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; }
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<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 u32 n_rows = in.n_rows; const u32 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; }
inline void Gen<T1, gen_type>::apply(Mat<typename T1::elem_type>& out) const { arma_extra_debug_sigprint(); // NOTE: we're assuming that the matrix has already been set to the correct size; // this is done by either the Mat contructor or operator=() if(is_same_type<gen_type, gen_ones_diag>::yes) { out.eye(); } else if(is_same_type<gen_type, gen_ones_full>::yes) { out.ones(); } else if(is_same_type<gen_type, gen_zeros >::yes) { out.zeros(); } else if(is_same_type<gen_type, gen_randu >::yes) { out.randu(); } else if(is_same_type<gen_type, gen_randn >::yes) { out.randn(); } }
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; 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; }
inline bool op_princomp::direct_princomp ( Mat<typename T1::elem_type>& coeff_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<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<eT> s; 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 hess ( Mat<typename T1::elem_type>& U, Mat<typename T1::elem_type>& H, const Base<typename T1::elem_type,T1>& X, const typename arma_blas_type_only<typename T1::elem_type>::result* junk = 0 ) { arma_extra_debug_sigprint(); arma_ignore(junk); arma_debug_check( void_ptr(&U) == void_ptr(&H), "hess(): 'U' is an alias of 'H'" ); typedef typename T1::elem_type eT; Col<eT> tao; const bool status = auxlib::hess(H, X.get_ref(), tao); if(H.n_rows == 0) { U.reset(); } else if(H.n_rows == 1) { U.ones(1, 1); } else if(H.n_rows == 2) { U.eye(2, 2); } else { U.eye(size(H)); Col<eT> v; for(uword i=0; i < H.n_rows-2; ++i) { // TODO: generate v in a more efficient manner; // TODO: the .ones() operation is an overkill, as most of v is overwritten afterwards v.ones(H.n_rows-i-1); v(span(1, H.n_rows-i-2)) = H(span(i+2, H.n_rows-1), i); U(span::all, span(i+1, H.n_rows-1)) -= tao(i) * (U(span::all, span(i+1, H.n_rows-1)) * v * v.t()); } U(span::all, H.n_rows-1) = U(span::all, H.n_rows-1) * (eT(1) - tao(H.n_rows-2)); for(uword i=0; i < H.n_rows-2; ++i) { H(span(i+2, H.n_rows-1), i).zeros(); } } if(status == false) { U.soft_reset(); H.soft_reset(); arma_debug_warn("hess(): decomposition failed"); } return status; }
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; }
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 u32 n_rows = in.n_rows; const u32 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; }