inline
arma::vec
numerical_gradient(const arma::vec& vals_inp, const double* step_size_inp, std::function<double (const arma::vec& vals_inp, arma::vec* grad_out, void* objfn_data)> objfn, void* objfn_data)
{
const size_t n_vals = vals_inp.n_elem;
const double step_size = (step_size_inp) ? *step_size_inp : 1e-04;
const double mach_eps = std::numeric_limits<double>::epsilon();
const arma::vec step_vec = arma::max(arma::abs(vals_inp), std::sqrt(step_size)*arma::ones(n_vals,1)) * std::pow(mach_eps,1.0/6.0);
arma::vec x_orig = vals_inp, x_term_1, x_term_2;
arma::vec grad_vec = arma::zeros(n_vals,1);
//
for (size_t i=0; i < n_vals; i++)
{
x_term_1 = x_orig;
x_term_2 = x_orig;
x_term_1(i) += step_vec(i);
x_term_2(i) -= step_vec(i);
//
double term_1 = objfn(x_term_1, nullptr, objfn_data);
double term_2 = -objfn(x_term_2, nullptr, objfn_data);
double denom_term = 2.0 * step_vec(i);
grad_vec(i) = (term_1 + term_2) / denom_term;
}
//
return grad_vec;
}
int main(void) {
printf("Loading Data ...\n");
const std::string kTrainDataFileName = "../../waterTrainData.txt";
const std::string kValDataFileName = "../../waterValData.txt";
const std::string kTestDataFileName = "../../waterTestData.txt";
DataDebug water_data(kTrainDataFileName,kValDataFileName,kTestDataFileName);
const int kTotFeatures = water_data.num_features()+1;
arma::vec theta_vec = arma::randu<arma::vec>(kTotFeatures,1);
theta_vec.zeros(kTotFeatures,1);
arma::vec gradient_vec = arma::randu<arma::vec>(kTotFeatures,1);
gradient_vec.zeros(kTotFeatures,1);
double lambda = 1.0;
LinearRegression lin_reg(theta_vec,gradient_vec,lambda);
printf("Program paused. Press enter to continue.\n");
std::cin.ignore();
// Computes cost for regularized linear regression.
std::vector<double> theta_stack_vec(kTotFeatures,1.0);
std::vector<double> grad_vec(kTotFeatures,0.0);
water_data.set_features(water_data.training_features());
water_data.set_labels(water_data.training_labels());
const double kInitCost = \
lin_reg.ComputeCost(theta_stack_vec,grad_vec,water_data);
printf("Cost at theta = [1 ; 1]: %.6f\n",kInitCost);
printf("(this value should be about 303.993192)\n");
printf("Program paused. Press enter to continue.\n");
std::cin.ignore();
// Computes gradient for regularized linear regression.
const double kReturnCode = lin_reg.ComputeGradient(water_data);
std::cout.setf(std::ios::fixed,std::ios::floatfield);
std::cout.precision(6);
printf("Gradient at theta = [1 ; 1]: \n");
lin_reg.gradient().t().raw_print(std::cout);
printf("(this value should be about [-15.303016; 598.250744])\n");
printf("Program paused. Press enter to continue.\n");
std::cin.ignore();
// Trains linear regression.
const int kReturnCode2 = lin_reg.Train(water_data);
printf("Program paused. Press enter to continue.\n");
std::cin.ignore();
// Generates values for learning curve.
const int kNumTrainEx = water_data.num_train_ex();
double *error_train = (double *)calloc(kNumTrainEx,sizeof(double));
double *error_val = (double *)calloc(kNumTrainEx,sizeof(double));
int use_poly = 0;
const int kReturnCode3 = \
LearningCurve(water_data,lin_reg,error_train,error_val,use_poly);
printf("# Training Examples\tTrain Error\tCross Validation Error\n");
for(unsigned int ex_index=0; ex_index<(unsigned int)kNumTrainEx; ex_index++)
{
printf("\t%d\t\t%.6f\t%.6f\n",ex_index+1,error_train[ex_index],\
error_val[ex_index]);
}
printf("Program paused. Press enter to continue.\n");
std::cin.ignore();
// Performs feature mapping for polynomial regression.
water_data.set_features(water_data.training_features());
const int kNumPolyFeatures = 8;
const int kReturnCode4 = water_data.PolyFeatures(kNumPolyFeatures);
const int kReturnCode5 = water_data.FeatureNormalize();
printf("Normalized Training Example 1: \n");
water_data.features_normalized().row(0).t().raw_print(std::cout);
printf("\n");
printf("Program paused. Press enter to continue.\n");
std::cin.ignore();
// Trains polynomial regression.
water_data.set_features(water_data.features_normalized());
water_data.set_labels(water_data.training_labels());
lin_reg.set_lambda(0.0);
const int kReturnCode6 = lin_reg.Train(water_data);
// Generates values for learning curve for polynomial regression.
use_poly = 1;
const int kReturnCode7 = \
LearningCurve(water_data,lin_reg,error_train,error_val,use_poly);
printf("Polynomial Regression (lambda = %.6f)\n",lin_reg.lambda());
printf("\n");
printf("# Training Examples\tTrain Error\tCross Validation Error\n");
for(unsigned int ex_index=0; ex_index<(unsigned int)kNumTrainEx; ex_index++)
{
printf("\t%d\t\t%.6f\t%.6f\n",ex_index+1,error_train[ex_index],\
error_val[ex_index]);
}
printf("Program paused. Press enter to continue.\n");
std::cin.ignore();
// Generates values for cross-validation curve for polynomial regression.
// Sets up vector of regularization parameters.
arma::rowvec lambda_vec = arma::ones<arma::rowvec>(10);
lambda_vec(0) = 0.0;
lambda_vec(1) = 0.001;
lambda_vec(2) = 0.003;
lambda_vec(3) = 0.01;
lambda_vec(4) = 0.03;
lambda_vec(5) = 0.1;
lambda_vec(6) = 0.3;
lambda_vec(7) = 1.0;
lambda_vec(8) = 3.0;
lambda_vec(9) = 10.0;
double *xval_error_train = (double *)calloc(10,sizeof(double));
double *xval_error_val = (double *)calloc(10,sizeof(double));
const int kReturnCode8 = \
ValidationCurve(water_data,lin_reg,xval_error_train,xval_error_val,lambda_vec);
printf("lambda\t\tTrain Error\tCross Validation Error\n");
for(unsigned int lambda_index=0; lambda_index<10; lambda_index++)
{
printf("%.6f\t%.6f\t%.6f\n",lambda_vec(lambda_index),\
xval_error_train[lambda_index],xval_error_val[lambda_index]);
}
printf("Program paused. Press enter to continue.\n");
std::cin.ignore();
// Frees memory.
free(error_train);
free(error_val);
free(xval_error_train);
free(xval_error_val);
return 0;
}
