- added basic optimization

SCE/SCE/DIFF.cpp

@@ -11,7 +11,7 @@ DIFF::~DIFF()
 }
 
 
-vector<long double> DIFF::diff()
+vector<long double> DIFF::diff(vector<long double> yvalues)
 {
 	vector<long double> diff = yvalues;
 	vector<long double> xdiff (diff.size()-1);
@@ -23,7 +23,7 @@ vector<long double> DIFF::diff()
 	return xdiff;
 }
 
-vector<long double> DIFF::backward_diff(vector<long double> y)
+vector<long double> DIFF::backward_diff(vector<long double> y, vector<long double> xvalues)
 {
 	vector<long double> temp;
 	temp.resize(y.size());
@@ -35,7 +35,7 @@ vector<long double> DIFF::backward_diff(vector<long double> y)
 	temp.at(y.size()-1) = 0;
 	return temp;
 }
-vector<long double> DIFF::forward_diff(vector<long double> y)
+vector<long double> DIFF::forward_diff(vector<long double> y, vector<long double> xvalues)
 {
 	vector<long double> temp;
 	temp.resize(y.size());
@@ -72,10 +72,12 @@ vector<long double> DIFF::mid_diff(vector<long double>y, vector<long double>x)
 	temp.at(i) = (y.at(i + 1) - y.at(i)) / (x.at(i + 1) - x.at(i));
 	temp.at(i) += (y.at(i + 1) - y.at(i - 1)) / (x.at(i + 1) - x.at(i - 1));
 	temp.at(i) /= 2;
+
 	for (; i < y.size() - 2; ++i)
 	{
 		temp.at(i) = (y.at(i + 1) - y.at(i - 1)) / (x.at(i + 1) - x.at(i - 1));
 	}
+
 	temp.at(i) += (y.at(i) - y.at(i - 1)) / (x.at(i) - x.at(i - 1));
 	temp.at(i) /= 2;
 	i++;

SCE/SCE/DIFF.h

@@ -5,13 +5,9 @@ using namespace std;
 class DIFF
 {
 public:
-	vector<long double> xvalues = {0, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200, 210, 220, 230, 240, 250};
+	vector<long double> diff(vector<long double>);
-	vector<long double> yvalues = {0, 2926, 10170, 21486, 33835, 45251, 55634, 65038, 73461, 80905, 87368, 92852, 97355, 100878, 103422, 104986, 106193, 110246, 119626, 136106, 162095, 199506, 238775, 277065, 314375, 350704};
+	vector<long double> forward_diff(vector<long double>, vector<long double>);
-	vector<long double> diff();
+	vector<long double> backward_diff(vector<long double>, vector<long double>);
-	
-
-	vector<long double> forward_diff(vector<long double>);
-	vector<long double> backward_diff(vector<long double>);
 	static vector<long double> central_diff(vector<long double>, vector<long double>);
 	static vector<long double> mid_diff(vector<long double>, vector<long double>);
 

SCE/SCE/SCE.cpp

@@ -3,11 +3,13 @@
 #include "lgs.h"
 #include "nlgs.h"
 #include "DIFF.h"
+#include "OPTIMIZATION.h"
 using namespace std;
 
 void cylinder();
 void lgs();
 void nlgs();
+void optimization();
 void diff();
 void print_array(long double* a, int size)
 {
@@ -37,6 +39,7 @@ int main()
 		cout << "1 Berechungen an einem Zylinder" << endl;
 		cout << "2 LGS loesen" << endl;
 		cout << "3 n.LGS loesen" << endl;
+		cout << "4 optimization" << endl;
 		cout << "5 numerische differentation" << endl;
 
 		cout << "e Beenden" << endl;
@@ -47,6 +50,7 @@ int main()
 			case '1': cylinder(); break;
 			case '2': lgs(); break;
 			case '3': nlgs(); break;
+			case '4': optimization(); break;
 			case '5': diff(); break;
 			
 			default: cout << "Okay, bye" << endl; break;
@@ -77,23 +81,75 @@ void nlgs()
 	NLGS nlgs;
 	cout << endl << "Bisektion: " << nlgs.bisektion(1,4,100) << endl;
 	cout << "Fixpunkt: " << nlgs.fixedpoint(1,100) << endl;
-	cout << "Newton: " <<nlgs.newton(1,100) << endl;
+	cout << "Newton: " << nlgs.newton(1,100) << endl;
 	cout << "skantenverfahren fehlt" << endl << endl;
 
 }
 
+void optimization()
+{
+	OPTIMIZATION opt;
+
+	long double lower_bound = -2, upper_bound = 2;		//upper / lower - _bounds instead of theta-vector
+	long double increments = 0.1;
+	
+	long double z = opt.g_von_theta(lower_bound, upper_bound);
+	long double which_theta = 1;
+
+	vector<long double> thetanew(2);
+	cout << "i" << "\t" << "z" << "\t" << "lb" << "\t" << "ub" << endl;
+
+	for(int i = 0; i < 41; i++)
+	{
+		
+		cout << i << "\t" << z << "\t" << lower_bound << "\t" << upper_bound << endl;
+		if (which_theta == 1)
+		{
+			thetanew.at(0) = lower_bound + increments;
+			thetanew.at(1) = upper_bound;
+		}
+		else
+		{
+			thetanew.at(0) = lower_bound;
+			thetanew.at(1) = upper_bound - increments;
+		}
+
+		long double znew = opt.g_von_theta(thetanew.at(0), thetanew.at(1));
+
+		if(znew > z)
+		{
+			z = znew;
+			lower_bound = thetanew.at(0);
+			upper_bound = thetanew.at(1);
+		}
+		else
+		{
+			if (which_theta == 1)
+				which_theta = 2;
+		}
+		
+	}
+	
+
+}
+
 void diff() {
 	//Plotter: https://www.desmos.com/calculator
 
 	DIFF diff;
+	vector<long double> xvalues = { 0, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200, 210, 220, 230, 240, 250 };
+	vector<long double> yvalues = { 0, 2926, 10170, 21486, 33835, 45251, 55634, 65038, 73461, 80905, 87368, 92852, 97355, 100878, 103422, 104986, 106193, 110246, 119626, 136106, 162095, 199506, 238775, 277065, 314375, 350704 };
 	vector<long double> AbfullX = {0, 5, 10, 15, 20 };
 	vector<long double> AbfullY = {1, 0.8811, 0.7366, 0.5430, 0.1698};
+
 	cout << "Erste Ableitung mit forward und backward" << endl;
-	print_array(diff.xvalues.data(), diff.forward_diff(diff.yvalues).data(), diff.xvalues.size());
+	print_array(xvalues.data(), diff.forward_diff(yvalues, xvalues).data(), xvalues.size());
-	print_array(diff.xvalues.data(), diff.central_diff(diff.yvalues, diff.xvalues).data(), diff.xvalues.size());
+	print_array(xvalues.data(), diff.central_diff(yvalues, xvalues).data(), xvalues.size());
+
 	cout << "Zweite Ableitung mit backward" << endl;
-	print_array(diff.xvalues.data(), diff.backward_diff(diff.forward_diff(diff.yvalues)).data(), diff.xvalues.size());
+	print_array(xvalues.data(), diff.backward_diff(diff.forward_diff(yvalues, xvalues), xvalues).data(), xvalues.size());
+
 	cout << "Erste Ableitung 6.1.2" << endl;
-	print_array(diff.xvalues.data(), diff.mid_diff(AbfullY, AbfullX).data(), AbfullX.size());
+	print_array(xvalues.data(), diff.mid_diff(AbfullY, AbfullX).data(), AbfullX.size());
 	
 }