void solve_nonlinear () {
for (size_t i = 0; i < signals.rows(); ++i) {
const Math::Vector<cost_value_type> signal (signals.row(i));
Math::Vector<cost_value_type> values (tensors.row(i));
cost.set_voxel (&signal, &values);
Math::Vector<cost_value_type> x (cost.size());
cost.init (x);
//Math::check_function_gradient (cost, x, 1e-10, true);
Math::GradientDescent<Cost> optim (cost);
try { optim.run (10000, 1e-8); }
catch (Exception& E) {
E.display();
}
//x = optim.state();
//Math::check_function_gradient (cost, x, 1e-10, true);
cost.get_values (values, optim.state());
}
}
void run ()
{
try {
Math::Matrix<value_type> directions = DWI::Directions::load_cartesian<value_type> (argument[0]);
report (str(argument[0]), directions);
}
catch (Exception& E) {
Math::Matrix<value_type> directions (str(argument[0]));
DWI::normalise_grad (directions);
if (directions.columns() < 3)
throw Exception ("unexpected matrix size for DW scheme \"" + str(argument[0]) + "\"");
print (str(argument[0]) + " [ " + str(directions.rows()) + " volumes ]\n");
DWI::Shells shells (directions);
for (size_t n = 0; n < shells.count(); ++n) {
Math::Matrix<value_type> subset (shells[n].count(), 3);
for (size_t i = 0; i < subset.rows(); ++i)
subset.row(i) = directions.row(shells[n].get_volumes()[i]).sub(0,3);
report ("\nb = " + str(shells[n].get_mean()), subset);
}
}
}
void run ()
{
Math::Matrix<value_type> directions = DWI::Directions::load_cartesian<value_type> (argument[0]);
size_t num_permutations = 1e8;
Options opt = get_options ("permutations");
if (opt.size())
num_permutations = opt[0][0];
Shared eddy_shared (directions, num_permutations);
Thread::run (Thread::multi (Processor (eddy_shared)), "eval thread");
auto& signs = eddy_shared.get_best_signs();
for (size_t n = 0; n < directions.rows(); ++n)
if (signs[n] < 0)
directions.row(n) *= -1.0;
bool cartesian = get_options("cartesian").size();
DWI::Directions::save (directions, argument[1], cartesian);
}
void report (const std::string& title, const Math::Matrix<value_type>& directions)
{
std::vector<value_type> NN_bipolar (directions.rows(), 0.0);
std::vector<value_type> NN_unipolar (directions.rows(), 0.0);
std::vector<value_type> E_bipolar (directions.rows(), 0.0);
std::vector<value_type> E_unipolar (directions.rows(), 0.0);
for (size_t i = 0; i < directions.rows()-1; ++i) {
for (size_t j = i+1; j < directions.rows(); ++j) {
value_type cos_angle = Math::dot (directions.row(i).sub(0,3), directions.row(j).sub(0,3));
NN_unipolar[i] = std::max (NN_unipolar[i], cos_angle);
NN_unipolar[j] = std::max (NN_unipolar[j], cos_angle);
cos_angle = std::abs(cos_angle);
NN_bipolar[i] = std::max (NN_bipolar[i], cos_angle);
NN_bipolar[j] = std::max (NN_bipolar[j], cos_angle);
value_type E =
Math::pow2 (directions(i,0) - directions(j,0)) +
Math::pow2 (directions(i,1) - directions(j,1)) +
Math::pow2 (directions(i,2) - directions(j,2));
E = value_type (1.0) / E;
E_unipolar[i] += E;
E_unipolar[j] += E;
value_type E2 =
Math::pow2 (directions(i,0) + directions(j,0)) +
Math::pow2 (directions(i,1) + directions(j,1)) +
Math::pow2 (directions(i,2) + directions(j,2));
E += value_type (1.0) / E2;
E_bipolar[i] += E;
E_bipolar[j] += E;
}
}
auto report_NN = [](const std::vector<value_type>& NN) {
value_type min = std::numeric_limits<value_type>::max();
value_type mean = 0.0;
value_type max = 0.0;
for (auto a : NN) {
a = (180.0/Math::pi) * std::acos (a);
mean += a;
min = std::min (min, a);
max = std::max (max, a);
}
mean /= NN.size();
print (" nearest-neighbour angles: mean = " + str(mean) + ", range [ " + str(min) + " - " + str(max) + " ]\n");
};
auto report_E = [](const std::vector<value_type>& E) {
value_type min = std::numeric_limits<value_type>::max();
value_type total = 0.0;
value_type max = 0.0;
for (auto e : E) {
total += e;
min = std::min (min, e);
max = std::max (max, e);
}
print (" energy: total = " + str(total) + ", mean = " + str(total/E.size()) + ", range [ " + str(min) + " - " + str(max) + " ]\n");
};
print (title + " [ " + str(directions.rows()) + " directions ]\n\n");
print (" Bipolar electrostatic repulsion model:\n");
report_NN (NN_bipolar);
report_E (E_bipolar);
print ("\n Unipolar electrostatic repulsion model:\n");
report_NN (NN_unipolar);
report_E (E_unipolar);
std::string lmax_results;
for (size_t lmax = 2; lmax <= Math::SH::LforN (directions.rows()); lmax += 2)
lmax_results += " " + str(DWI::condition_number_for_lmax (directions, lmax));
print ("\n Spherical Harmonic fit:\n condition numbers for lmax = " + str(2) + " -> "
+ str(Math::SH::LforN (directions.rows())) + ":" + lmax_results + "\n\n");
}
void run() {
Image::BufferPreload<float> data_in (argument[0], Image::Stride::contiguous_along_axis (3));
auto voxel_in = data_in.voxel();
Math::Matrix<value_type> grad (DWI::get_valid_DW_scheme<float> (data_in));
// Want to support non-shell-like data if it's just a straight extraction
// of all dwis or all bzeros i.e. don't initialise the Shells class
std::vector<size_t> volumes;
bool bzero = get_options ("bzero").size();
Options opt = get_options ("shell");
if (opt.size()) {
DWI::Shells shells (grad);
shells.select_shells (false, false);
for (size_t s = 0; s != shells.count(); ++s) {
DEBUG ("Including data from shell b=" + str(shells[s].get_mean()) + " +- " + str(shells[s].get_stdev()));
for (std::vector<size_t>::const_iterator v = shells[s].get_volumes().begin(); v != shells[s].get_volumes().end(); ++v)
volumes.push_back (*v);
}
// Remove DW information from header if b=0 is the only 'shell' selected
bzero = (shells.count() == 1 && shells[0].is_bzero());
} else {
const float bzero_threshold = File::Config::get_float ("BValueThreshold", 10.0);
for (size_t row = 0; row != grad.rows(); ++row) {
if ((bzero && (grad (row, 3) < bzero_threshold)) || (!bzero && (grad (row, 3) > bzero_threshold)))
volumes.push_back (row);
}
}
if (volumes.empty())
throw Exception ("No " + str(bzero ? "b=0" : "dwi") + " volumes present");
std::sort (volumes.begin(), volumes.end());
Image::Header header (data_in);
if (volumes.size() == 1)
header.set_ndim (3);
else
header.dim (3) = volumes.size();
Math::Matrix<value_type> new_grad (volumes.size(), grad.columns());
for (size_t i = 0; i < volumes.size(); i++)
new_grad.row (i) = grad.row (volumes[i]);
header.DW_scheme() = new_grad;
Image::Buffer<value_type> data_out (argument[1], header);
auto voxel_out = data_out.voxel();
Image::Loop outer ("extracting volumes...", 0, 3);
if (voxel_out.ndim() == 4) {
for (auto i = outer (voxel_out, voxel_in); i; ++i) {
for (size_t i = 0; i < volumes.size(); i++) {
voxel_in[3] = volumes[i];
voxel_out[3] = i;
voxel_out.value() = voxel_in.value();
}
}
} else {
const size_t volume = volumes[0];
for (auto i = outer (voxel_out, voxel_in); i; ++i) {
voxel_in[3] = volume;
voxel_out.value() = voxel_in.value();
}
}
}