comparison armadillo-2.4.4/include/armadillo_bits/op_princomp_meat.hpp @ 0:8b6102e2a9b0

Armadillo Library

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