Adding code for regular gauss algorithm.

2 files changed, 41 insertions, 0 deletions

diff --git a/math/gauss.cpp b/math/gauss.cpp
new file mode 100644
index 0000000..5faaa90
--- /dev/null
+++ b/math/gauss.cpp
@@ -0,0 +1,38 @@
+// Laufzeit: O(n^3)
+void swapLines(int n, int l1, int l2) {
+	for (int i = 0; i <= n; i++) swap(mat[l1][i], mat[l2][i]);
+}
+
+void normalLine(int n, int line) {
+	double factor = mat[line][line];
+	for (int i = 0; i <= n; i++) {
+		mat[line][i] /= factor;
+}}
+
+void takeAll(int n, int line) {
+	for (int i = 0; i < n; i++) {
+		if (i == line) continue;
+		double diff = mat[i][line];
+		for (int j = 0; j <= n; j++) {
+			mat[i][j] -= diff * mat[line][j];
+}}}
+
+int gauss(int n) { // Gibt zurück, ob das System (eindeutig) lösbar ist.
+	for (int i = 0; i < n; i++) {
+		int swappee = i; // Sucht Pivotzeile für bessere Stabilität.
+		for (int j = i + 1; j < n; j++)
+			if (abs(mat[j][i]) > abs(mat[i][i])) swappee = j;
+		swapLines(n, i, swappee);
+		if (abs(mat[i][i]) > EPSILON) {
+			normalLine(n, i);
+			takeAll(n, i);	
+	}} // Ab jetzt nur noch checks bzgl. Eindeutigkeit/Existenz der Lösung.
+	for (int i = 0; i < n; i++) {
+		bool allZero = true;
+		for (int j = i; j < n; j++)
+			if (abs(mat[i][j]) > EPSILON) allZero = false;
+		if (allZero && abs(mat[i][n]) > EPSILON) return INCONSISTENT;
+		if (allZero && abs(mat[i][n]) < EPSILON) return MULTIPLE;
+	}
+	return UNIQUE;
+}
diff --git a/math/math.tex b/math/math.tex
index 7d36c00..c06bd34 100644
--- a/math/math.tex
+++ b/math/math.tex
@@ -22,6 +22,9 @@ Sei $0 \leq x < n$. Definiere $d := \gcd(x, n)$.\newline
 \subsection{LGS über $\mathbb{F}_p$}
 \lstinputlisting{math/lgsFp.cpp}
 
+\subsection{LGS über $\mathbb{R}$}
+\lstinputlisting{math/gauss.cpp}
+
 \subsection{Chinesischer Restsatz}
 \begin{itemize}
 	\item Extrem anfällig gegen Overflows. Evtl. häufig 128-Bit Integer verwenden.