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 run()
{
// Read filenames
vector<std::string> filenames;
{
std::string folder = Path::dirname (argument[0]);
std::ifstream ifs (argument[0].c_str());
std::string temp;
while (getline (ifs, temp)) {
std::string filename (Path::join (folder, temp));
size_t p = filename.find_last_not_of(" \t");
if (std::string::npos != p)
filename.erase(p+1);
if (filename.size()) {
if (!MR::Path::exists (filename))
throw Exception ("Input connectome file not found: \"" + filename + "\"");
filenames.push_back (filename);
}
}
}
const MR::Connectome::matrix_type example_connectome = load_matrix (filenames.front());
if (example_connectome.rows() != example_connectome.cols())
throw Exception ("Connectome of first subject is not square (" + str(example_connectome.rows()) + " x " + str(example_connectome.cols()) + ")");
const MR::Connectome::node_t num_nodes = example_connectome.rows();
// Initialise enhancement algorithm
std::shared_ptr<Stats::EnhancerBase> enhancer;
switch (int(argument[1])) {
case 0: {
auto opt = get_options ("threshold");
if (!opt.size())
throw Exception ("For NBS algorithm, -threshold option must be provided");
enhancer.reset (new MR::Connectome::Enhance::NBS (num_nodes, opt[0][0]));
}
break;
case 1: {
std::shared_ptr<Stats::TFCE::EnhancerBase> base (new MR::Connectome::Enhance::NBS (num_nodes));
enhancer.reset (new Stats::TFCE::Wrapper (base));
load_tfce_parameters (*(dynamic_cast<Stats::TFCE::Wrapper*>(enhancer.get())));
if (get_options ("threshold").size())
WARN (std::string (argument[1]) + " is a threshold-free algorithm; -threshold option ignored");
}
break;
case 2: {
enhancer.reset (new MR::Connectome::Enhance::PassThrough());
if (get_options ("threshold").size())
WARN ("No enhancement algorithm being used; -threshold option ignored");
}
break;
default:
throw Exception ("Unknown enhancement algorithm");
}
size_t num_perms = get_option_value ("nperms", DEFAULT_NUMBER_PERMUTATIONS);
const bool do_nonstationary_adjustment = get_options ("nonstationary").size();
size_t nperms_nonstationary = get_option_value ("nperms_nonstationarity", DEFAULT_NUMBER_PERMUTATIONS_NONSTATIONARITY);
// Load design matrix
const matrix_type design = load_matrix (argument[2]);
if (size_t(design.rows()) != filenames.size())
throw Exception ("number of subjects does not match number of rows in design matrix");
// Load permutations file if supplied
auto opt = get_options("permutations");
vector<vector<size_t> > permutations;
if (opt.size()) {
permutations = Math::Stats::Permutation::load_permutations_file (opt[0][0]);
num_perms = permutations.size();
if (permutations[0].size() != (size_t)design.rows())
throw Exception ("number of rows in the permutations file (" + str(opt[0][0]) + ") does not match number of rows in design matrix");
}
// Load non-stationary correction permutations file if supplied
opt = get_options("permutations_nonstationary");
vector<vector<size_t> > permutations_nonstationary;
if (opt.size()) {
permutations_nonstationary = Math::Stats::Permutation::load_permutations_file (opt[0][0]);
nperms_nonstationary = permutations.size();
if (permutations_nonstationary[0].size() != (size_t)design.rows())
throw Exception ("number of rows in the nonstationary permutations file (" + str(opt[0][0]) + ") does not match number of rows in design matrix");
}
// Load contrast matrix
matrix_type contrast = load_matrix (argument[3]);
if (contrast.cols() > design.cols())
throw Exception ("too many contrasts for design matrix");
contrast.conservativeResize (contrast.rows(), design.cols());
const std::string output_prefix = argument[4];
// Load input data
// For compatibility with existing statistics code, symmetric matrix data is adjusted
// into vector form - one row per edge in the symmetric connectome. The Mat2Vec class
// deals with the re-ordering of matrix data into this form.
MR::Connectome::Mat2Vec mat2vec (num_nodes);
const size_t num_edges = mat2vec.vec_size();
matrix_type data (num_edges, filenames.size());
{
ProgressBar progress ("Loading input connectome data", filenames.size());
for (size_t subject = 0; subject < filenames.size(); subject++) {
const std::string& path (filenames[subject]);
MR::Connectome::matrix_type subject_data;
try {
subject_data = load_matrix (path);
} catch (Exception& e) {
throw Exception (e, "Error loading connectome data for subject #" + str(subject) + " (file \"" + path + "\"");
}
try {
MR::Connectome::to_upper (subject_data);
if (size_t(subject_data.rows()) != num_nodes)
throw Exception ("Connectome matrix is not the correct size (" + str(subject_data.rows()) + ", should be " + str(num_nodes) + ")");
} catch (Exception& e) {
throw Exception (e, "Connectome for subject #" + str(subject) + " (file \"" + path + "\") invalid");
}
for (size_t i = 0; i != num_edges; ++i)
data(i, subject) = subject_data (mat2vec(i).first, mat2vec(i).second);
++progress;
}
}
{
ProgressBar progress ("outputting beta coefficients, effect size and standard deviation...", contrast.cols() + 3);
const matrix_type betas = Math::Stats::GLM::solve_betas (data, design);
for (size_t i = 0; i < size_t(contrast.cols()); ++i) {
save_matrix (mat2vec.V2M (betas.col(i)), output_prefix + "_beta_" + str(i) + ".csv");
++progress;
}
const matrix_type abs_effects = Math::Stats::GLM::abs_effect_size (data, design, contrast);
save_matrix (mat2vec.V2M (abs_effects.col(0)), output_prefix + "_abs_effect.csv");
++progress;
const matrix_type std_effects = Math::Stats::GLM::std_effect_size (data, design, contrast);
matrix_type first_std_effect = mat2vec.V2M (std_effects.col (0));
for (MR::Connectome::node_t i = 0; i != num_nodes; ++i) {
for (MR::Connectome::node_t j = 0; j != num_nodes; ++j) {
if (!std::isfinite (first_std_effect (i, j)))
first_std_effect (i, j) = 0.0;
}
}
save_matrix (first_std_effect, output_prefix + "_std_effect.csv");
++progress;
const matrix_type stdevs = Math::Stats::GLM::stdev (data, design);
save_vector (stdevs.col(0), output_prefix + "_std_dev.csv");
}
Math::Stats::GLMTTest glm_ttest (data, design, contrast);
// If performing non-stationarity adjustment we need to pre-compute the empirical statistic
vector_type empirical_statistic;
if (do_nonstationary_adjustment) {
empirical_statistic = vector_type::Zero (num_edges);
if (permutations_nonstationary.size()) {
Stats::PermTest::PermutationStack perm_stack (permutations_nonstationary, "precomputing empirical statistic for non-stationarity adjustment...");
Stats::PermTest::precompute_empirical_stat (glm_ttest, enhancer, perm_stack, empirical_statistic);
} else {
Stats::PermTest::PermutationStack perm_stack (nperms_nonstationary, design.rows(), "precomputing empirical statistic for non-stationarity adjustment...", true);
Stats::PermTest::precompute_empirical_stat (glm_ttest, enhancer, perm_stack, empirical_statistic);
}
save_matrix (mat2vec.V2M (empirical_statistic), output_prefix + "_empirical.csv");
}
// Precompute default statistic and enhanced statistic
vector_type tvalue_output (num_edges);
vector_type enhanced_output (num_edges);
Stats::PermTest::precompute_default_permutation (glm_ttest, enhancer, empirical_statistic, enhanced_output, std::shared_ptr<vector_type>(), tvalue_output);
save_matrix (mat2vec.V2M (tvalue_output), output_prefix + "_tvalue.csv");
save_matrix (mat2vec.V2M (enhanced_output), output_prefix + "_enhanced.csv");
// Perform permutation testing
if (!get_options ("notest").size()) {
// FIXME Getting NANs in the null distribution
// Check: was result of pre-nulled subject data
vector_type null_distribution (num_perms);
vector_type uncorrected_pvalues (num_edges);
if (permutations.size()) {
Stats::PermTest::run_permutations (permutations, glm_ttest, enhancer, empirical_statistic,
enhanced_output, std::shared_ptr<vector_type>(),
null_distribution, std::shared_ptr<vector_type>(),
uncorrected_pvalues, std::shared_ptr<vector_type>());
} else {
Stats::PermTest::run_permutations (num_perms, glm_ttest, enhancer, empirical_statistic,
enhanced_output, std::shared_ptr<vector_type>(),
null_distribution, std::shared_ptr<vector_type>(),
uncorrected_pvalues, std::shared_ptr<vector_type>());
}
save_vector (null_distribution, output_prefix + "_null_dist.txt");
vector_type pvalue_output (num_edges);
Math::Stats::Permutation::statistic2pvalue (null_distribution, enhanced_output, pvalue_output);
save_matrix (mat2vec.V2M (pvalue_output), output_prefix + "_fwe_pvalue.csv");
save_matrix (mat2vec.V2M (uncorrected_pvalues), output_prefix + "_uncorrected_pvalue.csv");
}
}
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;
}