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,
const typename arma_not_cx<typename T1::elem_type>::result* junk
)
{
arma_extra_debug_sigprint();
arma_ignore(junk);
typedef typename T1::elem_type eT;
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<eT> s;
const bool svd_ok = 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<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;
}
inline
bool
op_princomp::direct_princomp
(
Mat< std::complex<typename T1::pod_type> >& coeff_out,
const Base< std::complex<typename T1::pod_type>, T1 >& X,
const typename arma_cx_only<typename T1::elem_type>::result* junk
)
{
arma_extra_debug_sigprint();
arma_ignore(junk);
typedef typename T1::pod_type T;
typedef std::complex<T> eT;
const unwrap<T1> Y( X.get_ref() );
const Mat<eT>& in = Y.M;
if(in.n_elem != 0)
{
// singular value decomposition
Mat<eT> U;
Col< T> s;
Mat<eT> tmp = in; tmp.each_row() -= mean(in);
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;
}
inline
bool
op_princomp::direct_princomp
(
Mat< std::complex<typename T1::pod_type> >& coeff_out,
Mat< std::complex<typename T1::pod_type> >& score_out,
Col< typename T1::pod_type >& latent_out,
Col< std::complex<typename T1::pod_type> >& tsquared_out,
const Base< std::complex<typename T1::pod_type>, T1 >& X,
const typename arma_cx_only<typename T1::elem_type>::result* junk
)
{
arma_extra_debug_sigprint();
arma_ignore(junk);
typedef typename T1::pod_type T;
typedef std::complex<T> eT;
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 = 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 = 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;
}