def test_row_mac_03(self):
det_before = m.det(self.mat_g)
m.row_mul_add(self.mat_g, 0, 2, 0.5)
det_after = m.det(self.mat_g)
self.mat_exp = [[0, -0.5, -1.0], [0, 1, 2], [-2, -1, 0]]
self.assertSequenceEqual(self.mat_g, self.mat_exp)
self.assertEqual(det_before, det_after)
def test_row_mac_02(self):
det_before = m.det(self.mat_g)
m.row_mul_add(self.mat_g, 1, 2, -1)
det_after = m.det(self.mat_g)
self.mat_exp = [[1, 0, -1], [2, 2, 2], [-2, -1, 0]]
self.assertSequenceEqual(self.mat_g, self.mat_exp)
self.assertEqual(det_before, det_after)
def test_row_mac_01(self):
det_before = m.det(self.mat_i)
m.row_mul_add(self.mat_i, 1, 0, 0.5)
det_after = m.det(self.mat_i)
self.mat_exp = [
[1, 0],
[0.5, 1.0],
]
self.assertSequenceEqual(self.mat_i, self.mat_exp)
self.assertEqual(det_before, det_after)
def matrix_inversion(eqs, varNames, api = False, ACCURACY = 4):
''' Matrix Inversion Method '''
if len(eqs) != len(eqs[0])-1 or len(varNames) != len(eqs):
raise Exception("Insufficient number of variables of equations.")
var_count = len(varNames)
delta_matrix = SquareMatrix([row[:-1] for row in eqs])
delta = det(delta_matrix)
if delta == 0:
raise Exception("Δ = 0, Matrix Inversion failed!")
const_matrix = Matrix([[row[-1]] for row in eqs])
adjoint = adj(delta_matrix)
res = (adjoint*const_matrix)*(1/delta) # actual solving step
adjointArray = adjoint.toList()
resArray = [q[0] for q in res]
result = [delta, adjointArray]
for i in range(var_count):
result.append((varNames[i], round(resArray[i], ACCURACY)))
if api:
return result
else:
print("Determinant = {0:.{1}f}".format(delta, ACCURACY))
print("Adjoint = " + str(adjointArray))
for name, value in result[2:]:
print("{0} = {1:.{2}f}".format(name, value, ACCURACY))
def setUp(self):
self.mj = pt.B
self.mp = pt.A
self.mt = pt.transp(pt.A)
self.mh = pt.det(pt.A)
self.mk = pt.matmult(pt.A, pt.B)
def test(size):
matrix = read_matrix(f'assets/input{size}.txt', size)
exp = read_int(f'assets/output{size}.txt')
act = det(matrix)
if exp == act:
print(f'Test passed. Answer: {act}')
else:
print(f'Test failed. Answer: {exp} Actual: {act}')
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 cramer(eqs, varNames, api = False, ACCURACY = 4):
''' Cramer's Rule '''
if len(eqs) != len(eqs[0])-1 or len(varNames) != len(eqs):
raise Exception("Insufficient number of variables of equations.")
var_count = len(varNames)
delta_matrix = SquareMatrix([row[:-1] for row in eqs])
delta = det(delta_matrix)
if delta == 0:
raise Exception("Δ = 0, Cramer's method failed!")
result = []
for i in range(var_count):
local_matrix = SquareMatrix([row[:i] + [row[-1]] + row[i+1:-1] for row in eqs])
result.append((varNames[i], round(det(local_matrix)/delta, ACCURACY)))
if api:
return result
else:
for name, value in result:
print("{0} = {1:.{2}f}".format(name, value, ACCURACY))
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("-------------------------------------------")
# Словарь функций
dictionary = {
'1':
matrix.add(data['first_matrix_dimensions'],
data['second_matrix_dimensions'], data['first_matrix'],
data['second_matrix']),
'2':
matrix.sub(data['first_matrix_dimensions'],
data['second_matrix_dimensions'], data['first_matrix'],
data['second_matrix']),
'3':
matrix.mult(data['first_matrix_dimensions'],
data['second_matrix_dimensions'], data['first_matrix'],
data['second_matrix']),
'4':
matrix.det(data['number'], data['first_matrix'])
}
# Вызов функции из словоря по списку входных данных
for param in calls:
if isinstance(dictionary[param],
list) and not (isinstance(dictionary[param][0], int) or
isinstance(dictionary[param][0], float)):
for i in range(len(dictionary[param])):
for j in range(len(dictionary[param][i])):
print(dictionary[param][i][j], '', end='')
print()
elif isinstance(dictionary[param],
list) and (isinstance(dictionary[param][0], int)
or isinstance(dictionary[param][0], float)):
for i in range(len(dictionary[param])):
def test_adj01(self):
self.mat_r = m.adjugate_matrix(self.mat_d)
d = m.det(self.mat_d)
self.mat_exp = [[d, 0, 0], [0, d, 0], [0, 0, d]]
self.assertEqual(m.mul_mat(self.mat_r, self.mat_d), self.mat_exp)
self.assertEqual(m.mul_mat(self.mat_d, self.mat_r), self.mat_exp)
def test_det03(self):
d = m.det(self.mat_a)
e = self.mat_a[0][0] * self.mat_a[1][1] - self.mat_a[0][
1] * self.mat_a[1][0]
self.assertEqual(d, e)
def test_det02(self):
d = m.det(self.mat_d)
self.assertEqual(d, 24.0)
def test_det01(self):
d = m.det(self.mat_i)
self.assertEqual(d, 1.0)
