# -*- 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 sympify
[docs]class Prefix(object):
"""
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).
"""
def __init__(self, name, abbrev, exponent, base=sympify(10)):
self.name = name
self.abbrev = abbrev
self.factor = base**exponent
def __str__(self):
return self.name
__repr__ = __str__
def __mul__(self, other):
fact = self.factor * other.factor
if fact == 1:
return 1
elif isinstance(other, Prefix):
# simplify prefix
for p in PREFIXES:
if PREFIXES[p].factor == fact:
return PREFIXES[p]
return fact
return self.factor * other
def __div__(self, other):
fact = self.factor / other.factor
if fact == 1:
return 1
elif isinstance(other, Prefix):
for p in PREFIXES:
if PREFIXES[p].factor == fact:
return PREFIXES[p]
return fact
return self.factor / other
__truediv__ = __div__
def __rdiv__(self, other):
if other == 1:
for p in PREFIXES:
if PREFIXES[p].factor == 1 / self.factor:
return PREFIXES[p]
return other / self.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.unitsystems.prefixes import (PREFIXES,
... prefix_unit)
>>> from sympy.physics.unitsystems.systems import mks
>>> m = mks["m"]
>>> pref = {"m": PREFIXES["m"], "c": PREFIXES["c"], "d": PREFIXES["d"]}
>>> prefix_unit(m, pref) #doctest: +SKIP
[cm, dm, mm]
"""
from sympy.physics.unitsystems.units import Unit
prefixed_units = []
for prefix in prefixes:
prefixed_units.append(Unit(unit, abbrev=unit.abbrev,
prefix=prefixes[prefix]))
return prefixed_units
# http://physics.nist.gov/cuu/Units/prefixes.html
PREFIXES = {
'Y': Prefix('yotta', 'Y', 24),
'Z': Prefix('zetta', 'Z', 21),
'E': Prefix('exa', 'E', 18),
'P': Prefix('peta', 'P', 15),
'T': Prefix('tera', 'T', 12),
'G': Prefix('giga', 'G', 9),
'M': Prefix('mega', 'M', 6),
'k': Prefix('kilo', 'k', 3),
'h': Prefix('hecto', 'h', 2),
'da': Prefix('deca', 'da', 1),
'd': Prefix('deci', 'd', -1),
'c': Prefix('centi', 'c', -2),
'm': Prefix('milli', 'm', -3),
'µ': Prefix('micro', 'µ', -6),
'n': Prefix('nano', 'n', -9),
'p': Prefix('pico', 'p', -12),
'f': Prefix('femto', 'f', -15),
'a': Prefix('atto', 'a', -18),
'z': Prefix('zepto', 'z', -21),
'y': Prefix('yocto', 'y', -24)
}
# http://physics.nist.gov/cuu/Units/binary.html
BIN_PREFIXES = {
'Ki': Prefix('kibi', 'Y', 10, 2),
'Mi': Prefix('mebi', 'Y', 20, 2),
'Gi': Prefix('gibi', 'Y', 30, 2),
'Ti': Prefix('tebi', 'Y', 40, 2),
'Pi': Prefix('pebi', 'Y', 50, 2),
'Ei': Prefix('exbi', 'Y', 60, 2)
}
