def __new__(cls, *expressions):
# All lists and tuples should already be unwrapped in
# as_tensor
if any(not isinstance(e, Expr) for e in expressions):
error("Expecting only UFL expressions in ListTensor constructor.")
# Get properties of the first expression
e0 = expressions[0]
sh = e0.ufl_shape
fi = e0.ufl_free_indices
fid = e0.ufl_index_dimensions
# Obviously, each subexpression must have the same shape
if any(sh != e.ufl_shape for e in expressions[1:]):
error(
"Cannot create a tensor by joining subexpressions with different shapes."
)
if any(fi != e.ufl_free_indices for e in expressions[1:]):
error(
"Cannot create a tensor where the components have different free indices."
)
if any(fid != e.ufl_index_dimensions for e in expressions[1:]):
error(
"Cannot create a tensor where the components have different free index dimensions."
)
# Simplify to Zero if possible
if all(isinstance(e, Zero) for e in expressions):
shape = (len(expressions), ) + sh
return Zero(shape, fi, fid)
return Operator.__new__(cls)
def __new__(cls, a, b):
# Conversion
a = as_ufl(a)
b = as_ufl(b)
# Type checking
if not is_true_ufl_scalar(a):
error("Cannot take the power of a non-scalar expression %s." %
ufl_err_str(a))
if not is_true_ufl_scalar(b):
error("Cannot raise an expression to a non-scalar power %s." %
ufl_err_str(b))
# Simplification
if isinstance(a, ScalarValue) and isinstance(b, ScalarValue):
return as_ufl(a._value**b._value)
if isinstance(b, Zero):
return IntValue(1)
if isinstance(a, Zero) and isinstance(b, ScalarValue):
if isinstance(b, ComplexValue):
error("Cannot raise zero to a complex power.")
bf = float(b)
if bf < 0:
error("Division by zero, cannot raise 0 to a negative power.")
else:
return zero()
if isinstance(b, ScalarValue) and b._value == 1:
return a
# Construction
self = Operator.__new__(cls)
self._init(a, b)
return self
def __new__(cls, a, b):
# Conversion
a = as_ufl(a)
b = as_ufl(b)
# Type checking
# TODO: Enabled workaround for nonscalar division in __div__,
# so maybe we can keep this assertion. Some algorithms may
# need updating.
if not is_ufl_scalar(a):
error("Expecting scalar nominator in Division.")
if not is_true_ufl_scalar(b):
error("Division by non-scalar is undefined.")
if isinstance(b, Zero):
error("Division by zero!")
# Simplification
# Simplification a/b -> a
if isinstance(a, Zero) or (isinstance(b, ScalarValue)
and b._value == 1):
return a
# Simplification "literal a / literal b" -> "literal value of
# a/b". Avoiding integer division by casting to float
if isinstance(a, ScalarValue) and isinstance(b, ScalarValue):
return as_ufl(float(a._value) / float(b._value))
# Simplification "a / a" -> "1"
# if not a.ufl_free_indices and not a.ufl_shape and a == b:
# return as_ufl(1)
# Construction
self = Operator.__new__(cls)
self._init(a, b)
return self
def __new__(cls, *expressions):
# All lists and tuples should already be unwrapped in
# as_tensor
if any(not isinstance(e, Expr) for e in expressions):
error("Expecting only UFL expressions in ListTensor constructor.")
# Get properties of the first expression
e0 = expressions[0]
sh = e0.ufl_shape
fi = e0.ufl_free_indices
fid = e0.ufl_index_dimensions
# Obviously, each subexpression must have the same shape
if any(sh != e.ufl_shape for e in expressions[1:]):
error("Cannot create a tensor by joining subexpressions with different shapes.")
if any(fi != e.ufl_free_indices for e in expressions[1:]):
error("Cannot create a tensor where the components have different free indices.")
if any(fid != e.ufl_index_dimensions for e in expressions[1:]):
error("Cannot create a tensor where the components have different free index dimensions.")
# Simplify to Zero if possible
if all(isinstance(e, Zero) for e in expressions):
shape = (len(expressions),) + sh
return Zero(shape, fi, fid)
return Operator.__new__(cls)
def __new__(cls, arg1, arg2):
if isinstance(arg1, (RealValue, Zero)) and isinstance(
arg2, (RealValue, Zero)):
return FloatValue(math.atan2(float(arg1), float(arg2)))
if isinstance(arg1,
(ComplexValue)) or isinstance(arg2, (ComplexValue)):
raise TypeError("Atan2 does not support complex numbers.")
return Operator.__new__(cls)
def __new__(cls, expression, indices):
# Simplify
if isinstance(expression, Zero):
fi, fid, sh = remove_indices(expression.ufl_free_indices,
expression.ufl_index_dimensions,
[ind.count() for ind in indices])
return Zero(sh, fi, fid)
# Construct
return Operator.__new__(cls)
def __new__(cls, expression, indices):
# Simplify
if isinstance(expression, Zero):
fi, fid, sh = remove_indices(expression.ufl_free_indices,
expression.ufl_index_dimensions,
[ind.count() for ind in indices])
return Zero(sh, fi, fid)
# Construct
return Operator.__new__(cls)
def __new__(cls, a):
a = as_ufl(a)
# Simplification
if isinstance(a, (Abs, Real, Imag, Zero)):
return a
if isinstance(a, Conj):
return a.ufl_operands[0]
if isinstance(a, ScalarValue):
return as_ufl(a._value.conjugate())
return Operator.__new__(cls)
def __new__(cls, a):
a = as_ufl(a)
# Simplification
if isinstance(a, (Zero, Abs)):
return a
if isinstance(a, Conj):
return Abs(a.ufl_operands[0])
if isinstance(a, ScalarValue):
return as_ufl(abs(a._value))
return Operator.__new__(cls)
def __new__(cls, a):
a = as_ufl(a)
# Simplification
if isinstance(a, Zero):
return a
if isinstance(a, (Real, Imag, Abs)):
return Zero(a.ufl_shape, a.ufl_free_indices, a.ufl_index_dimensions)
if isinstance(a, ScalarValue):
return as_ufl(a.imag())
return Operator.__new__(cls)
def __new__(cls, a):
a = as_ufl(a)
# Simplification
if isinstance(a, Conj):
a = a.ufl_operands[0]
if isinstance(a, Zero):
return a
if isinstance(a, ScalarValue):
return as_ufl(a.real())
if isinstance(a, Real):
a = a.ufl_operands[0]
return Operator.__new__(cls)
def __new__(cls, a, b):
# Make sure everything is an Expr
a = as_ufl(a)
b = as_ufl(b)
# Assert consistent tensor properties
sh = a.ufl_shape
fi = a.ufl_free_indices
fid = a.ufl_index_dimensions
if b.ufl_shape != sh:
error("Can't add expressions with different shapes.")
if b.ufl_free_indices != fi:
error("Can't add expressions with different free indices.")
if b.ufl_index_dimensions != fid:
error("Can't add expressions with different index dimensions.")
# Skip adding zero
if isinstance(a, Zero):
return b
elif isinstance(b, Zero):
return a
# Handle scalars specially and sort operands
sa = isinstance(a, ScalarValue)
sb = isinstance(b, ScalarValue)
if sa and sb:
# Apply constant propagation
return as_ufl(a._value + b._value)
elif sa:
# Place scalar first
# operands = (a, b)
pass # a, b = a, b
elif sb:
# Place scalar first
# operands = (b, a)
a, b = b, a
# elif a == b:
# # Replace a+b with 2*foo
# return 2*a
else:
# Otherwise sort operands in a canonical order
# operands = (b, a)
a, b = sorted_expr((a, b))
# construct and initialize a new Sum object
self = Operator.__new__(cls)
self._init(a, b)
return self
def __new__(cls, a, b):
# Conversion
a = as_ufl(a)
b = as_ufl(b)
# Type checking
# Make sure everything is scalar
if a.ufl_shape or b.ufl_shape:
error("Product can only represent products of scalars, "
"got\n\t%s\nand\n\t%s" % (ufl_err_str(a), ufl_err_str(b)))
# Simplification
if isinstance(a, Zero) or isinstance(b, Zero):
# Got any zeros? Return zero.
fi, fid = merge_unique_indices(a.ufl_free_indices,
a.ufl_index_dimensions,
b.ufl_free_indices,
b.ufl_index_dimensions)
return Zero((), fi, fid)
sa = isinstance(a, ScalarValue)
sb = isinstance(b, ScalarValue)
if sa and sb: # const * const = const
# FIXME: Handle free indices like with zero? I think
# IntValue may be index annotated now?
return as_ufl(a._value * b._value)
elif sa: # 1 * b = b
if a._value == 1:
return b
# a, b = a, b
elif sb: # a * 1 = a
if b._value == 1:
return a
a, b = b, a
# elif a == b: # a * a = a**2 # TODO: Why? Maybe just remove this?
# if not a.ufl_free_indices:
# return a**2
else: # a * b = b * a
# Sort operands in a semi-canonical order
# (NB! This is fragile! Small changes here can have large effects.)
a, b = sorted_expr((a, b))
# Construction
self = Operator.__new__(cls)
self._init(a, b)
return self
def __new__(cls, expression, multiindex):
if isinstance(expression, Zero):
# Zero-simplify indexed Zero objects
shape = expression.ufl_shape
efi = expression.ufl_free_indices
efid = expression.ufl_index_dimensions
fi = list(zip(efi, efid))
for pos, ind in enumerate(multiindex._indices):
if isinstance(ind, Index):
fi.append((ind.count(), shape[pos]))
fi = unique_sorted_indices(sorted(fi))
if fi:
fi, fid = zip(*fi)
else:
fi, fid = (), ()
return Zero(shape=(), free_indices=fi, index_dimensions=fid)
else:
return Operator.__new__(cls)
def __new__(cls, expression, multiindex):
if isinstance(expression, Zero):
# Zero-simplify indexed Zero objects
shape = expression.ufl_shape
efi = expression.ufl_free_indices
efid = expression.ufl_index_dimensions
fi = list(zip(efi, efid))
for pos, ind in enumerate(multiindex._indices):
if isinstance(ind, Index):
fi.append((ind.count(), shape[pos]))
fi = unique_sorted_indices(sorted(fi))
if fi:
fi, fid = zip(*fi)
else:
fi, fid = (), ()
return Zero(shape=(), free_indices=fi, index_dimensions=fid)
else:
return Operator.__new__(cls)
def __new__(cls, summand, index):
# Error checks
if not isinstance(summand, Expr):
error("Expecting Expr instance, got %s" % ufl_err_str(summand))
if not isinstance(index, MultiIndex):
error("Expecting MultiIndex instance, got %s" % ufl_err_str(index))
if len(index) != 1:
error("Expecting a single Index but got %d." % len(index))
# Simplification to zero
if isinstance(summand, Zero):
sh = summand.ufl_shape
j, = index
fi = summand.ufl_free_indices
fid = summand.ufl_index_dimensions
pos = fi.index(j.count())
fi = fi[:pos] + fi[pos+1:]
fid = fid[:pos] + fid[pos+1:]
return Zero(sh, fi, fid)
return Operator.__new__(cls)
def __new__(cls, summand, index):
# Error checks
if not isinstance(summand, Expr):
error("Expecting Expr instance, got %s" % ufl_err_str(summand))
if not isinstance(index, MultiIndex):
error("Expecting MultiIndex instance, got %s" % ufl_err_str(index))
if len(index) != 1:
error("Expecting a single Index but got %d." % len(index))
# Simplification to zero
if isinstance(summand, Zero):
sh = summand.ufl_shape
j, = index
fi = summand.ufl_free_indices
fid = summand.ufl_index_dimensions
pos = fi.index(j.count())
fi = fi[:pos] + fi[pos + 1:]
fid = fid[:pos] + fid[pos + 1:]
return Zero(sh, fi, fid)
return Operator.__new__(cls)
def __new__(cls, arg1, arg2):
if isinstance(arg1, (ScalarValue, Zero)) and isinstance(
arg2, (ScalarValue, Zero)):
return FloatValue(math.atan2(float(arg1), float(arg2)))
return Operator.__new__(cls)
def __new__(cls, arg1, arg2):
if isinstance(arg1, (RealValue, Zero)) and isinstance(arg2, (RealValue, Zero)):
return FloatValue(math.atan2(float(arg1), float(arg2)))
if isinstance(arg1, (ComplexValue)) or isinstance(arg2, (ComplexValue)):
raise TypeError("Atan2 does not support complex numbers.")
return Operator.__new__(cls)