void Eupdate2d(Field &EM, Loss &lass, int t){
// update electric field
#pragma omp parallel for
for (size_t dx = 1; dx < spacex - 1; dx++){
for (size_t dy = 1; dy < spacey - 1; dy++){
EM.Ez(dx,dy) = lass.EzE(dx,dy) * EM.Ez(dx,dy)
+ lass.EzH(dx,dy) * ((EM.Hy(dx, dy)
- EM.Hy(dx - 1, dy))
- (EM.Hx(dx,dy)
- EM.Hx(dx, dy - 1)));
}
}
//return EM;
}
// 2 dimensional functions for E / H movement
Field Hupdate2d(Field EM, Loss lass, int t){
// update magnetic field, x direction
for (size_t dx = 0; dx < spacex - 1; dx++){
for (size_t dy = 0; dy < spacey - 1; dy++){
EM.Hz(dx,dy) = lass.HzH(dx,dy) * EM.Hz(dx, dy)
+ lass.HzE(dx,dy) * ((EM.Ex(dx, dy + 1)
- EM.Ex(dx, dy))
- (EM.Ey(dx + 1,dy)
- EM.Ey(dx, dy)));
}
}
return EM;
}
Field Eupdate2d(Field EM, Loss lass, int t){
// update electric field
for (size_t dx = 0; dx < spacex - 1; dx++){
for (size_t dy = 1; dy < spacey - 1; dy++){
EM.Ex(dx,dy) = lass.ExE(dx,dy) * EM.Ex(dx,dy)
+ lass.ExH(dx,dy) * (EM.Hz(dx, dy) - EM.Hz(dx, dy - 1));
}
}
for (size_t dx = 1; dx < spacex - 1; dx++){
for (size_t dy = 0; dy < spacey - 1; dy++){
EM.Ey(dx,dy) = lass.EyE(dx,dy) * EM.Ey(dx,dy)
- lass.EyH(dx,dy) * (EM.Hz(dx, dy) - EM.Hz(dx - 1, dy));
}
}
return EM;
}
// TFSF boundaries
void TFSF(Field &EM, Loss &lass, Loss1d &lass1d, double Cour, double ppw){
int dx, dy, loc = 0;
// TFSF boundary
Bound first, last;
first.x = 10; last.x = 1990;
first.y = 10; last.y = 1490;
// Update along right edge!
dx = last.x;
for (int dy = first.y; dy <= last.y; dy++){
EM.Hy(dx,dy) += lass.HyE(dx, dy) * EM.Ez1d[dx];
}
// Updating along left edge
dx = first.x - 1;
for (int dy = first.y; dy <= last.y; dy++){
EM.Hy(dx,dy) -= lass.HyE(dx, dy) * EM.Ez1d[dx+1];
}
// Updating along top
dy = last.y;
for (int dx = first.x; dx <= last.x; dx++){
EM.Hx(dx,dy) -= lass.HxE(dx, dy) * EM.Ez1d[dx];
}
// Update along bot
dy = first.y - 1;
for (int dx = first.x; dx <= last.x; dx++){
EM.Hx(dx,dy) += lass.HxE(dx, dy) * EM.Ez1d[dx];
}
// Insert 1d grid stuff here. Update magnetic and electric field
Hupdate1d(EM, lass1d, EM.t);
Eupdate1d(EM, lass1d, EM.t);
//EM.Ez1d[10] = ricker(EM.t,0, Cour);
EM.Ez1d[10] = planewave(EM.t, loc, Cour, ppw);
EM.t++;
std::cout << EM.t << '\n';
// Check mag instead of ricker.
// Update along right
dx = last.x;
for (int dy = first.y; dy <= last.y; dy++){
EM.Ez(dx, dy) += lass.EzH(dx, dy) * EM.Hy1d[dx];
}
// Updating Ez along left
dx = first.x;
for (int dy = first.y; dy <= last.y; dy++){
EM.Ez(dx, dy) -= lass.EzH(dx, dy) * EM.Hy1d[dx - 1];
}
//return EM;
}
// TFSF boundaries
Field TFSF(Field EM, Loss lass, Loss1d lass1d, double Cour){
int dx, dy;
// TFSF boundary
Bound first, last;
first.x = 10; last.x = 390;
first.y = 10; last.y = 190;
// Update along right
dx = last.x;
for (int dy = first.y; dy <= last.y; dy++){
EM.Hz(dx, dy) -= lass.HzE(dx, dy) * EM.Ey1d[dx];
}
// Updating Hz along left
dx = first.x - 1;
for (int dy = first.y; dy <= last.y; dy++){
EM.Hz(dx, dy) += lass.HzE(dx, dy) * EM.Ey1d[dx + 1];
}
// Insert 1d grid stuff here. Update magnetic and electric field
Hupdate1d(EM, lass1d, EM.t);
Eupdate1d(EM, lass1d, EM.t);
//EM.Ey1d[10] = ricker(EM.t,0, Cour);
EM.Ey1d[10] = planewave(EM.t, 15, Cour, 30, 40);
EM.t++;
std::cout << EM.t << '\n';
// Check mag instead of ricker.
// Update along right edge!
dx = last.x;
for (int dy = first.y; dy <= last.y; dy++){
EM.Ey(dx,dy) -= lass.EyH(dx, dy) * EM.Hz1d[dx];
}
// Updating along left edge
dx = first.x;
for (int dy = first.y; dy <= last.y; dy++){
EM.Ey(dx,dy) += lass.EyH(dx, dy) * EM.Hz1d[dx-1];
}
// Updating along top
dy = last.y;
for (int dx = first.x; dx <= last.x; dx++){
EM.Ex(dx,dy) += lass.ExH(dx, dy) * EM.Hz1d[dx];
}
// Update along bot
dy = first.y;
for (int dx = first.x; dx <= last.x; dx++){
EM.Ex(dx,dy) -= lass.ExH(dx, dy) * EM.Hz1d[dx];
}
return EM;
}
// 2 dimensional functions for E / H movement
void Hupdate2d(Field &EM, Loss &lass, int t){
// update magnetic field, x direction
#pragma omp parallel for
for (size_t dx = 0; dx < spacex; dx++){
for (size_t dy = 0; dy < spacey - 1; dy++){
EM.Hx(dx,dy) = lass.HxH(dx,dy) * EM.Hx(dx, dy)
- lass.HxE(dx,dy) * (EM.Ez(dx,dy + 1)
- EM.Ez(dx,dy));
}
}
// update magnetic field, y direction
#pragma omp parallel for
for (size_t dx = 0; dx < spacex - 1; dx++){
for (size_t dy = 0; dy < spacey; dy++){
EM.Hy(dx,dy) = lass.HyH(dx,dy) * EM.Hy(dx,dy)
+ lass.HyE(dx,dy) * (EM.Ez(dx + 1,dy)
- EM.Ez(dx,dy));
}
}
//return EM;
}
int main(int argc, char** argv) {
try {
util::ProgramOptions::init(argc, argv);
logger::LogManager::init();
Hdf5CragStore cragStore(optionProjectFile.as<std::string>());
Hdf5VolumeStore volumeStore(optionProjectFile.as<std::string>());
Crag crag;
cragStore.retrieveCrag(crag);
NodeFeatures nodeFeatures(crag);
EdgeFeatures edgeFeatures(crag);
LOG_USER(logger::out) << "reading features" << std::endl;
cragStore.retrieveNodeFeatures(crag, nodeFeatures);
cragStore.retrieveEdgeFeatures(crag, edgeFeatures);
BundleOptimizer::Parameters parameters;
parameters.lambda = optionRegularizerWeight;
parameters.epsStrategy = BundleOptimizer::EpsFromGap;
BundleOptimizer optimizer(parameters);
BestEffort* bestEffort = 0;
OverlapLoss* overlapLoss = 0;
if (optionBestEffortFromProjectFile) {
LOG_USER(logger::out) << "reading best-effort" << std::endl;
bestEffort = new BestEffort(crag);
vigra::HDF5File project(
optionProjectFile.as<std::string>(),
vigra::HDF5File::OpenMode::ReadWrite);
project.cd("best_effort");
vigra::ArrayVector<int> beNodes;
vigra::MultiArray<2, int> beEdges;
project.readAndResize("nodes", beNodes);
project.readAndResize("edges", beEdges);
std::set<int> nodes;
for (int n : beNodes)
nodes.insert(n);
std::set<std::pair<int, int>> edges;
for (int i = 0; i < beEdges.shape(1); i++)
edges.insert(
std::make_pair(
std::min(beEdges(i, 0), beEdges(i, 1)),
std::max(beEdges(i, 0), beEdges(i, 1))));
for (Crag::NodeIt n(crag); n != lemon::INVALID; ++n)
bestEffort->node[n] = nodes.count(crag.id(n));
for (Crag::EdgeIt e(crag); e != lemon::INVALID; ++e)
bestEffort->edge[e] = edges.count(
std::make_pair(
std::min(crag.id(crag.u(e)), crag.id(crag.v(e))),
std::max(crag.id(crag.u(e)), crag.id(crag.v(e)))));
} else {
LOG_USER(logger::out) << "reading ground-truth" << std::endl;
ExplicitVolume<int> groundTruth;
volumeStore.retrieveGroundTruth(groundTruth);
LOG_USER(logger::out) << "finding best-effort solution" << std::endl;
overlapLoss = new OverlapLoss(crag, groundTruth);
bestEffort = new BestEffort(crag, *overlapLoss);
}
Loss* loss = 0;
bool destructLoss = false;
if (optionLoss.as<std::string>() == "hamming") {
LOG_USER(logger::out) << "using Hamming loss" << std::endl;
loss = new HammingLoss(crag, *bestEffort);
destructLoss = true;
} else if (optionLoss.as<std::string>() == "overlap") {
LOG_USER(logger::out) << "using overlap loss" << std::endl;
if (!overlapLoss) {
LOG_USER(logger::out) << "reading ground-truth" << std::endl;
ExplicitVolume<int> groundTruth;
volumeStore.retrieveGroundTruth(groundTruth);
LOG_USER(logger::out) << "finding best-effort solution" << std::endl;
overlapLoss = new OverlapLoss(crag, groundTruth);
}
loss = overlapLoss;
} else {
LOG_ERROR(logger::out)
<< "unknown loss: "
<< optionLoss.as<std::string>()
<< std::endl;
return 1;
}
if (optionNormalizeLoss) {
LOG_USER(logger::out) << "normalizing loss..." << std::endl;
loss->normalize(crag, MultiCut::Parameters());
}
Oracle oracle(
crag,
nodeFeatures,
edgeFeatures,
*loss,
*bestEffort);
std::vector<double> weights(nodeFeatures.dims() + edgeFeatures.dims(), 0);
optimizer.optimize(oracle, weights);
storeVector(weights, optionFeatureWeights);
if (destructLoss && loss != 0)
delete loss;
if (overlapLoss)
delete overlapLoss;
if (bestEffort)
delete bestEffort;
} catch (boost::exception& e) {
handleException(e, std::cerr);
}
}
// This is the function we writs the bulk of the code in
void FDTD(Field EM,
const int final_time, const double eps, const int space, Loss lass,
std::ofstream& output){
// For magnetic field:
// double offset = 0.00005;
// for electric field:
double offset = 0.05;
double loss = 0.0;
double Cour = 1.0 / sqrt(2.0);
// Relative permittivity
for (int dx = 0; dx < space; dx++){
for (int dy = 0; dy < space; dy++){
if (dx > 100 && dx < 150){
lass.EzH(dx, dy) = Cour * eps;
lass.EzE(dx, dy) = 1.0;
lass.HyH(dx, dy) = 1.0;
lass.HyE(dx, dy) = Cour / eps;
lass.HxE(dx, dy) = Cour / eps;
lass.HxH(dx, dy) = 1.0;
/*
lass.EzH(dx, dy) = eps / 9.0 /(1.0 - loss);
lass.EzE(dx, dy) = (1.0 - loss) / (1.0 + loss);
lass.HyH(dx, dy) = (1.0 - loss) / (1.0 + loss);
lass.HyE(dx, dy) = (1.0 / eps) / (1.0 + loss);
lass.HxE(dx, dy) = (1.0 / eps) / (1.0 + loss);
lass.HxH(dx, dy) = (1.0 - loss) / (1.0 + loss);
*/
}
else{
lass.EzH(dx, dy) = Cour * eps;
lass.EzE(dx, dy) = 1.0;
lass.HyH(dx, dy) = 1.0;
lass.HyE(dx, dy) = Cour / eps;
lass.HxE(dx, dy) = Cour / eps;
lass.HxH(dx, dy) = 1.0;
/*
lass.EzH(dx, dy) = eps;
lass.EzE(dx, dy) = 1.0;
lass.HyH(dx, dy) = 1.0;
lass.HyE(dx, dy) = (1.0 / eps);
lass.HxE(dx, dy) = (1.0 / eps);
lass.HxH(dx, dy) = 1.0;
*/
}
}
}
// Time looping
for (int t = 0; t < final_time; t++){
// Linking the final two elements for an ABC
for (int da = 0; da < space; da++){
EM.Hy(da,space - 1) = EM.Hy(da,space - 2);
EM.Hx(space - 1,da) = EM.Hx(space - 2,da);
}
// update magnetic field, y direction
for (int dx = 0; dx < space - 1; dx++){
for (int dy = 0; dy < space; dy++){
EM.Hy(dx,dy) = lass.HyH(dx,dy) * EM.Hy(dx,dy)
+ lass.HyE(dx,dy) * (EM.Ez(dx + 1,dy)
- EM.Ez(dx,dy));
}
}
// update magnetic field, x direction
for (int dx = 0; dx < space; dx++){
for (int dy = 0; dy < space - 1; dy++){
EM.Hx(dx,dy) = lass.HxH(dx,dy) * EM.Hx(dx, dy)
+ lass.HxE(dx,dy) * (EM.Ez(dx,dy + 1)
- EM.Ez(dx,dy));
}
}
// Correction to the H field for the TFSF boundary
// Hy[49] -= exp(-(t - 40.) * (t - 40.)/100.0) / eps;
// Hy[49] -= sin((t-10.0)*0.2)*0.0005;
// Linking the first two elements in the electric field
for (int dy = 0; dy < space; dy++){
EM.Ez(0,dy) = EM.Ez(1,dy);
EM.Ez(space - 1,dy) = EM.Ez(space - 2,dy);
}
// update electric field
for (int dx = 1; dx < space - 1; dx++){
for (int dy = 1; dy < space - 1; dy++){
EM.Ez(dx,dy) = lass.EzE(dx,dy) * EM.Ez(dx,dy)
+ lass.EzH[dx] * (EM.Hy(dx, dy)
- EM.Hy(dx - 1, dy)
- EM.Hx(dx,dy)
- EM.Hx(dx, dy - 1));
}
}
// set src for next step
for (int dy = 0; dy < space; dy++){
EM.Ez(50,dy) += exp(-((t + 1 - 40.) * (t + 1 - 40.))/100.0);
}
// EM.Ez[0] = 0;
// Ez[50] += sin((t - 10.0 + 1)*0.2)*0.0005;
/*
if (t > 0){
Ez[50] = sin(0.1 * t) / (0.1 * t);
}
else{
Ez[50] = 1;
}
*/
if (t % 50 == 0){
for (int dx = 0; dx < space; dx = dx + 50){
for (int dy = 0; dy < space; dy = dy + 50){
output << t << '\t' << dx <<'\t' << dy << '\t'
<< EM.Ez(dx, dy) << '\n';
//output << Ez(dx,dy) + (t * offset) << '\n';
//output << Hy[dx] + (t * offset) << '\n';
}
}
output << '\n' << '\n';
}
}
}
// Checking Absorbing Boundary Conditions (ABC)
void ABCcheck(Field &EM, Loss &lass){
// defining constant for ABC
double c1, c2, c3, temp1, temp2;
temp1 = sqrt(lass.EzH(0,0) * lass.HyE(0,0));
temp2 = 1.0 / temp1 + 2.0 + temp1;
c1 = -(1.0 / temp1 - 2.0 + temp1) / temp2;
c2 = -2.0 * (temp1 - 1.0 / temp1) / temp2;
c3 = 4.0 * (temp1 + 1.0 / temp1) / temp2;
size_t dx, dy;
// Setting ABC for top
for (dx = 0; dx < spacex; dx++){
EM.Ez(dx, spacey - 1) = c1 * (EM.Ez(dx, spacey - 3) + EM.Etop(0, 1, dx))
+ c2 * (EM.Etop(0, 0, dx) + EM.Etop(2, 0 , dx)
-EM.Ez(dx,spacey - 2) -EM.Etop(1, 1, dx))
+ c3 * EM.Etop(1, 0, dx) - EM.Etop(2, 1, dx);
// memorizing fields...
for (dy = 0; dy < 3; dy++){
EM.Etop(dy, 1, dx) = EM.Etop(dy, 0, dx);
EM.Etop(dy, 0, dx) = EM.Ez(dx, spacey - 1 - dy);
}
}
// Setting ABC for bottom
for (dx = 0; dx < spacex; dx++){
EM.Ez(dx,0) = c1 * (EM.Ez(dx, 2) + EM.Ebot(0, 1, dx))
+ c2 * (EM.Ebot(0, 0, dx) + EM.Ebot(2, 0 , dx)
-EM.Ez(dx,1) -EM.Ebot(1, 1, dx))
+ c3 * EM.Ebot(1, 0, dx) - EM.Ebot(2, 1, dx);
// memorizing fields...
for (dy = 0; dy < 3; dy++){
EM.Ebot(dy, 1, dx) = EM.Ebot(dy, 0, dx);
EM.Ebot(dy, 0, dx) = EM.Ez(dx, dy);
}
}
// ABC on right
for (dy = 0; dy < spacey; dy++){
EM.Ez(spacex - 1,dy) = c1 * (EM.Ez(spacex - 3,dy) + EM.Eright(0, 1, dy))
+ c2 * (EM.Eright(0, 0, dy) + EM.Eright(2, 0 , dy)
-EM.Ez(spacex - 2,dy) -EM.Eright(1, 1, dy))
+ c3 * EM.Eright(1, 0, dy) - EM.Eright(2, 1, dy);
// memorizing fields...
for (dx = 0; dx < 3; dx++){
EM.Eright(dx, 1, dy) = EM.Eright(dx, 0, dy);
EM.Eright(dx, 0, dy) = EM.Ez(spacex - 1 - dx, dy);
}
}
// Setting ABC for left side of grid. Woo!
for (dy = 0; dy < spacey; dy++){
EM.Ez(0,dy) = c1 * (EM.Ez(2,dy) + EM.Eleft(0, 1, dy))
+ c2 * (EM.Eleft(0, 0, dy) + EM.Eleft(2, 0 , dy)
-EM.Ez(1,dy) -EM.Eleft(1, 1, dy))
+ c3 * EM.Eleft(1, 0, dy) - EM.Eleft(2, 1, dy);
// memorizing fields...
for (dx = 0; dx < 3; dx++){
EM.Eleft(dx, 1, dy) = EM.Eleft(dx, 0, dy);
EM.Eleft(dx, 0, dy) = EM.Ez(dx, dy);
}
}
// return EM;
}
// Creating loss
void createloss2d(Loss &lass, double eps, double Cour,
double loss){
double radius = 400;
int sourcex = 450, sourcex2 = 250;
int sourcey = 750, sourcey2 = 100;
double dist, var, Q, epsp, mup, dist2, var_old;
double cutoff = 1.5;
for (size_t dx = 0; dx < spacex; dx++){
for (size_t dy = 0; dy < spacey; dy++){
dist = sqrt((dx - sourcex)*(dx - sourcex)
+ (dy - sourcey)*(dy - sourcey));
dist2 = sqrt((dx - sourcex2)*(dx - sourcex2)
+ (dy - sourcey2)*(dy - sourcey2));
// if (dx > 100 && dx < 150 && dy > 75 && dy < 125){
if (dist < radius){
// if (dist > 100000000){
Q = cbrt(-(radius / dist) + sqrt((radius/dist)
* (radius/dist) + (1.0/27.0)));
var = (Q - (1.0 / (3.0 * Q))) * (Q - (1.0 / (3.0 * Q)));
// var = radius / dist;
// var = 1.1;
if (abs(var - var_old) > cutoff){
var = var_old;
}
if (var > 10){
var = 10;
}
if (isnan(var)){
var = var_old;
}
epsp = eps / (var * var);
mup = 1 / (var * var);
/*
lass.EzH(dx, dy) = Cour * eps;
lass.EzE(dx, dy) = 1.0;
lass.HyH(dx, dy) = 1.0;
lass.HyE(dx, dy) = Cour / eps;
lass.HxE(dx, dy) = Cour / eps;
lass.HxH(dx, dy) = 1.0;
*/
lass.EzH(dx, dy) = Cour * epsp /(1.0 - loss);
lass.EzE(dx, dy) = (1.0 - loss) / (1.0 + loss);
lass.HyH(dx, dy) = (1.0 - loss) / (1.0 + loss);
lass.HyE(dx, dy) = Cour * (mup / eps) / (1.0 + loss);
lass.HxE(dx, dy) = Cour * (mup / eps) / (1.0 + loss);
lass.HxH(dx, dy) = (1.0 - loss) / (1.0 + loss);
/*
// PEC stuff
lass.EzH(dx, dy) = 0;
lass.EzE(dx, dy) = 0;
lass.HyH(dx, dy) = 0;
lass.HyE(dx, dy) = 0;
lass.HxE(dx, dy) = 0;
lass.HxH(dx, dy) = 0;
*/
var_old = var;
}
else{
/*
lass.EzH(dx, dy) = Cour * eps;
lass.EzE(dx, dy) = 1.0;
lass.HyH(dx, dy) = 1.0;
lass.HyE(dx, dy) = Cour / eps;
lass.HxE(dx, dy) = Cour / eps;
lass.HxH(dx, dy) = 1.0;
lass.EzH(dx, dy) = Cour * eps /(1.0 - loss);
lass.EzE(dx, dy) = (1.0 - loss) / (1.0 + loss);
lass.HyH(dx, dy) = (1.0 - loss) / (1.0 + loss);
lass.HyE(dx, dy) = Cour * (1.0 / eps) / (1.0 + loss);
lass.HxE(dx, dy) = Cour * (1.0 / eps) / (1.0 + loss);
lass.HxH(dx, dy) = (1.0 - loss) / (1.0 + loss);
*/
lass.EzH(dx, dy) = Cour * eps;
lass.EzE(dx, dy) = 1.0;
lass.HyH(dx, dy) = 1.0;
lass.HyE(dx, dy) = Cour * (1.0 / eps);
lass.HxE(dx, dy) = Cour * (1.0 / eps);
lass.HxH(dx, dy) = 1.0;
}
}
}
//return lass;
}
// Creating loss
Loss createloss2d(Loss lass, double eps, double Cour, double loss){
double radius = 40;
int sourcex = 200, sourcex2 = 100;
int sourcey = 100, sourcey2 = 100;
double dist, var, Q, epsp, mup, dist2;
for (size_t dx = 0; dx < spacex; dx++){
for (size_t dy = 0; dy < spacey; dy++){
dist = sqrt((dx - sourcex)*(dx - sourcex)
+ (dy - sourcey)*(dy - sourcey));
dist2 = sqrt((dx - sourcex2)*(dx - sourcex2)
+ (dy - sourcey2)*(dy - sourcey2));
// if (dx > 100 && dx < 150 && dy > 75 && dy < 125){
if (dist < radius){
Q = cbrt(-(radius / dist) + sqrt((radius/dist)
* (radius/dist) + (1.0/27.0)));
var = (Q - (1.0 / (3.0 * Q))) * (Q - (1.0/ (3.0 * Q)));
// var = 1.4;
if (abs(var) > 1000){
var = 1000;
}
if (isnan(var)){
var = 1000;
}
epsp = eps / (var * var);
mup = 1 / (var * var);
lass.ExH(dx, dy) = Cour * epsp /(1.0 - loss);
lass.ExE(dx, dy) = (1.0 - loss) / (1.0 + loss);
lass.EyE(dx, dy) = (1.0 - loss) / (1.0 + loss);
lass.EyH(dx, dy) = Cour * epsp / (1.0 + loss);
lass.HzE(dx, dy) = Cour * (mup / eps) / (1.0 + loss);
lass.HzH(dx, dy) = (1.0 - loss) / (1.0 + loss);
/*
// PEC stuff -- not complete!
lass.ExH(dx, dy) = 0;
lass.ExE(dx, dy) = 0;
lass.HzH(dx, dy) = 0;
lass.HzE(dx, dy) = 0;
lass.ExE(dx, dy) = 0;
lass.ExH(dx, dy) = 0;
*/
}
else{
lass.ExH(dx, dy) = Cour * eps;
lass.ExE(dx, dy) = 1.0;
lass.EyE(dx, dy) = 1.0;
lass.EyH(dx, dy) = Cour * eps;
lass.HzE(dx, dy) = Cour / eps;
lass.HzH(dx, dy) = 1.0;
}
}
}
return lass;
}