perf(matrix-calc): optimize determinant calculation to O(n^3) using Gaussian Elimination (steam-bell-92#733)

Author: dhruvpatel16120

math/Matrix-Calculator/Matrix-Calculator.py

@@ -167,13 +167,36 @@ def calculate_inverse(matrix):
                 matrix.append(row)
 
             def determinant(m):
-                if len(m) == 1:
+                n = len(m)
+                if n == 1:
                     return m[0][0]
-                if len(m) == 2:
+                if n == 2:
                     return m[0][0] * m[1][1] - m[0][1] * m[1][0]
-                det = 0
-                for c in range(len(m)):
-                    det += ((-1)**c) * m[0][c] * determinant([row[:c] + row[c+1:] for row in m[1:]])
+                
+                mat = [row[:] for row in m]
+                det = 1.0
+                
+                for i in range(n):
+                    pivot_row = i
+                    while pivot_row < n and abs(mat[pivot_row][i]) < 1e-9:
+                        pivot_row += 1
+                        
+                    if pivot_row == n:
+                        return 0.0
+                        
+                    if pivot_row != i:
+                        mat[i], mat[pivot_row] = mat[pivot_row], mat[i]
+                        det *= -1.0
+                        
+                    pivot_val = mat[i][i]
+                    for r in range(i + 1, n):
+                        factor = mat[r][i] / pivot_val
+                        for c in range(i, n):
+                            mat[r][c] -= factor * mat[i][c]
+                            
+                for i in range(n):
+                    det *= mat[i][i]
+                    
                 return det
 
             det_value = determinant(matrix)

tests/test_matrix_calculator.py

@@ -0,0 +1,93 @@
+import unittest
+import subprocess
+import os
+import sys
+
+class TestMatrixCalculator(unittest.TestCase):
+    def setUp(self):
+        self.script_path = os.path.join("math", "Matrix-Calculator", "Matrix-Calculator.py")
+
+    def run_script_with_input(self, user_input):
+        process = subprocess.Popen(
+            [sys.executable, self.script_path],
+            stdin=subprocess.PIPE,
+            stdout=subprocess.PIPE,
+            stderr=subprocess.PIPE,
+            text=True
+        )
+        stdout, stderr = process.communicate(input=user_input)
+        return stdout, stderr
+
+    def test_addition(self):
+        # Add two 2x2 matrices
+        # Matrix 1: [[1, 2], [3, 4]]
+        # Matrix 2: [[5, 6], [7, 8]]
+        # Expected Result: [[6.00, 8.00], [10.00, 12.00]]
+        user_input = "A\n2\n2\n1 2\n3 4\n5 6\n7 8\nQ\n"
+        stdout, _ = self.run_script_with_input(user_input)
+        self.assertIn("6.00\t8.00", stdout)
+        self.assertIn("10.00\t12.00", stdout)
+
+    def test_subtraction(self):
+        # Subtract two 2x2 matrices
+        user_input = "S\n2\n2\n5 6\n7 8\n1 2\n3 4\nQ\n"
+        stdout, _ = self.run_script_with_input(user_input)
+        self.assertIn("4.00\t4.00", stdout)
+        self.assertIn("4.00\t4.00", stdout)
+
+    def test_multiplication(self):
+        # Multiply 2x3 by 3x2 matrix
+        # Matrix 1: [[1, 2, 3], [4, 5, 6]] (2x3)
+        # Matrix 2: [[7, 8], [9, 1], [2, 3]] (3x2)
+        # Expected: [[31.00, 19.00], [85.00, 55.00]]
+        user_input = "M\n2\n3\n1 2 3\n4 5 6\n3\n2\n7 8\n9 1\n2 3\nQ\n"
+        stdout, _ = self.run_script_with_input(user_input)
+        self.assertIn("31.00\t19.00", stdout)
+        self.assertIn("85.00\t55.00", stdout)
+
+    def test_transpose(self):
+        # Transpose a 2x3 matrix
+        # Matrix: [[1, 2, 3], [4, 5, 6]]
+        # Expected: [[1.00, 4.00], [2.00, 5.00], [3.00, 6.00]]
+        user_input = "T\n2\n3\n1 2 3\n4 5 6\nQ\n"
+        stdout, _ = self.run_script_with_input(user_input)
+        self.assertIn("1.00\t4.00", stdout)
+        self.assertIn("2.00\t5.00", stdout)
+        self.assertIn("3.00\t6.00", stdout)
+
+    def test_determinant_3x3(self):
+        # Determinant of 3x3 matrix
+        # Matrix: [[1, 2, 3], [0, 4, 5], [1, 0, 6]]
+        # Expected Det: 1*(24) - 2*(-5) + 3*(-4) = 24 + 10 - 12 = 22
+        user_input = "D\n3\n1 2 3\n0 4 5\n1 0 6\nQ\n"
+        stdout, _ = self.run_script_with_input(user_input)
+        self.assertIn("Determinant: 22.00", stdout)
+
+    def test_determinant_with_row_swap(self):
+        # Determinant of a matrix that requires row swapping during pivot selection
+        # Matrix: [[0, 1], [1, 2]]
+        # Expected: -1
+        user_input = "D\n2\n0 1\n1 2\nQ\n"
+        stdout, _ = self.run_script_with_input(user_input)
+        self.assertIn("Determinant: -1.00", stdout)
+
+    def test_rank(self):
+        # Rank of a 3x3 matrix (linearly dependent)
+        # Matrix: [[1, 2, 3], [2, 4, 6], [1, 0, 1]]
+        # Expected Rank: 2
+        user_input = "R\n3\n3\n1 2 3\n2 4 6\n1 0 1\nQ\n"
+        stdout, _ = self.run_script_with_input(user_input)
+        self.assertIn("Rank of the Matrix: 2", stdout)
+
+    def test_inverse(self):
+        # Inverse of a 2x2 matrix
+        # Matrix: [[4, 7], [2, 6]]
+        # Det = 24 - 14 = 10
+        # Expected: [[0.6, -0.7], [-0.2, 0.4]]
+        user_input = "I\n2\n4 7\n2 6\nQ\n"
+        stdout, _ = self.run_script_with_input(user_input)
+        self.assertIn("0.60\t-0.70", stdout)
+        self.assertIn("-0.20\t0.40", stdout)
+
+if __name__ == "__main__":
+    unittest.main()