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;
}
const complex_matrix_type make_ug( const matrix_type& G, const matrix_type& A, const matrix_type& D ) const
{
assert( G.col() == 3 );
assert( A.col() == 3 );
assert( D.col() == 1 );
assert( A.row() == D.row() );
auto const M = make_matrix();
auto const S = G * ( M.inverse() );
matrix_type s( 1, S.row() );
for ( size_type i = 0; i < S.row(); ++ i )
{
s[0][i] = value_type( 0.5 ) * std::sqrt( std::inner_product( S.row_begin( i ), S.row_end( i ), S.row_begin( i ), value_type( 0 ) ) );
}
auto const piomega = 3.141592553590 * feng::inner_product( array_type( M[0][0], M[1][0], M[2][0] ),
feng::cross_product( array_type( M[0][1], M[1][1], M[2][1] ), array_type( M[0][2], M[1][2], M[2][2] ) ) );
auto const atomcellfacte = make_gaussian_electron( s, v0 );
const complex_matrix_type dwss = D * feng::pow( s, value_type( 2 ) );
const complex_matrix_type piag = A * G.transpose();
auto fact = feng::exp( - dwss - piag * complex_type( 0, 6.2831853071796 ) );
std::transform( fact.begin(), fact.end(), atomcellfacte.begin(), fact.begin(), [piomega]( const complex_type f, const value_type a )
{
return f * a / piomega;
} );
complex_matrix_type Ug( fact.col(), 1 );
for ( size_type i = 0; i < fact.col(); ++i )
{
Ug[i][0] = std::accumulate( fact.col_begin( i ), fact.col_end( i ), complex_type() );
//if ( std::abs(Ug[i][0].real()) < 1.0e-8 ) Ug[i][0].real(0);
//if ( std::abs(Ug[i][0].imag()) < 1.0e-8 ) Ug[i][0].imag(0);
}
return Ug;
}
void register_entry( size_matrix_type const& ar,
value_type alpha, complex_matrix_type const& lhs_matrix, complex_matrix_type const& rhs_matrix,
value_type beta, complex_matrix_type const& expm_matrix,
matrix_type const& intensity, size_type const column_index = 0 )
{
assert( ar.row() == ar.col() );
assert( ar.row() == lhs_matrix.row() );
assert( lhs_matrix.row() == lhs_matrix.col() );
assert( ar.row() == rhs_matrix.row() );
assert( ar.row() == intensity.row() );
assert( 1 == intensity.col() );
assert( (*(std::max_element(ar.begin(), ar.end()))) < ug_size );
assert( alpha >= value_type{0} );
assert( beta >= value_type{0} );
assert( alpha <= value_type{1} );
assert( beta <= value_type{1} );
assert( std::abs(alpha+beta-value_type{1}) < value_type{ 1.0e-10} );
//assert( c1_matrix.row() == ar.row() );
//assert( c1_matrix.col() == 1 );
assert( expm_matrix.row() == ar.row() );
assert( expm_matrix.col() == 1 );
assert( column_index < ar.row() );
size_type const n = ar.row();
size_type const m = ug_size;
matrix_type real_part(m, 1);
matrix_type imag_part(m, 1);
value_type norm_factor{0};
//norm only one column
//std::for_each( expm_matrix.col_begin( column_index ), expm_matrix.col_end( column_index ), [&norm_factor]( complex_type const& c ){ norm_factor += std::norm(c); } );
std::for_each( expm_matrix.begin(), expm_matrix.end(), [&norm_factor]( complex_type const& c ){ norm_factor += std::norm(c); } );
norm_factor /= static_cast<value_type>( expm_matrix.row() );
for ( size_type r = 0; r != ar.row(); ++r )
{
//for \beta C/2 C/2 part
extract_inner_product_coefficients( m, n, ar.row_begin(r), lhs_matrix.row_begin(r), rhs_matrix.col_begin(column_index), real_part.begin(), imag_part.begin() );
real_part *= alpha;
imag_part *= alpha;
//for \gamma E part
real_part[0][0] += beta * std::real( expm_matrix[r][column_index] );
imag_part[0][0] += beta * std::imag( expm_matrix[r][column_index] );
//real_part[0][0] += beta * std::real( expm_matrix[r][column_index] ) / norm_factor;
//imag_part[0][0] += beta * std::imag( expm_matrix[r][column_index] ) / norm_factor;
//needs modifying here
dsm.register_entry( intensity[r][0], real_part.begin(), imag_part.begin() );
}
#if 0
//register lambda, ensuring lambda to be 1
std::fill( real_part.begin(), real_part.end(), value_type{} );
value_type const factor = value_type{1.0};
value_type const weigh = factor * std::sqrt( static_cast<value_type>( intensity.row() ) );
real_part[0][0] = weigh;
imag_part[0][0] = weigh;
dsm.register_entry( value_type{2} * weigh * weigh, real_part.begin(), imag_part.begin() );
#endif
}
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;
}