def parse_unit(unit, unit_system=None):
"""
parses a unit string or unit expression and returns (factor,dimension,unit)
where factor is the correction factor to get to the base unit system,
dimension is the physical dimension as a Dimension object
and unit is the unit as an Expression containing Unit objects
Returns:
tuple of factor, dimension and unit
"""
if unit_system is None:
unit_system = DEF_UNIT_SYSTEM
if isinstance(unit, str):
if unit == "":
unit = S.One
else:
unit = parse_expr(unit, local_dict=unit_system)
for u in unit.free_symbols:
if not isinstance(u, Unit):
raise ValueError("%s is not a unit." % u.name)
#calculate dimension
dim = unit
factor = unit
for var in unit.free_symbols:
exp = unit.as_coeff_exponent(var)[1]
if exp == 0:
raise ValueError("%s is not a valid unit string." % unitStr)
dim = subs_symbols(dim, {var.name: var.dim})
factor = factor.subs(var, var.factor)
return (factor, dim_simplify(dim), unit)
def __new__(cls, name, dependency, unit_system, standard=True):
self = Unit.__new__(cls, name)
self.standard = standard
if isinstance(dependency, str):
self.dependency = parse_expr(dependency, local_dict=unit_system)
for u in self.dependency.free_symbols:
if not isinstance(u, Unit):
raise ValueError("%s is not a unit." % u.name)
else:
self.dependency = dependency
#calculate factor
self.factor = self.dependency
for var in self.dependency.free_symbols:
exponent = self.factor.as_coeff_exponent(var)[1]
self.factor *= var.factor**exponent
self.factor /= var**exponent
assert self.factor.is_number
#calculate dimension
dim = self.dependency
for var in self.dependency.free_symbols:
dim = subs_symbols(dim, {var.name: var.dim})
self.dim = dim_simplify(dim)
#calculate complexity
self.complexity = 0
for exponent in self.dim.values():
self.complexity += abs(exponent)
return self
def get_dimension(expr):
""" finds out physical dimension of a term containing quantities
Args:
- expr: Expr object possibly containing Quantity objects
Returns: Dimension object
"""
dim = expr
for var in expr.free_symbols:
if var.dim is None:
raise RuntimeError ("quantity '%s' doesn't have a dimension, yet." % var.name)
dim = subs_symbols(dim,{var.name:var.dim})
return dim_simplify(dim)