Added determinate function (#1429)

* Added determinate function

* Changed determinate function name

* Changed instance of .det() to .determinate()

* Added force_test() function

* Update tests.py

linear_algebra/README.md

@@ -45,7 +45,8 @@ This module contains some useful classes and functions for dealing with linear a
     - changeComponent(x,y,value) : changes the specified component.  
     - component(x,y) : returns the specified component.  
     - width() : returns the width of the matrix  
-    - height() : returns the height of the matrix  
+    - height() : returns the height of the matrix
+    - determinate() : returns the determinate of the matrix if it is square 
     - operator + : implements the matrix-addition.  
     - operator - _ implements the matrix-subtraction  
 

linear_algebra/src/lib.py

@@ -277,6 +277,33 @@ class Matrix(object):
         """
         return self.__height
 
+    def determinate(self) -> float:
+        """
+            returns the determinate of an nxn matrix using Laplace expansion
+        """
+        if self.__height == self.__width and self.__width >= 2:
+            total = 0
+            if self.__width > 2:
+                for x in range(0, self.__width):
+                    for y in range(0, self.__height):
+                        total += (
+                            self.__matrix[x][y]
+                            * (-1) ** (x + y)
+                            * Matrix(
+                                self.__matrix[0:x] + self.__matrix[x + 1 :],
+                                self.__width - 1,
+                                self.__height - 1,
+                            ).determinate()
+                        )
+            else:
+                return (
+                    self.__matrix[0][0] * self.__matrix[1][1]
+                    - self.__matrix[0][1] * self.__matrix[1][0]
+                )
+            return total
+        else:
+            raise Exception("matrix is not square")
+
     def __mul__(self, other):
         """
             implements the matrix-vector multiplication.

linear_algebra/src/tests.py

@@ -118,6 +118,13 @@ class Test(unittest.TestCase):
         A = Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]], 3, 3)
         self.assertEqual("|1,2,3|\n|2,4,5|\n|6,7,8|\n", str(A))
 
+    def test_determinate(self):
+        """
+            test for determinate()
+        """
+        A = Matrix([[1, 1, 4, 5], [3, 3, 3, 2], [5, 1, 9, 0], [9, 7, 7, 9]], 4, 4)
+        self.assertEqual(-376, A.determinate())
+
     def test__mul__matrix(self):
         A = Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]], 3, 3)
         x = Vector([1, 2, 3])
@@ -149,6 +156,13 @@ class Test(unittest.TestCase):
             str(squareZeroMatrix(5)),
         )
 
-
+def force_test() -> None:
+    """
+    This will ensure that pytest runs the unit tests above.
+    To explore https://github.com/TheAlgorithms/Python/pull/1124 uncomment the line below.
+    >>> # unittest.main()
+    """
+    pass
+    
 if __name__ == "__main__":
     unittest.main()