// 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 op_det
//! @{

template <typename T1>
inline bool op_det::apply_direct(typename T1::elem_type& out_val,
                                 const Base<typename T1::elem_type, T1>& expr) {
  arma_debug_sigprint();

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

  if (strip_diagmat<T1>::do_diagmat) {
    const strip_diagmat<T1> strip(expr.get_ref());

    out_val = op_det::apply_diagmat(strip.M);

    return true;
  }

  if (strip_trimat<T1>::do_trimat) {
    const strip_trimat<T1> strip(expr.get_ref());

    out_val = op_det::apply_trimat(strip.M);

    return true;
  }

  Mat<eT> A(expr.get_ref());

  arma_conform_check((A.is_square() == false),
                     "det(): given matrix must be square sized");

  const uword N = A.n_rows;

  if (N == 0) {
    out_val = eT(1);
    return true;
  }
  if (N == 1) {
    out_val = A[0];
    return true;
  }

  if ((is_cx<eT>::no) && (N <= 3)) {
    constexpr T det_min = std::numeric_limits<T>::epsilon();
    constexpr T det_max = T(1) / std::numeric_limits<T>::epsilon();

    eT det_val = eT(0);

    if (N == 2) {
      det_val = op_det::apply_tiny_2x2(A);
    }
    if (N == 3) {
      det_val = op_det::apply_tiny_3x3(A);
    }

    const T abs_det_val = std::abs(det_val);

    if ((abs_det_val > det_min) && (abs_det_val < det_max)) {
      out_val = det_val;
      return true;
    }

    // fallthrough if det_val is suspect
  }

  if (A.is_diagmat()) {
    out_val = op_det::apply_diagmat(A);
    return true;
  }

  const bool is_triu = trimat_helper::is_triu(A);
  const bool is_tril = is_triu ? false : trimat_helper::is_tril(A);

  if (is_triu || is_tril) {
    out_val = op_det::apply_trimat(A);
    return true;
  }

  return auxlib::det(out_val, A);
}

template <typename T1>
inline typename T1::elem_type op_det::apply_diagmat(
    const Base<typename T1::elem_type, T1>& expr) {
  arma_debug_sigprint();

  typedef typename T1::elem_type eT;

  const diagmat_proxy<T1> A(expr.get_ref());

  arma_conform_check((A.n_rows != A.n_cols), "det(): given matrix must be square sized");

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

  eT val = eT(1);

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

  return val;
}

template <typename T1>
inline typename T1::elem_type op_det::apply_trimat(
    const Base<typename T1::elem_type, T1>& expr) {
  arma_debug_sigprint();

  typedef typename T1::elem_type eT;

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

  const uword N = P.get_n_rows();

  arma_conform_check((N != P.get_n_cols()), "det(): given matrix must be square sized");

  eT val = eT(1);

  for (uword i = 0; i < N; ++i) {
    val *= P.at(i, i);
  }

  return val;
}

template <typename eT>
inline eT op_det::apply_tiny_2x2(const Mat<eT>& X) {
  arma_debug_sigprint();

  const eT* Xm = X.memptr();

  return (Xm[pos<0, 0>::n2] * Xm[pos<1, 1>::n2] - Xm[pos<0, 1>::n2] * Xm[pos<1, 0>::n2]);
}

template <typename eT>
inline eT op_det::apply_tiny_3x3(const Mat<eT>& X) {
  arma_debug_sigprint();

  const eT* Xm = X.memptr();

  // const double tmp1 = X.at(0,0) * X.at(1,1) * X.at(2,2);
  // const double tmp2 = X.at(0,1) * X.at(1,2) * X.at(2,0);
  // const double tmp3 = X.at(0,2) * X.at(1,0) * X.at(2,1);
  // const double tmp4 = X.at(2,0) * X.at(1,1) * X.at(0,2);
  // const double tmp5 = X.at(2,1) * X.at(1,2) * X.at(0,0);
  // const double tmp6 = X.at(2,2) * X.at(1,0) * X.at(0,1);
  // return (tmp1+tmp2+tmp3) - (tmp4+tmp5+tmp6);

  const eT val1 = Xm[pos<0, 0>::n3] * (Xm[pos<2, 2>::n3] * Xm[pos<1, 1>::n3] -
                                       Xm[pos<2, 1>::n3] * Xm[pos<1, 2>::n3]);
  const eT val2 = Xm[pos<1, 0>::n3] * (Xm[pos<2, 2>::n3] * Xm[pos<0, 1>::n3] -
                                       Xm[pos<2, 1>::n3] * Xm[pos<0, 2>::n3]);
  const eT val3 = Xm[pos<2, 0>::n3] * (Xm[pos<1, 2>::n3] * Xm[pos<0, 1>::n3] -
                                       Xm[pos<1, 1>::n3] * Xm[pos<0, 2>::n3]);

  return (val1 - val2 + val3);
}

//! @}
