# -*- coding: utf-8 -*-
"""
Module defining unit prefixe class and some constants.
Constant dict for SI and binary prefixes are defined as PREFIXES and
BIN_PREFIXES.
"""
from sympy import Expr, sympify
[docs]class Prefix(Expr):
"""
This class represent prefixes, with their name, symbol and factor.
Prefixes are used to create derived units from a given unit. They should
always be encapsulated into units.
The factor is constructed from a base (default is 10) to some power, and
it gives the total multiple or fraction. For example the kilometer km
is constructed from the meter (factor 1) and the kilo (10 to the power 3,
i.e. 1000). The base can be changed to allow e.g. binary prefixes.
A prefix multiplied by something will always return the product of this
other object times the factor, except if the other object:
- is a prefix and they can be combined into a new prefix;
- defines multiplication with prefixes (which is the case for the Unit
class).
"""
_op_priority = 13.0
is_commutative = True
def __new__(cls, name, abbrev, exponent, base=sympify(10)):
name = sympify(name)
abbrev = sympify(abbrev)
exponent = sympify(exponent)
base = sympify(base)
obj = Expr.__new__(cls, name, abbrev, exponent, base)
obj._name = name
obj._abbrev = abbrev
obj._scale_factor = base**exponent
obj._exponent = exponent
obj._base = base
return obj
@property
def name(self):
return self._name
@property
def abbrev(self):
return self._abbrev
@property
def scale_factor(self):
return self._scale_factor
@property
def base(self):
return self._base
def __str__(self):
# TODO: add proper printers and tests:
if self.base == 10:
return "Prefix(%r, %r, %r)" % (
str(self.name), str(self.abbrev), self._exponent)
else:
return "Prefix(%r, %r, %r, %r)" % (
str(self.name), str(self.abbrev), self._exponent, self.base)
__repr__ = __str__
def __mul__(self, other):
if not hasattr(other, "scale_factor"):
return super(Prefix, self).__mul__(other)
fact = self.scale_factor * other.scale_factor
if fact == 1:
return 1
elif isinstance(other, Prefix):
# simplify prefix
for p in PREFIXES:
if PREFIXES[p].scale_factor == fact:
return PREFIXES[p]
return fact
return self.scale_factor * other
def __div__(self, other):
if not hasattr(other, "scale_factor"):
return super(Prefix, self).__div__(other)
fact = self.scale_factor / other.scale_factor
if fact == 1:
return 1
elif isinstance(other, Prefix):
for p in PREFIXES:
if PREFIXES[p].scale_factor == fact:
return PREFIXES[p]
return fact
return self.scale_factor / other
__truediv__ = __div__
def __rdiv__(self, other):
if other == 1:
for p in PREFIXES:
if PREFIXES[p].scale_factor == 1 / self.scale_factor:
return PREFIXES[p]
return other / self.scale_factor
__rtruediv__ = __rdiv__
def prefix_unit(unit, prefixes):
"""
Return a list of all units formed by unit and the given prefixes.
You can use the predefined PREFIXES or BIN_PREFIXES, but you can also
pass as argument a subdict of them if you don't want all prefixed units.
>>> from sympy.physics.units.prefixes import (PREFIXES,
... prefix_unit)
>>> from sympy.physics.units.systems import MKS
>>> from sympy.physics.units import m
>>> pref = {"m": PREFIXES["m"], "c": PREFIXES["c"], "d": PREFIXES["d"]}
>>> prefix_unit(m, pref) #doctest: +SKIP
[cm, dm, mm]
"""
from sympy.physics.units.quantities import Quantity
prefixed_units = []
for prefix_abbr, prefix in prefixes.items():
quantity = Quantity(
"%s%s" % (prefix.name, unit.name),
abbrev=("%s%s" % (prefix.abbrev, unit.abbrev))
)
quantity.set_dimension(unit.dimension)
quantity.set_scale_factor(unit.scale_factor*prefix)
prefixed_units.append(quantity)
return prefixed_units
yotta = Prefix('yotta', 'Y', 24)
zetta = Prefix('zetta', 'Z', 21)
exa = Prefix('exa', 'E', 18)
peta = Prefix('peta', 'P', 15)
tera = Prefix('tera', 'T', 12)
giga = Prefix('giga', 'G', 9)
mega = Prefix('mega', 'M', 6)
kilo = Prefix('kilo', 'k', 3)
hecto = Prefix('hecto', 'h', 2)
deca = Prefix('deca', 'da', 1)
deci = Prefix('deci', 'd', -1)
centi = Prefix('centi', 'c', -2)
milli = Prefix('milli', 'm', -3)
micro = Prefix('micro', 'mu', -6)
nano = Prefix('nano', 'n', -9)
pico = Prefix('pico', 'p', -12)
femto = Prefix('femto', 'f', -15)
atto = Prefix('atto', 'a', -18)
zepto = Prefix('zepto', 'z', -21)
yocto = Prefix('yocto', 'y', -24)
# http://physics.nist.gov/cuu/Units/prefixes.html
PREFIXES = {
'Y': yotta,
'Z': zetta,
'E': exa,
'P': peta,
'T': tera,
'G': giga,
'M': mega,
'k': kilo,
'h': hecto,
'da': deca,
'd': deci,
'c': centi,
'm': milli,
'mu': micro,
'n': nano,
'p': pico,
'f': femto,
'a': atto,
'z': zepto,
'y': yocto,
}
kibi = Prefix('kibi', 'Y', 10, 2)
mebi = Prefix('mebi', 'Y', 20, 2)
gibi = Prefix('gibi', 'Y', 30, 2)
tebi = Prefix('tebi', 'Y', 40, 2)
pebi = Prefix('pebi', 'Y', 50, 2)
exbi = Prefix('exbi', 'Y', 60, 2)
# http://physics.nist.gov/cuu/Units/binary.html
BIN_PREFIXES = {
'Ki': kibi,
'Mi': mebi,
'Gi': gibi,
'Ti': tebi,
'Pi': pebi,
'Ei': exbi,
}
