// 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_expmat
//! @{

//! implementation based on:
//! Cleve Moler, Charles Van Loan.
//! Nineteen Dubious Ways to Compute the Exponential of a Matrix, Twenty-Five Years Later.
//! SIAM Review, Vol. 45, No. 1, 2003, pp. 3-49.
//! http://dx.doi.org/10.1137/S00361445024180

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

  const bool status = op_expmat::apply_direct(out, expr.m);

  if (status == false) {
    out.soft_reset();
    arma_stop_runtime_error("expmat(): given matrix appears ill-conditioned");
  }
}

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

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

  if (is_op_diagmat<T1>::value) {
    out = expr.get_ref();  // force the evaluation of diagmat()

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

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

    for (uword i = 0; i < N; ++i) {
      out.at(i, i) = std::exp(out.at(i, i));
    }

    return true;
  }

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

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

  if (A.is_diagmat()) {
    arma_debug_print("op_expmat: diag optimisation");

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

    out.zeros(N, N);

    for (uword i = 0; i < N; ++i) {
      out.at(i, i) = std::exp(A.at(i, i));
    }

    return true;
  }

  if ((arma_config::optimise_sym) && (auxlib::crippled_lapack(A) == false) &&
      sym_helper::is_approx_sym(A)) {
    arma_debug_print("op_expmat: symmetric/hermitian optimisation");

    Col<T> eigval;
    Mat<eT> eigvec;

    const bool eig_status = eig_sym_helper(eigval, eigvec, A, 'd', "expmat()");

    if (eig_status == false) {
      return false;
    }

    eigval = exp(eigval);

    out = eigvec * diagmat(eigval) * eigvec.t();

    return true;
  }

  const T norm_val = arma::norm(A, "inf");

  if (arma_isfinite(norm_val) == false) {
    return false;
  }

  const double log2_val = (norm_val > T(0)) ? double(eop_aux::log2(norm_val)) : double(0);

  int exponent = int(0);
  std::frexp(log2_val, &exponent);

  const uword s = uword((std::max)(int(0), exponent + int(1)));

  A /= eT(eop_aux::pow(double(2), double(s)));

  T c = T(0.5);

  Mat<eT> E(A.n_rows, A.n_rows, fill::eye);
  E += c * A;
  Mat<eT> D(A.n_rows, A.n_rows, fill::eye);
  D -= c * A;

  Mat<eT> X = A;

  bool positive = true;

  const uword N = 6;

  for (uword i = 2; i <= N; ++i) {
    c = c * T(N - i + 1) / T(i * (2 * N - i + 1));

    X = A * X;

    E += c * X;

    if (positive) {
      D += c * X;
    } else {
      D -= c * X;
    }

    positive = (positive) ? false : true;
  }

  if ((D.internal_has_nonfinite()) || (E.internal_has_nonfinite())) {
    return false;
  }

  const bool status = solve(out, D, E, solve_opts::no_approx);

  if (status == false) {
    return false;
  }

  for (uword i = 0; i < s; ++i) {
    out = out * out;
  }

  return true;
}

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

  const bool status = op_expmat_sym::apply_direct(out, in.m);

  if (status == false) {
    out.soft_reset();
    arma_stop_runtime_error("expmat_sym(): transformation failed");
  }
}

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

#if defined(ARMA_USE_LAPACK)
  {
    typedef typename T1::elem_type eT;
    typedef typename T1::pod_type T;

    const unwrap<T1> U(expr.get_ref());
    const Mat<eT>& X = U.M;

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

    if ((arma_config::check_conform) && (arma_config::warn_level > 0) &&
        (is_cx<eT>::yes) && (sym_helper::check_diag_imag(X) == false)) {
      arma_warn(1, "inv_sympd(): imaginary components on diagonal are non-zero");
    }

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

      out = X;

      eT* colmem = out.memptr();

      const uword N = X.n_rows;

      for (uword i = 0; i < N; ++i) {
        eT& out_ii = colmem[i];
        T out_ii_real = access::tmp_real(out_ii);

        out_ii = eT(std::exp(out_ii_real));

        colmem += N;
      }

      return true;
    }

    Col<T> eigval;
    Mat<eT> eigvec;

    const bool status = eig_sym_helper(eigval, eigvec, X, 'd', "expmat_sym()");

    if (status == false) {
      return false;
    }

    eigval = exp(eigval);

    out = eigvec * diagmat(eigval) * eigvec.t();

    return true;
  }
#else
  {
    arma_ignore(out);
    arma_ignore(expr);
    arma_stop_logic_error("expmat_sym(): use of LAPACK must be enabled");
    return false;
  }
#endif
}

//! @}
