// 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_inv_gen
//! @{

template <typename T1>
inline void op_inv_gen_default::apply(Mat<typename T1::elem_type>& out,
                                      const Op<T1, op_inv_gen_default>& X) {
  arma_debug_sigprint();

  const bool status = op_inv_gen_default::apply_direct(out, X.m, "inv()");

  if (status == false) {
    out.soft_reset();
    arma_stop_runtime_error("inv(): matrix is singular");
  }
}

template <typename T1>
inline bool op_inv_gen_default::apply_direct(Mat<typename T1::elem_type>& out,
                                             const Base<typename T1::elem_type, T1>& expr,
                                             const char* caller_sig) {
  arma_debug_sigprint();

  return op_inv_gen_full::apply_direct<T1, false>(out, expr, caller_sig, uword(0));
}

//

template <typename T1>
inline void op_inv_gen_full::apply(Mat<typename T1::elem_type>& out,
                                   const Op<T1, op_inv_gen_full>& X) {
  arma_debug_sigprint();

  const uword flags = X.aux_uword_a;

  const bool status = op_inv_gen_full::apply_direct(out, X.m, "inv()", flags);

  if (status == false) {
    out.soft_reset();
    arma_stop_runtime_error("inv(): matrix is singular");
  }
}

template <typename T1, const bool has_user_flags>
inline bool op_inv_gen_full::apply_direct(Mat<typename T1::elem_type>& out,
                                          const Base<typename T1::elem_type, T1>& expr,
                                          const char* caller_sig, const uword flags) {
  arma_debug_sigprint();

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

  if (has_user_flags == true) {
    arma_debug_print("op_inv_gen_full: has_user_flags = true");
  }
  if (has_user_flags == false) {
    arma_debug_print("op_inv_gen_full: has_user_flags = false");
  }

  const bool fast = has_user_flags && bool(flags & inv_opts::flag_fast);
  const bool allow_approx = has_user_flags && bool(flags & inv_opts::flag_allow_approx);
  const bool no_ugly = has_user_flags && bool(flags & inv_opts::flag_no_ugly);

  if (has_user_flags) {
    arma_debug_print("op_inv_gen_full: enabled flags:");

    if (fast) {
      arma_debug_print("fast");
    }
    if (allow_approx) {
      arma_debug_print("allow_approx");
    }
    if (no_ugly) {
      arma_debug_print("no_ugly");
    }

    arma_conform_check((fast && allow_approx),
                       "inv(): options 'fast' and 'allow_approx' are mutually exclusive");
    arma_conform_check((fast && no_ugly),
                       "inv(): options 'fast' and 'no_ugly' are mutually exclusive");
    arma_conform_check(
        (no_ugly && allow_approx),
        "inv(): options 'no_ugly' and 'allow_approx' are mutually exclusive");
  }

  if (no_ugly) {
    op_inv_gen_state<T> inv_state;

    const bool status = op_inv_gen_rcond::apply_direct(out, inv_state, expr);

    // workaround for bug in gcc 4.8
    const uword local_size = inv_state.size;
    const T local_rcond = inv_state.rcond;

    if ((status == false) ||
        (local_rcond <
         ((std::max)(local_size, uword(1)) * std::numeric_limits<T>::epsilon())) ||
        arma_isnan(local_rcond)) {
      return false;
    }

    return true;
  }

  if (allow_approx) {
    op_inv_gen_state<T> inv_state;

    Mat<eT> tmp;

    const bool status = op_inv_gen_rcond::apply_direct(tmp, inv_state, expr);

    // workaround for bug in gcc 4.8
    const uword local_size = inv_state.size;
    const T local_rcond = inv_state.rcond;

    if ((status == false) ||
        (local_rcond <
         ((std::max)(local_size, uword(1)) * std::numeric_limits<T>::epsilon())) ||
        arma_isnan(local_rcond)) {
      Mat<eT> A = expr.get_ref();

      if (inv_state.is_diag) {
        return op_pinv::apply_diag(out, A, T(0));
      }
      if (inv_state.is_sym) {
        return op_pinv::apply_sym(out, A, T(0), uword(0));
      }

      return op_pinv::apply_gen(out, A, T(0), uword(0));
    }

    out.steal_mem(tmp);

    return true;
  }

  out = expr.get_ref();

  arma_conform_check((out.is_square() == false), caller_sig,
                     ": given matrix must be square sized", [&]() { out.soft_reset(); });

  const uword N = out.n_rows;

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

  if (is_cx<eT>::no) {
    if (N == 1) {
      const eT a = out[0];

      out[0] = eT(1) / a;

      return (a != eT(0));
    } else if (N == 2) {
      const bool status = op_inv_gen_full::apply_tiny_2x2(out);

      if (status) {
        return true;
      }
    } else if (N == 3) {
      const bool status = op_inv_gen_full::apply_tiny_3x3(out);

      if (status) {
        return true;
      }
    }

    // fallthrough if optimisation failed
  }

  if (is_op_diagmat<T1>::value || out.is_diagmat()) {
    arma_debug_print("op_inv_gen_full: diag optimisation");

    eT* colmem = out.memptr();

    for (uword i = 0; i < N; ++i) {
      eT& out_ii = colmem[i];

      const eT src_val = out_ii;
      const eT inv_val = eT(1) / src_val;

      if (src_val == eT(0)) {
        return false;
      }

      out_ii = inv_val;

      colmem += N;
    }

    return true;
  }

  const strip_trimat<T1> strip(expr.get_ref());

  const bool is_triu_expr = strip.do_triu;
  const bool is_tril_expr = strip.do_tril;

  const bool is_triu_mat =
      (is_triu_expr || is_tril_expr) ? false : (trimat_helper::is_triu(out));
  const bool is_tril_mat = (is_triu_expr || is_tril_expr)
                               ? false
                               : ((is_triu_mat) ? false : trimat_helper::is_tril(out));

  if (is_triu_expr || is_tril_expr || is_triu_mat || is_tril_mat) {
    arma_debug_print("op_inv_gen_full: tri optimisation");

    return auxlib::inv_tr(out, ((is_triu_expr || is_triu_mat) ? uword(0) : uword(1)));
  }

  if ((arma_config::optimise_sym) && (auxlib::crippled_lapack(out) == false) &&
      (is_sym_expr<T1>::eval(expr.get_ref()) ||
       sym_helper::is_approx_sym(out, uword(100)))) {
    arma_debug_print("op_inv_gen_full: symmetric/hermitian optimisation");

    return auxlib::inv_sym(out);
  }

  return auxlib::inv(out);
}

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

  typedef typename get_pod_type<eT>::result T;

  // NOTE: assuming matrix X is square sized

  constexpr T det_min = std::numeric_limits<T>::epsilon();
  constexpr T det_max = T(1) / std::numeric_limits<T>::epsilon();

  eT* Xm = X.memptr();

  const eT a = Xm[pos<0, 0>::n2];
  const eT b = Xm[pos<0, 1>::n2];
  const eT c = Xm[pos<1, 0>::n2];
  const eT d = Xm[pos<1, 1>::n2];

  const eT det_val = (a * d - b * c);
  const T abs_det_val = std::abs(det_val);

  if ((abs_det_val < det_min) || (abs_det_val > det_max) || arma_isnan(det_val)) {
    return false;
  }

  Xm[pos<0, 0>::n2] = d / det_val;
  Xm[pos<0, 1>::n2] = -b / det_val;
  Xm[pos<1, 0>::n2] = -c / det_val;
  Xm[pos<1, 1>::n2] = a / det_val;

  return true;
}

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

  typedef typename get_pod_type<eT>::result T;

  // NOTE: assuming matrix X is square sized

  constexpr T det_min = std::numeric_limits<T>::epsilon();
  constexpr T det_max = T(1) / std::numeric_limits<T>::epsilon();

  Mat<eT> Y(3, 3, arma_nozeros_indicator());

  eT* Xm = X.memptr();
  eT* Ym = Y.memptr();

  const eT det_val = op_det::apply_tiny_3x3(X);
  const T abs_det_val = std::abs(det_val);

  if ((abs_det_val < det_min) || (abs_det_val > det_max) || arma_isnan(det_val)) {
    return false;
  }

  Ym[pos<0, 0>::n3] =
      (Xm[pos<2, 2>::n3] * Xm[pos<1, 1>::n3] - Xm[pos<2, 1>::n3] * Xm[pos<1, 2>::n3]) /
      det_val;
  Ym[pos<1, 0>::n3] =
      -(Xm[pos<2, 2>::n3] * Xm[pos<1, 0>::n3] - Xm[pos<2, 0>::n3] * Xm[pos<1, 2>::n3]) /
      det_val;
  Ym[pos<2, 0>::n3] =
      (Xm[pos<2, 1>::n3] * Xm[pos<1, 0>::n3] - Xm[pos<2, 0>::n3] * Xm[pos<1, 1>::n3]) /
      det_val;

  Ym[pos<0, 1>::n3] =
      -(Xm[pos<2, 2>::n3] * Xm[pos<0, 1>::n3] - Xm[pos<2, 1>::n3] * Xm[pos<0, 2>::n3]) /
      det_val;
  Ym[pos<1, 1>::n3] =
      (Xm[pos<2, 2>::n3] * Xm[pos<0, 0>::n3] - Xm[pos<2, 0>::n3] * Xm[pos<0, 2>::n3]) /
      det_val;
  Ym[pos<2, 1>::n3] =
      -(Xm[pos<2, 1>::n3] * Xm[pos<0, 0>::n3] - Xm[pos<2, 0>::n3] * Xm[pos<0, 1>::n3]) /
      det_val;

  Ym[pos<0, 2>::n3] =
      (Xm[pos<1, 2>::n3] * Xm[pos<0, 1>::n3] - Xm[pos<1, 1>::n3] * Xm[pos<0, 2>::n3]) /
      det_val;
  Ym[pos<1, 2>::n3] =
      -(Xm[pos<1, 2>::n3] * Xm[pos<0, 0>::n3] - Xm[pos<1, 0>::n3] * Xm[pos<0, 2>::n3]) /
      det_val;
  Ym[pos<2, 2>::n3] =
      (Xm[pos<1, 1>::n3] * Xm[pos<0, 0>::n3] - Xm[pos<1, 0>::n3] * Xm[pos<0, 1>::n3]) /
      det_val;

  const eT check_val = Xm[pos<0, 0>::n3] * Ym[pos<0, 0>::n3] +
                       Xm[pos<0, 1>::n3] * Ym[pos<1, 0>::n3] +
                       Xm[pos<0, 2>::n3] * Ym[pos<2, 0>::n3];

  const T max_diff = (is_float<T>::value)
                         ? T(1e-4)
                         : T(1e-10);  // empirically determined; may need tuning

  if (std::abs(T(1) - check_val) >= max_diff) {
    return false;
  }

  arrayops::copy(Xm, Ym, uword(3 * 3));

  return true;
}

template <typename T1>
inline bool op_inv_gen_rcond::apply_direct(
    Mat<typename T1::elem_type>& out, op_inv_gen_state<typename T1::pod_type>& out_state,
    const Base<typename T1::elem_type, T1>& expr) {
  arma_debug_sigprint();

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

  out = expr.get_ref();
  out_state.size = out.n_rows;
  out_state.rcond = T(0);

  arma_conform_check((out.is_square() == false),
                     "inv(): given matrix must be square sized",
                     [&]() { out.soft_reset(); });

  if (is_op_diagmat<T1>::value || out.is_diagmat()) {
    arma_debug_print("op_inv_gen_rcond: diag optimisation");

    out_state.is_diag = true;

    eT* colmem = out.memptr();

    T max_abs_src_val = T(0);
    T max_abs_inv_val = T(0);

    const uword N = out.n_rows;

    for (uword i = 0; i < N; ++i) {
      eT& out_ii = colmem[i];

      const eT src_val = out_ii;
      const eT inv_val = eT(1) / src_val;

      if (src_val == eT(0)) {
        return false;
      }

      out_ii = inv_val;

      const T abs_src_val = std::abs(src_val);
      const T abs_inv_val = std::abs(inv_val);

      max_abs_src_val = (abs_src_val > max_abs_src_val) ? abs_src_val : max_abs_src_val;
      max_abs_inv_val = (abs_inv_val > max_abs_inv_val) ? abs_inv_val : max_abs_inv_val;

      colmem += N;
    }

    out_state.rcond = T(1) / (max_abs_src_val * max_abs_inv_val);

    return true;
  }

  const strip_trimat<T1> strip(expr.get_ref());

  const bool is_triu_expr = strip.do_triu;
  const bool is_tril_expr = strip.do_tril;

  const bool is_triu_mat =
      (is_triu_expr || is_tril_expr) ? false : (trimat_helper::is_triu(out));
  const bool is_tril_mat = (is_triu_expr || is_tril_expr)
                               ? false
                               : ((is_triu_mat) ? false : trimat_helper::is_tril(out));

  if (is_triu_expr || is_tril_expr || is_triu_mat || is_tril_mat) {
    arma_debug_print("op_inv_gen_rcond: tri optimisation");

    return auxlib::inv_tr_rcond(out, out_state.rcond,
                                ((is_triu_expr || is_triu_mat) ? uword(0) : uword(1)));
  }

  if ((arma_config::optimise_sym) && (auxlib::crippled_lapack(out) == false) &&
      (is_sym_expr<T1>::eval(expr.get_ref()) ||
       sym_helper::is_approx_sym(out, uword(100)))) {
    arma_debug_print("op_inv_gen_rcond: symmetric/hermitian optimisation");

    out_state.is_sym = true;

    return auxlib::inv_sym_rcond(out, out_state.rcond);
  }

  return auxlib::inv_rcond(out, out_state.rcond);
}

//! @}
