def test_contract_automatrix_and_data():
numpy = import_module('numpy')
if numpy is None:
return
L = TensorIndexType('L')
S = TensorIndexType('S')
G = tensorhead('G', [L, S, S], [[1] * 3], matrix_behavior=True)
def G_data():
G.data = [[[1]]]
raises(ValueError, G_data)
L.data = [1, -1]
raises(ValueError, G_data)
S.data = [[1, 0], [0, 2]]
G.data = [
[[1, 2],
[3, 4]],
[[5, 6],
[7, 8]]
]
m0, m1, m2 = tensor_indices('m0:3', L)
s0, s1, s2 = tensor_indices('s0:3', S)
assert (G(-m0).data == numpy.array([
[[1, 4],
[3, 8]],
[[-5, -12],
[-7, -16]]
])).all()
(G(m0) * G(-m0)).data
G(m0, s0, -s1).data
c1 = G(m0, s0, -s1)*G(-m0, s1, -s2)
c2 = G(m0) * G(-m0)
assert (c1.data == c2.data).all()
del L.data
del S.data
del G.data
assert L.data is None
assert S.data is None
assert G.data is None
def test_noncommuting_components():
numpy = import_module("numpy")
if numpy is None:
skip("numpy not installed.")
euclid = TensorIndexType('Euclidean')
euclid.data = [1, 1]
i1, i2, i3 = tensor_indices('i1:4', euclid)
a, b, c, d = symbols('a b c d', commutative=False)
V1 = tensorhead('V1', [euclid] * 2, [[1]]*2)
V1.data = [[a, b], (c, d)]
V2 = tensorhead('V2', [euclid] * 2, [[1]]*2)
V2.data = [[a, c], [b, d]]
vtp = V1(i1, i2) * V2(-i2, -i1)
assert vtp == a ** 2 + b * c + c * b + d ** 2
assert vtp != a**2 + 2*b*c + d**2
Vc = b * V1(i1, -i1)
assert Vc.expand() == b * a + b * d
assert check_all(tsymmetry)
### TEST VALUED TENSORS ###
numpy = import_module('numpy')
if numpy:
minkowski = Matrix((
(1, 0, 0, 0),
(0, -1, 0, 0),
(0, 0, -1, 0),
(0, 0, 0, -1),
))
Lorentz = TensorIndexType('Lorentz', dim=4)
Lorentz.data = minkowski
i0, i1, i2, i3, i4 = tensor_indices('i0:5', Lorentz)
E, px, py, pz = symbols('E px py pz')
A = tensorhead('A', [Lorentz], [[1]])
A.data = [E, px, py, pz]
B = tensorhead('B', [Lorentz], [[1]], 'Gcomm')
B.data = range(4)
AB = tensorhead("AB", [Lorentz] * 2, [[1]]*2)
AB.data = minkowski
ba_matrix = Matrix((
(1, 2, 3, 4),
(5, 6, 7, 8),
(9, 0, -1, -2),
ret = sympy.Matrix(ret)
return ret
a, d, p, f, fx, fy, t, g, d2, d4 = sympy.symbols('a d p f fx fy t g d2 d4')
q = 1 - p
f = 0
d_index = TensorIndexType('d_index', dummy_fmt='L')
z_index = TensorIndexType('z_index', dummy_fmt='L')
PJ = [1, 1, 1]
d_index.data = [[PJ[0], 0, 0], [0, PJ[1], 0], [0, 0, PJ[2]]]
#d_index.data = [ [1, 0.5, 0], [0.5, 1, 0.5], [0, 0.5, 1 ] ]
print d_index.metric
P = tensorhead('P', [d_index, d_index, d_index], [[1], [1], [1]])
#R = tensorhead('R', [d_index, d_index], [[1], [1]])
R = tensorhead('R', [d_index, d_index, d_index, d_index], [[1], [1], [1], [1]])
S1 = tensorhead('S1', [d_index], [[1]])
S = tensorhead('S', [d_index, d_index], [[1], [1]])
#I = tensorhead('I', [d_index, d_index, d_index, d_index], [[1],[1],[1],[1]])
I = tensorhead(
'I',
[d_index, d_index, d_index, d_index, d_index, d_index, d_index, d_index],
[[1], [1], [1], [1], [1], [1], [1], [1]])
from sympy.tensor.tensor import tensor_indices, tensorhead, TensorIndexType, TensorType
import sympy
d_index = TensorIndexType('d_index', dummy_fmt='L')
#z_index = TensorIndexType('z_index', dummy_fmt='L')
P = tensorhead('P', [d_index, d_index, d_index], [[1], [1], [1]])
R = tensorhead('R', [d_index, d_index, d_index, d_index], [[1], [1], [1], [1]])
#I = tensorhead('I', [z_index, z_index, z_index, z_index], [[1]])
d_index.data = [1, 1, 1]
b0, b1, b2, b3, b4, b5 = tensor_indices('b0:6', d_index)
# 00 01 02
# 10 11 12
# 20 21 22
P.data = [
[
[1.0, 0.5, 0.0],
[0.5, .25, 0.0], #=0
[0.0, 0.0, 0.0]
],
[
[0.0, 0.5, 1.0],
[0.5, 0.5, 0.5], #=1
[1.0, 0.5, 0.0]
],
[
[0.0, 0.0, 0.0],
[0.0, .25, 0.5], #=2
[0.0, 0.5, 1.0]
assert check_all(tsymmetry)
### TEST VALUED TENSORS ###
numpy = import_module('numpy')
if numpy:
minkowski = Matrix((
(1, 0, 0, 0),
(0, -1, 0, 0),
(0, 0, -1, 0),
(0, 0, 0, -1),
))
Lorentz = TensorIndexType('Lorentz', dim=4)
Lorentz.data = minkowski
i0, i1, i2, i3, i4 = tensor_indices('i0:5', Lorentz)
E, px, py, pz = symbols('E px py pz')
A = tensorhead('A', [Lorentz], [[1]])
A.data = [E, px, py, pz]
B = tensorhead('B', [Lorentz], [[1]], 'Gcomm')
B.data = range(4)
AB = tensorhead("AB", [Lorentz] * 2, [[1]] * 2)
AB.data = minkowski
ba_matrix = Matrix((
(1, 2, 3, 4),
(5, 6, 7, 8),
(9, 0, -1, -2),
