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analyze/#8: Analyzed inverse of matrix function
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‎matrix/inverse_of_matrix.py

Lines changed: 99 additions & 62 deletions
Original file line numberDiff line numberDiff line change
@@ -5,6 +5,17 @@
55
from numpy import array
66

77

8+
flags = {
9+
1: False,
10+
2: False,
11+
3: False,
12+
4: False,
13+
5: False,
14+
6: False,
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7: False,
16+
}
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18+
819
def inverse_of_matrix(matrix: list[list[float]]) -> list[list[float]]:
920
"""
1021
A matrix multiplied with its inverse gives the identity matrix.
@@ -65,29 +76,42 @@ def inverse_of_matrix(matrix: list[list[float]]) -> list[list[float]]:
6576

6677
# Check if the provided matrix has 2 rows and 2 columns
6778
# since this implementation only works for 2x2 matrices
68-
if len(matrix) == 2 and len(matrix[0]) == 2 and len(matrix[1]) == 2:
79+
if len(matrix) == 2 and len(matrix[0]) == 2 and len(matrix[1]) == 2: # ID: 1
80+
flags[1] = True
81+
6982
# Calculate the determinant of the matrix
7083
determinant = float(
7184
d(matrix[0][0]) * d(matrix[1][1]) - d(matrix[1][0]) * d(matrix[0][1])
7285
)
73-
if determinant == 0:
86+
if determinant == 0: # ID: 2
87+
flags[2] = True
7488
raise ValueError("This matrix has no inverse.")
75-
76-
# Creates a copy of the matrix with swapped positions of the elements
77-
swapped_matrix = [[0.0, 0.0], [0.0, 0.0]]
78-
swapped_matrix[0][0], swapped_matrix[1][1] = matrix[1][1], matrix[0][0]
79-
swapped_matrix[1][0], swapped_matrix[0][1] = -matrix[1][0], -matrix[0][1]
80-
81-
# Calculate the inverse of the matrix
82-
return [
83-
[(float(d(n)) / determinant) or 0.0 for n in row] for row in swapped_matrix
84-
]
85-
elif (
89+
else: # ID: 3
90+
flags[3] = True
91+
# Creates a copy of the matrix with swapped positions of the elements
92+
swapped_matrix = [[0.0, 0.0], [0.0, 0.0]]
93+
swapped_matrix[0][0], swapped_matrix[1][1] = matrix[1][1], matrix[0][0]
94+
swapped_matrix[1][0], swapped_matrix[0][1] = -matrix[1][0], -matrix[0][1]
95+
96+
# Calculate the inverse of the matrix
97+
result = []
98+
for row in swapped_matrix:
99+
100+
res_row = []
101+
for n in row:
102+
res_row.append((float(d(n)) / determinant) or 0.0)
103+
104+
result.append(res_row)
105+
106+
return result
107+
108+
elif ( # ID: 4
86109
len(matrix) == 3
87110
and len(matrix[0]) == 3
88111
and len(matrix[1]) == 3
89112
and len(matrix[2]) == 3
90113
):
114+
flags[4] = True
91115
# Calculate the determinant of the matrix using Sarrus rule
92116
determinant = float(
93117
(
@@ -101,55 +125,68 @@ def inverse_of_matrix(matrix: list[list[float]]) -> list[list[float]]:
101125
+ (d(matrix[0][0]) * d(matrix[1][2]) * d(matrix[2][1]))
102126
)
103127
)
104-
if determinant == 0:
128+
if determinant == 0: # ID: 5
129+
flags[5] = True
105130
raise ValueError("This matrix has no inverse.")
106131

107-
# Creating cofactor matrix
108-
cofactor_matrix = [
109-
[d(0.0), d(0.0), d(0.0)],
110-
[d(0.0), d(0.0), d(0.0)],
111-
[d(0.0), d(0.0), d(0.0)],
112-
]
113-
cofactor_matrix[0][0] = (d(matrix[1][1]) * d(matrix[2][2])) - (
114-
d(matrix[1][2]) * d(matrix[2][1])
115-
)
116-
cofactor_matrix[0][1] = -(
117-
(d(matrix[1][0]) * d(matrix[2][2])) - (d(matrix[1][2]) * d(matrix[2][0]))
118-
)
119-
cofactor_matrix[0][2] = (d(matrix[1][0]) * d(matrix[2][1])) - (
120-
d(matrix[1][1]) * d(matrix[2][0])
121-
)
122-
cofactor_matrix[1][0] = -(
123-
(d(matrix[0][1]) * d(matrix[2][2])) - (d(matrix[0][2]) * d(matrix[2][1]))
124-
)
125-
cofactor_matrix[1][1] = (d(matrix[0][0]) * d(matrix[2][2])) - (
126-
d(matrix[0][2]) * d(matrix[2][0])
127-
)
128-
cofactor_matrix[1][2] = -(
129-
(d(matrix[0][0]) * d(matrix[2][1])) - (d(matrix[0][1]) * d(matrix[2][0]))
130-
)
131-
cofactor_matrix[2][0] = (d(matrix[0][1]) * d(matrix[1][2])) - (
132-
d(matrix[0][2]) * d(matrix[1][1])
133-
)
134-
cofactor_matrix[2][1] = -(
135-
(d(matrix[0][0]) * d(matrix[1][2])) - (d(matrix[0][2]) * d(matrix[1][0]))
136-
)
137-
cofactor_matrix[2][2] = (d(matrix[0][0]) * d(matrix[1][1])) - (
138-
d(matrix[0][1]) * d(matrix[1][0])
139-
)
132+
else: # ID: 6
133+
flags[6] = True
134+
# Creating cofactor matrix
135+
cofactor_matrix = [
136+
[d(0.0), d(0.0), d(0.0)],
137+
[d(0.0), d(0.0), d(0.0)],
138+
[d(0.0), d(0.0), d(0.0)],
139+
]
140+
cofactor_matrix[0][0] = (d(matrix[1][1]) * d(matrix[2][2])) - (
141+
d(matrix[1][2]) * d(matrix[2][1])
142+
)
143+
cofactor_matrix[0][1] = -(
144+
(d(matrix[1][0]) * d(matrix[2][2])) - (d(matrix[1][2]) * d(matrix[2][0]))
145+
)
146+
cofactor_matrix[0][2] = (d(matrix[1][0]) * d(matrix[2][1])) - (
147+
d(matrix[1][1]) * d(matrix[2][0])
148+
)
149+
cofactor_matrix[1][0] = -(
150+
(d(matrix[0][1]) * d(matrix[2][2])) - (d(matrix[0][2]) * d(matrix[2][1]))
151+
)
152+
cofactor_matrix[1][1] = (d(matrix[0][0]) * d(matrix[2][2])) - (
153+
d(matrix[0][2]) * d(matrix[2][0])
154+
)
155+
cofactor_matrix[1][2] = -(
156+
(d(matrix[0][0]) * d(matrix[2][1])) - (d(matrix[0][1]) * d(matrix[2][0]))
157+
)
158+
cofactor_matrix[2][0] = (d(matrix[0][1]) * d(matrix[1][2])) - (
159+
d(matrix[0][2]) * d(matrix[1][1])
160+
)
161+
cofactor_matrix[2][1] = -(
162+
(d(matrix[0][0]) * d(matrix[1][2])) - (d(matrix[0][2]) * d(matrix[1][0]))
163+
)
164+
cofactor_matrix[2][2] = (d(matrix[0][0]) * d(matrix[1][1])) - (
165+
d(matrix[0][1]) * d(matrix[1][0])
166+
)
140167

141-
# Transpose the cofactor matrix (Adjoint matrix)
142-
adjoint_matrix = array(cofactor_matrix)
143-
for i in range(3):
144-
for j in range(3):
145-
adjoint_matrix[i][j] = cofactor_matrix[j][i]
146-
147-
# Inverse of the matrix using the formula (1/determinant) * adjoint matrix
148-
inverse_matrix = array(cofactor_matrix)
149-
for i in range(3):
150-
for j in range(3):
151-
inverse_matrix[i][j] /= d(determinant)
152-
153-
# Calculate the inverse of the matrix
154-
return [[float(d(n)) or 0.0 for n in row] for row in inverse_matrix]
155-
raise ValueError("Please provide a matrix of size 2x2 or 3x3.")
168+
# Transpose the cofactor matrix (Adjoint matrix)
169+
adjoint_matrix = array(cofactor_matrix)
170+
for i in range(3):
171+
for j in range(3):
172+
adjoint_matrix[i][j] = cofactor_matrix[j][i]
173+
174+
# Inverse of the matrix using the formula (1/determinant) * adjoint matrix
175+
inverse_matrix = array(cofactor_matrix)
176+
for i in range(3):
177+
for j in range(3):
178+
inverse_matrix[i][j] /= d(determinant)
179+
180+
# Calculate the inverse of the matrix
181+
return [[float(d(n)) or 0.0 for n in row] for row in inverse_matrix]
182+
else:
183+
# ID: 7
184+
flags[7] = True
185+
raise ValueError("Please provide a matrix of size 2x2 or 3x3.")
186+
187+
188+
if __name__ == "__main__":
189+
import doctest
190+
doctest.testmod()
191+
192+
print(flags)

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