def test_mult_esc_mat(self):
self.assertEqual(
str(mat_op.mult_esc_mat(complex_cart(5, 2), self.mat_comp_a)),
'[[1 + 12i, 1 + 12i], [1 + 12i, 1 + 12i], [1 + 12i, 1 + 12i]]')
self.assertEqual(
str(mat_op.mult_esc_mat(complex_cart(5, 2), self.mat_comp_b)),
'[[3 + 7i, 6 + 14i, 9 + 21i], [3 + 7i, 6 + 14i, 9 + 21i], [3 + 7i, 6 + 14i, 9 + 21i]]'
)
def exp_complex_slit(mat):
A = mat
V = [complex_cart(0, 0) for i in range(len(mat))]
V[0] = complex_cart(1, 0)
V = mat_op.transpuesta(V)
for i in range(2):
C = mat_op.mult_mat(A, V)
A = mat_op.mult_mat(A, mat)
B = mat_op.transpuesta(C[:])
for i in range(len(B)):
B[i] = round(B[i].mod()**2, 2)
Plot(len(B), B)
return mat_op.transpuesta(B)
def mult_esc_mat(A, B):
m = len(B)
n = len(B[0])
ans = [[complex_cart(0, 0) for i in range(n)] for i in range(m)]
for i in range(m):
for j in range(n):
ans[i][j] = A * B[i][j]
return ans
def sum_vect(A, B):
if len(A) == len(B):
ans = [complex_cart(0, 0) for i in range(len(A))]
for i in range(len(A)):
ans[i] = A[i] + B[i]
return ans
else:
return 'Los vectores no tienen la misma dimension'
def product_in(A, B):
A = adjunta(A)
n = len(A)
m = len(B)
if n == m:
ans = complex_cart(0, 0)
for i in range(n):
ans += A[i][0] * B[i]
return ans
def inv_adit_mat(A):
m = len(A)
n = len(A[0])
ans = [[complex_cart(0, 0) for i in range(n)] for i in range(m)]
for i in range(m):
for j in range(n):
ans[i][j].a = -A[i][j].a
ans[i][j].b = -A[i][j].b
return ans
def unitary(A):
A = mult_mat(A, adjunta(A))
B = mult_mat(adjunta(A), A)
ans = True
if len(A) == len(A[0]):
identy = [[complex_cart(0, 0) for i in range(len(A[0]))]
for j in range(len(A))]
for i in range(len(A)):
identy[i][i] = complex_cart(1, 0)
for i in range(len(A)):
for j in range(len(A)):
if A[i][j].a == B[i][j].a and B[i][j].a == identy[i][j].a and A[
i][j].b == B[i][j].b and B[i][j].b == identy[i][j].b:
ans = True
else:
return False
else:
return ans
else:
print('La matriz no es cuadrada')
def inv_adi(A):
try:
ans = [complex_cart(0, 0) for i in range(len(A))]
for i in range(len(A)):
ans[i].a = -A[i].a
ans[i].b = -A[i].b
except:
ans = [0 for i in range(len(A))]
for i in range(len(A)):
ans[i] = -A[i]
finally:
return ans
def accion(A, B):
m, n = len(A), len(A[0])
m_b = len(B)
if n == m_b:
ans = [0 for i in range(m)]
for i in range(m):
suma = complex_cart(0, 0)
for j in range(n):
suma += A[i][j] * B[j]
ans[i] = suma
return ans
else:
return 'La acción no se puede calcular '
def mult_mat(A, B):
m_a = len(A)
n_a = len(A[0])
m_b = len(B)
n_b = len(B[0])
if n_a == m_b:
ans = [[complex_cart(0, 0) for i in range(len(B[0]))]
for i in range(len(A))]
for i in range(len(A)):
for j in range(len(B[0])):
for k in range(len(A[0])):
ans[i][j] += A[i][k] * B[k][j]
return ans
else:
return 'Error, el producto entre matrices no se puede'
def Measuring(observable, ket):
observable = [[
complex(observable[i][j].a, observable[i][j].b)
for j in range(len(observable[i]))
] for i in range(len(observable))]
A = np.array(observable)
eigenvalues, eigenvects = np.linalg.eig(A)
c = []
b = []
for i in range(len(eigenvects)):
d = []
b += [complex_cart(eigenvalues[i].real, eigenvalues[i].imag)]
for j in range(len(eigenvects[i])):
z = eigenvects[i][j]
d += [complex_cart(z.real, z.imag)]
c += [d]
if ket is None:
return (b, c)
else:
prob = []
for i in range(len(b)):
prob += [(mat_op.product_in(mat_op.transpuesta(ket),
c[i])).mod()**2]
return (b, c, prob)
def Quantum_states(x, ket, ket_a):
ket = mat_op.transpuesta(ket)
if ket_a is None:
ans = []
for i in range(len(ket)):
prob = (round((ket[i].mod()**2), 2)) / (round(
(mat_op.norma_vect(ket)**2), 2))
ans += [prob]
return ans[x]
else:
ket_a = mat_op.transpuesta(ket_a)
ans = mat_op.product_in(ket_a, ket)
norma_ket = mat_op.norma_vect(ket)
norma_ket_a = mat_op.norma_vect(ket_a)
b = norma_ket * norma_ket_a
return complex_cart(ans.a / b, ans.b / b)
def setUp(self):
self.mat_bool = [[False, False, False, False, False, False],
[False, False, False, False, False, False],
[False, True, False, False, False, True],
[False, False, False, True, False, False],
[False, False, True, False, False, False],
[True, False, False, False, True, False]]
self.vect_bool = [False, False, True, False, False, False]
self.mat_real = [[0, 1 / 6, 5 / 6], [1 / 3, 1 / 2, 1 / 6],
[2 / 3, 1 / 3, 0]]
self.vect_real = ([1 / 6, 1 / 6, 2 / 3])
A = [[complex_cart(0, 0) for i in range(8)] for j in range(8)]
A[1][0] = complex_cart(1 / math.sqrt(2), 0)
A[2][0] = complex_cart(1 / math.sqrt(2), 0)
A[3][1] = complex_cart(-1 / math.sqrt(6), 1 / math.sqrt(6))
A[3][3] = complex_cart(1, 0)
A[4][1] = complex_cart(-1 / math.sqrt(6), -1 / math.sqrt(6))
A[4][4] = complex_cart(1, 0)
A[5][1] = complex_cart(1 / math.sqrt(6), -1 / math.sqrt(6))
A[5][2] = complex_cart(-1 / math.sqrt(6), 1 / math.sqrt(6))
A[5][5] = complex_cart(1, 0)
A[6][2] = complex_cart(-1 / math.sqrt(6), -1 / math.sqrt(6))
A[6][6] = complex_cart(1, 0)
A[7][2] = complex_cart(1 / math.sqrt(6), -1 / math.sqrt(6))
A[7][7] = complex_cart(1, 0)
self.mat_compleja = A
B = [[complex_cart(0, 0) for i in range(3)] for j in range(3)]
B[0][0] = complex_cart(1 / math.sqrt(2), 0)
B[1][0] = complex_cart(0, -1 / math.sqrt(2))
B[0][1] = complex_cart(1 / math.sqrt(2), 0)
B[1][1] = complex_cart(0, 1 / math.sqrt(2))
B[2][2] = complex_cart(0, -1)
self.complex_mat = B
self.complex_vect = [
complex_cart(1 / math.sqrt(3), 0),
complex_cart(0, 2 / math.sqrt(15)),
complex_cart(math.sqrt(2 / 5), 0)
]
def Problem(x):
if x == '4.3.1':
observable = [[complex_cart(0, 0),
complex_cart(1, 0)],
[complex_cart(1, 0),
complex_cart(0, 0)]]
ket = [[complex_cart(1, 0)], [complex_cart(0, 0)]]
ans = Measuring(observable, ket)
return ans[1]
elif x == '4.3.2':
observable = [[complex_cart(0, 0),
complex_cart(1, 0)],
[complex_cart(1, 0),
complex_cart(0, 0)]]
ket = [[complex_cart(1, 0)], [complex_cart(0, 0)]]
ans = Measuring(observable, ket)
value = ans[0][0] * complex_cart(
ans[2][0], 0) + ans[0][1] * complex_cart(ans[2][1], 0)
print(value)
ans_1 = mat_op.mult_mat(observable, ket)
media = mat_op.product_in(mat_op.transpuesta(ans_1),
mat_op.transpuesta(ket))
print(media)
print(
'El valor de la distribucion hallado es igual al que se obtiene en el calculo de la media'
)
return (media)
elif x == '4.4.1':
U_1 = [[complex_cart(0, 0), complex_cart(1, 0)],
[complex_cart(1, 0), complex_cart(0, 0)]]
U_2 = [[
complex_cart(math.sqrt(2 / 4), 0),
complex_cart(math.sqrt(2 / 4), 0)
],
[
complex_cart(math.sqrt(2 / 4), 0),
complex_cart(-math.sqrt(2 / 4), 0)
]]
print(mat_op.unitary(U_1, ), mat_op.unitary(U_2))
print('Las dos matrices son unitarias')
U_3 = mat_op.mult_mat(U_1, U_2)
print(mat_op.unitary(U_3))
print('El producto de las matrices es unitario')
return [mat_op.unitary(U_3)]
elif x == '4.4.2':
U_n = [[
complex_cart(0, 0),
complex_cart(1 / math.sqrt(2), 0),
complex_cart(1 / math.sqrt(2), 0),
complex_cart(0, 0)
],
[
complex_cart(0, 1 / math.sqrt(2)),
complex_cart(0, 0),
complex_cart(0, 0),
complex_cart(1 / math.sqrt(2), 0)
],
[
complex_cart(1 / math.sqrt(2), 0),
complex_cart(0, 0),
complex_cart(0, 0),
complex_cart(0, 1 / math.sqrt(2))
],
[
complex_cart(0, 0),
complex_cart(1 / math.sqrt(2), 0),
complex_cart(-1 / math.sqrt(2), 0),
complex_cart(0, 0)
]]
state = state = mat_op.transpuesta([
complex_cart(1, 0),
complex_cart(0, 0),
complex_cart(0, 0),
complex_cart(0, 0)
])
ans = Dynamics(3, U_n, state)
return ans[3]
elif x == '4.5.2':
return 'hola'
else:
return 'EL ejercicio no fue propuesto'
def Identy(n):
ans = [[complex_cart(0, 0) for i in range(n)] for j in range(n)]
for i in range(n):
ans[i][i] = complex_cart(1, 0)
return ans
def test_accion(self):
a = [[complex_cart(-1, 0),
complex_cart(1, 1),
complex_cart(0, 0)],
[complex_cart(2, -1),
complex_cart(0, 0),
complex_cart(1, 0)],
[complex_cart(0, 0),
complex_cart(1, -1),
complex_cart(0, 1)]]
b = [complex_cart(1, 0), complex_cart(1, 1), complex_cart(0, 1)]
self.assertEqual(str(mat_op.accion(a, b)), '[-1 + 2i, 2 + 0i, 1 + 0i]')
def setUp(self):
"""Genera números complejos, unos en forma polar, y otros en forma
cartesiana"""
self.complex_a = complex_cart(1, 2)
self.complex_b = complex_cart(2, 4)
self.complex_c = complex_cart(-6, 2)
self.complex_d = complex_cart(-5, -8)
self.complex_e = complex_cart(0, 0)
self.complex_f = complex_cart(1, 1)
self.complex_h = complex_cart(1 / 2, 3 / 4)
self.complex_A = complex_polar(8, (3 * math.pi) / 4)
self.complex_B = complex_polar(3, (23 * math.pi) / 22)
self.complex_C = complex_polar(24, (3 * math.pi) / 5)
self.complex_D = complex_polar(4.47, 1.11)
self.mat_num_B = [[1, 2, 3], [1, 2, 3], [1, 2, 3]]
self.mat_num_A = [[1, 2], [1, 2], [1, 2]]
self.vect_num_C = [1, 2, 3]
self.vect_num_D = [1, 2, 3, 4]
self.mat_comp_a = [[complex_cart(1, 2),
complex_cart(1, 2)],
[complex_cart(1, 2),
complex_cart(1, 2)],
[complex_cart(1, 2),
complex_cart(1, 2)]]
self.mat_comp_b = [
[complex_cart(1, 1),
complex_cart(2, 2),
complex_cart(3, 3)],
[complex_cart(1, 1),
complex_cart(2, 2),
complex_cart(3, 3)],
[complex_cart(1, 1),
complex_cart(2, 2),
complex_cart(3, 3)]
]
self.vect_comp_c = [
complex_cart(1, 1),
complex_cart(2, 2),
complex_cart(3, 3)
]
self.vect_comp_d = [
complex_cart(1, 1),
complex_cart(2, 2),
complex_cart(3, 3),
complex_cart(4, 4)
]
def test_product_in(self):
a = [complex_cart(1, 0), complex_cart(0, 1), complex_cart(1, -3)]
b = [complex_cart(2, 1), complex_cart(0, 1), complex_cart(2, 0)]
self.assertEqual(str(mat_op.product_in(a, b)), '(5, 7)')
def test_norma_vect(self):
a = [complex_cart(3.4, 4.6), complex_cart(2.2, -7.1)]
b = [complex_cart(8.2, 5.3), complex_cart(8.1, -8.0)]
self.assertEqual(mat_op.norma_vect(a), 9.38)
self.assertEqual(mat_op.norma_vect(b), 15.0)
def test_unitary(self):
a = [[complex_cart(0, 0) for i in range(3)] for i in range(3)]
for i in range(3):
a[i][i] = complex_cart(0, 1)
self.assertEqual(mat_op.unitary(a), True)
self.assertEqual(mat_op.unitary(self.mat_comp_b), False)
def test_hermitian(self):
a = [[complex_cart(5, 0), complex_cart(3, 7)],
[complex_cart(3, -7), complex_cart(2, 0)]]
self.assertEqual(mat_op.hermitian(a), True)
self.assertEqual(mat_op.hermitian(self.mat_comp_b), False)
def test_mul_esc_vect(self):
self.assertEqual(mat_op.mul_esc_vect(5, self.vect_num_C), [5, 10, 15])
self.assertEqual(
str(mat_op.mul_esc_vect(complex_cart(5, 5), self.vect_comp_d)),
'[0 + 10i, 0 + 20i, 0 + 30i, 0 + 40i]')
