added support for inverse of 3x3 matrix (TheAlgorithms#7355)

* added support for inverse of 3x3 matrix

* Modified Docstring and improved code

* fixed an error

* Modified docstring

* Apply all suggestions from code review

Co-authored-by: Caeden Perelli-Harris <[email protected]>
Co-authored-by: Chris O <[email protected]>

Co-authored-by: Christian Clauss <[email protected]>
Co-authored-by: Caeden Perelli-Harris <[email protected]>
Co-authored-by: Chris O <[email protected]>

Author: 4 people

matrix/inverse_of_matrix.py

@@ -2,47 +2,154 @@
 
 from decimal import Decimal
 
+from numpy import array
+
 
 def inverse_of_matrix(matrix: list[list[float]]) -> list[list[float]]:
     """
     A matrix multiplied with its inverse gives the identity matrix.
-    This function finds the inverse of a 2x2 matrix.
+    This function finds the inverse of a 2x2 and 3x3 matrix.
     If the determinant of a matrix is 0, its inverse does not exist.
 
     Sources for fixing inaccurate float arithmetic:
     https://stackoverflow.com/questions/6563058/how-do-i-use-accurate-float-arithmetic-in-python
     https://docs.python.org/3/library/decimal.html
 
+    Doctests for 2x2
     >>> inverse_of_matrix([[2, 5], [2, 0]])
     [[0.0, 0.5], [0.2, -0.2]]
     >>> inverse_of_matrix([[2.5, 5], [1, 2]])
     Traceback (most recent call last):
-    ...
+        ...
     ValueError: This matrix has no inverse.
     >>> inverse_of_matrix([[12, -16], [-9, 0]])
     [[0.0, -0.1111111111111111], [-0.0625, -0.08333333333333333]]
     >>> inverse_of_matrix([[12, 3], [16, 8]])
     [[0.16666666666666666, -0.0625], [-0.3333333333333333, 0.25]]
     >>> inverse_of_matrix([[10, 5], [3, 2.5]])
     [[0.25, -0.5], [-0.3, 1.0]]
+
+    Doctests for 3x3
+    >>> inverse_of_matrix([[2, 5, 7], [2, 0, 1], [1, 2, 3]])
+    [[2.0, 5.0, -4.0], [1.0, 1.0, -1.0], [-5.0, -12.0, 10.0]]
+    >>> inverse_of_matrix([[1, 2, 2], [1, 2, 2], [3, 2, -1]])
+    Traceback (most recent call last):
+        ...
+    ValueError: This matrix has no inverse.
+
+    >>> inverse_of_matrix([[],[]])
+    Traceback (most recent call last):
+        ...
+    ValueError: Please provide a matrix of size 2x2 or 3x3.
+
+    >>> inverse_of_matrix([[1, 2], [3, 4], [5, 6]])
+    Traceback (most recent call last):
+        ...
+    ValueError: Please provide a matrix of size 2x2 or 3x3.
+
+    >>> inverse_of_matrix([[1, 2, 1], [0,3, 4]])
+    Traceback (most recent call last):
+        ...
+    ValueError: Please provide a matrix of size 2x2 or 3x3.
+
+    >>> inverse_of_matrix([[1, 2, 3], [7, 8, 9], [7, 8, 9]])
+    Traceback (most recent call last):
+        ...
+    ValueError: This matrix has no inverse.
+
+    >>> inverse_of_matrix([[1, 0, 0], [0, 1, 0], [0, 0, 1]])
+    [[1.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]]
     """
 
-    d = Decimal  # An abbreviation for conciseness
+    d = Decimal
 
     # Check if the provided matrix has 2 rows and 2 columns
     # since this implementation only works for 2x2 matrices
-    if len(matrix) != 2 or len(matrix[0]) != 2 or len(matrix[1]) != 2:
-        raise ValueError("Please provide a matrix of size 2x2.")
+    if len(matrix) == 2 and len(matrix[0]) == 2 and len(matrix[1]) == 2:
+        # Calculate the determinant of the matrix
+        determinant = float(
+            d(matrix[0][0]) * d(matrix[1][1]) - d(matrix[1][0]) * d(matrix[0][1])
+        )
+        if determinant == 0:
+            raise ValueError("This matrix has no inverse.")
+
+        # Creates a copy of the matrix with swapped positions of the elements
+        swapped_matrix = [[0.0, 0.0], [0.0, 0.0]]
+        swapped_matrix[0][0], swapped_matrix[1][1] = matrix[1][1], matrix[0][0]
+        swapped_matrix[1][0], swapped_matrix[0][1] = -matrix[1][0], -matrix[0][1]
+
+        # Calculate the inverse of the matrix
+        return [
+            [(float(d(n)) / determinant) or 0.0 for n in row] for row in swapped_matrix
+        ]
+    elif (
+        len(matrix) == 3
+        and len(matrix[0]) == 3
+        and len(matrix[1]) == 3
+        and len(matrix[2]) == 3
+    ):
+        # Calculate the determinant of the matrix using Sarrus rule
+        determinant = float(
+            (
+                (d(matrix[0][0]) * d(matrix[1][1]) * d(matrix[2][2]))
+                + (d(matrix[0][1]) * d(matrix[1][2]) * d(matrix[2][0]))
+                + (d(matrix[0][2]) * d(matrix[1][0]) * d(matrix[2][1]))
+            )
+            - (
+                (d(matrix[0][2]) * d(matrix[1][1]) * d(matrix[2][0]))
+                + (d(matrix[0][1]) * d(matrix[1][0]) * d(matrix[2][2]))
+                + (d(matrix[0][0]) * d(matrix[1][2]) * d(matrix[2][1]))
+            )
+        )
+        if determinant == 0:
+            raise ValueError("This matrix has no inverse.")
+
+        # Creating cofactor matrix
+        cofactor_matrix = [
+            [d(0.0), d(0.0), d(0.0)],
+            [d(0.0), d(0.0), d(0.0)],
+            [d(0.0), d(0.0), d(0.0)],
+        ]
+        cofactor_matrix[0][0] = (d(matrix[1][1]) * d(matrix[2][2])) - (
+            d(matrix[1][2]) * d(matrix[2][1])
+        )
+        cofactor_matrix[0][1] = -(
+            (d(matrix[1][0]) * d(matrix[2][2])) - (d(matrix[1][2]) * d(matrix[2][0]))
+        )
+        cofactor_matrix[0][2] = (d(matrix[1][0]) * d(matrix[2][1])) - (
+            d(matrix[1][1]) * d(matrix[2][0])
+        )
+        cofactor_matrix[1][0] = -(
+            (d(matrix[0][1]) * d(matrix[2][2])) - (d(matrix[0][2]) * d(matrix[2][1]))
+        )
+        cofactor_matrix[1][1] = (d(matrix[0][0]) * d(matrix[2][2])) - (
+            d(matrix[0][2]) * d(matrix[2][0])
+        )
+        cofactor_matrix[1][2] = -(
+            (d(matrix[0][0]) * d(matrix[2][1])) - (d(matrix[0][1]) * d(matrix[2][0]))
+        )
+        cofactor_matrix[2][0] = (d(matrix[0][1]) * d(matrix[1][2])) - (
+            d(matrix[0][2]) * d(matrix[1][1])
+        )
+        cofactor_matrix[2][1] = -(
+            (d(matrix[0][0]) * d(matrix[1][2])) - (d(matrix[0][2]) * d(matrix[1][0]))
+        )
+        cofactor_matrix[2][2] = (d(matrix[0][0]) * d(matrix[1][1])) - (
+            d(matrix[0][1]) * d(matrix[1][0])
+        )
 
-    # Calculate the determinant of the matrix
-    determinant = d(matrix[0][0]) * d(matrix[1][1]) - d(matrix[1][0]) * d(matrix[0][1])
-    if determinant == 0:
-        raise ValueError("This matrix has no inverse.")
+        # Transpose the cofactor matrix (Adjoint matrix)
+        adjoint_matrix = array(cofactor_matrix)
+        for i in range(3):
+            for j in range(3):
+                adjoint_matrix[i][j] = cofactor_matrix[j][i]
 
-    # Creates a copy of the matrix with swapped positions of the elements
-    swapped_matrix = [[0.0, 0.0], [0.0, 0.0]]
-    swapped_matrix[0][0], swapped_matrix[1][1] = matrix[1][1], matrix[0][0]
-    swapped_matrix[1][0], swapped_matrix[0][1] = -matrix[1][0], -matrix[0][1]
+        # Inverse of the matrix using the formula (1/determinant) * adjoint matrix
+        inverse_matrix = array(cofactor_matrix)
+        for i in range(3):
+            for j in range(3):
+                inverse_matrix[i][j] /= d(determinant)
 
-    # Calculate the inverse of the matrix
-    return [[float(d(n) / determinant) or 0.0 for n in row] for row in swapped_matrix]
+        # Calculate the inverse of the matrix
+        return [[float(d(n)) or 0.0 for n in row] for row in inverse_matrix]
+    raise ValueError("Please provide a matrix of size 2x2 or 3x3.")