spai-dynamic.hpp

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#ifndef VIENNACL_LINALG_DETAIL_SPAI_SPAI_DYNAMIC_HPP
#define VIENNACL_LINALG_DETAIL_SPAI_SPAI_DYNAMIC_HPP

/* =========================================================================
   Copyright (c) 2010-2015, Institute for Microelectronics,
                            Institute for Analysis and Scientific Computing,
                            TU Wien.
   Portions of this software are copyright by UChicago Argonne, LLC.

                            -----------------
                  ViennaCL - The Vienna Computing Library
                            -----------------

   Project Head:    Karl Rupp                   rupp@iue.tuwien.ac.at

   (A list of authors and contributors can be found in the manual)

   License:         MIT (X11), see file LICENSE in the base directory
============================================================================= */

#include <utility>
#include <iostream>
#include <fstream>
#include <string>
#include <algorithm>
#include <vector>
#include <math.h>
#include <map>
//#include "block_matrix.hpp"
//#include "block_vector.hpp"
//#include "benchmark-utils.hpp"
#include "boost/numeric/ublas/vector.hpp"
#include "boost/numeric/ublas/matrix.hpp"
#include "boost/numeric/ublas/matrix_proxy.hpp"
#include "boost/numeric/ublas/vector_proxy.hpp"
#include "boost/numeric/ublas/storage.hpp"
#include "boost/numeric/ublas/io.hpp"
#include "boost/numeric/ublas/lu.hpp"
#include "boost/numeric/ublas/triangular.hpp"
#include "boost/numeric/ublas/matrix_expression.hpp"
// ViennaCL includes
#include "viennacl/linalg/prod.hpp"
#include "viennacl/matrix.hpp"
#include "viennacl/compressed_matrix.hpp"
#include "viennacl/linalg/sparse_matrix_operations.hpp"
#include "viennacl/linalg/matrix_operations.hpp"
#include "viennacl/scalar.hpp"
#include "viennacl/linalg/cg.hpp"
#include "viennacl/linalg/inner_prod.hpp"
#include "viennacl/linalg/ilu.hpp"
#include "viennacl/ocl/backend.hpp"

#include "viennacl/linalg/detail/spai/block_matrix.hpp"
#include "viennacl/linalg/detail/spai/block_vector.hpp"
#include "viennacl/linalg/detail/spai/qr.hpp"
#include "viennacl/linalg/detail/spai/spai-static.hpp"
#include "viennacl/linalg/detail/spai/spai.hpp"
#include "viennacl/linalg/detail/spai/spai_tag.hpp"
#include "viennacl/linalg/opencl/kernels/spai.hpp"

namespace viennacl
{
namespace linalg
{
namespace detail
{
namespace spai
{

struct CompareSecond
{
  template<typename T1, typename T2>
  bool operator()(std::pair<T1, T2> const & left, std::pair<T1, T2> const & right)
  {
    return static_cast<double>(left.second) > static_cast<double>(right.second);
  }
};


template<typename MatrixT>
void composeNewR(MatrixT const & A,
                 MatrixT const & R_n,
                 MatrixT & R)
{
  typedef typename MatrixT::value_type        NumericType;

  vcl_size_t row_n = R_n.size1() - (A.size1() - R.size2());
  MatrixT C = boost::numeric::ublas::zero_matrix<NumericType>(R.size1() + row_n, R.size2() + A.size2());

  //write original R to new Composite R
  boost::numeric::ublas::project(C, boost::numeric::ublas::range(0,R.size1()), boost::numeric::ublas::range(0, R.size2())) += R;
  //write upper part of Q'*A_I_\hatJ, all columns and number of rows that equals to R.size2()
  boost::numeric::ublas::project(C, boost::numeric::ublas::range(0, R.size2()), boost::numeric::ublas::range(R.size2(),
                                                                                                            R.size2() + A.size2())) +=
  boost::numeric::ublas::project(A, boost::numeric::ublas::range(0, R.size2()), boost::numeric::ublas::range(0, A.size2()));

  //adding decomposed(QR) block to Composite R
  if (R_n.size1() > 0 && R_n.size2() > 0)
      boost::numeric::ublas::project(C,
                                     boost::numeric::ublas::range(R.size2(), R.size1() + row_n),
                                     boost::numeric::ublas::range(R.size2(), R.size2() + A.size2())) += R_n;
  R = C;
}

template<typename VectorT>
void composeNewVector(VectorT const & v_n,
                      VectorT       & v)
{
  typedef typename VectorT::value_type          NumericType;

  VectorT w  = boost::numeric::ublas::zero_vector<NumericType>(v.size() + v_n.size());
  boost::numeric::ublas::project(w, boost::numeric::ublas::range(0, v.size())) += v;
  boost::numeric::ublas::project(w, boost::numeric::ublas::range(v.size(), v.size() + v_n.size())) += v_n;
  v = w;
}

template<typename SparseVectorT, typename NumericT>
void sparse_norm_2(SparseVectorT const & v,
                   NumericT & norm)
{
  for (typename SparseVectorT::const_iterator vec_it  = v.begin(); vec_it != v.end(); ++vec_it)
    norm += (vec_it->second)*(vec_it->second);

  norm = std::sqrt(norm);
}

template<typename SparseVectorT, typename NumericT>
void sparse_inner_prod(SparseVectorT const & v1,
                       SparseVectorT const & v2,
                       NumericT & res_v)
{
  typename SparseVectorT::const_iterator v_it1 = v1.begin();
  typename SparseVectorT::const_iterator v_it2 = v2.begin();

  while ((v_it1 != v1.end())&&(v_it2 != v2.end()))
  {
    if (v_it1->first == v_it2->first)
    {
      res_v += (v_it1->second)*(v_it2->second);
      ++v_it1;
      ++v_it2;
    }
    else if (v_it1->first < v_it2->first)
      ++v_it1;
    else
      ++v_it2;
  }
}

template<typename SparseVectorT, typename NumericT>
bool buildAugmentedIndexSet(std::vector<SparseVectorT> const & A_v_c,
                            SparseVectorT const & res,
                            std::vector<unsigned int> & J,
                            std::vector<unsigned int> & J_u,
                            spai_tag const & tag)
{
  std::vector<std::pair<unsigned int, NumericT> > p;
  vcl_size_t cur_size = 0;
  NumericT inprod, norm2;

  for (typename SparseVectorT::const_iterator res_it = res.begin(); res_it != res.end(); ++res_it)
  {
    if (!isInIndexSet(J, res_it->first) && (std::fabs(res_it->second) > tag.getResidualThreshold()))
    {
      inprod = norm2 = 0;
      sparse_inner_prod(res, A_v_c[res_it->first], inprod);
      sparse_norm_2(A_v_c[res_it->first], norm2);
      p.push_back(std::pair<unsigned int, NumericT>(res_it->first, (inprod*inprod)/(norm2*norm2)));
    }
  }

  std::sort(p.begin(), p.end(), CompareSecond());
  while ((cur_size < J.size()) && (p.size() > 0))
  {
    J_u.push_back(p[0].first);
    p.erase(p.begin());
    cur_size++;
  }
  p.clear();
  return (cur_size > 0);
}

template<typename SparseVectorT>
void buildNewRowSet(std::vector<SparseVectorT> const & A_v_c,
                    std::vector<unsigned int>  const & I,
                    std::vector<unsigned int>  const & J_n,
                    std::vector<unsigned int>        & I_n)
{
  for (vcl_size_t i = 0; i < J_n.size(); ++i)
  {
    for (typename SparseVectorT::const_iterator col_it = A_v_c[J_n[i]].begin(); col_it!=A_v_c[J_n[i]].end(); ++col_it)
    {
      if (!isInIndexSet(I, col_it->first) && !isInIndexSet(I_n, col_it->first))
        I_n.push_back(col_it->first);
    }
  }
}

template<typename MatrixT>
void QRBlockComposition(MatrixT const & A_I_J,
                        MatrixT const & A_I_J_u,
                        MatrixT       & A_I_u_J_u)
{
  typedef typename MatrixT::value_type     NumericType;

  vcl_size_t row_n1 = A_I_J_u.size1() - A_I_J.size2();
  vcl_size_t row_n2 = A_I_u_J_u.size1();
  vcl_size_t row_n = row_n1 + row_n2;
  vcl_size_t col_n = A_I_J_u.size2();

  MatrixT C = boost::numeric::ublas::zero_matrix<NumericType>(row_n, col_n);
  boost::numeric::ublas::project(C,
                                 boost::numeric::ublas::range(0, row_n1),
                                 boost::numeric::ublas::range(0, col_n))
  += boost::numeric::ublas::project(A_I_J_u,
                                    boost::numeric::ublas::range(A_I_J.size2(), A_I_J_u.size1()),
                                    boost::numeric::ublas::range(0, col_n));

  boost::numeric::ublas::project(C,
                                 boost::numeric::ublas::range(row_n1, row_n1 + row_n2),
                                 boost::numeric::ublas::range(0, col_n)) += A_I_u_J_u;
  A_I_u_J_u = C;
}

template<typename SparseMatrixT,
         typename SparseVectorT,
         typename DenseMatrixT,
         typename VectorT>
void block_update(SparseMatrixT const & A,
                  std::vector<SparseVectorT> const & A_v_c,
                  std::vector<SparseVectorT>       & g_res,
                  std::vector<bool> & g_is_update,
                  std::vector<std::vector<unsigned int> >& g_I,
                  std::vector<std::vector<unsigned int> >& g_J,
                  std::vector<VectorT>      & g_b_v,
                  std::vector<DenseMatrixT> & g_A_I_J,
                  spai_tag const & tag)
{
  typedef typename DenseMatrixT::value_type     NumericType;


  std::vector<std::vector<unsigned int> > g_J_u(g_J.size());   // set of new column indices
  std::vector<std::vector<unsigned int> > g_I_u(g_J.size());   // set of new row indices
  std::vector<DenseMatrixT> g_A_I_J_u(g_J.size());             // matrix A(I, \tilde J), cf. Kallischko p.31-32
  std::vector<DenseMatrixT> g_A_I_u_J_u(g_J.size());           // matrix A(\tilde I, \tilde J), cf. Kallischko
  std::vector<VectorT>      g_b_v_u(g_J.size());               // new vector of beta coefficients from QR factorization

#ifdef VIENNACL_WITH_OPENMP
  #pragma omp parallel for
#endif
  for (long i = 0; i < static_cast<long>(g_J.size()); ++i)
  {
    if (g_is_update[static_cast<vcl_size_t>(i)])
    {
      if (buildAugmentedIndexSet<SparseVectorT, NumericType>(A_v_c, g_res[static_cast<vcl_size_t>(i)], g_J[static_cast<vcl_size_t>(i)], g_J_u[static_cast<vcl_size_t>(i)], tag))
      {
        //initialize matrix A_I_\hatJ
        initProjectSubMatrix(A, g_J_u[static_cast<vcl_size_t>(i)], g_I[static_cast<vcl_size_t>(i)], g_A_I_J_u[static_cast<vcl_size_t>(i)]);
        //multiplication of Q'*A_I_\hatJ
        apply_q_trans_mat(g_A_I_J[static_cast<vcl_size_t>(i)], g_b_v[static_cast<vcl_size_t>(i)], g_A_I_J_u[static_cast<vcl_size_t>(i)]);
        //building new rows index set \hatI
        buildNewRowSet(A_v_c, g_I[static_cast<vcl_size_t>(i)], g_J_u[static_cast<vcl_size_t>(i)], g_I_u[static_cast<vcl_size_t>(i)]);
        initProjectSubMatrix(A, g_J_u[static_cast<vcl_size_t>(i)], g_I_u[static_cast<vcl_size_t>(i)], g_A_I_u_J_u[static_cast<vcl_size_t>(i)]);
        //composition of block for new QR factorization
        QRBlockComposition(g_A_I_J[static_cast<vcl_size_t>(i)], g_A_I_J_u[static_cast<vcl_size_t>(i)], g_A_I_u_J_u[static_cast<vcl_size_t>(i)]);
        //QR factorization
        single_qr(g_A_I_u_J_u[static_cast<vcl_size_t>(i)], g_b_v_u[static_cast<vcl_size_t>(i)]);
        //composition of new R and new vector b_v
        composeNewR(g_A_I_J_u[static_cast<vcl_size_t>(i)], g_A_I_u_J_u[static_cast<vcl_size_t>(i)], g_A_I_J[static_cast<vcl_size_t>(i)]);
        composeNewVector(g_b_v_u[static_cast<vcl_size_t>(i)], g_b_v[static_cast<vcl_size_t>(i)]);
        //composition of new sets: I and J
        g_J[static_cast<vcl_size_t>(i)].insert(g_J[static_cast<vcl_size_t>(i)].end(), g_J_u[static_cast<vcl_size_t>(i)].begin(), g_J_u[static_cast<vcl_size_t>(i)].end());
        g_I[static_cast<vcl_size_t>(i)].insert(g_I[static_cast<vcl_size_t>(i)].end(), g_I_u[static_cast<vcl_size_t>(i)].begin(), g_I_u[static_cast<vcl_size_t>(i)].end());
      }
      else
      {
        g_is_update[static_cast<vcl_size_t>(i)] = false;
      }
    }
  }
}


/**************************************************** GPU SPAI Update ****************************************************************/


//performs Q'*A(I, \tilde J) on GPU
template<typename NumericT>
void block_q_multiplication(std::vector<std::vector<unsigned int> > const & g_J_u,
                            std::vector<std::vector<unsigned int> > const & g_I,
                            block_matrix & g_A_I_J_vcl,
                            block_vector & g_bv_vcl,
                            block_matrix & g_A_I_J_u_vcl,
                            std::vector<cl_uint> & g_is_update,
                            viennacl::context ctx)
{
  viennacl::ocl::context & opencl_ctx = const_cast<viennacl::ocl::context &>(ctx.opencl_context());
  unsigned int local_r_n = 0;
  unsigned int local_c_n = 0;
  unsigned int sz_blocks = 0;

  get_max_block_size(g_I,   local_r_n);
  get_max_block_size(g_J_u, local_c_n);

  //for debug
  std::vector<cl_uint> matrix_dims(g_I.size()*2, static_cast<cl_uint>(0));
  std::vector<cl_uint> blocks_ind(g_I.size() + 1, static_cast<cl_uint>(0));
  compute_blocks_size(g_I, g_J_u, sz_blocks, blocks_ind, matrix_dims);
  //std::vector<ScalarType> con_A_I_J(sz_blocks, static_cast<ScalarType>(0));

  viennacl::ocl::handle<cl_mem> g_is_update_vcl = opencl_ctx.create_memory(CL_MEM_READ_WRITE,
                                                                           static_cast<unsigned int>(sizeof(cl_uint)*(g_is_update.size())),
                                                                           &(g_is_update[0]));
  viennacl::linalg::opencl::kernels::spai<NumericT>::init(opencl_ctx);
  viennacl::ocl::kernel& block_q_kernel = opencl_ctx.get_kernel(viennacl::linalg::opencl::kernels::spai<NumericT>::program_name(), "block_q_mult");

  block_q_kernel.local_work_size(0,      local_c_n);
  block_q_kernel.global_work_size(0, 128*local_c_n);
  viennacl::ocl::enqueue(block_q_kernel(g_A_I_J_vcl.handle(), g_A_I_J_vcl.handle2(), g_A_I_J_u_vcl.handle(), g_A_I_J_u_vcl.handle2(),
                                        g_bv_vcl.handle(),
                                        g_bv_vcl.handle1(), g_A_I_J_vcl.handle1(), g_A_I_J_u_vcl.handle1(), g_is_update_vcl,
                                        viennacl::ocl::local_mem(static_cast<unsigned int>(sizeof(NumericT)*(local_r_n*local_c_n))),
                                        static_cast<cl_uint>(g_I.size())));
}

template<typename SizeT>
void assemble_qr_row_inds(std::vector<std::vector<SizeT> > const & g_I,
                          std::vector<std::vector<SizeT> > const & g_J,
                          std::vector<std::vector<SizeT> > const & g_I_u,
                          std::vector<std::vector<SizeT> >       & g_I_q)
{
#ifdef VIENNACL_WITH_OPENMP
  #pragma omp parallel for
#endif
  for (long i = 0; i < static_cast<long>(g_I.size()); ++i)
  {
    for (vcl_size_t j = g_J[static_cast<vcl_size_t>(i)].size(); j < g_I[static_cast<vcl_size_t>(i)].size(); ++j)
      g_I_q[static_cast<vcl_size_t>(i)].push_back(g_I[static_cast<vcl_size_t>(i)][j]);

    for (vcl_size_t j = 0; j < g_I_u[static_cast<vcl_size_t>(i)].size(); ++j)
      g_I_q[static_cast<vcl_size_t>(i)].push_back(g_I_u[static_cast<vcl_size_t>(i)][j]);
  }
}

template<typename NumericT>
void assemble_qr_block(std::vector<std::vector<unsigned int> > const & g_J,
                       std::vector<std::vector<unsigned int> > const& g_I,
                       std::vector<std::vector<unsigned int> > const& g_J_u,
                       std::vector<std::vector<unsigned int> > const& g_I_u,
                       std::vector<std::vector<unsigned int> >& g_I_q,
                       block_matrix & g_A_I_J_u_vcl,
                       viennacl::ocl::handle<cl_mem> & matrix_dimensions,
                       block_matrix & g_A_I_u_J_u_vcl,
                       std::vector<cl_uint> & g_is_update,
                       bool is_empty_block,
                       viennacl::context ctx)
{
  viennacl::ocl::context & opencl_ctx = const_cast<viennacl::ocl::context &>(ctx.opencl_context());

  //std::vector<std::vector<unsigned int> > g_I_q(g_I.size());
  assemble_qr_row_inds(g_I, g_J, g_I_u, g_I_q);
  unsigned int sz_blocks;
  std::vector<cl_uint> matrix_dims(g_I.size()*2, static_cast<cl_uint>(0));
  std::vector<cl_uint> blocks_ind(g_I.size() + 1, static_cast<cl_uint>(0));

  compute_blocks_size(g_I_q, g_J_u, sz_blocks, blocks_ind, matrix_dims);

  std::vector<NumericT> con_A_I_J_q(sz_blocks, static_cast<NumericT>(0));

  block_matrix g_A_I_J_q_vcl;
  //need to allocate memory for QR block
  g_A_I_J_q_vcl.handle() = opencl_ctx.create_memory(CL_MEM_READ_WRITE,
                                                    static_cast<unsigned int>(sizeof(NumericT)*sz_blocks),
                                                    &(con_A_I_J_q[0]));
  g_A_I_J_q_vcl.handle().context(opencl_ctx);

  g_A_I_J_q_vcl.handle1() = opencl_ctx.create_memory(CL_MEM_READ_WRITE,
                                                     static_cast<unsigned int>(sizeof(cl_uint)*2*static_cast<unsigned int>(g_I.size())),
                                                     &(matrix_dims[0]));
  g_A_I_J_q_vcl.handle1().context(opencl_ctx);

  g_A_I_J_q_vcl.handle2() = opencl_ctx.create_memory(CL_MEM_READ_WRITE,
                                                      static_cast<unsigned int>(sizeof(cl_uint)*static_cast<unsigned int>(g_I.size() + 1)),
                                                      &(blocks_ind[0]));
  g_A_I_J_q_vcl.handle2().context(opencl_ctx);

  viennacl::ocl::handle<cl_mem> g_is_update_vcl = opencl_ctx.create_memory(CL_MEM_READ_WRITE,
                                                                           static_cast<unsigned int>(sizeof(cl_uint)*(g_is_update.size())),
                                                                           &(g_is_update[0]));

  viennacl::linalg::opencl::kernels::spai<NumericT>::init(opencl_ctx);
  if (!is_empty_block)
  {
    viennacl::ocl::kernel& qr_assembly_kernel = opencl_ctx.get_kernel(viennacl::linalg::opencl::kernels::spai<NumericT>::program_name(), "block_qr_assembly");
    qr_assembly_kernel.local_work_size(0, 1);
    qr_assembly_kernel.global_work_size(0, 256);
    viennacl::ocl::enqueue(qr_assembly_kernel(matrix_dimensions,
                                              g_A_I_J_u_vcl.handle(),
                                              g_A_I_J_u_vcl.handle2(),
                                              g_A_I_J_u_vcl.handle1(),
                                              g_A_I_u_J_u_vcl.handle(),
                                              g_A_I_u_J_u_vcl.handle2(),
                                              g_A_I_u_J_u_vcl.handle1(),
                                              g_A_I_J_q_vcl.handle(),
                                              g_A_I_J_q_vcl.handle2(),
                                              g_A_I_J_q_vcl.handle1(),
                                              g_is_update_vcl,
                                              static_cast<unsigned int>(g_I.size())));
  }
  else
  {
    viennacl::ocl::kernel& qr_assembly_kernel = opencl_ctx.get_kernel(viennacl::linalg::opencl::kernels::spai<NumericT>::program_name(), "block_qr_assembly_1");
    qr_assembly_kernel.local_work_size(0, 1);
    qr_assembly_kernel.global_work_size(0, 256);
    viennacl::ocl::enqueue(qr_assembly_kernel(matrix_dimensions, g_A_I_J_u_vcl.handle(), g_A_I_J_u_vcl.handle2(),
                                              g_A_I_J_u_vcl.handle1(),
                                              g_A_I_J_q_vcl.handle(),
                                              g_A_I_J_q_vcl.handle2(), g_A_I_J_q_vcl.handle1(),
                                              g_is_update_vcl,
                                              static_cast<unsigned int>(g_I.size())));
  }
  g_A_I_u_J_u_vcl.handle() = g_A_I_J_q_vcl.handle();
  g_A_I_u_J_u_vcl.handle1() = g_A_I_J_q_vcl.handle1();
  g_A_I_u_J_u_vcl.handle2() = g_A_I_J_q_vcl.handle2();
}

template<typename NumericT>
void assemble_r(std::vector<std::vector<unsigned int> > & g_I,
                std::vector<std::vector<unsigned int> > & g_J,
                block_matrix & g_A_I_J_vcl,
                block_matrix & g_A_I_J_u_vcl,
                block_matrix & g_A_I_u_J_u_vcl,
                block_vector & g_bv_vcl,
                block_vector & g_bv_vcl_u,
                std::vector<cl_uint> & g_is_update,
                viennacl::context ctx)
{
  viennacl::ocl::context & opencl_ctx = const_cast<viennacl::ocl::context &>(ctx.opencl_context());
  std::vector<cl_uint> matrix_dims(g_I.size()*2, static_cast<cl_uint>(0));
  std::vector<cl_uint> blocks_ind(g_I.size() + 1, static_cast<cl_uint>(0));
  std::vector<cl_uint> start_bv_r_inds(g_I.size() + 1, 0);
  unsigned int sz_blocks, bv_size;

  compute_blocks_size(g_I, g_J, sz_blocks, blocks_ind, matrix_dims);
  get_size(g_J, bv_size);
  init_start_inds(g_J, start_bv_r_inds);

  std::vector<NumericT> con_A_I_J_r(sz_blocks, static_cast<NumericT>(0));
  std::vector<NumericT> b_v_r(bv_size, static_cast<NumericT>(0));

  block_matrix g_A_I_J_r_vcl;
  block_vector g_bv_r_vcl;
  g_A_I_J_r_vcl.handle() = opencl_ctx.create_memory(CL_MEM_READ_WRITE,
                                                    static_cast<unsigned int>(sizeof(NumericT)*sz_blocks),
                                                    &(con_A_I_J_r[0]));
  g_A_I_J_r_vcl.handle().context(opencl_ctx);

  g_A_I_J_r_vcl.handle1() = opencl_ctx.create_memory(CL_MEM_READ_WRITE,
                                                     static_cast<unsigned int>(sizeof(cl_uint)*2*static_cast<unsigned int>(g_I.size())),
                                                     &(matrix_dims[0]));
  g_A_I_J_r_vcl.handle1().context(opencl_ctx);

  g_A_I_J_r_vcl.handle2() = opencl_ctx.create_memory(CL_MEM_READ_WRITE,
                                                     static_cast<unsigned int>(sizeof(cl_uint)*static_cast<unsigned int>(g_I.size() + 1)),
                                                     &(blocks_ind[0]));
  g_A_I_J_r_vcl.handle2().context(opencl_ctx);

  g_bv_r_vcl.handle() = opencl_ctx.create_memory(CL_MEM_READ_WRITE,
                                                 static_cast<unsigned int>(sizeof(NumericT)*bv_size),
                                                 &(b_v_r[0]));
  g_bv_r_vcl.handle().context(opencl_ctx);

  g_bv_r_vcl.handle1() = opencl_ctx.create_memory(CL_MEM_READ_WRITE,
                                                  static_cast<unsigned int>(sizeof(cl_uint)*(g_I.size() + 1)),
                                                  &(start_bv_r_inds[0]));
  g_bv_r_vcl.handle().context(opencl_ctx);

  viennacl::ocl::handle<cl_mem> g_is_update_vcl = opencl_ctx.create_memory(CL_MEM_READ_WRITE,
                                                                           static_cast<unsigned int>(sizeof(cl_uint)*(g_is_update.size())),
                                                                           &(g_is_update[0]));
  viennacl::linalg::opencl::kernels::spai<NumericT>::init(opencl_ctx);
  viennacl::ocl::kernel& r_assembly_kernel = opencl_ctx.get_kernel(viennacl::linalg::opencl::kernels::spai<NumericT>::program_name(), "block_r_assembly");
  r_assembly_kernel.local_work_size(0, 1);
  r_assembly_kernel.global_work_size(0, 256);

  viennacl::ocl::enqueue(r_assembly_kernel(g_A_I_J_vcl.handle(), g_A_I_J_vcl.handle2(), g_A_I_J_vcl.handle1(),
                                          g_A_I_J_u_vcl.handle(), g_A_I_J_u_vcl.handle2(), g_A_I_J_u_vcl.handle1(),
                                          g_A_I_u_J_u_vcl.handle(), g_A_I_u_J_u_vcl.handle2(), g_A_I_u_J_u_vcl.handle1(),
                                          g_A_I_J_r_vcl.handle(), g_A_I_J_r_vcl.handle2(), g_A_I_J_r_vcl.handle1(),
                                          g_is_update_vcl, static_cast<cl_uint>(g_I.size())));

  viennacl::ocl::kernel & bv_assembly_kernel = opencl_ctx.get_kernel(viennacl::linalg::opencl::kernels::spai<NumericT>::program_name(), "block_bv_assembly");
  bv_assembly_kernel.local_work_size(0, 1);
  bv_assembly_kernel.global_work_size(0, 256);
  viennacl::ocl::enqueue(bv_assembly_kernel(g_bv_vcl.handle(), g_bv_vcl.handle1(), g_A_I_J_vcl.handle1(), g_bv_vcl_u.handle(),
                                            g_bv_vcl_u.handle1(), g_A_I_J_u_vcl.handle1(),
                                            g_bv_r_vcl.handle(), g_bv_r_vcl.handle1(), g_A_I_J_r_vcl.handle1(), g_is_update_vcl,
                                            static_cast<cl_uint>(g_I.size())));
  g_bv_vcl.handle() = g_bv_r_vcl.handle();
  g_bv_vcl.handle1() = g_bv_r_vcl.handle1();

  g_A_I_J_vcl.handle() = g_A_I_J_r_vcl.handle();
  g_A_I_J_vcl.handle2() = g_A_I_J_r_vcl.handle2();
  g_A_I_J_vcl.handle1() = g_A_I_J_r_vcl.handle1();
}

template<typename NumericT, unsigned int AlignmentV, typename SparseVectorT>
void block_update(viennacl::compressed_matrix<NumericT, AlignmentV> const & A,
                  std::vector<SparseVectorT> const & A_v_c,
                  std::vector<cl_uint> & g_is_update,
                  std::vector<SparseVectorT> & g_res,
                  std::vector<std::vector<unsigned int> > & g_J,
                  std::vector<std::vector<unsigned int> > & g_I,
                  block_matrix & g_A_I_J_vcl,
                  block_vector & g_bv_vcl,
                  spai_tag const & tag)
{
  viennacl::context ctx = viennacl::traits::context(A);
  //updated index set for columns
  std::vector<std::vector<unsigned int> > g_J_u(g_J.size());
  //updated index set for rows
  std::vector<std::vector<unsigned int> > g_I_u(g_J.size());
  //mixed index set of old and updated indices for rows
  std::vector<std::vector<unsigned int> > g_I_q(g_J.size());
  //GPU memory for A_I_\hatJ
  block_matrix g_A_I_J_u_vcl;
  //GPU memory for A_\hatI_\hatJ
  block_matrix g_A_I_u_J_u_vcl;
  bool is_empty_block;
  //GPU memory for new b_v
  block_vector g_bv_u_vcl;

#ifdef VIENNACL_WITH_OPENMP
  #pragma omp parallel for
#endif
  for (long i = 0; i < static_cast<long>(g_J.size()); ++i)
  {
    if (g_is_update[static_cast<vcl_size_t>(i)])
    {
      if (buildAugmentedIndexSet<SparseVectorT, NumericT>(A_v_c, g_res[static_cast<vcl_size_t>(i)], g_J[static_cast<vcl_size_t>(i)], g_J_u[static_cast<vcl_size_t>(i)], tag))
          buildNewRowSet(A_v_c, g_I[static_cast<vcl_size_t>(i)], g_J_u[static_cast<vcl_size_t>(i)], g_I_u[static_cast<vcl_size_t>(i)]);
    }
  }
  //assemble new A_I_J_u blocks on GPU and multiply them with Q'
  block_assembly(A, g_J_u, g_I, g_A_I_J_u_vcl, g_is_update, is_empty_block);
  //I have matrix A_I_J_u ready..
  block_q_multiplication<NumericT>(g_J_u, g_I, g_A_I_J_vcl, g_bv_vcl, g_A_I_J_u_vcl, g_is_update, ctx);
  //assemble A_\hatI_\hatJ
  block_assembly(A, g_J_u, g_I_u, g_A_I_u_J_u_vcl, g_is_update, is_empty_block);
  assemble_qr_block<NumericT>(g_J, g_I, g_J_u, g_I_u, g_I_q, g_A_I_J_u_vcl, g_A_I_J_vcl.handle1(),
                              g_A_I_u_J_u_vcl, g_is_update, is_empty_block, ctx);

  block_qr<NumericT>(g_I_q, g_J_u, g_A_I_u_J_u_vcl, g_bv_u_vcl, g_is_update, ctx);
  //concatanation of new and old indices
#ifdef VIENNACL_WITH_OPENMP
  #pragma omp parallel for
#endif
  for (long i = 0; i < static_cast<long>(g_J.size()); ++i)
  {
    g_J[static_cast<vcl_size_t>(i)].insert(g_J[static_cast<vcl_size_t>(i)].end(), g_J_u[static_cast<vcl_size_t>(i)].begin(), g_J_u[static_cast<vcl_size_t>(i)].end());
    g_I[static_cast<vcl_size_t>(i)].insert(g_I[static_cast<vcl_size_t>(i)].end(), g_I_u[static_cast<vcl_size_t>(i)].begin(), g_I_u[static_cast<vcl_size_t>(i)].end());
  }
  assemble_r<NumericT>(g_I, g_J, g_A_I_J_vcl, g_A_I_J_u_vcl, g_A_I_u_J_u_vcl,  g_bv_vcl,  g_bv_u_vcl, g_is_update, ctx);
}

}
}
}
}
#endif