void laplace2d() {
double nx = 31;
double ny = 31;
double c = 1;
double dx = 2/(nx-1);
double dy = 2/(ny-1);
double linorm_target = .01;
double linorm = 1;
// Make an output folder
std::string dir = "step9/";
Eigen::ArrayXd x; // Array containing our x values
x.setLinSpaced(nx,0,2); // Array is linearly spaced values from 0 to 2
Eigen::ArrayXd y; // Array containing our x values
y.setLinSpaced(ny,0,1);
// Arrays containing our calculated values
Eigen::ArrayXXd p;
Eigen::ArrayXXd pn;
// Initial Conditions
p.setZero(ny,nx);
pn.setZero(ny,nx);
//Set Boundary Conditions
p.block(0,0,ny,1) = Eigen::ArrayXXd::Constant(ny,1,0);
p.block(0,nx-1,ny,1) = y.block(0,0,ny,1);
p.block(0,0,1,nx) = p.block(1,0,1,nx);
p.block(ny-1,0,1,nx) = p.block(ny-2,0,1,nx);
while(linorm>linorm_target)
{
pn << p;
p.block(1,1,ny-2,nx-2) = (pow(dy,2)*(pn.block(2,1,ny-2,nx-2)+pn.block(0,1,ny-2,nx-2))+pow(dx,2)*(pn.block(1,2,ny-2,nx-2)+pn.block(1,0,ny-2,nx-2)))/(2*(pow(dx,2)+pow(dy,2)));
p(0,0) = (pow(dy,2)*(pn(1,0)+pn(ny-1,0))+pow(dx,2)*(pn(0,1)+pn(0,nx-1)))/(2*(pow(dx,2)+pow(dy,2)));
p(ny-1,nx-1) = (pow(dy,2)*(pn(0,nx-1)+pn(ny-2,nx-1))+pow(dx,2)*(pn(ny-1,0)+pn(ny-1,nx-2)))/(2*(pow(dx,2)+pow(dy,2)));
//Set Boundary Conditions
p.block(0,0,ny,1) = Eigen::ArrayXXd::Constant(ny,1,0);
p.block(0,nx-1,ny,1) = y.block(0,0,ny,1);
p.block(0,0,1,nx) = p.block(1,0,1,nx);
p.block(ny-1,0,1,nx) = p.block(ny-2,0,1,nx);
linorm = (p.cwiseAbs()-pn.cwiseAbs()).sum()/(pn.cwiseAbs()).sum();
}
ofstream writexdata((dir + "output.dat").c_str(), ios::out | ios::trunc);
writexdata << p << endl;
writexdata.close();
}
// apply the distmesh algorithm
std::tuple<Eigen::ArrayXXd, Eigen::ArrayXXi> distmesh::distmesh(
Functional const& distanceFunction, double const initialPointDistance,
Functional const& elementSizeFunction, Eigen::Ref<Eigen::ArrayXXd const> const boundingBox,
Eigen::Ref<Eigen::ArrayXXd const> const fixedPoints) {
// determine dimension of mesh
unsigned const dimension = boundingBox.cols();
// create initial distribution in bounding box
Eigen::ArrayXXd points = utils::createInitialPoints(distanceFunction,
initialPointDistance, elementSizeFunction, boundingBox, fixedPoints);
// create initial triangulation
Eigen::ArrayXXi triangulation = triangulation::delaunay(points);
// create buffer to store old point locations to calculate
// retriangulation and stop criterion
Eigen::ArrayXXd retriangulationCriterionBuffer = Eigen::ArrayXXd::Constant(
points.rows(), points.cols(), INFINITY);
Eigen::ArrayXXd stopCriterionBuffer = Eigen::ArrayXXd::Zero(
points.rows(), points.cols());
// main distmesh loop
Eigen::ArrayXXi edgeIndices;
for (unsigned step = 0; step < constants::maxSteps; ++step) {
// retriangulate if point movement is above threshold
if ((points - retriangulationCriterionBuffer).square().rowwise().sum().sqrt().maxCoeff() >
constants::retriangulationThreshold * initialPointDistance) {
// update triangulation
triangulation = triangulation::delaunay(points);
// reject triangles with circumcenter outside of the region
Eigen::ArrayXXd circumcenter = Eigen::ArrayXXd::Zero(triangulation.rows(), dimension);
for (int point = 0; point < triangulation.cols(); ++point) {
circumcenter += utils::selectIndexedArrayElements<double>(
points, triangulation.col(point)) / triangulation.cols();
}
triangulation = utils::selectMaskedArrayElements<int>(triangulation,
distanceFunction(circumcenter) < -constants::geometryEvaluationThreshold * initialPointDistance);
// find unique edge indices
edgeIndices = utils::findUniqueEdges(triangulation);
// store current points positions
retriangulationCriterionBuffer = points;
}
// calculate edge vectors and their length
auto const edgeVector = (utils::selectIndexedArrayElements<double>(points, edgeIndices.col(0)) -
utils::selectIndexedArrayElements<double>(points, edgeIndices.col(1))).eval();
auto const edgeLength = edgeVector.square().rowwise().sum().sqrt().eval();
// evaluate elementSizeFunction at midpoints of edges
auto const desiredElementSize = elementSizeFunction(0.5 *
(utils::selectIndexedArrayElements<double>(points, edgeIndices.col(0)) +
utils::selectIndexedArrayElements<double>(points, edgeIndices.col(1)))).eval();
// calculate desired edge length
auto const desiredEdgeLength = (desiredElementSize * (1.0 + 0.4 / std::pow(2.0, dimension - 1)) *
std::pow((edgeLength.pow(dimension).sum() / desiredElementSize.pow(dimension).sum()),
1.0 / dimension)).eval();
// calculate force vector for each edge
auto const forceVector = (edgeVector.colwise() *
((desiredEdgeLength - edgeLength) / edgeLength).max(0.0)).eval();
// store current points positions
stopCriterionBuffer = points;
// move points
for (int edge = 0; edge < edgeIndices.rows(); ++edge) {
if (edgeIndices(edge, 0) >= fixedPoints.rows()) {
points.row(edgeIndices(edge, 0)) += constants::deltaT * forceVector.row(edge);
}
if (edgeIndices(edge, 1) >= fixedPoints.rows()) {
points.row(edgeIndices(edge, 1)) -= constants::deltaT * forceVector.row(edge);
}
}
// project points outside of domain to boundary
utils::projectPointsToBoundary(distanceFunction, initialPointDistance, points);
// stop, when maximum points movement is below threshold
if ((points - stopCriterionBuffer).square().rowwise().sum().sqrt().maxCoeff() <
constants::pointsMovementThreshold * initialPointDistance) {
break;
}
}
return std::make_tuple(points, triangulation);
}
int main()
{
//initialisation
Eigen::ArrayXXd R = Eigen::ArrayXXd::Zero(FEATURE_SIZE, NO_OF_POSTAGS); //matrix R, dimension: Nf x Nw
std::default_random_engine generator;
std::normal_distribution<double> distr(0.0, 0.1);
//initialise the matrix R with small, random, non-zero numbers
for (int i = 0; i < R.rows(); i++) {
for (int j = 0; j < R.cols(); j++) {
double d = distr(generator);
//avoid having 0's as the weight, try to get all the coefficients initialised with small numbers
while (d == 0.0) {
d = distr(generator);
}
R(i, j) = d;
}
}
//initialise the matrix Q, of size feature_size x (no_of_postags * no_of_distance)
Eigen::ArrayXXd Q = Eigen::ArrayXXd::Zero(FEATURE_SIZE, NO_OF_POSTAGS);
for (int i = 0; i < Q.rows(); i++) {
for (int j = 0; j < Q.cols(); j++) {
double d = distr(generator);
//avoid having 0's as the weight, try to get all the coefficients initialised with small numbers
while (d == 0.0) {
d = distr(generator);
}
Q(i, j) = d;
}
}
//create an array of Ci (where each Ci is a matrix of Nf x Nf that governs the interaction between the ith feature and vn)
std::vector<Eigen::ArrayXXd> Ci;
for (int i = 0; i < 5; i++) {
Eigen::ArrayXXd Ci_temp = Eigen::ArrayXXd::Zero(FEATURE_SIZE, FEATURE_SIZE);
std::default_random_engine generator;
std::normal_distribution<double> distr(0.0, 0.1);
for (int j = 0; j < Ci_temp.rows(); j++) {
for (int k = 0; k < Ci_temp.cols(); k++) {
double d = distr(generator);
//avoid having 0's as the weight, try to get all the coefficients initialised with small numbers
while (d == 0.0) {
d = distr(generator);
}
Ci_temp(j, k) = d;
}
}
Ci.push_back(Ci_temp);
}
//initialise vi. We use a context of 5 (the postag of the head itself, the postag before the modifier, the postag after the modifier, the postag before the head, and the postag after the head)
//initialise vn. Both vi and vn are column vectors with all 0's and a single 1, which indicates the POS-tag we desire to get
//FOR NOW, we ignore the term br^transpose * R^transpose*vn, but find out what it is
//initialise the bias term bv
Eigen::ArrayXd bv;
//print the array of biases into an external file
std::ofstream final_postag_bias("final_postag_bias.txt");
if (!final_postag_bias.is_open()) {
std::cout << "fail to create final postag bias file" << std::endl;
}
/*std::map<std::string, int> big_pos_tag_map = get_postag_bias(bv, "distance_count.txt", "fine_pos_tags.txt");
std::cout << "size of big pos tag map = " << big_pos_tag_map.size() << std::endl;
for (std::map<std::string, int>::iterator it = big_pos_tag_map.begin(); it != big_pos_tag_map.end(); it++) {
final_postag_bias << "Pos tag " << it->first << " has bias value " << bv(it->second) << std::endl;
} */
/* create a pair between each "target pos tag" with a bias value (tested and correct)*/
//Eigen::ArrayXd word_bias_pair = Eigen::ArrayXd::Zero(NO_OF_POSTAGS_WITHOUT_DUMMY * NO_OF_DISTANCE);
int i_3 = -1;
std::ifstream fine_pos_tags("fine_pos_tags.txt");
std::string temp_string;
/*
while (getline(fine_pos_tags, temp_string)) {
for (int i = -MAX_DISTANCE; i <= MAX_DISTANCE; i++) {
if (i != 0) {
if (i == -49 || i == -45 || i == -40 || i == -35 || i == -30 || i == -25 || i == -20 || i == -15 || i == -10 || i == -5 || i == -4 || i == -3 || i == -2 || i == -1 || i == 1 || i == 2 || i == 3 || i == 4 || i == 5 || i == 6 || i == 11 || i == 16 || i == 21 || i == 26 || i == 31 || i == 36|| i == 41 || i == 46) {
i_3++;
std::stringstream sstm;
sstm << temp_string << i;
if (big_pos_tag_map.find(sstm.str()) == big_pos_tag_map.end()) {
std::cout << "ERROR" << std::endl;
} else {
int pos_tag_idx = big_pos_tag_map[sstm.str()];
//word_bias_pair(i_3) = bv(pos_tag_idx);
}
}
}
}
} */
/* end */
//main training part
std::map<std::string, int> mapping = postag_mapping("fine_pos_tags.txt");
fine_pos_tags.close();
//print out both the small and big mapping
//std::ofstream big_pos_tag_mapping("big_pos_tag_map.txt");
std::ofstream small_pos_tag_mapping("small_pos_tag_map.txt");
/*
for (std::map<std::string, int>::iterator it = big_pos_tag_map.begin(); it != big_pos_tag_map.end(); it++) {
big_pos_tag_mapping << it->first << " " << it->second << std::endl;
} */
for (std::map<std::string, int>::iterator it = mapping.begin(); it != mapping.end(); it++) {
small_pos_tag_mapping << it->first << " " << it->second << std::endl;
}
small_pos_tag_mapping.close();
//create the pairs
std::ifstream pairs ("real_pairs_medium.txt");
//initialise the gradient matrix
std::vector<Eigen::MatrixXd> dCi;
for (int i = 0; i < 5; i++) {
Eigen::MatrixXd temp = Eigen::MatrixXd::Zero(FEATURE_SIZE, FEATURE_SIZE);
dCi.push_back(temp);
}
Eigen::MatrixXd dR = Eigen::MatrixXd::Zero(FEATURE_SIZE, NO_OF_POSTAGS);
Eigen::MatrixXd dQ = Eigen::MatrixXd::Zero(FEATURE_SIZE, NO_OF_POSTAGS);
std::ofstream parameters ("parameters_each_epoch_small_trial_1_check_R.txt");
if (!parameters.is_open()) {
std::cout << "Error: output file not opening" << std::endl;
}
//initialise all the temporary variables outside the loop to save time on memory allocation on the heap (expensive)
//all these temporary variables are reset to zero using .setZero() method at the end of each loop
Eigen::MatrixXd tempC = Eigen::MatrixXd::Zero(FEATURE_SIZE, FEATURE_SIZE);
Eigen::MatrixXd temp_R_Model = Eigen::MatrixXd::Zero(FEATURE_SIZE, NO_OF_POSTAGS);
Eigen::MatrixXd temp_R_Data = Eigen::MatrixXd::Zero(FEATURE_SIZE, NO_OF_POSTAGS);
Eigen::MatrixXd temp_Q = Eigen::MatrixXd::Zero(FEATURE_SIZE, NO_OF_POSTAGS);
Eigen::MatrixXd temp_Q_Model = Eigen::MatrixXd::Zero(FEATURE_SIZE, NO_OF_POSTAGS);
Eigen::MatrixXd temp_Q_Data = Eigen::MatrixXd::Zero(FEATURE_SIZE, NO_OF_POSTAGS);
Eigen::VectorXd temp_Qw = Eigen::VectorXd::Zero(FEATURE_SIZE);
//Eigen::VectorXd dbias = Eigen::VectorXd::Zero(NO_OF_POSTAGS_WITHOUT_DUMMY * NO_OF_DISTANCE);
//Eigen::VectorXd temp_dbias = Eigen::VectorXd::Zero(NO_OF_POSTAGS_WITHOUT_DUMMY * NO_OF_DISTANCE);
Eigen::VectorXd tempCr = Eigen::VectorXd::Zero(FEATURE_SIZE);
Eigen::ArrayXd temp_e = Eigen::ArrayXd::Zero(NO_OF_POSTAGS);
/*
Eigen::MatrixXd temp_matrix = Eigen::MatrixXd::Zero(NO_OF_POSTAGS, FEATURE_SIZE);
Eigen::MatrixXd temp_matrix_2 = Eigen::MatrixXd::Zero(NO_OF_POSTAGS, FEATURE_SIZE); */
//calculate the normalising constant for the first time
std::ofstream gradient_check_R("gradient_check_R_big.txt");
Eigen::MatrixXd curr_dR = Eigen::MatrixXd::Zero(FEATURE_SIZE, NO_OF_POSTAGS); //DELETE THIS LATER
int no_of_iter = 0;
for (int i = 0; i < NO_OF_EPOCH; i++) {
if (!pairs.is_open()) {
std::cout << "Fail to open input file" << std::endl;
} else {
std::vector<std::string> temp;
std::string line;
while (getline(pairs, line)) {
if (line.size() > 1) {
no_of_iter++;
temp = split(line, ' ');
//initialise an array with the elements as the indices of: postag of the modifier, postag of the head, postag of before modifier, postag of after modifier, postag of before head, postag of after head
int arr_temp[6] = {mapping[temp[0]], mapping[temp[1]], mapping[temp[2]], mapping[temp[3]], mapping[temp[4]], mapping[temp[5]]};
if (no_of_iter % 10000 == 0) {
std::cout << no_of_iter << std::endl;
}
//calculate the normalising constant
double normalising_constant = 0.0;
for (int iter2 = 0; iter2 < 5; iter2++) {
tempCr += (Ci[iter2].matrix() * R.col(arr_temp[iter2+1]).matrix()); //prediction
}
for (int iter = 0; iter < Q.cols(); iter++) {
double temp = exp((tempCr.transpose() * Q.col(iter).matrix()));//dot product
temp_e(iter) = temp;
normalising_constant += temp;
}
//calculate all the gradient changes for each of the Ci, from dCi[0] to dCi[4]
//this operation is already efficient
for (int j = 0; j < 5; j++) {
for (int k = 0; k < Q.cols(); k++) {
tempC += (temp_e(k) * (Q.col(k).matrix() * R.col(arr_temp[j+1]).transpose().matrix()));
}
//normalise
tempC /= normalising_constant;
dCi[j] += (Q.col(arr_temp[0]).matrix() * R.col(arr_temp[j+1]).transpose().matrix() - tempC);
//reset the matrix tempC to prepare to calculate the next dCi[j]
tempC.setZero();
}
//calculate dQ VERIFY
for (int j = 0; j < 5; j++) {
temp_Qw += (Ci[j].matrix() * R.col(arr_temp[j+1]).matrix());
}
for (int j = 0; j < Q.cols(); j++) {
temp_Q_Model.col(j) += (temp_e(j) * temp_Qw);
}
temp_Q_Model /= normalising_constant;
temp_Q_Data.col(arr_temp[0]) = temp_Qw;
dQ += (temp_Q_Data - temp_Q_Model);
temp_Qw.setZero();
temp_Q_Model.setZero();
temp_Q_Data.setZero();
//calculate dR
//calculate dR with respect to data
for (int j = 0; j < 5; j++) {
temp_R_Data.col(arr_temp[j+1]) += Ci[j].transpose().matrix() * Q.col(arr_temp[0]).matrix();
}
//calculate dR with respect to model
for (int k = 0; k < Q.cols(); k++) {
for (int j = 0; j < 5; j++) {
temp_R_Model.col(arr_temp[j+1]) += (temp_e(k) * (Ci[j].transpose().matrix() * Q.col(k).matrix()));
}
}
temp_R_Model /= normalising_constant;
dR += (temp_R_Data - temp_R_Model);
if (no_of_iter % 1000 == 0) {
curr_dR = temp_R_Data - temp_R_Model;
}
temp_R_Data.setZero();
temp_R_Model.setZero();
//calculate dbias
//temp_dbias(arr_temp[0]) = 1.0;
//dbias += (temp_dbias - temp_e.matrix() / normalising_constant);
//temp_dbias(arr_temp[0]) = 0.0;
tempCr.setZero();
temp_e.setZero();
if (no_of_iter % 1000 == 0) {
Eigen::VectorXd temp = Eigen::VectorXd::Zero(FEATURE_SIZE);
gradient_check_R << "current data point = " << no_of_iter <<std::endl;
for (int j = 0; j < R.rows(); j++) {
for (int k = 0; k < R.cols(); k++) {
Eigen::ArrayXXd R_copy = R;
double result_1 = 0.0;
double result_2 = 0.0;
double temp_double = 0.0;
gradient_check_R << curr_dR(j, k) << " ";
R_copy(j, k) += EPSILON;
for (int iter2 = 0; iter2 < 5; iter2++) {
temp += (Ci[iter2].matrix() * R_copy.col(arr_temp[iter2+1]).matrix());
}
result_1 += temp.transpose() * Q.col(arr_temp[0]).matrix();
for (int l = 0; l < Q.cols(); l++) {
temp_double += exp(temp.transpose() * Q.col(l).matrix());
}
result_1 -= log(temp_double);
temp_double = 0.0;
//calculate result_2
R_copy(j, k) -= (2 * EPSILON);
temp.setZero();
for (int iter2 = 0; iter2 < 5; iter2++) {
temp += (Ci[iter2].matrix() * R_copy.col(arr_temp[iter2 + 1]).matrix());
}
result_2 += temp.transpose() * Q.col(arr_temp[0]).matrix();
for (int l = 0; l < Q.cols(); l++) {
temp_double += exp(temp.transpose() * Q.col(l).matrix());
}
result_2 -= log(temp_double);
temp.setZero();
gradient_check_R << (result_1 - result_2) / (2 * EPSILON) << std::endl;
}
}
curr_dR.setZero();
}
//update the gradient if no_of_iter mod mini batch size == 0, reset the gradient matrix to 0
if (no_of_iter % BATCH_SIZE == 0) {
double curr_learning_rate = LEARNING_RATE / (1 + no_of_iter * LEARNING_DECAY);
for (int j = 0; j < 5; j++) {
Ci[j] = Ci[j].matrix() + curr_learning_rate * dCi[j];
//reset the matrix dCi[j]
dCi[j].setZero();
}
//word_bias_pair = word_bias_pair + curr_learning_rate * dbias.array();
R = R.matrix() + curr_learning_rate * dR;
Q = Q.matrix() + curr_learning_rate * dQ;
dR.setZero();
dQ.setZero();
//dbias.setZero();
}
}
temp.clear();
}
pairs.close();
}
parameters << "Epoch number: " << i+1 << std::endl;
for (int j = 0; j < 5; j++) {
parameters << "Matrix C" << j+1 << std::endl;
parameters << Ci[j] << std::endl;
parameters << std::endl;
parameters << "End of matrix C" << j+1 << std::endl;
}
parameters << "Matrix R" << std::endl;
parameters << R << std::endl;
parameters << "End of matrix R" << std::endl;
parameters << "Matrix Q" << std::endl;
parameters << Q << std::endl;
parameters << "End of matrix Q" << std::endl;
//parameters << "Bias vector" << std::endl;
//parameters << word_bias_pair << std::endl;
//parameters << "End of bias vector" << std::endl;
pairs.open("real_pairs_medium.txt");
}
pairs.close();
parameters.close();
return 0;
}