def init_theta(X, Y):
"""
Initialization theta vector
:param X:
:param Y:
:return: Theta vector + Matrix for any class
"""
# Split X:
X1 = Matrix.from_list([X[i] for i in range(X.numrows) if Y[i][0] == 1])
X2 = Matrix.from_list([X[i] for i in range(X.numrows) if Y[i][0] == 0])
# A and B are avg data point of X1 and X2:
A = [sum([X1[i][1] for i in range(X1.numrows)])/X1.numrows, sum([X1[i][2] for i in range(X1.numrows)])/X1.numrows]
B = [sum([X2[i][1] for i in range(X2.numrows)])/X2.numrows, sum([X2[i][2] for i in range(X2.numrows)])/X2.numrows]
# Vector AB:
AB = [B[0] - A[0], B[1] - A[1]]
# I is midpoint between A and B:
I = [(A[0] + B[0])/2, (A[1] + B[1])/2]
# Get equation of AB's bisection:
theta1 = np.array([[-(AB[0]*I[0] + AB[1]*I[1])], [AB[0]], [AB[1]]])
# Scale theta:
div = theta1[0][0]
for i in range(len(theta1)):
if abs(theta1[i][0]) > abs(div):
div = theta1[i][0]
for i in range(len(theta1)):
theta1[i][0] /= div
# Return theta and matrix of any class
return [Matrix.from_list(theta1), X1, X2]
def get_matrix(data_input):
"""
Init X and Y matrix
:param data_input: input file path
:return: Matrix X and Y
"""
# Read data to dataframe df:
df = (pd.read_csv(data_input)).values
# Get X and Y:
X = Matrix.from_list([df[i][0:2] for i in range(len(df))])
Y = Matrix.from_list([df[i][2:] for i in range(len(df))])
# Append 1 into any row of X:
X = Matrix.from_list([np.insert(X[i], 0, (1,)) for i in range(len(df))])
# Return:
return [X, Y]
def get_matrix(var):
"""
Lay ma tran theta, X va Y
:param var: Ma tran tham so dau vao
:return: list 3 ma tran: theta, X va Y
"""
# Y la cot cuoi cung cua var, con lai thuoc X
X = [var[i] for i in range(len(var) - 1)]
Y = var[len(var) - 1]
# Them value 1 vao dau moi dong cua X
X.insert(0, [1 for i in range(len(var[0]))])
# Tao ma tran X va Y:
mX = Matrix.from_list(X)
mY = Matrix.from_list([Y])
# Tra ve theta, X va Y:
return [((mX * mX.trans()).inv()) * mX * mY.trans(), mX, mY]
def sigmoid_function(theta, X):
"""
Cacl sigmoid value
:param theta:
:param X:
:return:
"""
z = Matrix.from_list(X) * (-theta)
return 1.0 / (1 + np.exp(z[0][0]))
def update_equation(X, Y, theta, alpha):
"""
Update Decision Boundary
:param X:
:param Y:
:param theta:
:param alpha:
:return: New theta vector
"""
return theta - Matrix.from_list([[alpha * cost_function(X, Y, theta)] for i in range(theta.numrows)])
def __init__(self, key: list = None):
if not key:
key = Matrix.identity(3)
self.key_matrix = Matrix.from_list(key)
try:
determinant_modulus_inverse = pow(round(self.key_matrix.det()), -1,
26)
self.key_matrix_inverse = (determinant_modulus_inverse *
self.key_matrix.adjoint()) % 26
except:
raise Exception("Key matrix have to be modular inversible")
def encrypt(self, plaintext: str) -> str:
"""
Encrypt a given string, returning an encrypted string.
Overrides StringCipher.encrypt()
"""
no_space_plaintext = plaintext.replace(" ", "")
if not no_space_plaintext.isalpha():
raise Exception(
"Hill cipher only accept alphabets with or without spaces as plaintext"
)
lowercase_plaintext = no_space_plaintext.lower()
plaintext_mod_26_list = [
ord(char) - ord('a') for char in lowercase_plaintext
]
ciphertext_mod_26_list = []
block = self.key_matrix.numcols
offset = 0
while offset < len(plaintext_mod_26_list):
plaintext_slice = None
if len(plaintext_mod_26_list) - offset < block:
padding = [
0
for x in range(len(plaintext_mod_26_list), offset + block)
]
plaintext_slice = plaintext_mod_26_list[
offset:len(plaintext_mod_26_list)] + padding
else:
plaintext_slice = plaintext_mod_26_list[offset:offset + block]
plaintext_matrix_block = Matrix.from_list([[x]
for x in plaintext_slice
])
ciphertext_matrix_block = self.key_matrix * plaintext_matrix_block
for x in ciphertext_matrix_block.elements():
ciphertext_mod_26_list.append(x % 26)
offset += block
ciphertext = ''.join(
[chr(x + ord('a')) for x in ciphertext_mod_26_list]).upper()
return ciphertext
def infer(self, data_in):
"""Push data_in through network and give results."""
l3 = Matrix.from_list([data_in]) * self.l1 + self.b1
# l3 = NeuralNetwork._logistic(l3)
l3 = l3 * self.l2 + self.b2
# l3 = NeuralNetwork._logistic(l3)
e = [math.exp(elem) for elem in l3[0]]
s = sum(e)
odds = [elem / s for elem in e]
return self.argmax(odds)
def cost_function(X, Y, theta):
"""
Cacl avg cost value
:param X:
:param Y:
:param theta:
:return: Cost value
"""
m = X.numrows # Data length
# Cacl total cost:
cost = ([(-Y[i][0] * np.log(sigmoid_function(theta, [X[i]]))
- (1 - Y[i][0]) * np.log(1 - sigmoid_function(theta, [X[i]])))
* Matrix.from_list([[X[i][0]]]) for i in range(m)])
# Return avg cost:
return -sum([cost[i][0][0] for i in range(len(cost))])/m
def decrypt(self, ciphertext: str) -> str:
"""
Decrypt a given string, returning a plaintext string.
Overrides StringCipher.decrypt()
"""
if not ciphertext.isalpha():
raise Exception("Hill cipher only accept alphabets as ciphertext")
lowercase_ciphertext = ciphertext.lower()
ciphertext_mod_26_list = [
ord(char) - ord('a') for char in lowercase_ciphertext
]
plaintext_mod_26_list = []
block = self.key_matrix.numcols
offset = 0
while offset < len(ciphertext_mod_26_list):
ciphertext_slice = None
if len(ciphertext_mod_26_list) - offset < block:
padding = [
0
for x in range(len(ciphertext_mod_26_list), offset + block)
]
ciphertext_slice = ciphertext_mod_26_list[
offset:len(ciphertext_mod_26_list)] + padding
else:
ciphertext_slice = ciphertext_mod_26_list[offset:offset +
block]
ciphertext_matrix_block = Matrix.from_list(
[[x] for x in ciphertext_slice])
plaintext_matrix_block = self.key_matrix_inverse * ciphertext_matrix_block
for x in plaintext_matrix_block.elements():
plaintext_mod_26_list.append(round(x) % 26)
offset += block
plaintext = ''.join([chr(x + ord('a')) for x in plaintext_mod_26_list])
return plaintext
def update_equation(X, Y, theta, alpha, _lambda):
"""
Update Decision Boundary
:param X:
:param Y:
:param theta:
:param alpha:
:return: New theta vector
"""
temp = theta[0][0] # Save theta0 value
# Update theta(included theta0):
theta = theta - Matrix.from_list(
[[alpha * cost_function(X, Y, theta, _lambda)]
for i in range(theta.numrows)])
# Update theta0 by special way:
theta[0][0] = temp - alpha * cost_function(X, Y, theta, 0)
return theta
def colvec(l):
return Matrix.from_list([l]).trans()
def test_from_matrix(self):
assert P(Matrix.from_list([[0.4], [0.2], [0.1]])) == P([0.4, 0.2, 0.1])
from pymatrix import Matrix
import pandas as pd
import numpy as np
from Regularization import Hx, get_matrix
if __name__ == '__main__':
df1 = pd.read_csv("result.txt").values
df2 = (pd.read_csv("ex2data2.txt")).values
temp = get_matrix("ex2data2.txt")
X = temp[0]
Y = temp[1]
theta = Matrix.from_list(df1)
for i in range(len(df1)):
np.append(df1[i], 1 - Hx(theta, X, 6))
print df1