def __new__ (cls, arg, **options):
# print "Inverse(", arg, ")"
# print INVERTIBLE
if isinstance(arg, Inverse):
return arg.args[0]
if arg.is_Number:
return 1 / arg
arg_rank = expr_rank(arg)
if arg_rank == 1:
raise NotInvertibleError
if is_one(arg):
return arg
if is_zero(arg):
raise NotInvertibleError
# FIXME: Funky case trying to catch lower triangular or diagonal
# muls like T(P_0)*A*P_0
if arg in INVERTIBLE:
pass
elif isinstance(arg, TensorExpr) and not arg.has_inverse:
raise NotInvertibleError
elif isinstance(arg, Mul):
if arg.args[0] == S(-1):
return - Inverse(reduce(operator.mul, arg.args[1:]))
if not expr_invertible(arg):
raise NotInvertibleError
options['commutative'] = arg.is_commutative
return Basic.__new__(cls, arg, **options)
def expr_invertible(expr):
if expr.is_Number:
return True
if isinstance(expr, TensorExpr) and expr.has_inverse:
return True
elif isinstance(expr, Pow):
return expr_invertible(expr.args[0])
if isinstance(expr, Inverse):
return True
if expr in INVERTIBLE:
return True
er = expr_rank(expr)
if er == 1:
return False
if is_one(expr):
return True
if is_zero(expr):
return False
# FIXME: Funky case trying to catch lower triangular or diagonal
# muls like T(P_0)*A*P_0
if isinstance(expr, Mul):
return reduce(lambda acc, x: acc and expr_invertible(x), expr.args,
True)
if isinstance(expr, Pow):
return expr_invertible(expr.args[0])
def expr_invertible(expr):
if expr.is_Number:
return True
if isinstance(expr, TensorExpr) and expr.has_inverse:
return True
elif isinstance(expr, Pow):
return expr_invertible(expr.args[0])
if isinstance(expr, Inverse):
return True
if expr in INVERTIBLE:
return True
er = expr_rank(expr)
if er == 1:
return False
if is_one(expr):
return True
if is_zero(expr):
return False
# FIXME: Funky case trying to catch lower triangular or diagonal
# muls like T(P_0)*A*P_0
if isinstance(expr, Mul):
return reduce(lambda acc, x: acc and expr_invertible(x), expr.args, True)
if isinstance(expr, Pow):
return expr_invertible(expr.args[0])