// 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_trace
//! @{

template <typename T1>
arma_warn_unused inline typename T1::elem_type trace(
    const Base<typename T1::elem_type, T1>& X) {
  arma_debug_sigprint();

  typedef typename T1::elem_type eT;

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

  const uword N = (std::min)(P.get_n_rows(), P.get_n_cols());

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

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

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

  return val1 + val2;
}

template <typename T1>
arma_warn_unused inline typename T1::elem_type trace(const Op<T1, op_diagmat>& X) {
  arma_debug_sigprint();

  typedef typename T1::elem_type eT;

  const diagmat_proxy<T1> A(X.m);

  const uword N = (std::min)(A.n_rows, A.n_cols);

  eT val = eT(0);

  for (uword i = 0; i < N; ++i) {
    val += A[i];
  }

  return val;
}

//! speedup for trace(A*B); non-complex elements
template <typename T1, typename T2>
arma_warn_unused inline
    typename enable_if2<is_cx<typename T1::elem_type>::no, typename T1::elem_type>::result
    trace(const Glue<T1, T2, glue_times>& X) {
  arma_debug_sigprint();

  typedef typename T1::elem_type eT;

  const partial_unwrap<T1> tmp1(X.A);
  const partial_unwrap<T2> tmp2(X.B);

  const typename partial_unwrap<T1>::stored_type& A = tmp1.M;
  const typename partial_unwrap<T2>::stored_type& B = tmp2.M;

  const bool use_alpha = partial_unwrap<T1>::do_times || partial_unwrap<T2>::do_times;
  const eT alpha = use_alpha ? (tmp1.get_val() * tmp2.get_val()) : eT(0);

  arma_conform_assert_trans_mul_size<partial_unwrap<T1>::do_trans,
                                     partial_unwrap<T2>::do_trans>(
      A.n_rows, A.n_cols, B.n_rows, B.n_cols, "matrix multiplication");

  if ((A.n_elem == 0) || (B.n_elem == 0)) {
    return eT(0);
  }

  const uword A_n_rows = A.n_rows;
  const uword A_n_cols = A.n_cols;

  const uword B_n_rows = B.n_rows;
  const uword B_n_cols = B.n_cols;

  eT acc = eT(0);

  if ((partial_unwrap<T1>::do_trans == false) &&
      (partial_unwrap<T2>::do_trans == false)) {
    const uword N = (std::min)(A_n_rows, B_n_cols);

    eT acc1 = eT(0);
    eT acc2 = eT(0);

    for (uword k = 0; k < N; ++k) {
      const eT* B_colptr = B.colptr(k);

      // condition: A_n_cols = B_n_rows

      uword j;

      for (j = 1; j < A_n_cols; j += 2) {
        const uword i = (j - 1);

        const eT tmp_i = B_colptr[i];
        const eT tmp_j = B_colptr[j];

        acc1 += A.at(k, i) * tmp_i;
        acc2 += A.at(k, j) * tmp_j;
      }

      const uword i = (j - 1);

      if (i < A_n_cols) {
        acc1 += A.at(k, i) * B_colptr[i];
      }
    }

    acc = (acc1 + acc2);
  } else if ((partial_unwrap<T1>::do_trans == true) &&
             (partial_unwrap<T2>::do_trans == false)) {
    const uword N = (std::min)(A_n_cols, B_n_cols);

    for (uword k = 0; k < N; ++k) {
      const eT* A_colptr = A.colptr(k);
      const eT* B_colptr = B.colptr(k);

      // condition: A_n_rows = B_n_rows
      acc += op_dot::direct_dot(A_n_rows, A_colptr, B_colptr);
    }
  } else if ((partial_unwrap<T1>::do_trans == false) &&
             (partial_unwrap<T2>::do_trans == true)) {
    const uword N = (std::min)(A_n_rows, B_n_rows);

    for (uword k = 0; k < N; ++k) {
      // condition: A_n_cols = B_n_cols
      for (uword i = 0; i < A_n_cols; ++i) {
        acc += A.at(k, i) * B.at(k, i);
      }
    }
  } else if ((partial_unwrap<T1>::do_trans == true) &&
             (partial_unwrap<T2>::do_trans == true)) {
    const uword N = (std::min)(A_n_cols, B_n_rows);

    for (uword k = 0; k < N; ++k) {
      const eT* A_colptr = A.colptr(k);

      // condition: A_n_rows = B_n_cols
      for (uword i = 0; i < A_n_rows; ++i) {
        acc += A_colptr[i] * B.at(k, i);
      }
    }
  }

  return (use_alpha) ? (alpha * acc) : acc;
}

//! speedup for trace(A*B); complex elements
template <typename T1, typename T2>
arma_warn_unused inline typename enable_if2<is_cx<typename T1::elem_type>::yes,
                                            typename T1::elem_type>::result
trace(const Glue<T1, T2, glue_times>& X) {
  arma_debug_sigprint();

  typedef typename T1::pod_type T;
  typedef typename T1::elem_type eT;

  const partial_unwrap<T1> tmp1(X.A);
  const partial_unwrap<T2> tmp2(X.B);

  const typename partial_unwrap<T1>::stored_type& A = tmp1.M;
  const typename partial_unwrap<T2>::stored_type& B = tmp2.M;

  const bool use_alpha = partial_unwrap<T1>::do_times || partial_unwrap<T2>::do_times;
  const eT alpha = use_alpha ? (tmp1.get_val() * tmp2.get_val()) : eT(0);

  arma_conform_assert_trans_mul_size<partial_unwrap<T1>::do_trans,
                                     partial_unwrap<T2>::do_trans>(
      A.n_rows, A.n_cols, B.n_rows, B.n_cols, "matrix multiplication");

  if ((A.n_elem == 0) || (B.n_elem == 0)) {
    return eT(0);
  }

  const uword A_n_rows = A.n_rows;
  const uword A_n_cols = A.n_cols;

  const uword B_n_rows = B.n_rows;
  const uword B_n_cols = B.n_cols;

  eT acc = eT(0);

  if ((partial_unwrap<T1>::do_trans == false) &&
      (partial_unwrap<T2>::do_trans == false)) {
    const uword N = (std::min)(A_n_rows, B_n_cols);

    T acc_real = T(0);
    T acc_imag = T(0);

    for (uword k = 0; k < N; ++k) {
      const eT* B_colptr = B.colptr(k);

      // condition: A_n_cols = B_n_rows

      for (uword i = 0; i < A_n_cols; ++i) {
        // acc += A.at(k, i) * B_colptr[i];

        const std::complex<T>& xx = A.at(k, i);
        const std::complex<T>& yy = B_colptr[i];

        const T a = xx.real();
        const T b = xx.imag();

        const T c = yy.real();
        const T d = yy.imag();

        acc_real += (a * c) - (b * d);
        acc_imag += (a * d) + (b * c);
      }
    }

    acc = std::complex<T>(acc_real, acc_imag);
  } else if ((partial_unwrap<T1>::do_trans == true) &&
             (partial_unwrap<T2>::do_trans == false)) {
    const uword N = (std::min)(A_n_cols, B_n_cols);

    T acc_real = T(0);
    T acc_imag = T(0);

    for (uword k = 0; k < N; ++k) {
      const eT* A_colptr = A.colptr(k);
      const eT* B_colptr = B.colptr(k);

      // condition: A_n_rows = B_n_rows

      for (uword i = 0; i < A_n_rows; ++i) {
        // acc += std::conj(A_colptr[i]) * B_colptr[i];

        const std::complex<T>& xx = A_colptr[i];
        const std::complex<T>& yy = B_colptr[i];

        const T a = xx.real();
        const T b = xx.imag();

        const T c = yy.real();
        const T d = yy.imag();

        // take into account the complex conjugate of xx

        acc_real += (a * c) + (b * d);
        acc_imag += (a * d) - (b * c);
      }
    }

    acc = std::complex<T>(acc_real, acc_imag);
  } else if ((partial_unwrap<T1>::do_trans == false) &&
             (partial_unwrap<T2>::do_trans == true)) {
    const uword N = (std::min)(A_n_rows, B_n_rows);

    T acc_real = T(0);
    T acc_imag = T(0);

    for (uword k = 0; k < N; ++k) {
      // condition: A_n_cols = B_n_cols
      for (uword i = 0; i < A_n_cols; ++i) {
        // acc += A.at(k,i) * std::conj(B.at(k,i));

        const std::complex<T>& xx = A.at(k, i);
        const std::complex<T>& yy = B.at(k, i);

        const T a = xx.real();
        const T b = xx.imag();

        const T c = yy.real();
        const T d = -yy.imag();  // take the conjugate

        acc_real += (a * c) - (b * d);
        acc_imag += (a * d) + (b * c);
      }
    }

    acc = std::complex<T>(acc_real, acc_imag);
  } else if ((partial_unwrap<T1>::do_trans == true) &&
             (partial_unwrap<T2>::do_trans == true)) {
    const uword N = (std::min)(A_n_cols, B_n_rows);

    T acc_real = T(0);
    T acc_imag = T(0);

    for (uword k = 0; k < N; ++k) {
      const eT* A_colptr = A.colptr(k);

      // condition: A_n_rows = B_n_cols
      for (uword i = 0; i < A_n_rows; ++i) {
        // acc += std::conj(A_colptr[i]) * std::conj(B.at(k,i));

        const std::complex<T>& xx = A_colptr[i];
        const std::complex<T>& yy = B.at(k, i);

        const T a = xx.real();
        const T b = -xx.imag();  // take the conjugate

        const T c = yy.real();
        const T d = -yy.imag();  // take the conjugate

        acc_real += (a * c) - (b * d);
        acc_imag += (a * d) + (b * c);
      }
    }

    acc = std::complex<T>(acc_real, acc_imag);
  }

  return (use_alpha) ? eT(alpha * acc) : eT(acc);
}

//! trace of sparse object; generic version
template <typename T1>
arma_warn_unused inline typename T1::elem_type trace(
    const SpBase<typename T1::elem_type, T1>& expr) {
  arma_debug_sigprint();

  typedef typename T1::elem_type eT;

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

  const uword N = (std::min)(P.get_n_rows(), P.get_n_cols());

  eT acc = eT(0);

  if ((is_SpMat<typename SpProxy<T1>::stored_type>::value) &&
      (P.get_n_nonzero() >= 5 * N)) {
    const unwrap_spmat<typename SpProxy<T1>::stored_type> U(P.Q);

    const SpMat<eT>& X = U.M;

    for (uword i = 0; i < N; ++i) {
      acc += X.at(i, i);  // use binary search
    }
  } else {
    typename SpProxy<T1>::const_iterator_type it = P.begin();

    const uword P_n_nz = P.get_n_nonzero();

    for (uword i = 0; i < P_n_nz; ++i) {
      if (it.row() == it.col()) {
        acc += (*it);
      }

      ++it;
    }
  }

  return acc;
}

//! trace of sparse object; speedup for trace(A + B)
template <typename T1, typename T2>
arma_warn_unused inline typename T1::elem_type trace(
    const SpGlue<T1, T2, spglue_plus>& expr) {
  arma_debug_sigprint();

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

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

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

//! trace of sparse object; speedup for trace(A - B)
template <typename T1, typename T2>
arma_warn_unused inline typename T1::elem_type trace(
    const SpGlue<T1, T2, spglue_minus>& expr) {
  arma_debug_sigprint();

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

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

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

//! trace of sparse object; speedup for trace(A % B)
template <typename T1, typename T2>
arma_warn_unused inline typename T1::elem_type trace(
    const SpGlue<T1, T2, spglue_schur>& expr) {
  arma_debug_sigprint();

  typedef typename T1::elem_type eT;

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

  const SpMat<eT>& A = UA.M;
  const SpMat<eT>& B = UB.M;

  arma_conform_assert_same_size(A.n_rows, A.n_cols, B.n_rows, B.n_cols,
                                "element-wise multiplication");

  const uword N = (std::min)(A.n_rows, A.n_cols);

  eT acc = eT(0);

  for (uword i = 0; i < N; ++i) {
    acc += A.at(i, i) * B.at(i, i);
  }

  return acc;
}

//! trace of sparse object; speedup for trace(A*B)
template <typename T1, typename T2>
arma_warn_unused inline typename T1::elem_type trace(
    const SpGlue<T1, T2, spglue_times>& expr) {
  arma_debug_sigprint();

  typedef typename T1::elem_type eT;

  // better-than-nothing implementation

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

  const SpMat<eT>& A = UA.M;
  const SpMat<eT>& B = UB.M;

  arma_conform_assert_mul_size(A.n_rows, A.n_cols, B.n_rows, B.n_cols,
                               "matrix multiplication");

  if ((A.n_nonzero == 0) || (B.n_nonzero == 0)) {
    return eT(0);
  }

  const uword N = (std::min)(A.n_rows, B.n_cols);

  eT acc = eT(0);

  // TODO: the threshold may need tuning for complex matrices
  if ((A.n_nonzero >= 5 * N) || (B.n_nonzero >= 5 * N)) {
    for (uword k = 0; k < N; ++k) {
      typename SpMat<eT>::const_col_iterator B_it = B.begin_col_no_sync(k);
      typename SpMat<eT>::const_col_iterator B_it_end = B.end_col_no_sync(k);

      while (B_it != B_it_end) {
        const eT B_val = (*B_it);
        const uword i = B_it.row();

        acc += A.at(k, i) * B_val;

        ++B_it;
      }
    }
  } else {
    const SpMat<eT> AB = A * B;

    acc = trace(AB);
  }

  return acc;
}

//! trace of sparse object; speedup for trace(A.t()*B); non-complex elements
template <typename T1, typename T2>
arma_warn_unused inline
    typename enable_if2<is_cx<typename T1::elem_type>::no, typename T1::elem_type>::result
    trace(const SpGlue<SpOp<T1, spop_htrans>, T2, spglue_times>& expr) {
  arma_debug_sigprint();

  typedef typename T1::elem_type eT;

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

  const SpMat<eT>& A = UA.M;
  const SpMat<eT>& B = UB.M;

  // NOTE: deliberately swapped A.n_rows and A.n_cols to take into account the requested
  // transpose operation
  arma_conform_assert_mul_size(A.n_cols, A.n_rows, B.n_rows, B.n_cols,
                               "matrix multiplication");

  if ((A.n_nonzero == 0) || (B.n_nonzero == 0)) {
    return eT(0);
  }

  const uword N = (std::min)(A.n_cols, B.n_cols);

  eT acc = eT(0);

  if ((A.n_nonzero >= 5 * N) || (B.n_nonzero >= 5 * N)) {
    for (uword k = 0; k < N; ++k) {
      typename SpMat<eT>::const_col_iterator B_it = B.begin_col_no_sync(k);
      typename SpMat<eT>::const_col_iterator B_it_end = B.end_col_no_sync(k);

      while (B_it != B_it_end) {
        const eT B_val = (*B_it);
        const uword i = B_it.row();

        acc += A.at(i, k) * B_val;

        ++B_it;
      }
    }
  } else {
    const SpMat<eT> AtB = A.t() * B;

    acc = trace(AtB);
  }

  return acc;
}

//! trace of sparse object; speedup for trace(A.t()*B); complex elements
template <typename T1, typename T2>
arma_warn_unused inline typename enable_if2<is_cx<typename T1::elem_type>::yes,
                                            typename T1::elem_type>::result
trace(const SpGlue<SpOp<T1, spop_htrans>, T2, spglue_times>& expr) {
  arma_debug_sigprint();

  typedef typename T1::elem_type eT;

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

  const SpMat<eT>& A = UA.M;
  const SpMat<eT>& B = UB.M;

  // NOTE: deliberately swapped A.n_rows and A.n_cols to take into account the requested
  // transpose operation
  arma_conform_assert_mul_size(A.n_cols, A.n_rows, B.n_rows, B.n_cols,
                               "matrix multiplication");

  if ((A.n_nonzero == 0) || (B.n_nonzero == 0)) {
    return eT(0);
  }

  const uword N = (std::min)(A.n_cols, B.n_cols);

  eT acc = eT(0);

  // TODO: the threshold may need tuning for complex matrices
  if ((A.n_nonzero >= 5 * N) || (B.n_nonzero >= 5 * N)) {
    for (uword k = 0; k < N; ++k) {
      typename SpMat<eT>::const_col_iterator B_it = B.begin_col_no_sync(k);
      typename SpMat<eT>::const_col_iterator B_it_end = B.end_col_no_sync(k);

      while (B_it != B_it_end) {
        const eT B_val = (*B_it);
        const uword i = B_it.row();

        acc += std::conj(A.at(i, k)) * B_val;

        ++B_it;
      }
    }
  } else {
    const SpMat<eT> AtB = A.t() * B;

    acc = trace(AtB);
  }

  return acc;
}

//! @}
