max@0: // Copyright (C) 2010-2011 NICTA (www.nicta.com.au)
max@0: // Copyright (C) 2010-2011 Conrad Sanderson
max@0: // Copyright (C) 2010 Dimitrios Bouzas
max@0: // Copyright (C) 2011 Stanislav Funiak
max@0: // 
max@0: // This file is part of the Armadillo C++ library.
max@0: // It is provided without any warranty of fitness
max@0: // for any purpose. You can redistribute this file
max@0: // and/or modify it under the terms of the GNU
max@0: // Lesser General Public License (LGPL) as published
max@0: // by the Free Software Foundation, either version 3
max@0: // of the License or (at your option) any later version.
max@0: // (see http://www.opensource.org/licenses for more info)
max@0: 
max@0: 
max@0: //! \addtogroup op_princomp
max@0: //! @{
max@0: 
max@0: 
max@0: 
max@0: //! \brief
max@0: //! principal component analysis -- 4 arguments version
max@0: //! computation is done via singular value decomposition
max@0: //! coeff_out    -> principal component coefficients
max@0: //! score_out    -> projected samples
max@0: //! latent_out   -> eigenvalues of principal vectors
max@0: //! tsquared_out -> Hotelling's T^2 statistic
max@0: template<typename eT>
max@0: inline
max@0: bool
max@0: op_princomp::direct_princomp
max@0:   (
max@0:         Mat<eT>& coeff_out,
max@0:         Mat<eT>& score_out,
max@0:         Col<eT>& latent_out, 
max@0:         Col<eT>& tsquared_out,
max@0:   const Mat<eT>& in
max@0:   )
max@0:   {
max@0:   arma_extra_debug_sigprint();
max@0: 
max@0:   const uword n_rows = in.n_rows;
max@0:   const uword n_cols = in.n_cols;
max@0:   
max@0:   if(n_rows > 1) // more than one sample
max@0:     {
max@0:     // subtract the mean - use score_out as temporary matrix
max@0:     score_out = in - repmat(mean(in), n_rows, 1);
max@0:  	  
max@0:     // singular value decomposition
max@0:     Mat<eT> U;
max@0:     Col<eT> s;
max@0:     
max@0:     const bool svd_ok = svd(U,s,coeff_out,score_out);
max@0:     
max@0:     if(svd_ok == false)
max@0:       {
max@0:       return false;
max@0:       }
max@0:     
max@0:     
max@0:     //U.reset();  // TODO: do we need this ?  U will get automatically deleted anyway
max@0:     
max@0:     // normalize the eigenvalues
max@0:     s /= std::sqrt( double(n_rows - 1) );
max@0:     
max@0:     // project the samples to the principals
max@0:     score_out *= coeff_out;
max@0:     
max@0:     if(n_rows <= n_cols) // number of samples is less than their dimensionality
max@0:       {
max@0:       score_out.cols(n_rows-1,n_cols-1).zeros();
max@0:       
max@0:       //Col<eT> s_tmp = zeros< Col<eT> >(n_cols);
max@0:       Col<eT> s_tmp(n_cols);
max@0:       s_tmp.zeros();
max@0:       
max@0:       s_tmp.rows(0,n_rows-2) = s.rows(0,n_rows-2);
max@0:       s = s_tmp;
max@0:           
max@0:       // compute the Hotelling's T-squared
max@0:       s_tmp.rows(0,n_rows-2) = eT(1) / s_tmp.rows(0,n_rows-2);
max@0:       
max@0:       const Mat<eT> S = score_out * diagmat(Col<eT>(s_tmp));   
max@0:       tsquared_out = sum(S%S,1); 
max@0:       }
max@0:     else
max@0:       {
max@0:       // compute the Hotelling's T-squared   
max@0:       const Mat<eT> S = score_out * diagmat(Col<eT>( eT(1) / s));
max@0:       tsquared_out = sum(S%S,1);
max@0:       }
max@0:             
max@0:     // compute the eigenvalues of the principal vectors
max@0:     latent_out = s%s;
max@0:     }
max@0:   else // 0 or 1 samples
max@0:     {
max@0:     coeff_out.eye(n_cols, n_cols);
max@0:     
max@0:     score_out.copy_size(in);
max@0:     score_out.zeros();
max@0:     
max@0:     latent_out.set_size(n_cols);
max@0:     latent_out.zeros();
max@0:     
max@0:     tsquared_out.set_size(n_rows);
max@0:     tsquared_out.zeros();
max@0:     }
max@0:   
max@0:   return true;
max@0:   }
max@0: 
max@0: 
max@0: 
max@0: //! \brief
max@0: //! principal component analysis -- 3 arguments version
max@0: //! computation is done via singular value decomposition
max@0: //! coeff_out    -> principal component coefficients
max@0: //! score_out    -> projected samples
max@0: //! latent_out   -> eigenvalues of principal vectors
max@0: template<typename eT>
max@0: inline
max@0: bool
max@0: op_princomp::direct_princomp
max@0:   (
max@0:         Mat<eT>& coeff_out,
max@0:         Mat<eT>& score_out,
max@0:         Col<eT>& latent_out,
max@0:   const Mat<eT>& in
max@0:   )
max@0:   {
max@0:   arma_extra_debug_sigprint();
max@0:   
max@0:   const uword n_rows = in.n_rows;
max@0:   const uword n_cols = in.n_cols;
max@0:   
max@0:   if(n_rows > 1) // more than one sample
max@0:     {
max@0:     // subtract the mean - use score_out as temporary matrix
max@0:     score_out = in - repmat(mean(in), n_rows, 1);
max@0:  	  
max@0:     // singular value decomposition
max@0:     Mat<eT> U;
max@0:     Col<eT> s;
max@0:     
max@0:     const bool svd_ok = svd(U,s,coeff_out,score_out);
max@0:     
max@0:     if(svd_ok == false)
max@0:       {
max@0:       return false;
max@0:       }
max@0:     
max@0:     
max@0:     // U.reset();
max@0:     
max@0:     // normalize the eigenvalues
max@0:     s /= std::sqrt( double(n_rows - 1) );
max@0:     
max@0:     // project the samples to the principals
max@0:     score_out *= coeff_out;
max@0:     
max@0:     if(n_rows <= n_cols) // number of samples is less than their dimensionality
max@0:       {
max@0:       score_out.cols(n_rows-1,n_cols-1).zeros();
max@0:       
max@0:       Col<eT> s_tmp = zeros< Col<eT> >(n_cols);
max@0:       s_tmp.rows(0,n_rows-2) = s.rows(0,n_rows-2);
max@0:       s = s_tmp;
max@0:       }
max@0:       
max@0:     // compute the eigenvalues of the principal vectors
max@0:     latent_out = s%s;
max@0:     
max@0:     }
max@0:   else // 0 or 1 samples
max@0:     {
max@0:     coeff_out.eye(n_cols, n_cols);
max@0:     
max@0:     score_out.copy_size(in);
max@0:     score_out.zeros();
max@0:     
max@0:     latent_out.set_size(n_cols);
max@0:     latent_out.zeros(); 
max@0:     }
max@0:   
max@0:   return true;
max@0:   }
max@0: 
max@0: 
max@0: 
max@0: //! \brief
max@0: //! principal component analysis -- 2 arguments version
max@0: //! computation is done via singular value decomposition
max@0: //! coeff_out    -> principal component coefficients
max@0: //! score_out    -> projected samples
max@0: template<typename eT>
max@0: inline
max@0: bool
max@0: op_princomp::direct_princomp
max@0:   (
max@0:         Mat<eT>& coeff_out,
max@0:         Mat<eT>& score_out,
max@0:   const Mat<eT>& in
max@0:   )
max@0:   {
max@0:   arma_extra_debug_sigprint();
max@0:   
max@0:   const uword n_rows = in.n_rows;
max@0:   const uword n_cols = in.n_cols;
max@0:   
max@0:   if(n_rows > 1) // more than one sample
max@0:     {
max@0:     // subtract the mean - use score_out as temporary matrix
max@0:     score_out = in - repmat(mean(in), n_rows, 1);
max@0:  	  
max@0:     // singular value decomposition
max@0:     Mat<eT> U;
max@0:     Col<eT> s;
max@0:     
max@0:     const bool svd_ok = svd(U,s,coeff_out,score_out);
max@0:     
max@0:     if(svd_ok == false)
max@0:       {
max@0:       return false;
max@0:       }
max@0:     
max@0:     // U.reset();
max@0:     
max@0:     // normalize the eigenvalues
max@0:     s /= std::sqrt( double(n_rows - 1) );
max@0:     
max@0:     // project the samples to the principals
max@0:     score_out *= coeff_out;
max@0:     
max@0:     if(n_rows <= n_cols) // number of samples is less than their dimensionality
max@0:       {
max@0:       score_out.cols(n_rows-1,n_cols-1).zeros();
max@0:       
max@0:       Col<eT> s_tmp = zeros< Col<eT> >(n_cols);
max@0:       s_tmp.rows(0,n_rows-2) = s.rows(0,n_rows-2);
max@0:       s = s_tmp;
max@0:       }
max@0:     }
max@0:   else // 0 or 1 samples
max@0:     {
max@0:     coeff_out.eye(n_cols, n_cols);
max@0:     score_out.copy_size(in);
max@0:     score_out.zeros();
max@0:     }
max@0:   
max@0:   return true;
max@0:   }
max@0: 
max@0: 
max@0: 
max@0: //! \brief
max@0: //! principal component analysis -- 1 argument version
max@0: //! computation is done via singular value decomposition
max@0: //! coeff_out    -> principal component coefficients
max@0: template<typename eT>
max@0: inline
max@0: bool
max@0: op_princomp::direct_princomp
max@0:   (
max@0:         Mat<eT>& coeff_out,
max@0:   const Mat<eT>& in
max@0:   )
max@0:   {
max@0:   arma_extra_debug_sigprint();
max@0:   
max@0:   if(in.n_elem != 0)
max@0:     {
max@0:     // singular value decomposition
max@0:     Mat<eT> U;
max@0:     Col<eT> s;
max@0:     
max@0:     const Mat<eT> tmp = in - repmat(mean(in), in.n_rows, 1);
max@0:     
max@0:     const bool svd_ok = svd(U,s,coeff_out, tmp);
max@0:     
max@0:     if(svd_ok == false)
max@0:       {
max@0:       return false;
max@0:       }
max@0:     }
max@0:   else
max@0:     {
max@0:     coeff_out.eye(in.n_cols, in.n_cols);
max@0:     }
max@0:   
max@0:   return true;
max@0:   }
max@0: 
max@0: 
max@0: 
max@0: //! \brief
max@0: //! principal component analysis -- 4 arguments complex version
max@0: //! computation is done via singular value decomposition
max@0: //! coeff_out    -> principal component coefficients
max@0: //! score_out    -> projected samples
max@0: //! latent_out   -> eigenvalues of principal vectors
max@0: //! tsquared_out -> Hotelling's T^2 statistic
max@0: template<typename T>
max@0: inline
max@0: bool
max@0: op_princomp::direct_princomp
max@0:   (
max@0:         Mat< std::complex<T> >& coeff_out,
max@0:         Mat< std::complex<T> >& score_out,
max@0:         Col<T>&                 latent_out,
max@0:         Col< std::complex<T> >& tsquared_out,
max@0:   const Mat< std::complex<T> >& in
max@0:   )
max@0:   {
max@0:   arma_extra_debug_sigprint();
max@0:   
max@0:   typedef std::complex<T> eT;
max@0:   
max@0:   const uword n_rows = in.n_rows;
max@0:   const uword n_cols = in.n_cols;
max@0:   
max@0:   if(n_rows > 1) // more than one sample
max@0:     {
max@0:     // subtract the mean - use score_out as temporary matrix
max@0:     score_out = in - repmat(mean(in), n_rows, 1);
max@0:  	  
max@0:     // singular value decomposition
max@0:     Mat<eT> U;
max@0:     Col<T> s;
max@0:     
max@0:     const bool svd_ok = svd(U,s,coeff_out,score_out); 
max@0:     
max@0:     if(svd_ok == false)
max@0:       {
max@0:       return false;
max@0:       }
max@0:     
max@0:     
max@0:     //U.reset();
max@0:     
max@0:     // normalize the eigenvalues
max@0:     s /= std::sqrt( double(n_rows - 1) );
max@0:     
max@0:     // project the samples to the principals
max@0:     score_out *= coeff_out;
max@0:     
max@0:     if(n_rows <= n_cols) // number of samples is less than their dimensionality
max@0:       {
max@0:       score_out.cols(n_rows-1,n_cols-1).zeros();
max@0:       
max@0:       Col<T> s_tmp = zeros< Col<T> >(n_cols);
max@0:       s_tmp.rows(0,n_rows-2) = s.rows(0,n_rows-2);
max@0:       s = s_tmp;
max@0:           
max@0:       // compute the Hotelling's T-squared   
max@0:       s_tmp.rows(0,n_rows-2) = 1.0 / s_tmp.rows(0,n_rows-2);
max@0:       const Mat<eT> S = score_out * diagmat(Col<T>(s_tmp));                     
max@0:       tsquared_out = sum(S%S,1); 
max@0:       }
max@0:     else
max@0:       {
max@0:       // compute the Hotelling's T-squared   
max@0:       const Mat<eT> S = score_out * diagmat(Col<T>(T(1) / s));                     
max@0:       tsquared_out = sum(S%S,1);
max@0:       }
max@0:     
max@0:     // compute the eigenvalues of the principal vectors
max@0:     latent_out = s%s;
max@0:     
max@0:     }
max@0:   else // 0 or 1 samples
max@0:     {
max@0:     coeff_out.eye(n_cols, n_cols);
max@0:     
max@0:     score_out.copy_size(in);
max@0:     score_out.zeros();
max@0:       
max@0:     latent_out.set_size(n_cols);
max@0:     latent_out.zeros();
max@0:       
max@0:     tsquared_out.set_size(n_rows);
max@0:     tsquared_out.zeros();
max@0:     }
max@0:   
max@0:   return true;
max@0:   }
max@0: 
max@0: 
max@0: 
max@0: //! \brief
max@0: //! principal component analysis -- 3 arguments complex version
max@0: //! computation is done via singular value decomposition
max@0: //! coeff_out    -> principal component coefficients
max@0: //! score_out    -> projected samples
max@0: //! latent_out   -> eigenvalues of principal vectors
max@0: template<typename T>
max@0: inline
max@0: bool
max@0: op_princomp::direct_princomp
max@0:   (
max@0:         Mat< std::complex<T> >& coeff_out,
max@0:         Mat< std::complex<T> >& score_out,
max@0:         Col<T>&                 latent_out,
max@0:   const Mat< std::complex<T> >& in
max@0:   )
max@0:   {
max@0:   arma_extra_debug_sigprint();
max@0:   
max@0:   typedef std::complex<T> eT;
max@0:   
max@0:   const uword n_rows = in.n_rows;
max@0:   const uword n_cols = in.n_cols;
max@0:   
max@0:   if(n_rows > 1) // more than one sample
max@0:     {
max@0:     // subtract the mean - use score_out as temporary matrix
max@0:     score_out = in - repmat(mean(in), n_rows, 1);
max@0:  	  
max@0:     // singular value decomposition
max@0:     Mat<eT> U;
max@0:     Col< T> s;
max@0:     
max@0:     const bool svd_ok = svd(U,s,coeff_out,score_out);
max@0:     
max@0:     if(svd_ok == false)
max@0:       {
max@0:       return false;
max@0:       }
max@0:     
max@0:     
max@0:     // U.reset();
max@0:     
max@0:     // normalize the eigenvalues
max@0:     s /= std::sqrt( double(n_rows - 1) );
max@0:     
max@0:     // project the samples to the principals
max@0:     score_out *= coeff_out;
max@0:     
max@0:     if(n_rows <= n_cols) // number of samples is less than their dimensionality
max@0:       {
max@0:       score_out.cols(n_rows-1,n_cols-1).zeros();
max@0:       
max@0:       Col<T> s_tmp = zeros< Col<T> >(n_cols);
max@0:       s_tmp.rows(0,n_rows-2) = s.rows(0,n_rows-2);
max@0:       s = s_tmp;
max@0:       }
max@0:       
max@0:     // compute the eigenvalues of the principal vectors
max@0:     latent_out = s%s;
max@0: 
max@0:     }
max@0:   else // 0 or 1 samples
max@0:     {
max@0:     coeff_out.eye(n_cols, n_cols);
max@0: 
max@0:     score_out.copy_size(in);
max@0:     score_out.zeros();
max@0: 
max@0:     latent_out.set_size(n_cols);
max@0:     latent_out.zeros();
max@0:     }
max@0:   
max@0:   return true;
max@0:   }
max@0: 
max@0: 
max@0: 
max@0: //! \brief
max@0: //! principal component analysis -- 2 arguments complex version
max@0: //! computation is done via singular value decomposition
max@0: //! coeff_out    -> principal component coefficients
max@0: //! score_out    -> projected samples
max@0: template<typename T>
max@0: inline
max@0: bool
max@0: op_princomp::direct_princomp
max@0:   (
max@0:         Mat< std::complex<T> >& coeff_out,
max@0:         Mat< std::complex<T> >& score_out,
max@0:   const Mat< std::complex<T> >& in
max@0:   )
max@0:   {
max@0:   arma_extra_debug_sigprint();
max@0:   
max@0:   typedef std::complex<T> eT;
max@0:   
max@0:   const uword n_rows = in.n_rows;
max@0:   const uword n_cols = in.n_cols;
max@0:   
max@0:   if(n_rows > 1) // more than one sample
max@0:     {
max@0:     // subtract the mean - use score_out as temporary matrix
max@0:     score_out = in - repmat(mean(in), n_rows, 1);
max@0:  	  
max@0:     // singular value decomposition
max@0:     Mat<eT> U;
max@0:     Col< T> s;
max@0:     
max@0:     const bool svd_ok = svd(U,s,coeff_out,score_out);
max@0:     
max@0:     if(svd_ok == false)
max@0:       {
max@0:       return false;
max@0:       }
max@0:     
max@0:     // U.reset();
max@0:     
max@0:     // normalize the eigenvalues
max@0:     s /= std::sqrt( double(n_rows - 1) );
max@0: 
max@0:     // project the samples to the principals
max@0:     score_out *= coeff_out;
max@0: 
max@0:     if(n_rows <= n_cols) // number of samples is less than their dimensionality
max@0:       {
max@0:       score_out.cols(n_rows-1,n_cols-1).zeros();
max@0:       }
max@0: 
max@0:     }
max@0:   else // 0 or 1 samples
max@0:     {
max@0:     coeff_out.eye(n_cols, n_cols);
max@0:     
max@0:     score_out.copy_size(in);
max@0:     score_out.zeros();
max@0:     }
max@0:   
max@0:   return true;
max@0:   }
max@0: 
max@0: 
max@0: 
max@0: //! \brief
max@0: //! principal component analysis -- 1 argument complex version
max@0: //! computation is done via singular value decomposition
max@0: //! coeff_out    -> principal component coefficients
max@0: template<typename T>
max@0: inline
max@0: bool
max@0: op_princomp::direct_princomp
max@0:   (
max@0:         Mat< std::complex<T> >& coeff_out,
max@0:   const Mat< std::complex<T> >& in
max@0:   )
max@0:   {
max@0:   arma_extra_debug_sigprint();
max@0:   
max@0:   typedef typename std::complex<T> eT;
max@0:   
max@0:   if(in.n_elem != 0)
max@0:     {
max@0:  	  // singular value decomposition
max@0:  	  Mat<eT> U;
max@0:     Col< T> s;
max@0:     
max@0:     const Mat<eT> tmp = in - repmat(mean(in), in.n_rows, 1);
max@0:     
max@0:     const bool svd_ok = svd(U,s,coeff_out, tmp);
max@0:     
max@0:     if(svd_ok == false)
max@0:       {
max@0:       return false;
max@0:       }
max@0:     }
max@0:   else
max@0:     {
max@0:     coeff_out.eye(in.n_cols, in.n_cols);
max@0:     }
max@0:   
max@0:   return true;
max@0:   }
max@0: 
max@0: 
max@0: 
max@0: template<typename T1>
max@0: inline
max@0: void
max@0: op_princomp::apply
max@0:   (
max@0:         Mat<typename T1::elem_type>& out,
max@0:   const Op<T1,op_princomp>&          in
max@0:   )
max@0:   {
max@0:   arma_extra_debug_sigprint();
max@0:   
max@0:   typedef typename T1::elem_type eT;
max@0:   
max@0:   const unwrap_check<T1> tmp(in.m, out);
max@0:   const Mat<eT>& A     = tmp.M;
max@0:   
max@0:   const bool status = op_princomp::direct_princomp(out, A);
max@0:   
max@0:   if(status == false)
max@0:     {
max@0:     out.reset();
max@0:     
max@0:     arma_bad("princomp(): failed to converge");
max@0:     }
max@0:   }
max@0: 
max@0: 
max@0: 
max@0: //! @}