// SPDX-License-Identifier: Apache-2.0
//
// Copyright 2008-2016 Conrad Sanderson (http://conradsanderson.id.au)
// Copyright 2008-2016 National ICT Australia (NICTA)
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
// http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
// ------------------------------------------------------------------------

//! \addtogroup fn_accu
//! @{

template <typename T1>
arma_hot inline typename T1::elem_type accu_proxy_linear(const Proxy<T1>& P) {
  arma_extra_debug_sigprint();

  typedef typename T1::elem_type eT;

  eT val = eT(0);

  typename Proxy<T1>::ea_type Pea = P.get_ea();

  const uword n_elem = P.get_n_elem();

  if (arma_config::openmp && Proxy<T1>::use_mp && mp_gate<eT>::eval(n_elem)) {
#if defined(ARMA_USE_OPENMP)
    {
      // NOTE: using parallelisation with manual reduction workaround to take into account
      // complex numbers; NOTE: OpenMP versions lower than 4.0 do not support user-defined
      // reduction

      const int n_threads_max = mp_thread_limit::get();
      const uword n_threads_use =
          (std::min)(uword(podarray_prealloc_n_elem::val), uword(n_threads_max));
      const uword chunk_size = n_elem / n_threads_use;

      podarray<eT> partial_accs(n_threads_use);

#pragma omp parallel for schedule(static) num_threads(int(n_threads_use))
      for (uword thread_id = 0; thread_id < n_threads_use; ++thread_id) {
        const uword start = (thread_id + 0) * chunk_size;
        const uword endp1 = (thread_id + 1) * chunk_size;

        eT acc = eT(0);
        for (uword i = start; i < endp1; ++i) {
          acc += Pea[i];
        }

        partial_accs[thread_id] = acc;
      }

      for (uword thread_id = 0; thread_id < n_threads_use; ++thread_id) {
        val += partial_accs[thread_id];
      }

      for (uword i = (n_threads_use * chunk_size); i < n_elem; ++i) {
        val += Pea[i];
      }
    }
#endif
  } else {
#if defined(__FAST_MATH__)
    {
      if (P.is_aligned()) {
        typename Proxy<T1>::aligned_ea_type Pea_aligned = P.get_aligned_ea();

        for (uword i = 0; i < n_elem; ++i) {
          val += Pea_aligned.at_alt(i);
        }
      } else {
        for (uword i = 0; i < n_elem; ++i) {
          val += Pea[i];
        }
      }
    }
#else
    {
      eT val1 = eT(0);
      eT val2 = eT(0);

      uword i, j;
      for (i = 0, j = 1; j < n_elem; i += 2, j += 2) {
        val1 += Pea[i];
        val2 += Pea[j];
      }

      if (i < n_elem) {
        val1 += Pea[i];
      }

      val = val1 + val2;
    }
#endif
  }

  return val;
}

template <typename T1>
arma_hot inline typename T1::elem_type accu_proxy_at_mp(const Proxy<T1>& P) {
  arma_extra_debug_sigprint();

  typedef typename T1::elem_type eT;

  eT val = eT(0);

#if defined(ARMA_USE_OPENMP)
  {
    const uword n_rows = P.get_n_rows();
    const uword n_cols = P.get_n_cols();

    if (n_cols == 1) {
      const int n_threads_max = mp_thread_limit::get();
      const uword n_threads_use =
          (std::min)(uword(podarray_prealloc_n_elem::val), uword(n_threads_max));
      const uword chunk_size = n_rows / n_threads_use;

      podarray<eT> partial_accs(n_threads_use);

#pragma omp parallel for schedule(static) num_threads(int(n_threads_use))
      for (uword thread_id = 0; thread_id < n_threads_use; ++thread_id) {
        const uword start = (thread_id + 0) * chunk_size;
        const uword endp1 = (thread_id + 1) * chunk_size;

        eT acc = eT(0);
        for (uword i = start; i < endp1; ++i) {
          acc += P.at(i, 0);
        }

        partial_accs[thread_id] = acc;
      }

      for (uword thread_id = 0; thread_id < n_threads_use; ++thread_id) {
        val += partial_accs[thread_id];
      }

      for (uword i = (n_threads_use * chunk_size); i < n_rows; ++i) {
        val += P.at(i, 0);
      }
    } else if (n_rows == 1) {
      const int n_threads_max = mp_thread_limit::get();
      const uword n_threads_use =
          (std::min)(uword(podarray_prealloc_n_elem::val), uword(n_threads_max));
      const uword chunk_size = n_cols / n_threads_use;

      podarray<eT> partial_accs(n_threads_use);

#pragma omp parallel for schedule(static) num_threads(int(n_threads_use))
      for (uword thread_id = 0; thread_id < n_threads_use; ++thread_id) {
        const uword start = (thread_id + 0) * chunk_size;
        const uword endp1 = (thread_id + 1) * chunk_size;

        eT acc = eT(0);
        for (uword i = start; i < endp1; ++i) {
          acc += P.at(0, i);
        }

        partial_accs[thread_id] = acc;
      }

      for (uword thread_id = 0; thread_id < n_threads_use; ++thread_id) {
        val += partial_accs[thread_id];
      }

      for (uword i = (n_threads_use * chunk_size); i < n_cols; ++i) {
        val += P.at(0, i);
      }
    } else {
      podarray<eT> col_accs(n_cols);

      const int n_threads = mp_thread_limit::get();

#pragma omp parallel for schedule(static) num_threads(n_threads)
      for (uword col = 0; col < n_cols; ++col) {
        eT val1 = eT(0);
        eT val2 = eT(0);

        uword i, j;
        for (i = 0, j = 1; j < n_rows; i += 2, j += 2) {
          val1 += P.at(i, col);
          val2 += P.at(j, col);
        }

        if (i < n_rows) {
          val1 += P.at(i, col);
        }

        col_accs[col] = val1 + val2;
      }

      val = arrayops::accumulate(col_accs.memptr(), n_cols);
    }
  }
#else
  { arma_ignore(P); }
#endif

  return val;
}

template <typename T1>
arma_hot inline typename T1::elem_type accu_proxy_at(const Proxy<T1>& P) {
  arma_extra_debug_sigprint();

  typedef typename T1::elem_type eT;

  if (arma_config::openmp && Proxy<T1>::use_mp && mp_gate<eT>::eval(P.get_n_elem())) {
    return accu_proxy_at_mp(P);
  }

  const uword n_rows = P.get_n_rows();
  const uword n_cols = P.get_n_cols();

  eT val = eT(0);

  if (n_rows != 1) {
    eT val1 = eT(0);
    eT val2 = eT(0);

    for (uword col = 0; col < n_cols; ++col) {
      uword i, j;
      for (i = 0, j = 1; j < n_rows; i += 2, j += 2) {
        val1 += P.at(i, col);
        val2 += P.at(j, col);
      }

      if (i < n_rows) {
        val1 += P.at(i, col);
      }
    }

    val = val1 + val2;
  } else {
    for (uword col = 0; col < n_cols; ++col) {
      val += P.at(0, col);
    }
  }

  return val;
}

//! accumulate the elements of a matrix
template <typename T1>
arma_warn_unused arma_hot inline
    typename enable_if2<is_arma_type<T1>::value, typename T1::elem_type>::result
    accu(const T1& X) {
  arma_extra_debug_sigprint();

  const Proxy<T1> P(X);

  if (is_Mat<typename Proxy<T1>::stored_type>::value ||
      is_subview_col<typename Proxy<T1>::stored_type>::value) {
    const quasi_unwrap<typename Proxy<T1>::stored_type> tmp(P.Q);

    return arrayops::accumulate(tmp.M.memptr(), tmp.M.n_elem);
  }

  return (Proxy<T1>::use_at) ? accu_proxy_at(P) : accu_proxy_linear(P);
}

//! explicit handling of multiply-and-accumulate
template <typename T1, typename T2>
arma_warn_unused inline typename T1::elem_type accu(
    const eGlue<T1, T2, eglue_schur>& expr) {
  arma_extra_debug_sigprint();

  typedef eGlue<T1, T2, eglue_schur> expr_type;

  typedef typename expr_type::proxy1_type::stored_type P1_stored_type;
  typedef typename expr_type::proxy2_type::stored_type P2_stored_type;

  const bool have_direct_mem_1 =
      (is_Mat<P1_stored_type>::value) || (is_subview_col<P1_stored_type>::value);
  const bool have_direct_mem_2 =
      (is_Mat<P2_stored_type>::value) || (is_subview_col<P2_stored_type>::value);

  if (have_direct_mem_1 && have_direct_mem_2) {
    const quasi_unwrap<P1_stored_type> tmp1(expr.P1.Q);
    const quasi_unwrap<P2_stored_type> tmp2(expr.P2.Q);

    return op_dot::direct_dot(tmp1.M.n_elem, tmp1.M.memptr(), tmp2.M.memptr());
  }

  const Proxy<expr_type> P(expr);

  return (Proxy<expr_type>::use_at) ? accu_proxy_at(P) : accu_proxy_linear(P);
}

//! explicit handling of Hamming norm (also known as zero norm)
template <typename T1>
arma_warn_unused inline uword accu(const mtOp<uword, T1, op_rel_noteq>& X) {
  arma_extra_debug_sigprint();

  typedef typename T1::elem_type eT;

  const eT val = X.aux;

  const Proxy<T1> P(X.m);

  uword n_nonzero = 0;

  if (Proxy<T1>::use_at == false) {
    typedef typename Proxy<T1>::ea_type ea_type;

    ea_type A = P.get_ea();
    const uword n_elem = P.get_n_elem();

    for (uword i = 0; i < n_elem; ++i) {
      n_nonzero += (A[i] != val) ? uword(1) : uword(0);
    }
  } else {
    const uword P_n_cols = P.get_n_cols();
    const uword P_n_rows = P.get_n_rows();

    if (P_n_rows == 1) {
      for (uword col = 0; col < P_n_cols; ++col) {
        n_nonzero += (P.at(0, col) != val) ? uword(1) : uword(0);
      }
    } else {
      for (uword col = 0; col < P_n_cols; ++col)
        for (uword row = 0; row < P_n_rows; ++row) {
          n_nonzero += (P.at(row, col) != val) ? uword(1) : uword(0);
        }
    }
  }

  return n_nonzero;
}

template <typename T1>
arma_warn_unused inline uword accu(const mtOp<uword, T1, op_rel_eq>& X) {
  arma_extra_debug_sigprint();

  typedef typename T1::elem_type eT;

  const eT val = X.aux;

  const Proxy<T1> P(X.m);

  uword n_nonzero = 0;

  if (Proxy<T1>::use_at == false) {
    typedef typename Proxy<T1>::ea_type ea_type;

    ea_type A = P.get_ea();
    const uword n_elem = P.get_n_elem();

    for (uword i = 0; i < n_elem; ++i) {
      n_nonzero += (A[i] == val) ? uword(1) : uword(0);
    }
  } else {
    const uword P_n_cols = P.get_n_cols();
    const uword P_n_rows = P.get_n_rows();

    if (P_n_rows == 1) {
      for (uword col = 0; col < P_n_cols; ++col) {
        n_nonzero += (P.at(0, col) == val) ? uword(1) : uword(0);
      }
    } else {
      for (uword col = 0; col < P_n_cols; ++col)
        for (uword row = 0; row < P_n_rows; ++row) {
          n_nonzero += (P.at(row, col) == val) ? uword(1) : uword(0);
        }
    }
  }

  return n_nonzero;
}

template <typename T1, typename T2>
arma_warn_unused inline uword accu(const mtGlue<uword, T1, T2, glue_rel_noteq>& X) {
  arma_extra_debug_sigprint();

  const Proxy<T1> PA(X.A);
  const Proxy<T2> PB(X.B);

  arma_debug_assert_same_size(PA, PB, "operator!=");

  uword n_nonzero = 0;

  if ((Proxy<T1>::use_at == false) && (Proxy<T2>::use_at == false)) {
    typedef typename Proxy<T1>::ea_type PA_ea_type;
    typedef typename Proxy<T2>::ea_type PB_ea_type;

    PA_ea_type A = PA.get_ea();
    PB_ea_type B = PB.get_ea();
    const uword n_elem = PA.get_n_elem();

    for (uword i = 0; i < n_elem; ++i) {
      n_nonzero += (A[i] != B[i]) ? uword(1) : uword(0);
    }
  } else {
    const uword PA_n_cols = PA.get_n_cols();
    const uword PA_n_rows = PA.get_n_rows();

    if (PA_n_rows == 1) {
      for (uword col = 0; col < PA_n_cols; ++col) {
        n_nonzero += (PA.at(0, col) != PB.at(0, col)) ? uword(1) : uword(0);
      }
    } else {
      for (uword col = 0; col < PA_n_cols; ++col)
        for (uword row = 0; row < PA_n_rows; ++row) {
          n_nonzero += (PA.at(row, col) != PB.at(row, col)) ? uword(1) : uword(0);
        }
    }
  }

  return n_nonzero;
}

template <typename T1, typename T2>
arma_warn_unused inline uword accu(const mtGlue<uword, T1, T2, glue_rel_eq>& X) {
  arma_extra_debug_sigprint();

  const Proxy<T1> PA(X.A);
  const Proxy<T2> PB(X.B);

  arma_debug_assert_same_size(PA, PB, "operator==");

  uword n_nonzero = 0;

  if ((Proxy<T1>::use_at == false) && (Proxy<T2>::use_at == false)) {
    typedef typename Proxy<T1>::ea_type PA_ea_type;
    typedef typename Proxy<T2>::ea_type PB_ea_type;

    PA_ea_type A = PA.get_ea();
    PB_ea_type B = PB.get_ea();
    const uword n_elem = PA.get_n_elem();

    for (uword i = 0; i < n_elem; ++i) {
      n_nonzero += (A[i] == B[i]) ? uword(1) : uword(0);
    }
  } else {
    const uword PA_n_cols = PA.get_n_cols();
    const uword PA_n_rows = PA.get_n_rows();

    if (PA_n_rows == 1) {
      for (uword col = 0; col < PA_n_cols; ++col) {
        n_nonzero += (PA.at(0, col) == PB.at(0, col)) ? uword(1) : uword(0);
      }
    } else {
      for (uword col = 0; col < PA_n_cols; ++col)
        for (uword row = 0; row < PA_n_rows; ++row) {
          n_nonzero += (PA.at(row, col) == PB.at(row, col)) ? uword(1) : uword(0);
        }
    }
  }

  return n_nonzero;
}

//! accumulate the elements of a subview (submatrix)
template <typename eT>
arma_warn_unused arma_hot inline eT accu(const subview<eT>& X) {
  arma_extra_debug_sigprint();

  const uword X_n_rows = X.n_rows;
  const uword X_n_cols = X.n_cols;

  if (X_n_rows == 1) {
    const Mat<eT>& m = X.m;

    const uword col_offset = X.aux_col1;
    const uword row_offset = X.aux_row1;

    eT val1 = eT(0);
    eT val2 = eT(0);

    uword i, j;
    for (i = 0, j = 1; j < X_n_cols; i += 2, j += 2) {
      val1 += m.at(row_offset, col_offset + i);
      val2 += m.at(row_offset, col_offset + j);
    }

    if (i < X_n_cols) {
      val1 += m.at(row_offset, col_offset + i);
    }

    return val1 + val2;
  }

  if (X_n_cols == 1) {
    return arrayops::accumulate(X.colptr(0), X_n_rows);
  }

  eT val = eT(0);

  for (uword col = 0; col < X_n_cols; ++col) {
    val += arrayops::accumulate(X.colptr(col), X_n_rows);
  }

  return val;
}

template <typename eT>
arma_warn_unused arma_hot inline eT accu(const subview_col<eT>& X) {
  arma_extra_debug_sigprint();

  return arrayops::accumulate(X.colmem, X.n_rows);
}

//

template <typename T1>
arma_hot inline typename T1::elem_type accu_cube_proxy_linear(const ProxyCube<T1>& P) {
  arma_extra_debug_sigprint();

  typedef typename T1::elem_type eT;

  eT val = eT(0);

  typename ProxyCube<T1>::ea_type Pea = P.get_ea();

  const uword n_elem = P.get_n_elem();

  if (arma_config::openmp && ProxyCube<T1>::use_mp && mp_gate<eT>::eval(n_elem)) {
#if defined(ARMA_USE_OPENMP)
    {
      // NOTE: using parallelisation with manual reduction workaround to take into account
      // complex numbers; NOTE: OpenMP versions lower than 4.0 do not support user-defined
      // reduction

      const int n_threads_max = mp_thread_limit::get();
      const uword n_threads_use =
          (std::min)(uword(podarray_prealloc_n_elem::val), uword(n_threads_max));
      const uword chunk_size = n_elem / n_threads_use;

      podarray<eT> partial_accs(n_threads_use);

#pragma omp parallel for schedule(static) num_threads(int(n_threads_use))
      for (uword thread_id = 0; thread_id < n_threads_use; ++thread_id) {
        const uword start = (thread_id + 0) * chunk_size;
        const uword endp1 = (thread_id + 1) * chunk_size;

        eT acc = eT(0);
        for (uword i = start; i < endp1; ++i) {
          acc += Pea[i];
        }

        partial_accs[thread_id] = acc;
      }

      for (uword thread_id = 0; thread_id < n_threads_use; ++thread_id) {
        val += partial_accs[thread_id];
      }

      for (uword i = (n_threads_use * chunk_size); i < n_elem; ++i) {
        val += Pea[i];
      }
    }
#endif
  } else {
#if defined(__FAST_MATH__)
    {
      if (P.is_aligned()) {
        typename ProxyCube<T1>::aligned_ea_type Pea_aligned = P.get_aligned_ea();

        for (uword i = 0; i < n_elem; ++i) {
          val += Pea_aligned.at_alt(i);
        }
      } else {
        for (uword i = 0; i < n_elem; ++i) {
          val += Pea[i];
        }
      }
    }
#else
    {
      eT val1 = eT(0);
      eT val2 = eT(0);

      uword i, j;
      for (i = 0, j = 1; j < n_elem; i += 2, j += 2) {
        val1 += Pea[i];
        val2 += Pea[j];
      }

      if (i < n_elem) {
        val1 += Pea[i];
      }

      val = val1 + val2;
    }
#endif
  }

  return val;
}

template <typename T1>
arma_hot inline typename T1::elem_type accu_cube_proxy_at_mp(const ProxyCube<T1>& P) {
  arma_extra_debug_sigprint();

  typedef typename T1::elem_type eT;

  eT val = eT(0);

#if defined(ARMA_USE_OPENMP)
  {
    const uword n_rows = P.get_n_rows();
    const uword n_cols = P.get_n_cols();
    const uword n_slices = P.get_n_slices();

    podarray<eT> slice_accs(n_slices);

    const int n_threads = mp_thread_limit::get();

#pragma omp parallel for schedule(static) num_threads(n_threads)
    for (uword slice = 0; slice < n_slices; ++slice) {
      eT val1 = eT(0);
      eT val2 = eT(0);

      for (uword col = 0; col < n_cols; ++col) {
        uword i, j;
        for (i = 0, j = 1; j < n_rows; i += 2, j += 2) {
          val1 += P.at(i, col, slice);
          val2 += P.at(j, col, slice);
        }

        if (i < n_rows) {
          val1 += P.at(i, col, slice);
        }
      }

      slice_accs[slice] = val1 + val2;
    }

    val = arrayops::accumulate(slice_accs.memptr(), slice_accs.n_elem);
  }
#else
  { arma_ignore(P); }
#endif

  return val;
}

template <typename T1>
arma_hot inline typename T1::elem_type accu_cube_proxy_at(const ProxyCube<T1>& P) {
  arma_extra_debug_sigprint();

  typedef typename T1::elem_type eT;

  if (arma_config::openmp && ProxyCube<T1>::use_mp && mp_gate<eT>::eval(P.get_n_elem())) {
    return accu_cube_proxy_at_mp(P);
  }

  const uword n_rows = P.get_n_rows();
  const uword n_cols = P.get_n_cols();
  const uword n_slices = P.get_n_slices();

  eT val1 = eT(0);
  eT val2 = eT(0);

  for (uword slice = 0; slice < n_slices; ++slice)
    for (uword col = 0; col < n_cols; ++col) {
      uword i, j;
      for (i = 0, j = 1; j < n_rows; i += 2, j += 2) {
        val1 += P.at(i, col, slice);
        val2 += P.at(j, col, slice);
      }

      if (i < n_rows) {
        val1 += P.at(i, col, slice);
      }
    }

  return (val1 + val2);
}

//! accumulate the elements of a cube
template <typename T1>
arma_warn_unused arma_hot inline typename T1::elem_type accu(
    const BaseCube<typename T1::elem_type, T1>& X) {
  arma_extra_debug_sigprint();

  const ProxyCube<T1> P(X.get_ref());

  if (is_Cube<typename ProxyCube<T1>::stored_type>::value) {
    unwrap_cube<typename ProxyCube<T1>::stored_type> tmp(P.Q);

    return arrayops::accumulate(tmp.M.memptr(), tmp.M.n_elem);
  }

  return (ProxyCube<T1>::use_at) ? accu_cube_proxy_at(P) : accu_cube_proxy_linear(P);
}

//! explicit handling of multiply-and-accumulate (cube version)
template <typename T1, typename T2>
arma_warn_unused inline typename T1::elem_type accu(
    const eGlueCube<T1, T2, eglue_schur>& expr) {
  arma_extra_debug_sigprint();

  typedef eGlueCube<T1, T2, eglue_schur> expr_type;

  typedef typename ProxyCube<T1>::stored_type P1_stored_type;
  typedef typename ProxyCube<T2>::stored_type P2_stored_type;

  if (is_Cube<P1_stored_type>::value && is_Cube<P2_stored_type>::value) {
    const unwrap_cube<P1_stored_type> tmp1(expr.P1.Q);
    const unwrap_cube<P2_stored_type> tmp2(expr.P2.Q);

    return op_dot::direct_dot(tmp1.M.n_elem, tmp1.M.memptr(), tmp2.M.memptr());
  }

  const ProxyCube<expr_type> P(expr);

  return (ProxyCube<expr_type>::use_at) ? accu_cube_proxy_at(P)
                                        : accu_cube_proxy_linear(P);
}

//

template <typename T>
arma_warn_unused inline typename arma_scalar_only<T>::result accu(const T& x) {
  return x;
}

//! accumulate values in a sparse object
template <typename T1>
arma_warn_unused inline typename T1::elem_type accu(
    const SpBase<typename T1::elem_type, T1>& expr) {
  arma_extra_debug_sigprint();

  typedef typename T1::elem_type eT;

  const SpProxy<T1> P(expr.get_ref());

  const uword N = P.get_n_nonzero();

  if (N == 0) {
    return eT(0);
  }

  if (SpProxy<T1>::use_iterator == false) {
    // direct counting
    return arrayops::accumulate(P.get_values(), N);
  }

  if (is_SpSubview<typename SpProxy<T1>::stored_type>::value) {
    const SpSubview<eT>& sv = reinterpret_cast<const SpSubview<eT>&>(P.Q);

    if (sv.n_rows == sv.m.n_rows) {
      const SpMat<eT>& m = sv.m;
      const uword col = sv.aux_col1;

      return arrayops::accumulate(&(m.values[m.col_ptrs[col]]), N);
    }
  }

  typename SpProxy<T1>::const_iterator_type it = P.begin();

  eT val = eT(0);

  for (uword i = 0; i < N; ++i) {
    val += (*it);
    ++it;
  }

  return val;
}

//! explicit handling of accu(A + B), where A and B are sparse matrices
template <typename T1, typename T2>
arma_warn_unused inline typename T1::elem_type accu(
    const SpGlue<T1, T2, spglue_plus>& expr) {
  arma_extra_debug_sigprint();

  const unwrap_spmat<T1> UA(expr.A);
  const unwrap_spmat<T2> UB(expr.B);

  arma_debug_assert_same_size(UA.M.n_rows, UA.M.n_cols, UB.M.n_rows, UB.M.n_cols,
                              "addition");

  return (accu(UA.M) + accu(UB.M));
}

//! explicit handling of accu(A - B), where A and B are sparse matrices
template <typename T1, typename T2>
arma_warn_unused inline typename T1::elem_type accu(
    const SpGlue<T1, T2, spglue_minus>& expr) {
  arma_extra_debug_sigprint();

  const unwrap_spmat<T1> UA(expr.A);
  const unwrap_spmat<T2> UB(expr.B);

  arma_debug_assert_same_size(UA.M.n_rows, UA.M.n_cols, UB.M.n_rows, UB.M.n_cols,
                              "subtraction");

  return (accu(UA.M) - accu(UB.M));
}

//! explicit handling of accu(A % B), where A and B are sparse matrices
template <typename T1, typename T2>
arma_warn_unused inline typename T1::elem_type accu(
    const SpGlue<T1, T2, spglue_schur>& expr) {
  arma_extra_debug_sigprint();

  typedef typename T1::elem_type eT;

  const SpProxy<T1> px(expr.A);
  const SpProxy<T2> py(expr.B);

  typename SpProxy<T1>::const_iterator_type x_it = px.begin();
  typename SpProxy<T1>::const_iterator_type x_it_end = px.end();

  typename SpProxy<T2>::const_iterator_type y_it = py.begin();
  typename SpProxy<T2>::const_iterator_type y_it_end = py.end();

  eT acc = eT(0);

  while ((x_it != x_it_end) || (y_it != y_it_end)) {
    if (x_it == y_it) {
      acc += ((*x_it) * (*y_it));

      ++x_it;
      ++y_it;
    } else {
      const uword x_it_col = x_it.col();
      const uword x_it_row = x_it.row();

      const uword y_it_col = y_it.col();
      const uword y_it_row = y_it.row();

      if ((x_it_col < y_it_col) ||
          ((x_it_col == y_it_col) && (x_it_row < y_it_row)))  // if y is closer to the end
      {
        ++x_it;
      } else  // x is closer to the end
      {
        ++y_it;
      }
    }
  }

  return acc;
}

template <typename T1, typename spop_type>
arma_warn_unused inline typename T1::elem_type accu(const SpOp<T1, spop_type>& expr) {
  arma_extra_debug_sigprint();

  typedef typename T1::elem_type eT;

  const bool is_vectorise = (is_same_type<spop_type, spop_vectorise_row>::yes) ||
                            (is_same_type<spop_type, spop_vectorise_col>::yes) ||
                            (is_same_type<spop_type, spop_vectorise_all>::yes);

  if (is_vectorise) {
    return accu(expr.m);
  }

  const SpMat<eT> tmp = expr;

  return accu(tmp);
}

//! @}
