cholesky.h

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/*
 *  This file is a part of TiledArray.
 *  Copyright (C) 2020 Virginia Tech
 *
 *  This program is free software: you can redistribute it and/or modify
 *  it under the terms of the GNU General Public License as published by
 *  the Free Software Foundation, either version 3 of the License, or
 *  (at your option) any later version.
 *
 *  This program is distributed in the hope that it will be useful,
 *  but WITHOUT ANY WARRANTY; without even the implied warranty of
 *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 *  GNU General Public License for more details.
 *
 *  You should have received a copy of the GNU General Public License
 *  along with this program.  If not, see <http://www.gnu.org/licenses/>.
 *
 *  David Williams-Young
 *  Computational Research Division, Lawrence Berkeley National Laboratory
 *
 *  cholesky.h
 *  Created:    8 June, 2020
 *
 */
#ifndef TILEDARRAY_MATH_LINALG_SCALAPACK_CHOL_H__INCLUDED
#define TILEDARRAY_MATH_LINALG_SCALAPACK_CHOL_H__INCLUDED
 
#include <TiledArray/config.h>
#if TILEDARRAY_HAS_SCALAPACK
 
#include <TiledArray/math/linalg/forward.h>
#include <TiledArray/math/linalg/scalapack/util.h>
 
#include <scalapackpp/factorizations/potrf.hpp>
#include <scalapackpp/linear_systems/posv.hpp>
#include <scalapackpp/linear_systems/trtrs.hpp>
#include <scalapackpp/matrix_inverse/trtri.hpp>
 
namespace TiledArray::math::linalg::scalapack {
 
template <typename Array>
auto cholesky(const Array& A, TiledRange l_trange = TiledRange(),
              size_t NB = default_block_size()) {
  auto& world = A.world();
  auto world_comm = world.mpi.comm().Get_mpi_comm();
  blacspp::Grid grid = blacspp::Grid::square_grid(world_comm);
 
  world.gop.fence();  // stage ScaLAPACK execution
  auto matrix = scalapack::array_to_block_cyclic(A, grid, NB, NB);
  world.gop.fence();  // stage ScaLAPACK execution
 
  auto [M, N] = matrix.dims();
  if (M != N) TA_EXCEPTION("Matrix must be square for Cholesky");
 
  auto [Mloc, Nloc] = matrix.dist().get_local_dims(N, N);
  auto desc = matrix.dist().descinit_noerror(N, N, Mloc);
 
  auto info = scalapackpp::ppotrf(blacspp::Triangle::Lower, N,
                                  matrix.local_mat().data(), 1, 1, desc);
  if (info) TA_EXCEPTION("Cholesky Failed");
 
  // Zero out the upper triangle
  zero_triangle(blacspp::Triangle::Upper, matrix);
 
  if (l_trange.rank() == 0) l_trange = A.trange();
 
  world.gop.fence();
  auto L = scalapack::block_cyclic_to_array<Array>(matrix, l_trange);
  world.gop.fence();
 
  return L;
}
 
template <bool Both, typename Array>
auto cholesky_linv(const Array& A, TiledRange l_trange = TiledRange(),
                   size_t NB = default_block_size()) {
  using value_type = typename Array::element_type;
 
  auto& world = A.world();
  auto world_comm = world.mpi.comm().Get_mpi_comm();
  blacspp::Grid grid = blacspp::Grid::square_grid(world_comm);
 
  world.gop.fence();  // stage ScaLAPACK execution
  auto matrix = scalapack::array_to_block_cyclic(A, grid, NB, NB);
  world.gop.fence();  // stage ScaLAPACK execution
 
  auto [M, N] = matrix.dims();
  if (M != N) TA_EXCEPTION("Matrix must be square for Cholesky");
 
  auto [Mloc, Nloc] = matrix.dist().get_local_dims(N, N);
  auto desc = matrix.dist().descinit_noerror(N, N, Mloc);
 
  auto info = scalapackpp::ppotrf(blacspp::Triangle::Lower, N,
                                  matrix.local_mat().data(), 1, 1, desc);
  if (info) TA_EXCEPTION("Cholesky Failed");
 
  // Zero out the upper triangle
  zero_triangle(blacspp::Triangle::Upper, matrix);
 
  // Copy L if needed
  std::shared_ptr<scalapack::BlockCyclicMatrix<value_type>> L_sca = nullptr;
  if constexpr (Both) {
    L_sca = std::make_shared<scalapack::BlockCyclicMatrix<value_type>>(
        world, grid, N, N, NB, NB);
    L_sca->local_mat() = matrix.local_mat();
  }
 
  // Compute inverse
  info =
      scalapackpp::ptrtri(blacspp::Triangle::Lower, blacspp::Diagonal::NonUnit,
                          N, matrix.local_mat().data(), 1, 1, desc);
  if (info) TA_EXCEPTION("TRTRI Failed");
 
  if (l_trange.rank() == 0) l_trange = A.trange();
 
  world.gop.fence();
  auto Linv = scalapack::block_cyclic_to_array<Array>(matrix, l_trange);
  world.gop.fence();
 
  if constexpr (Both) {
    auto L = scalapack::block_cyclic_to_array<Array>(*L_sca, l_trange);
    world.gop.fence();
    return std::tuple(L, Linv);
  } else {
    return Linv;
  }
}
 
template <typename Array>
auto cholesky_solve(const Array& A, const Array& B,
                    TiledRange x_trange = TiledRange(),
                    size_t NB = default_block_size()) {
  auto& world = A.world();
  /*
  if( world != B.world() ) {
    TA_EXCEPTION("A and B must be distributed on same MADWorld context");
  }
  */
  auto world_comm = world.mpi.comm().Get_mpi_comm();
  blacspp::Grid grid = blacspp::Grid::square_grid(world_comm);
 
  world.gop.fence();  // stage ScaLAPACK execution
  auto A_sca = scalapack::array_to_block_cyclic(A, grid, NB, NB);
  auto B_sca = scalapack::array_to_block_cyclic(B, grid, NB, NB);
  world.gop.fence();  // stage ScaLAPACK execution
 
  auto [M, N] = A_sca.dims();
  if (M != N) TA_EXCEPTION("A must be square for Cholesky Solve");
 
  auto [B_N, NRHS] = B_sca.dims();
  if (B_N != N) TA_EXCEPTION("A and B dims must agree");
 
  scalapackpp::scalapack_desc desc_a, desc_b;
  {
    auto [Mloc, Nloc] = A_sca.dist().get_local_dims(N, N);
    desc_a = A_sca.dist().descinit_noerror(N, N, Mloc);
  }
 
  {
    auto [Mloc, Nloc] = B_sca.dist().get_local_dims(N, NRHS);
    desc_b = B_sca.dist().descinit_noerror(N, NRHS, Mloc);
  }
 
  auto info = scalapackpp::pposv(blacspp::Triangle::Lower, N, NRHS,
                                 A_sca.local_mat().data(), 1, 1, desc_a,
                                 B_sca.local_mat().data(), 1, 1, desc_b);
  if (info) TA_EXCEPTION("Cholesky Solve Failed");
 
  if (x_trange.rank() == 0) x_trange = B.trange();
 
  world.gop.fence();
  auto X = scalapack::block_cyclic_to_array<Array>(B_sca, x_trange);
  world.gop.fence();
 
  return X;
}
 
template <typename Array>
auto cholesky_lsolve(Op trans, const Array& A, const Array& B,
                     TiledRange l_trange = TiledRange(),
                     TiledRange x_trange = TiledRange(),
                     size_t NB = default_block_size()) {
  auto& world = A.world();
  /*
  if( world != B.world() ) {
    TA_EXCEPTION("A and B must be distributed on same MADWorld context");
  }
  */
  auto world_comm = world.mpi.comm().Get_mpi_comm();
  blacspp::Grid grid = blacspp::Grid::square_grid(world_comm);
 
  world.gop.fence();  // stage ScaLAPACK execution
  auto A_sca = scalapack::array_to_block_cyclic(A, grid, NB, NB);
  auto B_sca = scalapack::array_to_block_cyclic(B, grid, NB, NB);
  world.gop.fence();  // stage ScaLAPACK execution
 
  auto [M, N] = A_sca.dims();
  if (M != N) TA_EXCEPTION("A must be square for Cholesky Solve");
 
  auto [B_N, NRHS] = B_sca.dims();
  if (B_N != N) TA_EXCEPTION("A and B dims must agree");
 
  scalapackpp::scalapack_desc desc_a, desc_b;
  {
    auto [Mloc, Nloc] = A_sca.dist().get_local_dims(N, N);
    desc_a = A_sca.dist().descinit_noerror(N, N, Mloc);
  }
 
  {
    auto [Mloc, Nloc] = B_sca.dist().get_local_dims(N, NRHS);
    desc_b = B_sca.dist().descinit_noerror(N, NRHS, Mloc);
  }
 
  auto info = scalapackpp::ppotrf(blacspp::Triangle::Lower, N,
                                  A_sca.local_mat().data(), 1, 1, desc_a);
  if (info) TA_EXCEPTION("Cholesky Failed");
 
  info = scalapackpp::ptrtrs(
      blacspp::Triangle::Lower, to_scalapackpp_transposeflag(trans),
      blacspp::Diagonal::NonUnit, N, NRHS, A_sca.local_mat().data(), 1, 1,
      desc_a, B_sca.local_mat().data(), 1, 1, desc_b);
  if (info) TA_EXCEPTION("TRTRS Failed");
 
  // Zero out the upper triangle
  zero_triangle(blacspp::Triangle::Upper, A_sca);
 
  if (l_trange.rank() == 0) l_trange = A.trange();
  if (x_trange.rank() == 0) x_trange = B.trange();
 
  world.gop.fence();
  auto L = scalapack::block_cyclic_to_array<Array>(A_sca, l_trange);
  auto X = scalapack::block_cyclic_to_array<Array>(B_sca, x_trange);
  world.gop.fence();
 
  return std::tuple(L, X);
}
 
}  // namespace TiledArray::math::linalg::scalapack
 
#endif  // TILEDARRAY_HAS_SCALAPACK
#endif  // TILEDARRAY_MATH_LINALG_SCALAPACK_CHOL_H__INCLUDED