Added matrix functions adj, trans, cof, inv.

common.py

@@ -28,6 +28,10 @@ def __repr__(self):
     (r'sqrt',               'OPR'),
     (r'exp',                'OPR'),
     (r'det',                'OPR'),
+    (r'adj',                'OPR'),
+    (r'trans',              'OPR'),
+    (r'cof',                'OPR'),
+    (r'inv',                'OPR'),
     (r'[a-zA-Z_]+',         'IDT'),
     (r'=',                  'EQL'),
     (r'\+',                 'ADD'),

rules.py

@@ -1,6 +1,7 @@
 """
 This file contains methods to handle calculation of all the rules.
 """
+import copy
 import math
 import operator
 from typing import List, Union
@@ -21,7 +22,7 @@ def pow(tokens: List[Union[Token, Value, RuleMatch]]) -> Value:
 
 
 def opr(tokens: List[Union[Token, Value, RuleMatch]]) -> Value:
-    return Value(Type.Number, {'sqrt': math.sqrt, 'exp': math.exp, 'det': det}[tokens[0].value](tokens[1].value.value))
+    return Value(Type.Number, {'sqrt': math.sqrt, 'exp': math.exp, 'det': det, 'trans': trans, 'cof': cof, 'adj': adj, 'inv': inv}[tokens[0].value](tokens[1].value.value))
 
 
 def neg(tokens: List[Union[Token, Value, RuleMatch]]) -> Value:
@@ -59,6 +60,39 @@ def det(matrix: List[List[float]]) -> float:
     return sum(cofactors)
 
 
+def trans(matrix: List[List[float]]) -> List[List[float]]:
+    return list(map(list, zip(*matrix)))
+
+
+def cof(matrix: List[List[float]]) -> List[List[float]]:
+    # TODO: This code is pretty ugly.
+
+    cofactor_matrix = []
+
+    for row in range(len(matrix)):
+        cofactor_matrix.append([])
+
+        for col in range(len(matrix[row])):
+            minor = copy.deepcopy(matrix)
+            del minor[row]
+
+            for r in minor:
+                del r[col]
+
+            cofactor_matrix[row].append(det(minor) * (1 if (row + col) % 2 is 0 else -1))
+
+    return cofactor_matrix
+
+
+def adj(matrix: List[List[float]]) -> List[List[float]]:
+    return trans(cof(matrix))
+
+
+def inv(matrix: List[List[float]]):
+    multiplier = 1 / det(matrix)
+    return [[cell * multiplier for cell in row] for row in adj(matrix)]
+
+
 calc_map = {
     'add': add,
     'mul': mul,

tests.py

@@ -103,11 +103,25 @@ def runTest(self):
         self.assertEqual(evaluate('det([1,2,3|4,5,6|7,8,8])'), 3.0)
 
         self.assertEqual(evaluate('[1,2|4,5]'), [[1.0, 2.0], [4.0, 5.0]])
+        self.assertEqual(evaluate('trans([1,2|4,5])'), [[1.0, 4.0], [2.0, 5.0]])
+
+        self.assertEqual(evaluate('inv([1,4,7|3,0,5|-1,9,11])'), [[45/8, -19/8, -5/2], [19/4, -9/4, -2], [-27/8, 13/8, 3/2]])
+
         self.assertEqual(evaluate('[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]])
 
         self.assertEqual(evaluate('[1,0,0,0|0,1,0,0|0,0,1,0|0,0,0,1]'), [[1.0, 0.0, 0.0, 0.0], [0.0, 1.0, 0.0, 0.0], [0.0, 0.0, 1.0, 0.0], [0.0, 0.0, 0.0, 1.0]])
         self.assertEqual(evaluate('det([1,3,5,7|2,4,6,8|9,7,5,4|8,6,5,9])'), 2.0)
 
+        self.assertEqual(evaluate('cof([1,2,3|0,4,5|1,0,6])'), [[24, 5, -4], [-12, 3, 2], [-2, -5, 4]])
+
+        # Since we have floating-point issues, we have to test each value individually.
+        calc = evaluate('inv([1,2,3|0,4,5|1,0,6])')
+        ans = [[12/11, -6/11, -1/11], [5/22, 3/22, -5/22], [-2/11, 1/11, 2/11]]
+
+        for row in range(len(calc)):
+            for col in range(len(calc)):
+                self.assertAlmostEqual(calc[row][col], ans[row][col])
+
         # for _ in range(10):
         #     mat = [[random.randint(1, 100) for _ in range(10)] for _ in range(10)]
         #     mat_str = '[' + '|'.join([','.join(map(str, line)) for line in mat]) + ']'