From f8033ef4acbead25cf342b85ccd9631a7a46b6e5 Mon Sep 17 00:00:00 2001
From: Patrice Matz <ofjokg@gmail.com>
Date: Thu, 7 Dec 2017 19:05:44 +0100
Subject: [PATCH] -hier haste Basedow ;P - also: differential stuff

---
 SCE/SCE/DIFF.cpp | 74 ++++++++++++++++++++++++++++++++++++++++++++++++
 SCE/SCE/DIFF.h   | 23 +++++++++++++++
 SCE/SCE/SCE.cpp  | 37 +++++++++++++++++++++++-
 SCE/SCE/nlgs.cpp | 14 ++++-----
 SCE/SCE/nlgs.h   |  6 ++--
 5 files changed, 143 insertions(+), 11 deletions(-)
 create mode 100644 SCE/SCE/DIFF.cpp
 create mode 100644 SCE/SCE/DIFF.h

diff --git a/SCE/SCE/DIFF.cpp b/SCE/SCE/DIFF.cpp
new file mode 100644
index 0000000..ec72ba2
--- /dev/null
+++ b/SCE/SCE/DIFF.cpp
@@ -0,0 +1,74 @@
+#include "DIFF.h"
+using namespace std;
+
+DIFF::DIFF()
+{
+	y1values.resize(yvalues.size());
+}
+
+
+DIFF::~DIFF()
+{
+}
+
+
+vector<long double> DIFF::diff()
+{
+	vector<long double> diff = yvalues;
+	vector<long double> xdiff (diff.size()-1);
+	for(unsigned int i = 0; i < xdiff.size(); i++)
+	{
+		xdiff.at(i) = diff.at(i+1) - diff.at(i);
+	}
+
+	return xdiff;
+}
+
+vector<long double> DIFF::forward_diff()
+{
+	for(unsigned int i=0; i < xvalues.size()-1; i++)
+	{
+		y1values.at(i) = (yvalues.at(i + 1) - yvalues.at(i)) / (xvalues.at(i + 1) - xvalues.at(i));
+	}
+	y1values.at(25) = 0;
+	return y1values;
+}
+
+vector<long double> DIFF::backward_diff()
+{
+	
+	for (unsigned int i = 1; i < xvalues.size(); i++)
+	{
+		y1values.at(i) = (yvalues.at(i) - yvalues.at(i-1)) / (xvalues.at(i) - xvalues.at(i-1));
+	}
+	y1values.at(0) = 0;
+	return y1values;
+}
+
+vector<long double> DIFF::backward_diff(vector<long double> y)
+{
+	vector<long double> temp;
+	temp.resize(y.size());
+
+	for (unsigned int i = 0; i < y.size() - 1; i++)
+	{
+		temp.at(i) = (y.at(i + 1) - y.at(i)) / (xvalues.at(i + 1) - xvalues.at(i));
+	}
+	temp.at(25) = 0;
+	return temp;
+}
+vector<long double> DIFF::forward_diff(vector<long double> y)
+{
+	vector<long double> temp;
+	temp.resize(y.size());
+
+	for (unsigned int i = 1; i < y.size(); i++)
+	{
+		temp.at(i) = (y.at(i) - y.at(i - 1)) / (xvalues.at(i) - xvalues.at(i - 1));
+	}
+	temp.at(0) = 0;
+	return temp;
+}
+
+
+
diff --git a/SCE/SCE/DIFF.h b/SCE/SCE/DIFF.h
new file mode 100644
index 0000000..6e39461
--- /dev/null
+++ b/SCE/SCE/DIFF.h
@@ -0,0 +1,23 @@
+#pragma once
+#include <vector>
+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> 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> y1values; //y-values of 1st derivative
+	vector<long double> y2values; //y-values of 2nd derivative
+	vector<long double> diff();
+	vector<long double> forward_diff();
+	vector<long double> backward_diff();
+
+	vector<long double> forward_diff(vector<long double>);
+	vector<long double> backward_diff(vector<long double>);
+
+
+	DIFF();
+	~DIFF();
+};
+
diff --git a/SCE/SCE/SCE.cpp b/SCE/SCE/SCE.cpp
index 81ada93..36cc688 100644
--- a/SCE/SCE/SCE.cpp
+++ b/SCE/SCE/SCE.cpp
@@ -2,11 +2,31 @@
 #include <iostream>
 #include "lgs.h"
 #include "nlgs.h"
+#include "DIFF.h"
 using namespace std;
 
 void cylinder();
 void lgs();
 void nlgs();
+void diff();
+void print_array(long double* a, int size)
+{
+	cout << endl;
+	for(int i = 0; i < size; i++)
+	{
+		cout << a[i] << "\t";
+	}
+	cout << endl << endl;
+}
+void print_array(long double* a, long double* b,  int size)
+{
+	cout << endl;
+	for (int i = 0; i < size; i++)
+	{
+		cout << a[i] << "," << b[i] << endl;
+	}
+	cout << endl << endl;
+}
 
 int main()
 {
@@ -17,6 +37,7 @@ int main()
 		cout << "1 Berechungen an einem Zylinder" << endl;
 		cout << "2 LGS loesen" << endl;
 		cout << "3 n.LGS loesen" << endl;
+		cout << "5 numerische differentation" << endl;
 
 		cout << "e Beenden" << endl;
 		
@@ -26,6 +47,7 @@ int main()
 			case '1': cylinder(); break;
 			case '2': lgs(); break;
 			case '3': nlgs(); break;
+			case '5': diff(); break;
 			
 			default: cout << "Okay, bye" << endl; break;
 		}
@@ -52,5 +74,18 @@ void lgs()
 
 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 << "skantenverfahren fehlt" << endl << endl;
+
 }
+
+void diff() {
+	DIFF diff;
+	
+	print_array(diff.xvalues.data(), diff.forward_diff().data(), diff.xvalues.size());
+	print_array(diff.xvalues.data(), diff.backward_diff(diff.forward_diff()).data(), diff.xvalues.size());
+	
+}
\ No newline at end of file
diff --git a/SCE/SCE/nlgs.cpp b/SCE/SCE/nlgs.cpp
index e491d54..6fe826a 100644
--- a/SCE/SCE/nlgs.cpp
+++ b/SCE/SCE/nlgs.cpp
@@ -4,24 +4,24 @@
 using namespace std;
 
 
-long double nlgs::function(long double x)
+long double NLGS::function(long double x)
 {
 	return (pow(x, 4) - x - 10);
 }
 
-long double nlgs::function_fixedpoint(long double x)
+long double NLGS::function_fixedpoint(long double x)
 {
 	return pow(x+10, 1/4);
 }
 
-long double nlgs::function_derived(long double x)
+long double NLGS::function_derived(long double x)
 {
 	return 4 * pow(x, 3) - 1;
 }
 
 
 
-long double  nlgs::bisektion(long double A, long double B , int limit)
+long double  NLGS::bisektion(long double A, long double B , int limit)
 {
 	long double a = A, b = B, c;
 	for (int i = limit; i--;) 
@@ -33,7 +33,7 @@ long double  nlgs::bisektion(long double A, long double B , int limit)
 	return c;
 }
 
-long double  nlgs::fixedpoint(long double start, int limit)
+long double  NLGS::fixedpoint(long double start, int limit)
 {
 	long double x = start;
 	for(int i = limit ; i-- ;)
@@ -43,7 +43,7 @@ long double  nlgs::fixedpoint(long double start, int limit)
 	return x;
 }
 
-long double  nlgs::newton(long double start, int limit)
+long double  NLGS::newton(long double start, int limit)
 {
 	long double x = start;
 	for (int i = limit; i--;)
@@ -53,7 +53,7 @@ long double  nlgs::newton(long double start, int limit)
 	return x;
 }
 
-long double nlgs::secant(long double A, long double B, int limit)
+long double NLGS::secant(long double A, long double B, int limit)
 {
 	long double a = A, b = B;
 	for (int i = limit; i--;)
diff --git a/SCE/SCE/nlgs.h b/SCE/SCE/nlgs.h
index e05b7de..fd03ec6 100644
--- a/SCE/SCE/nlgs.h
+++ b/SCE/SCE/nlgs.h
@@ -1,5 +1,5 @@
 #pragma once
-class nlgs
+class NLGS
 {
 private:
 	long double function(long double);
@@ -11,7 +11,7 @@ public:
 	long double fixedpoint(long double, int);					//start, number of iterations
 	long double newton(long double, int);						//start, number of iterations
 	long double secant(long double, long double, int);			//a, b, number of iterations
-	nlgs(){};
-	~nlgs(){};
+	NLGS(){};
+	~NLGS(){};
 };