void _0000_singular_value_decomposition()
{
// load
feng::matrix<double> m;
m.load_txt( "./images/Teacher.txt" );
// normalize
auto const mx = *std::max_element( m.begin(), m.end() );
auto const mn = *std::min_element( m.begin(), m.end() );
m = ( m - mn ) / ( mx - mn + 1.0e-10 );
// take a snapshot
m.save_as_bmp( "./images/0000_singular_value_decomposition.bmp", "gray" );
// adding noise
auto const[r, c] = m.shape();
m += feng::rand<double>( r, c, 2 );
// record noisy matrix
m.save_as_bmp( "./images/0001_singular_value_decomposition.bmp", "gray" );
// execute svd
auto const& svd = feng::singular_value_decomposition( m );
// check svd result
if (svd) // case successful
{
// extracted svd result matrices, u, v w
auto const& [u, v, w] = (*svd);
// try to reconstruct matrix using u * v * w'
auto const& m_ = u * v * (w.transpose());
// record reconstructed matrix
m_.save_as_bmp( "./images/0002_singular_value_decomposition.bmp", "gray" );
auto dm = std::min( r, c );
auto factor = 2UL;
while ( dm >= factor )
{
auto new_dm = dm / factor;
feng::matrix<double> const new_u{ u, std::make_pair(0UL, r), std::make_pair(0UL, new_dm) };
feng::matrix<double> const new_v{ v, std::make_pair(0UL, new_dm), std::make_pair(0UL, new_dm) };
feng::matrix<double> const new_w{ w, std::make_pair(0UL, c), std::make_pair(0UL, new_dm) };
auto const& new_m = new_u * new_v * new_w.transpose();
new_m.save_as_bmp( "./images/0003_singular_value_decomposition_"+std::to_string(new_dm)+".bmp", "gray" );
factor *= 2UL;
}
}
else
{
void eigen_hermitian( const Complex_Matrix1& A, Complex_Matrix2& V, feng::matrix<T,D,A_>& Lambda, const T_ eps = T_( 1.0e-10 ) )
{
Lambda.resize( A.row(), A.col() );
Lambda = T(0);
return eigen_hermitian_impl( A, V, Lambda.diag_begin(), eps);
}
std::size_t cyclic_eigen_jacobi( const Matrix1& A, Matrix2& V, feng::matrix<T,D,A_>& Lambda, std::size_t const max_rot = 80, const T_ eps = T_( 1.0e-10 ) )
{
Lambda.resize( A.row(), A.col() );
Lambda = T(0);
return cyclic_eigen_jacobi( A, V, Lambda.diag_begin(), max_rot, eps );
}