value_type iterate( matrix_type const& initial_matrix, matrix_type& result_matrix )
{
triple_homotopy_fitting<value_type> thf{ug_size};
size_type const tilt_number = diag_matrix.row();
matrix_type intensity{ intensity_matrix.col(), 1 };
for ( size_type index = 0; index != tilt_number; ++index )
{
std::copy( intensity_matrix.row_begin(index), intensity_matrix.row_end(index), intensity.col_begin(0) );
//TODO -- optimizaton here
thf.register_entry( ar,
//C1 approximation
alpha(progress_ratio), make_coefficient_matrix( thickness, diag_matrix.row_begin(index), diag_matrix.row_end(index), column_index ),
//C/2 * C/2 approximation
beta(progress_ratio), make_coefficient_matrix( thickness/2.0, diag_matrix.row_begin(index), diag_matrix.row_end(index) ), expm( make_structure_matrix(ar, initial_matrix, diag_matrix.row_begin(index), diag_matrix.row_end(index) ), thickness/2.0, column_index ),
//standard expm
gamma(progress_ratio), make_scattering_matrix( ar, initial_matrix, diag_matrix.row_begin(index), diag_matrix.row_end(index), thickness, column_index ),
intensity, column_index );
}
result_matrix.resize( ug_size, 1 );
value_type const residual = thf.output( result_matrix.begin() );
/*
std::cout << "\n current residual is " << residual << "\n";
std::cout << "\n current ug is \n" << result_matrix.transpose() << "\n";
*/
return residual;
}
void fit()
{
std::cerr << "\nbefore the fit, thickness is set to be " << thickness << "\n";
assert( ug_size );
assert( ar_dim );
assert( column_index < ar_dim );
assert( std::abs(std::real(thickness)) < 1.0e-10 );
assert( std::imag(thickness) > 1.0e-10 );
assert( diag_matrix.col() == ar_dim );
assert( diag_matrix.row() == intensity_matrix.row() );
assert( intensity_matrix.col() == ar_dim );
assert( initial_ug.row() == ug_size );
assert( initial_ug.col() == 1 );
assert( ar.row() == ar.col() );
assert( ar_dim == ar.row() );
assert( progress_ratio >= value_type{0} );
assert( progress_ratio <= value_type{1} );
assert( alpha );
assert( beta );
assert( gamma );
new_residual = iterate( initial_ug, new_ug );
matrix_type second_ug{ initial_ug };
size_type current_iteration = 0;
matrix_vector_type vm;
vector_type vr;
vm.push_back( new_ug );
vr.push_back( new_residual );
value_type best_residual_so_far = new_residual;
while ( true )
{
value_type const second_residual = iterate( new_ug, second_ug );
bool break_flag = false;
//??
if ( best_residual_so_far > max_iteration * second_residual ) break_flag = true;
best_residual_so_far = std::min( second_residual, best_residual_so_far );
if( ++current_iteration > max_iteration ) break_flag = true;
new_ug.swap( second_ug );
new_residual = second_residual;
vm.push_back( new_ug );
vr.push_back( new_residual );
if ( break_flag ) break;
}
size_type const elite_index = std::distance( vr.begin(), std::min_element( vr.begin(), vr.end() ) );
std::copy( vm[elite_index].begin(), vm[elite_index].end(), new_ug.begin() );
//std::cout << "\ncurrent elite residual is " << vr[elite_index] << ", at iteration " << current_iteration << std::endl;
}
value_type output( Output_Iterator oit )
{
fit();
std::copy( new_ug.begin(), new_ug.end(), oit );
return new_residual;
}