def getGradient(features, weight, target):
"""
This function calculates gradient of LSE( 2(A^T)Ax - 2(A^T)b )
"""
# gradient = 2(A^T)Ax - 2(A^T)b
features_T = mat.transpose(features)
gradient = 2 * mat.mul(mat.mul(features_T, features), weight)
gradient -= 2 * mat.mul(features_T, target)
return gradient
def newtonmethod(hession_inv, gradient, weight):
"""
Using newton's method to optimize the answer.
xn = xn-1
"""
# x1 = x0 - (H^-1)(gradient)
return weight - mat.mul(hession_inv, gradient)
def genb(features, y):
"""
input: A, b
output: (A^T)(b)
"""
y = np.array(y).reshape(-1, 1)
b = mat.mul(mat.transpose(features), y)
return b
def getHessionInv(features):
"""
This function calculates hession matrix of LSE( 2(A^T)A )
"""
# hession = 2(A^T)A
features_T = mat.transpose(features)
hession = 2 * mat.mul(features_T, features)
return mat.inv(hession)
def genmatrix(features, rate):
"""
input: A, rate
output: (A^T)(A) - (rate)(I)
This function will return (A^T)(A) - rate * I
"""
matrix = mat.mul(mat.transpose(features), features)
matrix -= rate * np.eye(matrix.shape[0])
return matrix
def d_hill(ciphertext, key):
# your code here
if len(ciphertext) == 0:
print('Error(d_hill): invalid ciphertext')
return ''
new_key = ''
if len(key) > 4:
new_key += key[:4]
elif len(key) == 4:
new_key += key
else:
new_key += key
counter = 0
while len(new_key) < 4:
new_key += key[counter]
counter += 1
baseString = utilities_A4.get_lower()
key_matrix = matrix.new_matrix(2, 2, 0)
count = 0
for i in range(2):
for j in range(2):
key_matrix[i][j] = baseString.index(new_key[count].lower())
count += 1
if mod.gcd(matrix.det(key_matrix), 26) != 1:
print('Error(d_hill): key is not invertible')
return ''
inverse_key_matrix = matrix.inverse(key_matrix, 26)
plaintext = ''
non_alpha = utilities_A4.get_nonalpha(ciphertext)
blocks = utilities_A4.text_to_blocks(
utilities_A4.remove_nonalpha(ciphertext), 2)
for block in blocks:
block_m = matrix.new_matrix(2, 1, 0)
block_m[0][0] = baseString.index(block[0].lower())
block_m[1][0] = baseString.index(block[1].lower())
result_m = matrix.matrix_mod(matrix.mul(inverse_key_matrix, block_m),
26)
plaintext += baseString[result_m[0][0]].lower()
plaintext += baseString[result_m[1][0]].lower()
plaintext = utilities_A4.insert_nonalpha(plaintext, non_alpha)
while plaintext[-1] == 'q':
plaintext = plaintext[:-1]
return plaintext
def testMul(self):
lhs = OrderedSet(['a', 'b', 'c', 'd', 'e', 'f', 'g', 'h'])
rhs = OrderedSet(['1', '2', '3', '4', '5', '6', '7', '8'])
prod = mul(lhs, rhs)
result = OrderedSet(['a1', 'a2', 'a3', 'a4', 'a5', 'a6', 'a7', 'a8',
'b1', 'b2', 'b3', 'b4', 'b5', 'b6', 'b7', 'b8',
'c1', 'c2', 'c3', 'c4', 'c5', 'c6', 'c7', 'c8',
'd1', 'd2', 'd3', 'd4', 'd5', 'd6', 'd7', 'd8',
'e1', 'e2', 'e3', 'e4', 'e5', 'e6', 'e7', 'e8',
'f1', 'f2', 'f3', 'f4', 'f5', 'f6', 'f7', 'f8',
'g1', 'g2', 'g3', 'g4', 'g5', 'g6', 'g7', 'g8',
'h1', 'h2', 'h3', 'h4', 'h5', 'h6', 'h7', 'h8'])
self.assertEqual(prod, result)
def __init__(self, filename):
super(PygameInterpreter, self).__init__(filename)
# Font
if os.path.exists(DIR_FONT):
font_name = DIR_FONT
else:
self.error("No {0}. Falling back to pygame default font.".format(
DIR_FONT))
font_name = None # pygame default
self.font = pygame.font.Font(font_name, FONT_SIZE)
# pixel positioning
self.text_height = self.font.get_linesize()
border_width = int(self.text_height * BORDER_WIDTH_MULTIPLIER)
self.text_topleft = [border_width] * 2
txt_area_size = matrix.sub(self.resolution,
matrix.mul(self.text_topleft, [2, 2]))
self.row_length = txt_area_size[0]
# text placing
self.linenumber = 0
self.remaining_row = self.row_length
self.text = []
self.text_states = []
# setup
self.clearwait = False
#~ # black filter
#~ self.darkening = 0
# buttons
self.buttons = []
# menu
self.rmenu = None
# saving
# normally this should be read in from the savenumber command
self.savenumber = 20
self.saves = dict()
def __init__(self, filename):
super(PygameInterpreter, self).__init__(filename)
# Font
if os.path.exists(DIR_FONT):
font_name = DIR_FONT
else:
self.error( "No {0}. Falling back to pygame default font.".format(DIR_FONT) )
font_name = None # pygame default
self.font = pygame.font.Font(font_name, FONT_SIZE)
# pixel positioning
self.text_height = self.font.get_linesize()
border_width = int(self.text_height*BORDER_WIDTH_MULTIPLIER)
self.text_topleft = [border_width]*2
txt_area_size = matrix.sub( self.resolution, matrix.mul(self.text_topleft, [2, 2]) )
self.row_length = txt_area_size[0]
# text placing
self.linenumber = 0
self.remaining_row = self.row_length
self.text = []
self.text_states = []
# setup
self.clearwait = False
#~ # black filter
#~ self.darkening = 0
# buttons
self.buttons = []
# menu
self.rmenu = None
# saving
# normally this should be read in from the savenumber command
self.savenumber = 20
self.saves = dict()
def test_q4():
print("-------------------------------------------")
print("Testing Q4: Matrix Library")
filename = 'q4_solution.txt'
outFile = open(filename, 'w')
print()
outFile.write('1- Testing is_vector:\n')
outFile.write('is_vector({}) = {}\n'.format([], matrix.is_vector([])))
outFile.write('is_vector({}) = {}\n'.format([10], matrix.is_vector([10])))
outFile.write('is_vector({}) = {}\n'.format([10, 20],
matrix.is_vector([10, 20])))
outFile.write('is_vector({}) = {}\n'.format(10, matrix.is_vector(10)))
outFile.write('is_vector({}) = {}\n'.format([3, 4.5],
matrix.is_vector([3, 4.5])))
outFile.write('is_vector({}) = {}\n'.format([[]], matrix.is_vector([[]])))
outFile.write('is_vector({}) = {}\n'.format([[1, 2], [3, 4]],
matrix.is_vector([[1, 2],
[3, 4]])))
outFile.write('\n')
outFile.write('2- Testing is_matrix')
A = []
outFile.write('is_matrix({}) = {}\n'.format(A, matrix.is_matrix(A)))
A = [5]
outFile.write('is_matrix({}) = {}\n'.format(A, matrix.is_matrix(A)))
A = [[1, 2], [3, 4]]
outFile.write('is_matrix({}) = {}\n'.format(A, matrix.is_matrix(A)))
A = [[1], [2], [3]]
outFile.write('is_matrix({}) = {}\n'.format(A, matrix.is_matrix(A)))
A = [[1, 2, 3], [4, 5, 6]]
outFile.write('is_matrix({}) = {}\n'.format(A, matrix.is_matrix(A)))
A = 5
outFile.write('is_matrix({}) = {}\n'.format(A, matrix.is_matrix(A)))
A = [5.5]
outFile.write('is_matrix({}) = {}\n'.format(A, matrix.is_matrix(A)))
A = [[1, 2, 3], [4, 5]]
outFile.write('is_matrix({}) = {}\n'.format(A, matrix.is_matrix(A)))
outFile.write('\n')
print('3- Testing print_matrix')
A = []
print('print_matrix({})='.format(A))
matrix.print_matrix(A)
A = [10, 20, 30]
print('print_matrix({})='.format(A))
matrix.print_matrix(A)
A = [[10], [20], [30]]
print('print_matrix({})='.format(A))
matrix.print_matrix(A)
A = [[10, 20, 30], [40, 50, 60], [70, 80, 10]]
print('print_matrix({})='.format(A))
matrix.print_matrix(A)
A = [[10, 20, 30], [40, 50, 60], [70, 80]]
print('print_matrix({})='.format(A))
print(matrix.print_matrix(A))
print()
outFile.write('4/5/6- Testing size functions\n')
A = []
outFile.write('get_rowCount({}) = {}\n'.format(A,
matrix.get_rowCount(A)))
outFile.write('get_ColumnCount({}) = {}\n'.format(
A, matrix.get_columnCount(A)))
outFile.write('get_size({}) = {}\n'.format(A, matrix.get_size(A)))
outFile.write('\n')
A = [1, 2, 3]
outFile.write('get_rowCount({}) = {}\n'.format(A,
matrix.get_rowCount(A)))
outFile.write('get_ColumnCount({}) = {}\n'.format(
A, matrix.get_columnCount(A)))
outFile.write('get_size({}) = {}\n'.format(A, matrix.get_size(A)))
outFile.write('\n')
A = [[1, 2], [3, 4], [5, 6]]
outFile.write('get_rowCount({}) = {}\n'.format(A,
matrix.get_rowCount(A)))
outFile.write('get_ColumnCount({}) = {}\n'.format(
A, matrix.get_columnCount(A)))
outFile.write('get_size({}) = {}\n'.format(A, matrix.get_size(A)))
outFile.write('\n')
A = [[1, 2], [3]]
outFile.write('get_rowCount({}) = {}\n'.format(A,
matrix.get_rowCount(A)))
outFile.write('get_ColumnCount({}) = {}\n'.format(
A, matrix.get_columnCount(A)))
outFile.write('get_size({}) = {}\n'.format(A, matrix.get_size(A)))
outFile.write('\n')
outFile.write('7- Testing is_square\n')
A = []
outFile.write('is_square({}) = {}\n'.format(A, matrix.is_square(A)))
A = [5]
outFile.write('is_square({}) = {}\n'.format(A, matrix.is_square(A)))
A = [5, 6]
outFile.write('is_square({}) = {}\n'.format(A, matrix.is_square(A)))
A = [[1, 2], [3, 4]]
outFile.write('is_square({}) = {}\n'.format(A, matrix.is_square(A)))
A = [5.5]
outFile.write('is_square({}) = {}\n'.format(A, matrix.is_square(A)))
outFile.write('\n')
outFile.write('8/9/10- Testing getter functions\n')
A = [[1, 2, 3], [4, 5, 6]]
i = 0
j = 1
outFile.write('get_row({},{}) = {}\n'.format(A, i, matrix.get_row(A,
i)))
outFile.write('get_Column({},{}) = {}\n'.format(A, j,
matrix.get_column(A, j)))
outFile.write('get_element({},{},{}) = {}\n'.format(
A, i, j, matrix.get_element(A, i, j)))
outFile.write('\n')
i = 2
j = 2
outFile.write('get_row({},{}) = {}\n'.format(A, i, matrix.get_row(A,
i)))
outFile.write('get_Column({},{}) = {}\n'.format(A, j,
matrix.get_column(A, j)))
outFile.write('get_element({},{},{}) = {}\n'.format(
A, i, j, matrix.get_element(A, i, j)))
outFile.write('\n')
i = 1
j = 3
outFile.write('get_row({},{}) = {}\n'.format(A, i, matrix.get_row(A,
i)))
outFile.write('get_Column({},{}) = {}\n'.format(A, j,
matrix.get_column(A, j)))
outFile.write('get_element({},{},{}) = {}\n'.format(
A, i, j, matrix.get_element(A, i, j)))
outFile.write('\n')
A = [[1, 2, 3], []]
outFile.write('get_row({},{}) = {}\n'.format(A, i, matrix.get_row(A,
i)))
outFile.write('get_Column({},{}) = {}\n'.format(A, j,
matrix.get_column(A, j)))
outFile.write('get_element({},{},{}) = {}\n'.format(
A, i, j, matrix.get_element(A, i, j)))
outFile.write('\n')
outFile.write('11- Testing new_matrix\n')
r = 0
c = 0
pad = 0
outFile.write('new_matrix({},{},{})=\n{}\n'.format(
r, c, pad, matrix.new_matrix(r, c, pad)))
c = 1
outFile.write('new_matrix({},{},{})=\n{}\n'.format(
r, c, pad, matrix.new_matrix(r, c, pad)))
r = 1
outFile.write('new_matrix({},{},{})=\n{}\n'.format(
r, c, pad, matrix.new_matrix(r, c, pad)))
r = 2
c = 1
outFile.write('new_matrix({},{},{})=\n{}\n'.format(
r, c, pad, matrix.new_matrix(r, c, pad)))
c = 2
r = 1
outFile.write('new_matrix({},{},{})=\n{}\n'.format(
r, c, pad, matrix.new_matrix(r, c, pad)))
c = 3
r = 3
outFile.write('new_matrix({},{},{})=\n{}\n'.format(
r, c, pad, matrix.new_matrix(r, c, pad)))
r = -1
outFile.write('new_matrix({},{},{})=\n{}\n'.format(
r, c, pad, matrix.new_matrix(r, c, pad)))
r = 3
c = -5
outFile.write('new_matrix({},{},{})=\n{}\n'.format(
r, c, pad, matrix.new_matrix(r, c, pad)))
c = 5
pad = 3.5
outFile.write('new_matrix({},{},{})=\n{}\n'.format(
r, c, pad, matrix.new_matrix(r, c, pad)))
outFile.write('\n')
outFile.write('12- Testing get_I\n')
size = -1
outFile.write('get_I({}) = {}\n'.format(size, matrix.get_I(size)))
size = 0
outFile.write('get_I({}) = {}\n'.format(size, matrix.get_I(size)))
size = 1
outFile.write('get_I({}) = {}\n'.format(size, matrix.get_I(size)))
size = 2
outFile.write('get_I({}) = {}\n'.format(size, matrix.get_I(size)))
size = 3
outFile.write('get_I({}) = {}\n'.format(size, matrix.get_I(size)))
outFile.write('\n')
outFile.write('13- Testing is_identity\n')
A = [1]
outFile.write('is_identity({}) = {}\n'.format(A, matrix.is_identity(A)))
A = matrix.get_I(3)
outFile.write('is_identity({}) = {}\n'.format(A, matrix.is_identity(A)))
A = [[1, 0], [1, 1]]
outFile.write('is_identity({}) = {}\n'.format(A, matrix.is_identity(A)))
A = [[1, 0], [0, 1, 0]]
outFile.write('is_identity({}) = {}\n'.format(A, matrix.is_identity(A)))
outFile.write('\n')
outFile.write('14- Testing scalar_mul\n')
A = [[1, 2], [3, 4]]
c = 10
outFile.write('scalar_mul({},{}) = {}\n'.format(A, c,
matrix.scalar_mul(c, A)))
A = [1, 2, 3, 4]
outFile.write('scalar_mul({},{}) = {}\n'.format(A, c,
matrix.scalar_mul(c, A)))
A = []
outFile.write('scalar_mul({},{}) = {}\n'.format(A, c,
matrix.scalar_mul(c, A)))
A = [1, 2, 3, [4]]
outFile.write('scalar_mul({},{}) = {}\n'.format(A, c,
matrix.scalar_mul(c, A)))
A = [[1, 2], [3, 4]]
c = [10]
outFile.write('scalar_mul({},{}) = {}\n'.format(A, c,
matrix.scalar_mul(c, A)))
outFile.write('\n')
outFile.write('15- Testing mul\n')
A = [[1, 2], [3, 4]]
B = [[10, 20], [30, 40]]
outFile.write('mul({},{})=\n{}\n'.format(A, c, matrix.mul(A, B)))
A = [[1, 2, 3], [5, 6, 7]]
B = [[10, 20], [30, 40], [50, 60]]
outFile.write('mul({},{})= {}\n'.format(A, c, matrix.mul(A, B)))
A = [5]
B = [10]
outFile.write('mul({},{})= {}\n'.format(A, B, matrix.mul(A, B)))
A = [0, 1, 2]
B = [[0], [1], [2]]
outFile.write('mul({},{})= {}\n'.format(A, B, matrix.mul(A, B)))
A = [[0], 1]
B = [1, 0]
outFile.write('mul({},{})= {}\n'.format(A, B, matrix.mul(A, B)))
A = [1, 0]
B = [[0], 1]
outFile.write('mul({},{})= {}\n'.format(A, B, matrix.mul(A, B)))
A = [[1, 2, 3], [5, 6, 7]]
B = [[10, 20], [30, 40], [50, 60]]
outFile.write('mul({},{})= {}\n'.format(B, A, matrix.mul(B, A)))
A = [[1, 2, 3], [5, 6, 7]]
B = [[10, 20], [30, 40]]
outFile.write('mul({},{})= {}\n'.format(A, B, matrix.mul(A, B)))
outFile.write('\n')
outFile.write('16- Testing matrix_mod\n')
A = [[1, 2], [3, 4]]
m = 2
outFile.write('matrix_mod({},{})= {}\n'.format(A, m,
matrix.matrix_mod(A, m)))
A = [1, 2, 3, 4]
m = 2
outFile.write('matrix_mod({},{})= {}\n'.format(A, m,
matrix.matrix_mod(A, m)))
A = [[3], [5]]
m = 3
outFile.write('matrix_mod({},{})= {}\n'.format(A, m,
matrix.matrix_mod(A, m)))
A = [[3], [5]]
m = 0
outFile.write('matrix_mod({},{})= {}\n'.format(A, m,
matrix.matrix_mod(A, m)))
A = [3, [5]]
m = 6
outFile.write('matrix_mod({},{})= {}\n'.format(A, m,
matrix.matrix_mod(A, m)))
outFile.write('\n')
outFile.write('17- Testing det\n')
A = [[1, 2], [3, 4]]
outFile.write('det({})= {}\n'.format(A, matrix.det(A)))
A = [10]
outFile.write('det({})= {}\n'.format(A, matrix.det(A)))
A = [[1, 1, 1], [2, 2, 2], [3, 3, 3]]
outFile.write('det({})= {}\n'.format(A, matrix.det(A)))
A = [[1, 1, 1], [2, 2]]
outFile.write('det({})= {}\n'.format(A, matrix.det(A)))
outFile.write('\n')
outFile.write('18- Testing inverse\n')
A = [[1, 4], [8, 11]]
m = 26
outFile.write('inverse({},{})= {}\n'.format(A, m, matrix.inverse(A, m)))
A = [[4, 3], [1, 1]]
m = 5
outFile.write('inverse({},{})= {}\n'.format(A, m, matrix.inverse(A, m)))
A = [[1, 4], [8, 10]]
m = 26
outFile.write('inverse({},{})= {}\n'.format(A, m, matrix.inverse(A, m)))
A = [1, 4, 8, 10]
m = 15
outFile.write('inverse({},{})= {}\n'.format(A, m, matrix.inverse(A, m)))
A = [[4, 3], [1, 1]]
m = -5
outFile.write('inverse({},{})= {}\n'.format(A, m, matrix.inverse(A, m)))
A = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]
m = 7
outFile.write('inverse({},{})= {}\n'.format(A, m, matrix.inverse(A, m)))
A = [[1, 2, 3], [4, 5]]
m = 7
outFile.write('inverse({},{})= {}\n'.format(A, m, matrix.inverse(A, m)))
outFile.close()
print('Comparing q4_solution with q4_sample:')
print(utilities_A4.compare_files('q4_solution.txt', 'q4_sample.txt'))
print()
print("-------------------------------------------")