def __new__(typ, name, **kwargs):
obj = IndexedBase.__new__(typ, name)
return obj
def __new__(cls, label, shape=None, function=None):
obj = IndexedBase.__new__(cls, label, shape)
obj.function = function
return obj
def __new__(typ, name, **kwargs):
obj = IndexedBase.__new__(typ, name)
return obj
def __new__(cls, name, rdim, coordinates=None):
if isinstance(rdim, (tuple, list, Tuple)):
if not len(rdim) == 1:
raise ValueError(
'> Expecting a tuple, list, Tuple of length 1')
rdim = rdim[0]
obj = IndexedBase.__new__(cls, name, shape=(rdim))
if coordinates is None:
_coordinates = [Symbol(name) for name in ['x', 'y', 'z'][:rdim]]
else:
if not isinstance(coordinates, (list, tuple, Tuple)):
raise TypeError('> Expecting list, tuple, Tuple')
for a in coordinates:
if not isinstance(a, (str, Symbol)):
raise TypeError('> Expecting str or Symbol')
_coordinates = [Symbol(name) for name in coordinates]
obj._name = name
obj._rdim = rdim
obj._coordinates = _coordinates
obj._jacobian = None
obj._det_jacobian = None
obj._covariant = None
obj._contravariant = None
obj._hessian = None
# ...
if not (obj._expressions is None):
coords = ['x', 'y', 'z'][:rdim]
# ...
args = []
for i in coords:
x = obj._expressions[i]
x = sympify(x)
args.append(x)
args = Tuple(*args)
# ...
# ...
lcoords = ['x1', 'x2', 'x3'][:rdim]
lcoords = [Symbol(i) for i in lcoords]
constants = list(set(args.free_symbols) - set(lcoords))
# subs constants as Constant objects instead of Symbol
d = {}
for i in constants:
# TODO shall we add the type?
# by default it is real
d[i] = Constant(i.name)
args = args.subs(d)
# ...
obj._expressions = args
# ...
return obj
def __new__(cls, label, shape=None, **kw_args):
return IndexedBase.__new__(cls, label, shape, **kw_args)
def __new__(cls, name, dim=None, **kwargs):
ldim = kwargs.pop('ldim', cls._ldim)
pdim = kwargs.pop('pdim', cls._pdim)
coordinates = kwargs.pop('coordinates', None)
evaluate = kwargs.pop('evaluate', True)
dims = [dim, ldim, pdim]
for i, d in enumerate(dims):
if isinstance(d,
(tuple, list, Tuple, Matrix, ImmutableDenseMatrix)):
if not len(d) == 1:
raise ValueError(
'> Expecting a tuple, list, Tuple of length 1')
dims[i] = d[0]
dim, ldim, pdim = dims
if dim is None:
assert ldim is not None
assert pdim is not None
assert pdim >= ldim
else:
ldim = dim
pdim = dim
obj = IndexedBase.__new__(cls, name, shape=pdim)
if not evaluate:
return obj
if coordinates is None:
_coordinates = [Symbol(name) for name in ['x', 'y', 'z'][:pdim]]
else:
if not isinstance(coordinates, (list, tuple, Tuple)):
raise TypeError('> Expecting list, tuple, Tuple')
for a in coordinates:
if not isinstance(a, (str, Symbol)):
raise TypeError('> Expecting str or Symbol')
_coordinates = [Symbol(u) for u in coordinates]
obj._name = name
obj._ldim = ldim
obj._pdim = pdim
obj._coordinates = tuple(_coordinates)
obj._jacobian = kwargs.pop('jacobian', JacobianSymbol(obj))
obj._is_minus = None
obj._is_plus = None
lcoords = ['x1', 'x2', 'x3'][:ldim]
lcoords = [Symbol(i) for i in lcoords]
obj._logical_coordinates = Tuple(*lcoords)
# ...
if not (obj._expressions is None):
coords = ['x', 'y', 'z'][:pdim]
# ...
args = []
for i in coords:
x = obj._expressions[i]
x = sympify(x)
args.append(x)
args = Tuple(*args)
# ...
zero_coords = ['x1', 'x2', 'x3'][ldim:]
for i in zero_coords:
x = sympify(i)
args = args.subs(x, 0)
# ...
constants = list(set(args.free_symbols) - set(lcoords))
constants_values = {a.name: Constant(a.name) for a in constants}
# subs constants as Constant objects instead of Symbol
constants_values.update(kwargs)
d = {a: constants_values[a.name] for a in constants}
args = args.subs(d)
obj._expressions = args
obj._constants = tuple(
a for a in constants
if isinstance(constants_values[a.name], Symbol))
args = [obj[i] for i in range(pdim)]
exprs = obj._expressions
subs = list(zip(_coordinates, exprs))
if obj._jac is None and obj._inv_jac is None:
obj._jac = Jacobian(obj).subs(list(zip(args, exprs)))
obj._inv_jac = obj._jac.inv()
elif obj._inv_jac is None:
obj._jac = ImmutableDenseMatrix(sympify(obj._jac)).subs(subs)
obj._inv_jac = obj._jac.inv()
elif obj._jac is None:
obj._inv_jac = ImmutableDenseMatrix(sympify(
obj._inv_jac)).subs(subs)
obj._jac = obj._inv_jac.inv()
else:
obj._jac = ImmutableDenseMatrix(sympify(obj._jac)).subs(subs)
obj._inv_jac = ImmutableDenseMatrix(sympify(
obj._inv_jac)).subs(subs)
else:
obj._jac = Jacobian(obj)
obj._metric = obj._jac.T * obj._jac
obj._metric_det = obj._metric.det()
return obj