def lorentz_transform(self, transformation_matrix):
"""
Performs a Lorentz transform on the tensor.
Parameters
----------
transformation_matrix : ~sympy.tensor.array.dense_ndim_array.ImmutableDenseNDimArray or list
Sympy Array or multi-dimensional list containing Sympy Expressions
Returns
-------
~einsteinpy.symbolic.metric.MetricTensor
lorentz transformed tensor
"""
t = super(MetricTensor, self).lorentz_transform(transformation_matrix)
return MetricTensor(
t.tensor(),
syms=self.syms,
config=self._config,
name=_change_name(self.name, context="__lt"),
)
def change_config(self, newconfig="lll", metric=None):
"""
Changes the index configuration(contravariant/covariant)
Parameters
----------
newconfig : str
Specify the new configuration. Defaults to 'lll'
metric : ~einsteinpy.symbolic.metric.MetricTensor or None
Parent metric tensor for changing indices.
Already assumes the value of the metric tensor from which it was initialized if passed with None.
Compulsory if not initialized with 'from_metric'. Defaults to None.
Returns
-------
~einsteinpy.symbolic.christoffel.ChristoffelSymbols
New tensor with new configuration. Defaults to 'lll'
Raises
------
Exception
Raised when a parent metric could not be found.
"""
if metric is None:
metric = self._parent_metric
if metric is None:
raise Exception(
"Parent Metric not found, can't do configuration change")
new_tensor = _change_config(self, metric, newconfig)
new_obj = ChristoffelSymbols(
new_tensor,
self.syms,
config=newconfig,
parent_metric=metric,
name=_change_name(self.name, context="__" + newconfig),
)
return new_obj
def lorentz_transform(self, transformation_matrix):
"""
Performs a Lorentz transform on the tensor.
Parameters
----------
transformation_matrix : ~sympy.tensor.array.dense_ndim_array.ImmutableDenseNDimArray or list
Sympy Array or multi-dimensional list containing Sympy Expressions
Returns
-------
~einsteinpy.symbolic.tensor.BaseRelativityTensor
lorentz transformed tensor(or vector)
"""
tm = sympy.Array(transformation_matrix)
t = self.tensor()
for i in range(self.order):
if self.config[i] == "u":
t = simplify(
tensorcontraction(tensorproduct(tm, t), (1, 2 + i)))
else:
t = simplify(
tensorcontraction(tensorproduct(tm, t), (0, 2 + i)))
dest = list(range(len(t.shape)))
dest.remove(0)
dest.insert(i, 0)
t = sympy.permutedims(t, dest)
return BaseRelativityTensor(
t,
syms=self.syms,
config=self.config,
parent_metric=None,
variables=self.variables,
functions=self.functions,
name=_change_name(self.name, context="__lt"),
)
def change_config(self, newconfig="uu"):
"""
Changes the index configuration(contravariant/covariant)
Parameters
----------
newconfig : str
Specify the new configuration. Defaults to 'uu'
Returns
-------
~einsteinpy.symbolic.metric.MetricTensor
New Metric with new configuration. Defaults to 'uu'
Raises
------
ValueError
Raised when new configuration is not 'll' or 'uu'.
This constraint is in place because we are dealing with Metric Tensor.
"""
if newconfig == self.config:
return self
if newconfig == "uu" or newconfig == "ll":
inv_met = MetricTensor(
sympy.simplify(sympy.Matrix(self.arr.tolist()).inv()).tolist(),
self.syms,
config=newconfig,
name=_change_name(self.name, context="__" + newconfig),
)
inv_met._invmetric = self
return inv_met
raise ValueError(
"Configuration can't have one upper and one lower index in Metric Tensor."
)
def test_change_name(curr_name, context, expected):
altered_name = _change_name(curr_name, context)
assert altered_name == expected
