// 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 glue_mvnrnd
//! @{

// implementation based on:
// James E. Gentle.
// Generation of Random Numbers.
// Computational Statistics, pp. 305-331, 2009.
// http://dx.doi.org/10.1007/978-0-387-98144-4_7

template <typename T1, typename T2>
inline void glue_mvnrnd_vec::apply(Mat<typename T1::elem_type>& out,
                                   const Glue<T1, T2, glue_mvnrnd_vec>& expr) {
  arma_extra_debug_sigprint();

  const bool status = glue_mvnrnd::apply_direct(out, expr.A, expr.B, uword(1));

  if (status == false) {
    out.soft_reset();
    arma_stop_runtime_error(
        "mvnrnd(): given covariance matrix is not symmetric positive semi-definite");
  }
}

template <typename T1, typename T2>
inline void glue_mvnrnd::apply(Mat<typename T1::elem_type>& out,
                               const Glue<T1, T2, glue_mvnrnd>& expr) {
  arma_extra_debug_sigprint();

  const bool status = glue_mvnrnd::apply_direct(out, expr.A, expr.B, expr.aux_uword);

  if (status == false) {
    out.soft_reset();
    arma_stop_runtime_error(
        "mvnrnd(): given covariance matrix is not symmetric positive semi-definite");
  }
}

template <typename T1, typename T2>
inline bool glue_mvnrnd::apply_direct(Mat<typename T1::elem_type>& out,
                                      const Base<typename T1::elem_type, T1>& M,
                                      const Base<typename T1::elem_type, T2>& C,
                                      const uword N) {
  arma_extra_debug_sigprint();

  typedef typename T1::elem_type eT;

  const quasi_unwrap<T1> UM(M.get_ref());
  const quasi_unwrap<T2> UC(C.get_ref());

  arma_debug_check((UM.M.is_colvec() == false) && (UM.M.is_empty() == false),
                   "mvnrnd(): given mean must be a column vector");
  arma_debug_check((UC.M.is_square() == false),
                   "mvnrnd(): given covariance matrix must be square sized");
  arma_debug_check(
      (UM.M.n_rows != UC.M.n_rows),
      "mvnrnd(): number of rows in given mean vector and covariance matrix must match");

  if (UM.M.is_empty() || UC.M.is_empty()) {
    out.set_size(0, N);
    return true;
  }

  if ((arma_config::debug) && (auxlib::rudimentary_sym_check(UC.M) == false)) {
    arma_debug_warn_level(1, "mvnrnd(): given matrix is not symmetric");
  }

  bool status = false;

  if (UM.is_alias(out) || UC.is_alias(out)) {
    Mat<eT> tmp;

    status = glue_mvnrnd::apply_noalias(tmp, UM.M, UC.M, N);

    out.steal_mem(tmp);
  } else {
    status = glue_mvnrnd::apply_noalias(out, UM.M, UC.M, N);
  }

  return status;
}

template <typename eT>
inline bool glue_mvnrnd::apply_noalias(Mat<eT>& out, const Mat<eT>& M, const Mat<eT>& C,
                                       const uword N) {
  arma_extra_debug_sigprint();

  Mat<eT> D;

  const bool chol_status =
      op_chol::apply_direct(D, C, 1);  // '1' means "lower triangular"

  if (chol_status == false) {
    // C is not symmetric positive definite, so find approximate square root of C

    Col<eT> eigval;  // NOTE: eT is constrained to be real (ie. float or double) in
                     // fn_mvnrnd.hpp
    Mat<eT> eigvec;

    const bool eig_status = eig_sym_helper(eigval, eigvec, C, 'd', "mvnrnd()");

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

    eT* eigval_mem = eigval.memptr();
    const uword eigval_n_elem = eigval.n_elem;

    // since we're doing an approximation, tolerate tiny negative eigenvalues

    const eT tol = eT(-100) * Datum<eT>::eps * norm(C, "fro");

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

    for (uword i = 0; i < eigval_n_elem; ++i) {
      const eT val = eigval_mem[i];

      if ((val < tol) || (arma_isfinite(val) == false)) {
        return false;
      }
    }

    for (uword i = 0; i < eigval_n_elem; ++i) {
      if (eigval_mem[i] < eT(0)) {
        eigval_mem[i] = eT(0);
      }
    }

    Mat<eT> DD = eigvec * diagmat(sqrt(eigval));

    D.steal_mem(DD);
  }

  out = D * randn<Mat<eT> >(M.n_rows, N);

  if (N == 1) {
    out += M;
  } else if (N > 1) {
    out.each_col() += M;
  }

  return true;
}

//! @}
