-
Notifications
You must be signed in to change notification settings - Fork 0
/
Matrix.py
175 lines (119 loc) · 4.88 KB
/
Matrix.py
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
import numpy as np
import matplotlib.pyplot as plt
class Matrix:
"""Representation of an n-dimensional linear transformation"""
def __init__(self, dimensions, elements):
self.dimensions = dimensions
self.elements = elements
self.arr = np.zeros((self.dimensions, self.dimensions))
for i in range(dimensions) :
for j in range(dimensions) :
self.arr[i][j] = elements[i * (dimensions) + j]
def equals(self, other):
if self.dimensions != other.dimensions:
return False
for i in range(len(self.elements)):
if self.elements[i] != other.elements[i]:
return False
return True
def get_element(self,r, c):
return self.arr[r][c]
def get_row(self, i):
return self.arr[i]
def get_col(self, i):
return [c[i] for c in self.arr]
def copy(self):
elements = []
for i in range(0,self.dimensions):
for j in range(0,self.dimensions):
elements.append(self.arr[i][j])
return Matrix(self.dimensions, elements)
def multiply(self, other):
assert (isinstance(other,Matrix))
elements = []
val = 0
# Selecting sub row of first matrix
for i in range(self.dimensions):
sub_1 = self.get_row(i)
# Selecting sub column of second matrix
for j in range(len(sub_1)):
val = 0
sub_2 = other.get_col(j)
# Multiplying element by element in sub matrices
for k in range(len(sub_1)):
val += sub_1[k] * sub_2[k]
# Appeding to the resultant element list
elements.append(val)
return Matrix(self.dimensions, elements)
def getcofactor(self, m, i, j):
return [row[: j] + row[j+1:] for row in (m[: i] + m[i+1:])]
"""
def modulus(self):
# if given matrix is of order
# 2*2 then simply return det
# value by cross multiplying
# elements of matrix.
if(self.dimensions == 2):
value = self.get_element(0,0) * self.get_element(1,1) - self.get_element(1,0) * self.get_element(0,1)
return value
# initialize Sum to zero
Sum = 0
# loop to traverse each column
# of matrix a.
for current_column in range(self.dimensions):
# calculating the sign corresponding
# to co-factor of that sub matrix.
sign = (-1) ** (current_column)
# calling the function recursily to
# get determinant value of
# sub matrix obtained.
sub_det = self.modulus(self.getcofactor(self, 0, current_column))
# adding the calculated determinant
# value of particular column
# matrix to total Sum.
Sum += (sign * self.get_element(0,[current_column] * sub_det))
# returning the final Sum
temp = [0]*self.dimensions # temporary array for storing row
total = 1
det = 1 # initialize result
# loop for traversing the diagonal elements
for i in range(0, n):
index = i # initialize the index
# finding the index which has non zero value
while(mat[index][i] == 0 and index < n):
index += 1
if(index == n): # if there is non zero element
# the determinat of matrix as zero
continue
if(index != i):
# loop for swaping the diagonal element row and index row
for j in range(0, n):
mat[index][j], mat[i][j] = mat[i][j], mat[index][j]
# determinant sign changes when we shift rows
# go through determinant properties
det = det*int(pow(-1, index-i))
# storing the values of diagonal row elements
for j in range(0, n):
temp[j] = mat[i][j]
# traversing every row below the diagonal element
for j in range(i+1, n):
num1 = temp[i] # value of diagonal element
num2 = mat[j][i] # value of next row element
# traversing every column of row
# and multiplying to every row
for k in range(0, n):
# multiplying to make the diagonal
# element and next row element equal
mat[j][k] = (num1*mat[j][k]) - (num2*temp[k])
total = total * num1 # Det(kA)=kDet(A);
# mulitplying the diagonal elements to get determinant
for i in range(0, n):
det = det*mat[i][i]
return int(det/total) # Det(kA)/k=Det(A);
"""
def inverse(self):
return
def eigenvalues(self):
return
def eigenvector(self):
return