Matrix
BeamEndContact3D::ExpMap(Vector th)
// this function computes the exp map of the given vector
{
double sf1;
double sf2;
double sf3;
double theta; // vector norm
Vector theta_vec(BEC3_NUM_DIM); // input vector
Matrix sk_theta(BEC3_NUM_DIM,BEC3_NUM_DIM); // skew of vector
Matrix theta_theta(BEC3_NUM_DIM,BEC3_NUM_DIM); // dyadic product of vector
Matrix Q(BEC3_NUM_DIM,BEC3_NUM_DIM); // Exonential Map Vector
// initialize theta variables
Q.Zero();
sk_theta.Zero();
theta_theta.Zero();
theta_vec = th;
theta = theta_vec.Norm();
sk_theta = GetSkew(theta_vec);
int i, j;
for (int i = 0; i<3; i++) {
for (int j = 0; j<3; j++) {
theta_theta(i,j) = theta_vec(i)*theta_vec(j);
}
}
// determine local variables
sf1 = cos(theta);
if (theta > 5.0e-3) {
sf2 = (sin(theta))/theta;
} else {
// small theta approximation
sf2 = 1.0 - theta*theta/6.0 + pow(theta,4.0)/120.0;
}
if (theta > 0.1) {
sf3 = (1.0-cos(theta))/(theta*theta);
} else {
// small theta approximation
sf3 = 0.5 - theta*theta/24.0 + pow(theta, 4.0)/720.0
-pow(theta,6.0)/40320.0 + pow(theta, 8.0)/3628800.0;
}
// compute exponental map vector
Q = sf1*mEye1 + sf2*sk_theta + sf3*theta_theta;
return Q;
}
int main(void) {
const std::string kDataFileName = "../../microChipData.txt";
DataMapped micro_chip_data(kDataFileName);
const int kNumFeatures = micro_chip_data.num_features();
arma::vec theta_vec = arma::randu<arma::vec>(kNumFeatures+1,1);
theta_vec.zeros(kNumFeatures+1,1);
arma::vec gradient_vec = arma::randu<arma::vec>(kNumFeatures+1,1);
gradient_vec.zeros(kNumFeatures+1,1);
const int kNumTrainEx = micro_chip_data.num_train_ex();
arma::vec predictions_vec = arma::randu<arma::vec>(kNumTrainEx,1);
const double kLambda = 1.0;
const int kNumIterations = 400;
RegularizedLogisticRegression reg_log_reg(kNumIterations,theta_vec,\
gradient_vec,predictions_vec,kLambda);
// Computes initial cost.
const std::vector<double> kTheta(kNumFeatures+1,0.0);
std::vector<double> grad(kNumFeatures+1,0.0);
const double kInitCost = reg_log_reg.ComputeCost(kTheta,grad,micro_chip_data);
printf("Cost at initial theta (zeros): %.6f\n",kInitCost);
printf("\n");
printf("Program paused. Press enter to continue.\n");
std::cin.ignore();
// Uses MMA algorithm to solve for optimum weights and cost.
nlopt::opt opt(nlopt::LD_MMA,kNumFeatures+1);
WrapperStruct wrap_struct;
wrap_struct.reg_log_reg = ®_log_reg;
wrap_struct.data_mapped = µ_chip_data;
opt.set_min_objective(ComputeCostWrapper,&wrap_struct);
opt.set_xtol_rel(1e-4);
std::vector<double> nlopt_theta(kNumFeatures+1,0.0);
double min_cost = 0.0;
nlopt::result nlopt_result = opt.optimize(nlopt_theta,min_cost);
for(int feature_index=0; feature_index<(kNumFeatures+1); feature_index++)
{
theta_vec(feature_index) = nlopt_theta[feature_index];
}
// Computes accuracy on training set.
const int kReturnCode2 = reg_log_reg.LabelPrediction(micro_chip_data);
const arma::vec trainingPredict = reg_log_reg.predictions();
const arma::vec trainingLabels = micro_chip_data.training_labels();
int num_train_match = 0;
for(int example_index=0; example_index<kNumTrainEx; example_index++)
{
if (trainingPredict(example_index) == trainingLabels(example_index))
{
num_train_match++;
}
}
printf("Train Accuracy: %.6f\n",(100.0*num_train_match/kNumTrainEx));
return 0;
}
