# 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.

"""

import io

import re

from fractions import Fraction

import numpy as np

from numpy import finfo

_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(1.0 - 4.0 * _float_finfo.epsneg)

_JUST_ABOVE_UNITY = float(1.0 + 4.0 * _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 namespace.items():

# 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 = f":math:`{unit._represents.to_string('latex')[1:-1]}`"

aliases = ", ".join(f"``{x}``" for x in unit.aliases)

yield (

unit,

doc,

represents,

aliases,

"Yes" if unit.name in has_prefixes else "No",

)

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

"""

)

template = """

* - ``{}``

- {}

- {}

- {}

- {}

"""

for unit_summary in _iter_unit_summary(namespace):

docstring.write(template.format(*unit_summary))

return docstring.getvalue()

def generate_prefixonly_unit_summary(namespace):

"""

Generates table entries for units in a namespace that are just prefixes

without the base unit. Note that this is intended to be used *after*

`generate_unit_summary` and therefore does not include the table header.

Parameters

----------

namespace : dict

A namespace containing units that are prefixes but do *not* have the

base unit in their namespace.

Returns

-------

docstring : str

A docstring containing a summary table of the units.

"""

from . import PrefixUnit

faux_namespace = {}

for unit in namespace.values():

if isinstance(unit, PrefixUnit):

base_unit = unit.represents.bases[0]

faux_namespace[base_unit.name] = base_unit

docstring = io.StringIO()

template = """

* - Prefixes for ``{}``

- {} prefixes

- {}

- {}

- Only

"""

for unit_summary in _iter_unit_summary(faux_namespace):

docstring.write(template.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

# Maximum speed for regular case where scale is a float.

if scale.__class__ is float:

return scale

# We cannot have numpy scalars, since they don't autoconvert to

# complex if necessary. They are also slower.

if hasattr(scale, "dtype"):

scale = scale.item()

# All classes that scale can be (int, float, complex, Fraction)

# have an "imag" attribute.

if scale.imag:

if abs(scale.real) > abs(scale.imag):

if is_effectively_unity(scale.imag / scale.real + 1):

return scale.real

elif is_effectively_unity(scale.real / scale.imag + 1):

return complex(0.0, scale.imag)

return scale

else:

return scale.real

def maybe_simple_fraction(p, max_denominator=100):

"""Fraction very close to x with denominator at most max_denominator.

The fraction has to be such that fraction/x is unity to within 4 ulp.

If such a fraction does not exist, returns the float number.

The algorithm is that of `fractions.Fraction.limit_denominator`, but

sped up by not creating a fraction to start with.

"""

if p == 0 or p.__class__ is int:

return p

n, d = p.as_integer_ratio()

a = n // d

# Normally, start with 0,1 and 1,0; here we have applied first iteration.

n0, d0 = 1, 0

n1, d1 = a, 1

while d1 <= max_denominator:

if _JUST_BELOW_UNITY <= n1 / (d1 * p) <= _JUST_ABOVE_UNITY:

return Fraction(n1, d1)

n, d = d, n - a * d

a = n // d

n0, n1 = n1, n0 + a * n1

d0, d1 = d1, d0 + a * d1

return p

def validate_power(p):

"""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

"""

denom = getattr(p, "denominator", None)

if denom is None:

try:

p = float(p)

except Exception:

p = np.asanyarray(p)

if ((first := p.flat[0]) == p).all():

p = float(first)

else:

raise ValueError(

"Quantities and Units may only be raised to a scalar power"

)

# This returns either a (simple) Fraction or the same float.

p = maybe_simple_fraction(p)

# If still a float, nothing more to be done.

if isinstance(p, float):

return p

# Otherwise, check for simplifications.

denom = p.denominator

if denom == 1:

p = p.numerator

elif (denom & (denom - 1)) == 0:

# Above is a bit-twiddling hack to see if denom is a power of two.

# If so, float does not lose precision and will speed things up.

p = float(p)

return p

def resolve_fractions(a, b):

"""

If either input is a Fraction, convert the other to a Fraction

(at least if it does not have a ridiculous denominator).

This ensures that any operation involving a Fraction will use

rational arithmetic and preserve precision.

"""

# We short-circuit on the most common cases of int and float, since

# isinstance(a, Fraction) is very slow for any non-Fraction instances.

a_is_fraction = (

a.__class__ is not int and a.__class__ is not float and isinstance(a, Fraction)

)

b_is_fraction = (

b.__class__ is not int and b.__class__ is not float and isinstance(b, Fraction)

)

if a_is_fraction and not b_is_fraction:

b = maybe_simple_fraction(b)

elif not a_is_fraction and b_is_fraction:

a = maybe_simple_fraction(a)

return a, b

def quantity_asanyarray(a, dtype=None):

from .quantity import Quantity

if (

not isinstance(a, np.ndarray)

and not np.isscalar(a)

and any(isinstance(x, Quantity) for x in a)

):

return Quantity(a, dtype=dtype)

else:

# skip over some dtype deprecation.

dtype = np.float64 if dtype is np.inexact else dtype

return np.asanyarray(a, dtype=dtype)