def test_change_config():
x, y, z = sympy.symbols("x y z")
list3d = np.zeros((3, 3, 3), dtype=int).tolist()
for i in range(3):
list3d[i][i][i] = (x**i) * (y * (2 - i)) + i * z
list3d[1][2][0] = list3d[1][0][2] = x * y * z
list3d[2][1][0] = list3d[2][0][1] = 4 * y
metriclist = np.identity(3).tolist()
metric = MetricTensor(metriclist, (x, y, z), "uu")
ch = ChristoffelSymbols(list3d, (x, y, z), "ull", parent_metric=metric)
chr_new = ch.change_config("llu")
for t in range(3):
i, j, k = t % 3, (int(t / 3)) % 3, (int(t / (3**2))) % 3
assert sympy.simplify(ch[i, j, k] - chr_new[i, j, k]) == 0
def test_TypeError():
testarr = np.ones((4, 4, 4), dtype=int).tolist()
syms = 0
try:
obj = ChristoffelSymbols(testarr, syms)
assert False
except TypeError:
assert True
def test_no_exception_raised_passing_christoffel_with_unconventional_indices():
sch = schwarzschild_metric()
ch = ChristoffelSymbols.from_metric(sch)
ch2 = ch.change_config("uuu")
try:
rm = RiemannCurvatureTensor.from_christoffels(ch2)
assert True
except:
assert False
def test_properties():
sch_inv = schwarzschild_metric()
ch = ChristoffelSymbols.from_metric(sch_inv)
assert ch.parent_metric == ch._parent_metric
# test change_config, should raise ValueError
ch._parent_metric = None
try:
ch_new = ch.change_config("lll")
assert False
except Exception:
return True
def get_christoffel_symbols(self, input_vectors=None):
"""
returns the christoffel symbols in the standard order:
`cf[i,j,k]`= $\Gamma^i_{jk}$
einsteinpy is used to obtain the tensor
"""
cf = ChristoffelSymbols.from_metric(self.get_metric_tensor())
if input_vectors is not None:
cf = self.model.apply(cf.tensor(), input_vectors)
return cf
def test_wrong_number_of_indices_ValueError():
x, y, z = sympy.symbols("x y z")
list3d = np.zeros((3, 3, 3), dtype=int).tolist()
for i in range(3):
list3d[i][i][i] = (x**i) * (y * (2 - i)) + i * z
list3d[1][2][0] = list3d[1][0][2] = x * y * z
list3d[2][1][0] = list3d[2][0][1] = 4 * y
try:
ch = ChristoffelSymbols(list3d, (x, y, z), "ulll")
assert False
except ValueError:
assert True
def test_ChristoffelSymbols():
sch = schwarzschild_metric()
chl = ChristoffelSymbols.from_metric(sch)
mat = chl.tensor()
symbolstr = "t r theta phi"
syms = sympy.symbols(symbolstr)
G, M, c, a = sympy.symbols("G M c a")
assert (
sympy.simplify(mat[2, 3, 3] -
(-1 * sympy.cos(syms[2]) * sympy.sin(syms[2]))) == 0)
assert sympy.simplify(mat[3, 3, 1] - syms[1] / (syms[1]**2)) == 0
assert (sympy.simplify((mat[1, 1, 1].subs({a: (2 * G * M / (c**2))})) -
(G * M /
(2 * G * M * syms[1] - c**2 * syms[1]**2))) == 0)
assert chl.symbols() == syms
def christoffel_symbol(self):
from einsteinpy.symbolic import ChristoffelSymbols
return ChristoffelSymbols.from_metric(self.metric_tensor)
def get_tensor():
metric = AntiDeSitter()
return ChristoffelSymbols.from_metric(metric)