"""
units
=====
The pynbody units module consists of a set of classes for tracking units.
It relates closely to the :mod:`~pynbody.array` module, which defines
an extension to numpy arrays which carries unit information.
Making units
------------
Units are generated and used at various points through the pynbody
framework. Quite often the functions where users interact with units
simply accept strings.
You can also make units yourself in two ways. Either you can create a string, and
instantiate a Unit like this:
>>> units.Unit("Msol kpc**-3")
>>> units.Unit("2.1e12 m_p cm**-2/3")
Or you can do it within python, using the named Unit objects
>>> units.Msol * units.kpc**-3
>>> 2.1e12 * units.m_p * units.cm**(-2,3)
In the last example, either a tuple describing a fraction or a
Fraction instance (from the standard python module fractions) is
acceptable.
Getting conversion ratios
-------------------------
To convert one unit to another, use the ``ratio`` member function:
>>> units.Msol.ratio(units.kg)
1.99e30
>>> (units.Msol / units.kpc**3).ratio(units.m_p/units.cm**3)
4.04e-8
If the units cannot be converted, a UnitsException is raised:
>>> units.Msol.ratio(units.kpc)
UnitsException
Specifying numerical values
---------------------------
Sometimes it's necessary to specify a numerical value in the course
of a conversion. For instance, consider a comoving distance; this
can be specified in pynbody units as follows:
>>> comoving_kpc = units.kpc * units.a
where units.a represents the scalefactor. We can attempt to convert
this to a physical distance as follows
>>> comoving_kpc.ratio(units.kpc)
but this fails, throwing a UnitsException. On the other hand we
can specify a value for the scalefactor when we request the conversion
>>> comoving_kpc.ratio(units.kpc, a=0.5)
0.5
and the conversion completes with the expected result. The units
module also defines units.h for the dimensionless hubble constant,
which can be used similarly. *By default, all conversions happening
within a specific simulation context should pass in values for
a and h as a matter of routine.*
Any IrreducibleUnit (see below) can have a value specified in this way,
but a and h are envisaged to be the most useful applications.
Defining new base units
-----------------------
The units module is fully extensible: you can define and name your own
units which then integrate with all the standard functions.
.. code-block:: python
litre = units.NamedUnit("litre",0.001*units.m**3)
gallon = units.NamedUnit("gallon",0.004546*units.m**3)
gallon.ratio(litre) # 4.546
(units.pc**3).ratio(litre) # 2.94e52
You can even define completely new dimensions.
.. code-block:: python
V = units.IrreducibleUnit("V") # define a volt
C = units.NamedUnit("C", units.J/V) # define a coulomb
q = units.NamedUnit("q", 1.60217646e-19*C) # elementary charge
F = units.NamedUnit("F", C/V) # Farad
epsilon0 = 8.85418e-12 *F/units.m
>>> (q*V).ratio("eV")
1.000
>>> ((q**2)/(4*math.pi*epsilon0*units.m**2)).ratio("N")
2.31e-28
"""
import re
import keyword
import numpy as np
from . import backcompat
from .backcompat import fractions
import functools
Fraction = fractions.Fraction
_registry = {}
[docs]class UnitsException(Exception):
pass
[docs]class UnitBase(object):
"""Base class for units. To instantiate a unit, call the :func:`pynbody.units.Unit`
factory function."""
def __init__(self):
raise ValueError("Cannot directly initialize abstract base class")
pass
def __pow__(self, p):
if isinstance(p, tuple):
p = Fraction(p[0], p[1])
if not (isinstance(p, Fraction) or isinstance(p, int)):
if isinstance(p, float):
raise ValueError("Units can only be raised to integer or fractional powers. Use python's built-in fractions module or a tuple: e.g. unit**(1,2) represents a square root.")
else :
raise ValueError("Units can only be raised to integer or fractional powers")
return CompositeUnit(1, [self], [p]).simplify()
def __truediv__(self, m):
return self.__div__(m)
def __rtruediv__(self, m):
return self.__rdiv__(m)
def __div__(self, m):
if hasattr(m, "_no_unit"):
return NoUnit()
if isinstance(m, UnitBase):
return CompositeUnit(1, [self, m], [1, -1]).simplify()
else:
return CompositeUnit(1.0 / m, [self], [1]).simplify()
def __rdiv__(self, m):
return CompositeUnit(m, [self], [-1]).simplify()
def __mul__(self, m):
if hasattr(m, "_no_unit"):
return NoUnit()
elif hasattr(m, "units"):
return m * self
elif isinstance(m, UnitBase):
return CompositeUnit(1, [self, m], [1, 1]).simplify()
else:
return CompositeUnit(m, [self], [1]).simplify()
def __rmul__(self, m):
return CompositeUnit(m, [self], [1]).simplify()
def __add__(self, m):
scale = m.in_units(self) if hasattr(m, 'in_units') else m/float(self)
if hasattr(scale, 'units'):
scale.units = 1
return self * (1.0 + scale)
def __sub__(self, m):
return self + (-m)
def __repr__(self):
return 'Unit("' + str(self) + '")'
def __eq__(self, other):
try:
return self.ratio(other) == 1.
except UnitsException:
return False
def __ne__(self, other):
return not (self == other)
def __lt__(self, other):
return self.ratio(other) < 1.
def __gt__(self, other):
return self.ratio(other) > 1.
def __le__(self, other):
return self.ratio(other) <= 1.
def __ge__(self, other):
return self.ratio(other) >= 1.
def __neg__(self):
return self * (-1)
def __float__(self):
return 1.
def __hash__(self):
return id(self)
def simplify(self):
return self
def is_dimensionless(self):
return False
[docs] def ratio(self, other, **substitutions):
"""Get the conversion ratio between this Unit and another
specified unit.
Keyword arguments, if specified, give numerical substitutions
for the named unit. This is most useful for specifying values
for cosmological quantities like 'a' and 'h', but can also
be used for any IrreducibleUnit.
>>> Unit("1 Mpc a").ratio("kpc", a=0.25)
250.0
>>> Unit("1 Mpc").ratio("Msol")
UnitsException: not convertible
>>> Unit("1 Mpc").ratio("Msol", kg=25.0, m=50.0)
3.1028701506345152e-08
"""
if isinstance(other, str):
other = Unit(other)
if hasattr(other, "_no_unit"):
raise UnitsException("Unknown units")
try:
return (self / other).dimensionless_constant(**substitutions)
except UnitsException:
raise UnitsException("Not convertible")
[docs] def in_units(self, *a, **kw):
"""Alias for ratio"""
return self.ratio(*a, **kw)
[docs] def irrep(self):
"""Return a unit equivalent to this one (may be identical) but
expressed in terms of the currently defined IrreducibleUnit
instances."""
return self
def _register_unit(self, st):
if st in _registry:
raise UnitsException("Unit with this name already exists")
if "**" in st or "^" in st or " " in st:
# will cause problems for simple string parser in Unit() factory
raise UnitsException("Unit names cannot contain '**' or '^' or spaces")
_registry[st] = self
def __deepcopy__(self, memo):
# This may look odd, but the units conversion will be very
# broken after deep-copying if we don't guarantee that a given
# physical unit corresponds to only one instance
return self
[docs]class NoUnit(UnitBase):
def __init__(self):
self._no_unit = True
[docs] def ratio(self, other, **substitutions):
if isinstance(other, NoUnit):
return 1
else:
raise UnitsException("Unknown units")
def dimensional_project(self, *args):
raise UnitsException("Unknown units")
def is_dimensionless(self):
return True
def simplify(self):
return self
def __pow__(self, a):
return self
def __div__(self, a):
return self
def __rdiv__(self, a):
return self
def __mul__(self, a):
return self
def __rmul__(self, a):
return self
def __repr__(self):
return "NoUnit()"
def latex(self):
return ""
[docs] def irrep(self):
return self
no_unit = NoUnit()
def _resurrect_named_unit(unit_name, unit_latex, represents):
if unit_name in _registry:
return _registry[unit_name]
else:
if represents is None:
nu = IrreducibleUnit(unit_name)
else:
nu = NamedUnit(unit_name, represents)
nu._latex = unit_latex
return nu
[docs]class IrreducibleUnit(UnitBase):
def __init__(self, st):
self._st_rep = st
self._register_unit(st)
def __reduce__(self):
return (_resurrect_named_unit, (self._st_rep, None, None))
def __str__(self):
return self._st_rep
def latex(self):
return r"\mathrm{" + self._st_rep + "}"
[docs] def irrep(self):
return CompositeUnit(1, [self], [1])
[docs]class NamedUnit(UnitBase):
def __init__(self, st, represents):
self._st_rep = st
if isinstance(represents, str):
represents = Unit(represents)
self._represents = represents
self._register_unit(st)
def __reduce__(self):
return (_resurrect_named_unit, (self._st_rep, getattr(self, '_latex', None), self._represents))
def __str__(self):
return self._st_rep
def latex(self):
if hasattr(self, '_latex'):
return self._latex
return r"\mathrm{" + self._st_rep + "}"
[docs] def irrep(self):
return self._represents.irrep()
[docs]class CompositeUnit(UnitBase):
def __init__(self, scale, bases, powers):
"""Initialize a composite unit.
Direct use of this function is not recommended. Instead use the
factory function Unit(...)."""
if scale == 1.:
scale = 1
self._scale = scale
self._bases = bases
self._powers = powers
[docs] def latex(self):
"""Returns a LaTeX representation of this unit.
Prefactors are converted into exponent notation. Named units by default
are represented by the string '\mathrm{unit_name}', although this can
be overriden in the pynbody configuration files or by setting
unit_name._latex."""
if self._scale != 1:
x = ("%.2e" % self._scale).split('e')
s = x[0]
ex = x[1].lstrip('0+')
if len(ex) > 0 and ex[0] == '-':
ex = '-' + (ex[1:]).lstrip('0')
if ex != '':
s += r"\times 10^{" + ex + "}"
else:
s = ""
for b, p in zip(self._bases, self._powers):
if s != "":
s += r"\," + b.latex()
else:
s = b.latex()
if p != 1:
s += "^{"
s += str(p)
s += "}"
return s
def __str__(self):
s = None
if len(self._bases) == 0:
return "%.2e" % self._scale
if self._scale != 1:
s = "%.2e" % self._scale
for b, p in zip(self._bases, self._powers):
if s is not None:
s += " " + str(b)
else:
s = str(b)
if p != 1:
s += "**"
if isinstance(p, Fraction):
s += str(p)
else:
s += str(p)
return s
def __float__(self):
return float(self._scale)
def _expand(self, expand_to_irrep=False):
"""Internal routine to expand any pointers to composite units
into direct pointers to the base units. If expand_to_irrep is
True, everything is expressed in irreducible units.
A _gather will normally be necessary to sanitize the unit
after an _expand."""
trash = []
for i, (b, p) in enumerate(zip(self._bases, self._powers)):
if isinstance(b, NamedUnit) and expand_to_irrep:
b = b._represents.irrep()
if isinstance(b, CompositeUnit):
if expand_to_irrep:
b = b.irrep()
trash.append(i)
self._scale *= b._scale ** p
for b_sub, p_sub in zip(b._bases, b._powers):
self._bases.append(b_sub)
self._powers.append(p_sub * p)
trash.sort()
for offset, i in enumerate(trash):
del self._bases[i - offset]
del self._powers[i - offset]
def _gather(self):
"""Internal routine to gather together powers of the same base
units, then order the base units by their power (descending)"""
trash = []
bases = list(set(self._bases))
powers = [sum([p for bi, p in zip(self._bases, self._powers)
if bi is b])
for b in bases]
bp = sorted([x for x in zip(powers, bases) if x[0] != 0],
reverse=True,
key=lambda x: x[0])
# Py2 only: cmp=lambda x, y: cmp(x[0], y[0]))
if len(bp) != 0:
self._powers, self._bases = list(map(list, list(zip(*bp))))
else:
self._powers, self._bases = [], []
[docs] def copy(self):
"""Create a copy which is 'shallow' in the sense that it
references exactly the same underlying base units, but where
the list of those units can be manipulated separately."""
return CompositeUnit(self._scale, self._bases[:], self._powers[:])
def __copy__(self):
"""For compatibility with python copy module"""
return self.copy()
def simplify(self):
self._expand()
self._gather()
return self
[docs] def irrep(self):
"""Return a new unit which represents this unit expressed
solely in terms of IrreducibleUnit bases."""
x = self.copy()
x._expand(True)
x._gather()
return x
[docs] def is_dimensionless(self):
"""Returns true if this unit actually translates into a scalar
quantity."""
x = self.irrep()
if len(x._powers) == 0:
return True
[docs] def dimensionless_constant(self, **substitutions):
"""If this unit is dimensionless, return its scalar quantity.
Direct use of this function is not recommended. It is generally
better to use the ratio function instead.
Provide keyword arguments to set values for named IrreducibleUnits --
see the ratio function for more information."""
x = self.irrep()
c = x._scale
for xb, xp in zip(x._bases, x._powers):
if str(xb) in substitutions:
c *= substitutions[str(xb)] ** xp
else:
raise UnitsException("Not dimensionless")
return c
def _power_of(self, base):
if base in self._bases:
return self._powers[self._bases.index(base)]
else:
return 0
[docs] def dimensional_project(self, basis_units):
"""Work out how to express the dimensions of this unit relative to the
specified list of basis units.
This is used by the framework when making inferences about sensible units to
use in various situations.
For example, you can represent a length as an energy divided by a force:
>>> Unit("23 kpc").dimensional_project(["J", "N"])
array([1, -1], dtype=object)
However it's not possible to represent a length by energy alone:
>>> Unit("23 kpc").dimensional_project(["J"])
UnitsException: Basis units do not span dimensions of specified unit
This function also doesn't know what to do if the result is ambiguous:
>>> Unit("23 kpc").dimensional_project(["J", "N", "kpc"])
UnitsException: Basis units are not linearly independent
"""
vec_irrep = [Unit(x).irrep() for x in basis_units]
me_irrep = self.irrep()
bases = set(me_irrep._bases)
for vec in vec_irrep:
bases.update(vec._bases)
bases = list(bases)
matrix = np.zeros((len(bases), len(vec_irrep)), dtype=Fraction)
for base_i, base in enumerate(bases):
for vec_i, vec in enumerate(vec_irrep):
matrix[base_i, vec_i] = vec._power_of(base)
# The matrix calculated above describes the transformation M
# such that v = M.d where d is the sought-after powers of the
# specified base vectors, and v is the powers in terms of the
# base units in the list bases.
#
# To invert, since M is possibly rectangular, we use the
# solution to the least-squares problem [minimize (v-M.d)^2]
# which is d = (M^T M)^(-1) M^T v.
#
# If the solution to that does not solve v = M.d, there is no
# admissable solution to v=M.d, i.e. the supplied base vectors do not
# span
# the requires space.
#
# If (M^T M) is singular, the vectors are not linearly independent, so
# any
# solution would not be unique.
M_T_M = np.dot(matrix.transpose(), matrix)
from . import util
try:
M_T_M_inv = util.rational_matrix_inv(M_T_M)
except np.linalg.linalg.LinAlgError:
raise UnitsException("Basis units are not linearly independent")
my_powers = [me_irrep._power_of(base) for base in bases]
candidate = np.dot(M_T_M_inv, np.dot(matrix.transpose(), my_powers))
# Because our method involves a loss of information (multiplying
# by M^T), we could get a spurious solution. Check this is not the
# case...
if any(np.dot(matrix, candidate) != my_powers):
# Spurious solution, meaning the base vectors did not span the
# units required in the first place.
raise UnitsException(
"Basis units do not span dimensions of specified unit")
return candidate
[docs]def Unit(s):
"""
Class factory for units. Given a string s, creates
a Unit object.
The string format is:
[<scale>] [<unit_name>][**<rational_power>] [[<unit_name>] ... ]
for example:
"1.e30 kg"
"kpc**2"
"26.2 m s**-1"
"""
if isinstance(s, UnitBase):
return s
elif isinstance(s, int):
s = str(s)
x = s.split()
try:
scale = float(x[0])
del x[0]
except (ValueError, IndexError):
scale = 1.0
units = []
powers = []
for com in x:
if "**" in com or "^" in com:
s = com.split("**" if "**" in com else "^")
try:
u = _registry[s[0]]
except KeyError:
raise ValueError("Unknown unit " + s[0])
p = Fraction(s[1])
if p.denominator == 1:
p = p.numerator
else:
u = _registry[com]
p = 1
units.append(u)
powers.append(p)
return CompositeUnit(scale, units, powers)
[docs]def takes_arg_in_units(*args, **orig_kwargs):
"""
Returns a decorator to create a function which auto-converts input
to given units.
**Usage:**
.. code-block:: python
@takes_arg_in_units((2, "Msol"), (1, "kpc"), ("blob", "erg"))
def my_function(arg0, arg1, arg2, blob=22) :
print "Arg 2 is",arg2,"Msol"
print "Arg 1 is",arg1,"kpc"
print "blob is",blob,"ergs"
>>> My_function(22, "1.e30 kg", 23, blob="12 J")
Input 3 is 0.5 Msol
Input 2 is 23 kpc
"""
context_arg = orig_kwargs.get('context_arg', None)
kwargs = [x for x in args if hasattr(x[0], '__len__')]
args = [x for x in args if not hasattr(x[0], '__len__')]
def decorator_fn(x):
@functools.wraps(x)
def wrapper_fn(*fn_args, **fn_kwargs):
context = {}
if context_arg is not None:
context = fn_args[context_arg].conversion_context()
fn_args = list(fn_args)
for arg_num, arg_units in args:
if isinstance(fn_args[arg_num], str):
fn_args[arg_num] = Unit(fn_args[arg_num])
if hasattr(fn_args[arg_num], "in_units"):
fn_args[arg_num] = fn_args[
arg_num].in_units(arg_units, **context)
for arg_name, arg_units in kwargs:
if isinstance(fn_kwargs[arg_name], str):
fn_kwargs[arg_name] = Unit(fn_kwargs[arg_name])
if hasattr(fn_kwargs[arg_name], "in_units"):
fn_kwargs[arg_name] = fn_kwargs[
arg_name].in_units(arg_units, **context)
return x(*fn_args, **fn_kwargs)
return wrapper_fn
return decorator_fn
from . import config_parser
def __is_clean_name(s):
if re.search('[^0-9a-zA-Z_]', s):
return False
if re.search('^[^a-zA-Z_]+', s):
return False
if keyword.iskeyword(s):
return False
return True
for new_unit_name in map(str.strip, config_parser.get('irreducible-units', 'names').split(",")):
new_unit = IrreducibleUnit(new_unit_name)
if __is_clean_name(new_unit_name):
globals()[new_unit_name] = new_unit
for new_unit_name, new_unit_definition in config_parser.items("named-units"):
new_unit = NamedUnit(new_unit_name, new_unit_definition)
if __is_clean_name(new_unit_name):
globals()[new_unit_name] = new_unit
for unit_name, latex in config_parser.items("units-latex"):
_registry[unit_name]._latex = latex
_default_units = {}
for a_, b_ in config_parser.items("default-array-dimensions"):
_default_units[a_] = Unit(b_)
[docs]def has_unit(obj):
"""Returns True if the specified object has a meaningful units attribute"""
if hasattr(obj, 'units') and isinstance(obj.units, UnitBase):
return not hasattr(obj.units, '_no_unit')
else:
return False
has_units = has_unit
def get_item_with_unit(array, item):
if has_unit(array):
return array[item]*array.units
else:
return array[item]
[docs]def is_unit(obj):
"""Returns True if the specified object represents a unit"""
return isinstance(obj, UnitBase)
[docs]def is_unit_like(obj):
"""Returns True if the specified object is itself a unit or
otherwise exposes unit information"""
return is_unit(obj) or has_unit(obj)
