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cheby.cc
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cheby.cc
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// chebyschev bound code
#include <cmath>
#include <limits>
#include <iostream>
#include <fstream>
#include "cheby.h"
using namespace std;
// Function to find mean.
double mean(vector<double> &values) {
double n = values.size();
double sum = 0.0;
for(int i = 0; i < n; i++) {
sum = sum + values[i];
}
return sum / n;
}
double std_dev(vector <double> &values, double mean) {
double n = values.size();
double std_dev = 0.0;
for(int i = 0; i < n; i++) {
std_dev += pow(values[i] - mean, 2);
}
return sqrt(std_dev / n);
}
double interpolate(vector<double> &xData, vector<double> &yData, double x, bool extrapolate) {
int size = xData.size();
double x1;
double y1;
double x2;
double y2;
// find value of i such that x lies between points at indices i and i+1 of xData
for (int i = 0; i < size; i++) {
// if we exceed the range in xData, return -1
if (i == size - 1) return -1;
if ((x >= xData[i] && x <= xData[i+1]) || (x <= xData[i] && x >= xData[i+1])) {
x1 = xData[i];
y1 = yData[i];
x2 = xData[i+1];
y2 = yData[i+1];
break;
}
}
// gradient
double dydx = (y2 - y1) / (x2 - x1);
// linear interpolation
return y2 + dydx * (x - x1);
}
double calculate_sample_lambda(int N, double bound) {
for (double l = (sqrt(1.0/bound)); l <= N; l += 0.01) {
double a = (1.0/(N + 1.0));
double b = (N + 1)*((pow(N,2)) - 1 + N*(pow(l,2)));
double c = pow(N,2)*pow(l,2);
if (a*floor(b/c) < bound) {
return l;
}
}
return 0.0;
}
vector <vector <double> > chebyshev(vector <vector <double> > &X_vals, vector <vector <double> > &Y_vals, double confidence, double step) {
int n = X_vals.size();
// create vector of values interpolating each point
double max_val = fmax(pv_max, cells_max * kWh_in_one_cell);
// step size of chebyshev curve
//double step = 0.2;
double lambda = calculate_sample_lambda(n, 1 - confidence);
vector <double> cheby_X;
vector <double> cheby_Y;
for (double X_val = 0.0; X_val <= max_val; X_val += step) {
vector <double> Y_set;
// find value of Y at X_val for every curve
for (int trace = 0; trace < X_vals.size(); trace++) {
double interpolated_Y = interpolate(X_vals[trace], Y_vals[trace], X_val, false);
if (interpolated_Y >= 0) {
Y_set.push_back(interpolated_Y);
}
else {
// as soon as a single curve is not added, break out of the loop because we dont care about
// these values anymore.
//cout << "trace " << trace << " didnt have a value for x=" << X_val << endl;
break;
}
}
// count it only if every curve had an interpolation value for X_val
if (Y_set.size() == X_vals.size()) {
double Y_mean = mean(Y_set);
double Y_std = std_dev(Y_set, Y_mean);
cheby_X.push_back(X_val);
cheby_Y.push_back(lambda*Y_std + Y_mean);
//cout << X_val << " " << lambda*Y_std + Y_mean << endl;
}
}
vector <vector <double> > return_vector(2);
return_vector[0] = cheby_X;
return_vector[1] = cheby_Y;
return return_vector;
}
SimulationResult calculate_sample_bound(vector < vector <SimulationResult> > &sizing_curves, double epsilon, double confidence) {
int n = sizing_curves.size();
#ifdef DEBUG
cout << "calculate_sample_bound: sizing_curve.size() = " << n << ", epsilon = " << epsilon << ", confidence = " << confidence << endl;
#endif
// create arrays for all B and C values
vector < vector <double> > B_values(n);
vector < vector <double> > C_values(n);
for (int i = 0; i < n; ++i) {
int n_curve = sizing_curves[i].size();
vector <double> Bs;
vector <double> Cs;
double last_B = -1, last_C = -1;
for (auto& sim_result: sizing_curves[i]) {
//if (sim_result.B != last_B && sim_result.C != last_C) {
Bs.push_back(sim_result.B);
Cs.push_back(sim_result.C);
//last_B = sim_result.B;
//last_C = sim_result.C;
//}
}
B_values[i] = Bs;
C_values[i] = Cs;
}
vector <vector <double> > cheby_on_B = chebyshev(C_values, B_values, confidence, cells_step*kWh_in_one_cell);
vector <vector <double> > cheby_on_C = chebyshev(B_values, C_values, confidence, pv_step);
#ifdef DEBUG
// print chebyshev curves to files.
cout << "DEBUG: cheby_on_C" << endl;
cout << cheby_on_C[0].size() << endl;
for (int i = 0; i < cheby_on_C[0].size(); i++) {
cout << cheby_on_C[0][i] << "\t" << cheby_on_C[1][i] << endl;
}
cout << "DEBUG: cheby_on_B" << endl;
cout << cheby_on_B[0].size() << endl;
for (int i = 0; i < cheby_on_B[0].size(); i++) {
cout << cheby_on_B[1][i] << "\t" << cheby_on_B[0][i] << endl;
}
#endif
// search the upper envelope for the cheapest system
double lowest_cost = numeric_limits<double>::infinity();
double lowest_B;
double lowest_C;
for (double B_val = 0.0; B_val <= cells_max * kWh_in_one_cell; B_val += cells_step * kWh_in_one_cell) {
double C1 = interpolate(cheby_on_B[1], cheby_on_B[0], B_val, false);
double C2 = interpolate(cheby_on_C[0], cheby_on_C[1], B_val, false);
if (C1 < 0 || C2 < 0) {
continue;
}
double C_max = fmax(C1, C2);
// ensure this value is on the search grid by rounding up to the nearest pv_step value
if (fmod(C_max, pv_step) != 0) {
C_max = C_max - fmod(C_max, pv_step) + pv_step;
}
double cost = B_inv * (B_val / kWh_in_one_cell) + PV_inv * C_max;
if (cost < lowest_cost) {
lowest_cost = cost;
lowest_B = B_val;
lowest_C = C_max;
// cout << lowest_B << " " << lowest_C << " " << lowest_cost << endl;
}
}
return SimulationResult(lowest_B, lowest_C, lowest_cost);
}