From 687ec9b6b129ee6c01ab329907544da99b2ad8a0 Mon Sep 17 00:00:00 2001
From: teridax <sven.vogel123@web.de>
Date: Thu, 27 Apr 2023 14:25:57 +0200
Subject: [PATCH] added matrix

---
 main.py            |   2 +
 matrix/__init__.py | 165 +++++++++++++++++++++++++++++++++++++++++++++
 2 files changed, 167 insertions(+)
 create mode 100644 matrix/__init__.py

diff --git a/main.py b/main.py
index e6d3e2a..0a457cb 100644
--- a/main.py
+++ b/main.py
@@ -16,6 +16,7 @@
 
 import fixpoint_approximation
 import linear_approximation
+import matrix
 import newton_polynom
 import zero_point_approximation
 
@@ -25,3 +26,4 @@ if __name__ == '__main__':
     fixpoint_approximation.test()
     newton_polynom.test()
     zero_point_approximation.test()
+    matrix.test()
diff --git a/matrix/__init__.py b/matrix/__init__.py
new file mode 100644
index 0000000..d067cf4
--- /dev/null
+++ b/matrix/__init__.py
@@ -0,0 +1,165 @@
+import math
+
+
+class Matrix:
+
+    def __init__(self, rows, cols):
+        self.rows = rows
+        self.cols = cols
+
+        self.fields = []
+
+        # initialize to identity matrix
+        for x in range(rows):
+            row = []
+
+            for y in range(cols):
+                row.append(float(x == y))
+
+            self.fields.append(row)
+
+    def __str__(self):
+        return self.fields.__str__()
+
+    # convert this matrix to identity
+    def to_identity(self):
+        for x in range(self.rows):
+            for y in range(self.cols):
+                self.fields[x][y] = float(x == y)
+
+    def transpose(self):
+        result = Matrix(self.cols, self.rows)
+
+        for x in range(self.rows):
+            for y in range(self.cols):
+                result.fields[y][x] = self.fields[x][y]
+
+        return result
+
+    def __mul__(self, other):
+        result = Matrix(self.rows, other.cols)
+
+        for x in range(self.rows):
+            for y in range(other.cols):
+                sum = 0
+
+                for i in range(self.cols):
+                    sum += self.fields[x][i] * other.fields[i][y]
+
+                result.fields[x][y] = sum
+
+        return result
+
+    def scale(self, other):
+        result = Matrix(self.rows, other.cols)
+
+        for x in range(self.rows):
+            for y in range(other.cols):
+
+                result.fields[x][y] = self.fields[x][y] * other
+
+        return result
+
+    def __add__(self, other):
+        result = Matrix(self.rows, self.cols)
+
+        for x in range(self.rows):
+            for y in range(self.cols):
+                result.fields[x][y] = self.fields[x][y] + other.fields[x][y]
+
+        return result
+
+    def __sub__(self, other):
+        result = Matrix(self.rows, self.cols)
+
+        for x in range(self.rows):
+            for y in range(self.cols):
+                result.fields[x][y] = self.fields[x][y] - other.fields[x][y]
+
+        return result
+
+    def slice(self, row_min, row_max, col_min, col_max):
+        rows = row_max - row_min
+        cols = col_max - col_min
+
+        result = Matrix(rows, cols)
+
+        for x in range(row_min, row_max):
+            for y in range(col_min, col_max):
+                result.fields[x][y] = self.fields[x][y]
+
+        return result
+
+    def exclude_row_and_col(self, i):
+        result = Matrix(self.rows - 1, self.cols - 1)
+
+        for x in range(i):
+            for y in range(i):
+                result.fields[x][y] = self.fields[x][y]
+
+        for x in range(i + 1, self.rows - 1):
+            for y in range(i + 1, self.cols - 1):
+                result.fields[x][y] = self.fields[x][y]
+
+        return result
+
+    def determinant(self):
+        if self.rows == 2 and self.cols == 2:
+            return self.fields[0][0] * self.fields[1][1] - self.fields[0][1] * self.fields[1][0]
+
+        # Satz von Sarrus
+        if self.rows == 3 and self.cols == 3:
+            aei = self.fields[0][0] * self.fields[1][1] * self.fields[2][2]
+            bfg = self.fields[0][1] * self.fields[1][2] * self.fields[2][0]
+            cdh = self.fields[0][2] * self.fields[1][0] * self.fields[2][1]
+            ceg = self.fields[0][2] * self.fields[1][1] * self.fields[2][0]
+            afh = self.fields[0][0] * self.fields[1][2] * self.fields[2][1]
+            bdi = self.fields[0][1] * self.fields[1][0] * self.fields[2][2]
+            return aei + bfg + cdh - ceg - afh - bdi
+
+        # Laplace
+        if self.rows == self.cols:
+            # perform laplace on 2nd row
+            self.__laplace_row(1)
+
+    def __laplace_row(self, i):
+        sum = 0
+        for i in range(self.rows):
+            sum += math.pow(-1, i + 1) * self.exclude_row_and_col(i).determinant()
+
+        return sum
+
+    def cramer(self, vector, order):
+        return Matrix.from_vector(vector, order).determinant() / self.determinant()
+
+    @classmethod
+    def from_array(cls, array):
+        matrix = Matrix(rows=len(array), cols=len(array[0]))
+
+        for y in range(matrix.cols):
+            for x in range(matrix.rows):
+                matrix.fields[x][y] = array[x][y]
+
+        return matrix
+
+    @classmethod
+    def from_vector(cls, vector, column):
+        matrix = Matrix(rows=len(vector), cols=len(vector))
+
+        for y in range(matrix.rows):
+            matrix.fields[y][column] = vector[y]
+
+        return matrix
+
+def test():
+    mat1 = Matrix.from_array([
+        [2, -4],
+        [3, 1],
+        [-2, 1]
+    ])
+    mat2 = Matrix.from_array([
+        [2, -2, 3],
+        [-3, 4, -4]
+    ])
+
+    print(mat1 * mat2)