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units.py
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units.py
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# Copyright 2016 by Harold Fellermann
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program. If not, see <http://www.gnu.org/licenses/>.
"""Dimensional quantities for unit aware calculations.
Quantities are values with an associated unit of a given dimension,
such as 3.3 meters, 50 seconds, 42 meters per second.
This is straight forward:
Quantity(3.3, m=1)
Quantity(50, s=1)
Quantity(42, m=1, s=-1)
The first argument is the quantity's value and the keyword arguments
it's unit. Each label specifies a dimension and the number gives its
exponent. There is no restriction to the label employed, other than
being a valid python identifier -- which allows the user to calculate
in arbitrary units. Many standard units together with their metric
multiples are already defined in the module (and creating own ones is
a one-liner). With those, the handling of units becomes much simpler:
>>> 3.3*meter
Quantity(3.3, m=1)
>>> 50*second
Quantity(50, s=1)
>>> 42*meter/second
Quantity(42, s=-1, m=1)
Arithmetics are type safe, e.g. it is an error to add quantities of
different dimensions (with the exception that adding and subtracting 0
is allowed). Arithmetics take care of the proper handling of dimensions:
>>> v = 45*mile/hour
>>> print 3*hour * v
217261.44 m
>>> print 3*hour * v / kilometer
217.26144
When raising quantities to fractional powers, such as second**0.5, it
can be safer to use proper fractions to avoid floating point errors:
>>> from fractions import Fraction
>>> print second**Fraction(1,2)
1.0 s^1/2
"""
from decimal import Decimal, getcontext
class Quantity(object) :
def __init__(self, value, **opts) :
if type(value) is Quantity :
self.value = value.value
opts = dict(value.unit)
elif isinstance(value, str) :
self.value = Empirical(value)
else :
self.value = value
self.unit = opts
def __hash__(self) :
return hash(repr(self))
def __repr__(self) :
unit = self.unit
return '%s(%s, %s)' % (
type(self).__name__,
self.value,
', '.join('%s=%s' % (item, unit[item]) for item in self.unit)
)
def __str__(self) :
def expstr(u,e) :
return ('%s^%s' % (u,e)) if e!=1 else u
unit = self.unit
unitstr = ' '.join(expstr(u,unit[u]) for u in unit)
return "%s %s" % (self.value, unitstr)
# comparison
def __nonzero__(self) :
return bool(self.value)
def __eq__(self, other) :
if not isinstance(other, Quantity) :
if not self.unit :
return self.value == other
else :
raise NotImplementedError
return self.value == other.value and self.unit == other.unit
def __ne__(self, other) :
if not isinstance(other, Quantity) :
if not self.unit :
return self.value != other
else :
raise NotImplementedError
return self.value != other.value or self.unit != other.unit
def __le__(self, other) :
if not isinstance(other, Quantity) :
if not self.unit :
return self.value <= other
else :
raise NotImplementedError
if self.unit != other.unit :
raise TypeError("No ordering relation is defined for units of different dimension")
return self.value <= other.value
def __ge__(self, other) :
if not isinstance(other, Quantity) :
if not self.unit :
return self.value >= other
else :
raise NotImplementedError
if self.unit != other.unit :
raise TypeError("No ordering relation is defined for units of different dimension")
return self.value >= other.value
def __lt__(self, other) :
if not isinstance(other, Quantity) :
if not self.unit :
return self.value < other
else :
raise NotImplementedError
if self.unit != other.unit :
raise TypeError("No ordering relation is defined for units of different dimension")
return self.value < other.value
def __gt__(self, other) :
if not isinstance(other, Quantity) :
if not self.unit :
return self.value > other
else :
raise NotImplementedError
if self.unit != other.unit :
raise TypeError("No ordering relation is defined for units of different dimension")
return self.value > other.value
# conversion
def __int__(self) :
if self.unit :
raise TypeError("Cannot convert dimensional quantity into int.")
return int(self.value)
def __long__(self) :
if self.unit :
raise TypeError("Cannot convert dimensional quantity into long.")
return long(self.value)
def __float__(self) :
if self.unit :
raise TypeError("Cannot convert dimensional quantity into float.")
return float(self.value)
def __complex__(self) :
if self.unit :
raise TypeError("Cannot convert dimensional quantity into complex.")
return complex(self.value)
# arithmetics
def __pos__(self) :
return Quantity(+self.value, **self.unit)
def __neg__(self) :
return Quantity(-self.value, **self.unit)
def __abs__(self) :
return Quantity(abs(self.value), **self.unit)
def __add__(self,other) :
if not isinstance(other, Quantity) and not other :
return Quantity(self)
elif not isinstance(other, Quantity) :
if not self.unit :
return Quantity(self.value + other)
else :
raise TypeError("Cannot add %s and %s." % (self, other))
if self.unit != other.unit :
raise TypeError("Cannot add %s and %s." % (self, other))
else :
return Quantity(self.value + other.value, **self.unit)
def __radd__(self,other) :
if not isinstance(other, Quantity) and not other :
return Quantity(self)
elif not isinstance(other, Quantity) and not self.unit :
return self + other
else :
raise TypeError("Cannot add %s and %s." % (self, other))
def __sub__(self,other) :
if not isinstance(other, Quantity) and not other :
return Quantity(self)
if not isinstance(other, Quantity) :
if not self.unit :
return Quantity(self.value - other)
else :
raise TypeError("Cannot add %s and %s." % (self, other))
if self.unit != other.unit :
raise TypeError("Cannot subtract %s and %s." % (self, other))
else :
return Quantity(self.value - other.value, **self.unit)
def __rsub__(self,other) :
if not isinstance(other, Quantity) and not other :
return Quantity(-self.value, **self.unit)
elif not isinstance(other, Quantity) and not self.unit :
return -self + other
else :
raise TypeError("Cannot subtract %s and %s." % (self, other))
def __mul__(self, other) :
if isinstance(other, Quantity) :
unit = dict(self.unit)
for u in other.unit :
unit[u] = unit.get(u,0) + other.unit[u]
return Quantity(self.value * other.value, **unit).simplify()
else :
return Quantity(self.value * other, **self.unit)
def __rmul__(self, other) :
return Quantity(self.value * other, **self.unit).simplify()
def __div__(self, other) :
if isinstance(other, Quantity) :
unit = dict(self.unit)
for u in other.unit :
unit[u] = unit.get(u,0) - other.unit[u]
return Quantity(self.value / other.value, **unit).simplify()
else :
return Quantity(self.value / other, **self.unit)
def __rdiv__(self, other) :
unit = dict((u,-self.unit[u]) for u in self.unit)
return Quantity(other / self.value, **unit).simplify()
def __divmod__(self, other) :
raise RuntimeError('XXX')
def __floordiv__(self, other) :
if isinstance(other, Quantity) :
unit = dict(self.unit)
for u in other.unit :
unit[u] = unit.get(u,0) - other.unit[u]
return Quantity(self.value // other.value, **unit).simplify()
else :
return Quantity(self.value // other, **self.unit)
def __mod__(self, other) :
raise RuntimeError('XXX')
def __pow__(self, other) :
unit = dict((u,self.unit[u]*other) for u in self.unit)
return Quantity(self.value**other, **unit)
def simplify(self) :
unit = self.unit
if not any(unit.values()) : return float(self.value)
zeros = [u for u in unit if unit[u]==0]
for u in zeros : del self.unit[u]
return self
def as_latex(self, unit, format="%g") :
try :
string = str(format % (self/unit))
except TypeError :
raise ValueError("Cannot convert %s to %s" % (self, unit))
if 'e' in string :
mantisse,exponent = string.split('e')
if exponent.startswith('+') :
exponent = exponent[1:].lstrip('0')
return r'%s \times 10^{%s}' % (mantisse,exponent)
else :
return string
def inject_metric_unit(namespace, name, quantity) :
factors = {
'tera' : int(1e12),
'giga' : int(1e9),
'mega' : int(1e6),
'kilo' : int(1e3),
'hecto' : int(1e2),
'deca' : int(1e1),
'' : int(1e0),
'deci' : 1e-1,
'centi' : 1e-2,
'milli' : 1e-3,
'micro' : 1e-6,
'nano' : 1e-9,
'pico' : 1e-12,
'femto' : 1e-15,
}
for prefix in factors :
namespace[prefix+name] = factors[prefix]*quantity
# standard units
from fractions import Fraction
# SI base units
inject_metric_unit(globals(), 'meter', Quantity(1, m = Fraction(1)) )
inject_metric_unit(globals(), 'second', Quantity(1, s = Fraction(1)) )
inject_metric_unit(globals(), 'gram', Quantity(1e-3,kg = Fraction(1)) )
inject_metric_unit(globals(), 'ampere', Quantity(1, A = Fraction(1)) )
inject_metric_unit(globals(), 'kelvin', Quantity(1, K = Fraction(1)) )
inject_metric_unit(globals(), 'candela', Quantity(1, cd = Fraction(1)) )
inject_metric_unit(globals(), 'mol', Quantity(1, mol = Fraction(1)) )
inject_metric_unit(globals(), 'bit', Quantity(1, bit = Fraction(1)) )
# Units officially accepted for use with the SI
minute = 60*second
hour = 60*minute
day = 24*hour
hectare = (100*meter)**2
inject_metric_unit(globals(), 'liter', (0.1*meter)**3 )
inject_metric_unit(globals(), 'tonne', 1000*kilogram )
# derived units
inject_metric_unit(globals(), 'hertz', second**-1 )
inject_metric_unit(globals(), 'newton', kilogram*meter/second**2 )
inject_metric_unit(globals(), 'pascal', newton/meter**2 )
inject_metric_unit(globals(), 'joule', newton*meter )
inject_metric_unit(globals(), 'watt', joule/second )
inject_metric_unit(globals(), 'coulomb', ampere*second )
inject_metric_unit(globals(), 'volt', watt/ampere )
inject_metric_unit(globals(), 'farad', coulomb/volt )
inject_metric_unit(globals(), 'ohm', volt/ampere )
inject_metric_unit(globals(), 'carnot', joule/kelvin )
# common units not officially sanctioned
angstrom = 0.1*nanometer
dyne = 1e-5*newton
erg = 100*nanojoule
cal = 4.184*joule
kcal = 1000*cal
inject_metric_unit(globals(), 'bar', 1.e5*pascal )
inject_metric_unit(globals(), 'clausius', kcal/kelvin )
# non-metric units
mile = 1.609344*kilometer
gallon = 3.78541178*liter
inch = 2.54*centimeter
# constants
Avogadro = 6.02214179e23/mol
Boltzmann = 1.3806488e-23*joule/kelvin
Planck = 6.62606957e-34*joule*second