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// 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_extra_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_extra_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_extra_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_extra_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_extra_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");
}
}
//! @}
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