (den.need_sync<memory_space>())
        const_cast<vector_type&>(den).sync<memory_space>();

      auto num_2d = num.getLocalView<memory_space>();
      auto num_1d = Kokkos::subview (num_2d, Kokkos::ALL(), 0);
      auto den_2d = den.getLocalView<memory_space>();
      auto den_1d = Kokkos::subview (den_2d, Kokkos::ALL(), 0);

      scalar_type minimum;
      Min<scalar_type> min_reducer(minimum);

      Kokkos::parallel_reduce ("minQuotient", Kokkos::RangePolicy<execution_space>(0, N),
        KOKKOS_LAMBDA (const local_ordinal_type &i, scalar_type &local_min)
        {
          if (den_1d(i) != zero)
            min_reducer.join(local_min, num_1d(i)/den_1d(i));
        }, min_reducer);

      return minimum;
    }


  } // namespace TpetraVector

} // namespace Sundials

#endif // _TPETRA_SUNDIALS_VECTOR_KERNELS_HPP_
