def test_arithmetics():
a = list2tensor([3 for i in range(9)], (3, 3), (1, -1))
b = list2tensor([7 for i in range(9)], (3, 3), (1, -1))
c1 = a + b
c2 = b + a
assert c1 == c2
d1 = a - b
d2 = b - a
assert d1 == d2 * (-1)
e1 = a * 5
e2 = 5 * a
e3 = copy(a)
e3 *= 5
assert e1 == e2 == e3
f1 = a / 5
f2 = copy(a)
f2 /= 5
assert f1 == f2
assert f1[0, 0] == f1[0, 1] == f1[0, 2] == f1[1, 0] == f1[1, 1] == \
f1[1, 2] == f1[2, 0] == f1[2, 1] == f1[2, 2] == 3 / 5
assert type(a) == type(b) == type(c1) == type(c2) == type(d1) == type(d2) \
== type(e1) == type(e2) == type(e3) == type(f1)
def test_raise_index():
x, y, z, w, r, phi = symbols('x y z w r phi')
A = list2tensor([1, 0, 0, 0, r**2, 0, 0, 0, (r**2) * sin(phi)], (3, 3),
(-1, -1))
original_A = copy(A)
T = list2tensor([w, x, 0, y, z, 0, 0, y**2, x * y * w], (3, 3), (-1, -1))
original_T = copy(T)
S1 = raise_index(T, A, 1)
assert S1.ind_char == (1, -1)
# check that original A and T not changed
assert original_A == A
assert original_T == T
S2 = raise_index(T, A, 2)
# w x/r**2 0
# y z/r**2 0
# 0 y**2/r**2 w*x*y/(r**2*sin(phi))
assert S2.ind_char == (-1, 1)
assert S2[0, 0] == w
assert S2[0, 1] == x / r**2
assert S2[0, 2] == S2[1, 2] == S2[2, 0] == 0
assert S2[1, 0] == y
assert S2[1, 1] == z / r**2
assert S2[2, 1] == y**2 / r**2
assert S2[2, 2] == w * x * y / (r**2 * sin(phi))
S3 = raise_index(T, A, 1, 2)
S4 = raise_index(T, A, *[1, 2])
assert S3 == S4
assert S3.ind_char == S4.ind_char == (1, 1)
def test_lower_index():
x, y, z, w, r, phi = symbols('x y z w r phi')
A = list2tensor([1, 0, 0, 0, r**2, 0, 0, 0, (r**2) * sin(phi)], (3, 3),
(-1, -1))
original_A = copy(A)
T = list2tensor([w, x, 0, y, z, 0, 0, y**2, x * y * w], (3, 3), (1, 1))
original_T = copy(T)
S1 = lower_index(T, A, 1)
assert S1.ind_char == (-1, 1)
assert original_A == A
assert original_T == T
# w x 0
# r**2*y r**2*z 0
# 0 r**2*y**2*sin(phi) r**2*w*x*y*sin(phi)
assert S1[0, 0] == w
assert S1[0, 1] == x
assert S1[0, 2] == S1[1, 2] == S1[2, 0] == 0
assert S1[1, 0] == r**2 * y
assert S1[1, 1] == r**2 * z
assert S1[2, 1] == r**2 * y**2 * sin(phi)
assert S1[2, 2] == r**2 * w * x * y * sin(phi)
S2 = lower_index(T, A, 2)
assert S2.ind_char == (1, -1)
S3 = lower_index(T, A, 1, 2)
S4 = lower_index(T, A, *[1, 2])
assert S3 == S4
assert S3.ind_char == S4.ind_char == (-1, -1)
def test_df_varlist():
x1, x2, x3 = symbols('x1 x2 x3')
f = x1**2 * x2 + sin(x2 * x3 - x2)
var_list = [x1, x2, x3]
assert df(f, var_list) == [
2 * x1 * x2, x1**2 + (x3 - 1) * cos(x2 * x3 - x2),
x2 * cos(x2 * x3 - x2)
]
assert isinstance(df(f, var_list), list)
assert df(f, var_list, 'l') == [
2 * x1 * x2, x1**2 + (x3 - 1) * cos(x2 * x3 - x2),
x2 * cos(x2 * x3 - x2)
]
assert isinstance(df(f, var_list, 'l'), list)
assert df(f, var_list, 'a') == list2arraypy([
2 * x1 * x2, x1**2 + (x3 - 1) * cos(x2 * x3 - x2),
x2 * cos(x2 * x3 - x2)
])
assert isinstance(df(f, var_list, 'a'), Arraypy)
assert df(f, var_list, 't') == list2tensor([
2 * x1 * x2, x1**2 + (x3 - 1) * cos(x2 * x3 - x2),
x2 * cos(x2 * x3 - x2)
])
assert isinstance(df(f, var_list, 't'), TensorArray)
assert df(f, var_list, 't').type_pq == (0, 1)
def test_df_var_tnsr0():
x1, x2, x3 = symbols('x1 x2 x3')
f = x1**2 * x2 + sin(x2 * x3 - x2)
var_tnsr0 = TensorArray(Arraypy(3), (1))
var_tnsr0[0] = x1
var_tnsr0[1] = x2
var_tnsr0[2] = x3
assert df(f, var_tnsr0) == [
2 * x1 * x2, x1**2 + (x3 - 1) * cos(x2 * x3 - x2),
x2 * cos(x2 * x3 - x2)
]
assert isinstance(df(f, var_tnsr0), list)
assert df(f, var_tnsr0, 'l') == [
2 * x1 * x2, x1**2 + (x3 - 1) * cos(x2 * x3 - x2),
x2 * cos(x2 * x3 - x2)
]
assert isinstance(df(f, var_tnsr0, 'l'), list)
assert df(f, var_tnsr0, 'a') == list2arraypy([
2 * x1 * x2, x1**2 + (x3 - 1) * cos(x2 * x3 - x2),
x2 * cos(x2 * x3 - x2)
])
assert isinstance(df(f, var_tnsr0, 'a'), Arraypy)
assert df(f, var_tnsr0, 't') == list2tensor([
2 * x1 * x2, x1**2 + (x3 - 1) * cos(x2 * x3 - x2),
x2 * cos(x2 * x3 - x2)
])
assert isinstance(df(f, var_tnsr0, 't'), TensorArray)
assert df(f, var_tnsr0, 't').type_pq == (0, 1)
def test_tensor_contract():
tensor = list2tensor(list(range(9)), (3, 3), (1, -1))
# 0 1 2
# 3 4 5
# 6 7 8
assert tensor.rank == 2
# contract of matrix will be summ of diagonal elements: 0 + 4 + 8 == 12
res_tensor = tensor.contract(1, 2)
assert res_tensor.rank == 1
assert len(res_tensor) == 1
assert res_tensor[0] == 12
def test_equality():
first_list = [1, 2, 3, 4]
second_list = [1, 2, 3, 4]
third_list = [4, 3, 2, 1]
assert first_list == second_list
assert first_list != third_list
first_arraypy = list2arraypy(first_list, (2, 2))
second_arraypy = list2arraypy(second_list, (2, 2))
third_arraypy = list2arraypy(third_list, (2, 2))
fourth_arraypy = list2arraypy(first_list, 4)
assert first_arraypy == second_arraypy
second_arraypy[0, 0] = 0
assert first_arraypy != second_arraypy
assert first_arraypy != third_arraypy
assert first_arraypy != fourth_arraypy
first_tensor = list2tensor(first_list, (2, 2), (1, 1))
second_tensor = list2tensor(second_list, (2, 2), (1, 1))
third_tensor = list2tensor(second_list, (2, 2), (-1, 1))
assert first_tensor == second_tensor
assert first_tensor != third_tensor
def test_converting_functions():
arr_list = [1, 2, 3, 4]
arr_matrix = Matrix(((1, 2), (3, 4)))
# list
arr_arraypy = list2arraypy(arr_list, (2, 2))
assert (isinstance(arr_arraypy, Arraypy))
arr_tensor = list2tensor(arr_list, (2, 2), (-1, -1))
assert (isinstance(arr_tensor, TensorArray))
# Matrix
arr_arraypy = matrix2arraypy(arr_matrix)
assert (isinstance(arr_arraypy, Arraypy))
arr_tensor = matrix2tensor(arr_matrix, (-1, -1))
assert (isinstance(arr_tensor, TensorArray))