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# Licensed under a 3-clause BSD style license - see LICENSE.rst
"""
Miscellaneous utilities for `astropy.units`.
None of the functions in the module are meant for use outside of the
package.
"""
from __future__ import (absolute_import, division, print_function,
unicode_literals)
import numbers
import io
import re
from fractions import Fraction
import numpy as np
from numpy import finfo
from ..extern import six
_float_finfo = finfo(float)
# take float here to ensure comparison with another float is fast
# give a little margin since often multiple calculations happened
_JUST_BELOW_UNITY = float(1.-4.*_float_finfo.epsneg)
_JUST_ABOVE_UNITY = float(1.+4.*_float_finfo.eps)
def _get_first_sentence(s):
"""
Get the first sentence from a string and remove any carriage
returns.
"""
x = re.match(r".*?\S\.\s", s)
if x is not None:
s = x.group(0)
return s.replace('\n', ' ')
def _iter_unit_summary(namespace):
"""
Generates the ``(unit, doc, represents, aliases, prefixes)``
tuple used to format the unit summary docs in `generate_unit_summary`.
"""
from . import core
# Get all of the units, and keep track of which ones have SI
# prefixes
units = []
has_prefixes = set()
for key, val in six.iteritems(namespace):
# Skip non-unit items
if not isinstance(val, core.UnitBase):
continue
# Skip aliases
if key != val.name:
continue
if isinstance(val, core.PrefixUnit):
# This will return the root unit that is scaled by the prefix
# attached to it
has_prefixes.add(val._represents.bases[0].name)
else:
units.append(val)
# Sort alphabetically, case insensitive
units.sort(key=lambda x: x.name.lower())
for unit in units:
doc = _get_first_sentence(unit.__doc__).strip()
represents = ''
if isinstance(unit, core.Unit):
represents = ":math:`{0}`".format(
unit._represents.to_string('latex')[1:-1])
aliases = ', '.join('``{0}``'.format(x) for x in unit.aliases)
yield (unit, doc, represents, aliases, unit.name in has_prefixes)
def generate_unit_summary(namespace):
"""
Generates a summary of units from a given namespace. This is used
to generate the docstring for the modules that define the actual
units.
Parameters
----------
namespace : dict
A namespace containing units.
Returns
-------
docstring : str
A docstring containing a summary table of the units.
"""
docstring = io.StringIO()
docstring.write("""
.. list-table:: Available Units
:header-rows: 1
:widths: 10 20 20 20 1
* - Unit
- Description
- Represents
- Aliases
- SI Prefixes
""")
for unit_summary in _iter_unit_summary(namespace):
docstring.write("""
* - ``{0}``
- {1}
- {2}
- {3}
- {4!s:.1}
""".format(*unit_summary))
return docstring.getvalue()
def is_effectively_unity(value):
# value is *almost* always real, except, e.g., for u.mag**0.5, when
# it will be complex. Use try/except to ensure normal case is fast
try:
return _JUST_BELOW_UNITY <= value <= _JUST_ABOVE_UNITY
except TypeError: # value is complex
return (_JUST_BELOW_UNITY <= value.real <= _JUST_ABOVE_UNITY and
_JUST_BELOW_UNITY <= value.imag + 1 <= _JUST_ABOVE_UNITY)
def sanitize_scale(scale):
if is_effectively_unity(scale):
return 1.0
if np.iscomplex(scale): # scale is complex
if scale == 0.0:
return 0.0
if abs(scale.real) > abs(scale.imag):
if is_effectively_unity(scale.imag/scale.real + 1):
scale = scale.real
else:
if is_effectively_unity(scale.real/scale.imag + 1):
scale = complex(0., scale.imag)
return scale
def validate_power(p, support_tuples=False):
"""Convert a power to a floating point value, an integer, or a Fraction.
If a fractional power can be represented exactly as a floating point
number, convert it to a float, to make the math much faster; otherwise,
retain it as a `fractions.Fraction` object to avoid losing precision.
Conversely, if the value is indistinguishable from a rational number with a
low-numbered denominator, convert to a Fraction object.
Parameters
----------
p : float, int, Rational, Fraction
Power to be converted
"""
if isinstance(p, (numbers.Rational, Fraction)):
denom = p.denominator
if denom == 1:
p = int(p.numerator)
# This is bit-twiddling hack to see if the integer is a
# power of two
elif (denom & (denom - 1)) == 0:
p = float(p)
else:
try:
p = float(p)
except Exception:
if not np.isscalar(p):
raise ValueError("Quantities and Units may only be raised "
"to a scalar power")
else:
raise
if (p % 1.0) == 0.0:
# Denominators of 1 can just be integers.
p = int(p)
elif (p * 8.0) % 1.0 == 0.0:
# Leave alone if the denominator is exactly 2, 4 or 8, since this
# can be perfectly represented as a float, which means subsequent
# operations are much faster.
pass
else:
# Convert floats indistinguishable from a rational to Fraction.
# Here, we do not need to test values that are divisors of a higher
# number, such as 3, since it is already addressed by 6.
for i in (10, 9, 7, 6):
scaled = p * float(i)
if((scaled + 4. * _float_finfo.eps) % 1.0 <
8. * _float_finfo.eps):
p = Fraction(int(round(scaled)), i)
break
return p
def resolve_fractions(a, b):
"""
If either input is a Fraction, convert the other to a Fraction.
This ensures that any operation involving a Fraction will use
rational arithmetic and preserve precision.
"""
a_is_fraction = isinstance(a, Fraction)
b_is_fraction = isinstance(b, Fraction)
if a_is_fraction and not b_is_fraction:
b = Fraction(b)
elif not a_is_fraction and b_is_fraction:
a = Fraction(a)
return a, b
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