// 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_princomp
//! @{

//! \brief
//! principal component analysis -- 4 arguments version
//! computation is done via singular value decomposition
//! coeff_out    -> principal component coefficients
//! score_out    -> projected samples
//! latent_out   -> eigenvalues of principal vectors
//! tsquared_out -> Hotelling's T^2 statistic
template <typename T1>
inline bool op_princomp::direct_princomp(Mat<typename T1::elem_type>& coeff_out,
                                         Mat<typename T1::elem_type>& score_out,
                                         Col<typename T1::pod_type>& latent_out,
                                         Col<typename T1::elem_type>& tsquared_out,
                                         const Base<typename T1::elem_type, T1>& X) {
  arma_debug_sigprint();

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

  const unwrap_check<T1> Y(X.get_ref(), score_out);
  const Mat<eT>& in = Y.M;

  const uword n_rows = in.n_rows;
  const uword n_cols = in.n_cols;

  if (n_rows > 1)  // more than one sample
  {
    // subtract the mean - use score_out as temporary matrix
    score_out = in;
    score_out.each_row() -= mean(in);

    // singular value decomposition
    Mat<eT> U;
    Col<T> s;

    const bool svd_ok = (n_rows >= n_cols) ? svd_econ(U, s, coeff_out, score_out)
                                           : svd(U, s, coeff_out, score_out);

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

    // normalize the eigenvalues
    s /= std::sqrt(double(n_rows - 1));

    // project the samples to the principals
    score_out *= coeff_out;

    if (n_rows <= n_cols)  // number of samples is less than their dimensionality
    {
      score_out.cols(n_rows - 1, n_cols - 1).zeros();

      Col<T> s_tmp(n_cols, arma_zeros_indicator());

      s_tmp.rows(0, n_rows - 2) = s.rows(0, n_rows - 2);
      s = s_tmp;

      // compute the Hotelling's T-squared
      s_tmp.rows(0, n_rows - 2) = T(1) / s_tmp.rows(0, n_rows - 2);

      const Mat<eT> S = score_out * diagmat(Col<T>(s_tmp));
      tsquared_out = sum(S % S, 1);
    } else {
      // compute the Hotelling's T-squared
      // TODO: replace with more robust approach
      const Mat<eT> S = score_out * diagmat(Col<T>(T(1) / s));
      tsquared_out = sum(S % S, 1);
    }

    // compute the eigenvalues of the principal vectors
    latent_out = s % s;
  } else  // 0 or 1 samples
  {
    coeff_out.eye(n_cols, n_cols);

    score_out.copy_size(in);
    score_out.zeros();

    latent_out.set_size(n_cols);
    latent_out.zeros();

    tsquared_out.set_size(n_rows);
    tsquared_out.zeros();
  }

  return true;
}

//! \brief
//! principal component analysis -- 3 arguments version
//! computation is done via singular value decomposition
//! coeff_out    -> principal component coefficients
//! score_out    -> projected samples
//! latent_out   -> eigenvalues of principal vectors
template <typename T1>
inline bool op_princomp::direct_princomp(Mat<typename T1::elem_type>& coeff_out,
                                         Mat<typename T1::elem_type>& score_out,
                                         Col<typename T1::pod_type>& latent_out,
                                         const Base<typename T1::elem_type, T1>& X) {
  arma_debug_sigprint();

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

  const unwrap_check<T1> Y(X.get_ref(), score_out);
  const Mat<eT>& in = Y.M;

  const uword n_rows = in.n_rows;
  const uword n_cols = in.n_cols;

  if (n_rows > 1)  // more than one sample
  {
    // subtract the mean - use score_out as temporary matrix
    score_out = in;
    score_out.each_row() -= mean(in);

    // singular value decomposition
    Mat<eT> U;
    Col<T> s;

    const bool svd_ok = (n_rows >= n_cols) ? svd_econ(U, s, coeff_out, score_out)
                                           : svd(U, s, coeff_out, score_out);

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

    // normalize the eigenvalues
    s /= std::sqrt(double(n_rows - 1));

    // project the samples to the principals
    score_out *= coeff_out;

    if (n_rows <= n_cols)  // number of samples is less than their dimensionality
    {
      score_out.cols(n_rows - 1, n_cols - 1).zeros();

      Col<T> s_tmp(n_cols, arma_zeros_indicator());

      s_tmp.rows(0, n_rows - 2) = s.rows(0, n_rows - 2);
      s = s_tmp;
    }

    // compute the eigenvalues of the principal vectors
    latent_out = s % s;
  } else  // 0 or 1 samples
  {
    coeff_out.eye(n_cols, n_cols);

    score_out.copy_size(in);
    score_out.zeros();

    latent_out.set_size(n_cols);
    latent_out.zeros();
  }

  return true;
}

//! \brief
//! principal component analysis -- 2 arguments version
//! computation is done via singular value decomposition
//! coeff_out    -> principal component coefficients
//! score_out    -> projected samples
template <typename T1>
inline bool op_princomp::direct_princomp(Mat<typename T1::elem_type>& coeff_out,
                                         Mat<typename T1::elem_type>& score_out,
                                         const Base<typename T1::elem_type, T1>& X) {
  arma_debug_sigprint();

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

  const unwrap_check<T1> Y(X.get_ref(), score_out);
  const Mat<eT>& in = Y.M;

  const uword n_rows = in.n_rows;
  const uword n_cols = in.n_cols;

  if (n_rows > 1)  // more than one sample
  {
    // subtract the mean - use score_out as temporary matrix
    score_out = in;
    score_out.each_row() -= mean(in);

    // singular value decomposition
    Mat<eT> U;
    Col<T> s;

    const bool svd_ok = (n_rows >= n_cols) ? svd_econ(U, s, coeff_out, score_out)
                                           : svd(U, s, coeff_out, score_out);

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

    // project the samples to the principals
    score_out *= coeff_out;

    if (n_rows <= n_cols)  // number of samples is less than their dimensionality
    {
      score_out.cols(n_rows - 1, n_cols - 1).zeros();
    }
  } else  // 0 or 1 samples
  {
    coeff_out.eye(n_cols, n_cols);
    score_out.copy_size(in);
    score_out.zeros();
  }

  return true;
}

//! \brief
//! principal component analysis -- 1 argument version
//! computation is done via singular value decomposition
//! coeff_out    -> principal component coefficients
template <typename T1>
inline bool op_princomp::direct_princomp(Mat<typename T1::elem_type>& coeff_out,
                                         const Base<typename T1::elem_type, T1>& X) {
  arma_debug_sigprint();

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

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

  if (in.n_elem != 0) {
    Mat<eT> tmp = in;
    tmp.each_row() -= mean(in);

    // singular value decomposition
    Mat<eT> U;
    Col<T> s;

    const bool svd_ok = (in.n_rows >= in.n_cols) ? svd_econ(U, s, coeff_out, tmp)
                                                 : svd(U, s, coeff_out, tmp);

    if (svd_ok == false) {
      return false;
    }
  } else {
    coeff_out.eye(in.n_cols, in.n_cols);
  }

  return true;
}

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

  const bool status = op_princomp::direct_princomp(out, in.m);

  if (status == false) {
    out.soft_reset();

    arma_stop_runtime_error("princomp(): decomposition failed");
  }
}

//! @}
