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Decomposing and Composing Units
*******************************
.. _decomposing:
Reducing a Unit to Its Irreducible Parts
========================================
A unit or quantity can be decomposed into its irreducible parts using
the `Unit.decompose() <astropy.units.core.UnitBase.decompose>` or
`Quantity.decompose() <astropy.units.quantity.Quantity.decompose>`
methods.
Examples
--------
.. EXAMPLE START: Reducing a Unit to Its Irreducible Parts
To decompose a unit with :meth:`~astropy.units.core.UnitBase.decompose`::
>>> from astropy import units as u
>>> u.Ry
Unit("Ry")
>>> u.Ry.decompose()
Unit("2.17987e-18 m2 kg / s2")
To get the list of units in the decomposition, the
`~astropy.units.core.UnitBase.bases` and `~astropy.units.core.UnitBase.powers`
properties can be used::
>>> Ry = u.Ry.decompose()
>>> [unit**power for unit, power in zip(Ry.bases, Ry.powers)]
[Unit("m2"), Unit("kg"), Unit("1 / s2")]
You can limit the selection of units that you want to decompose by
using the ``bases`` keyword argument::
>>> u.Ry.decompose(bases=[u.m, u.N])
Unit("2.17987e-18 N m")
This is also useful to decompose to a particular system. For example,
to decompose the Rydberg unit of energy in terms of `CGS
<https://en.wikipedia.org/wiki/Centimetre-gram-second_system_of_units>`_
units::
>>> u.Ry.decompose(bases=u.cgs.bases)
Unit("2.17987e-11 cm2 g / s2")
Finally, if you want to know how a unit was defined::
>>> u.Ry.represents
Unit("13.6057 eV")
.. EXAMPLE END
Automatically Composing a Unit into More Complex Units
======================================================
Conversely, a unit may be recomposed back into more complex units
using the :meth:`~astropy.units.core.UnitBase.compose` method. Since there
may be multiple equally good results, a list is always returned.
Examples
--------
.. EXAMPLE START: Recomposing a Unit into More Complex Units
To recompose a unit with :meth:`~astropy.units.core.UnitBase.compose`::
>>> x = u.Ry.decompose()
>>> x.compose()
[Unit("Ry"),
Unit("2.17987e-62 foe"),
Unit("2.17987e-18 J"),
Unit("2.17987e-11 erg"),
Unit("13.6057 eV")]
Some other interesting examples::
>>> (u.s ** -1).compose() # doctest: +SKIP
[Unit("Bq"), Unit("Hz"), Unit("2.7027e-11 Ci")]
Composition can be combined with :ref:`unit_equivalencies`::
>>> (u.s ** -1).compose(equivalencies=u.spectral()) # doctest: +SKIP
[Unit("m"),
Unit("Hz"),
Unit("J"),
Unit("Bq"),
Unit("3.24078e-17 pc"),
Unit("1.057e-16 lyr"),
Unit("6.68459e-12 AU"),
Unit("1.4378e-09 solRad"),
Unit("0.01 k"),
Unit("100 cm"),
Unit("1e+06 micron"),
Unit("1e+07 erg"),
Unit("1e+10 Angstrom"),
Unit("3.7e+10 Ci"),
Unit("4.58743e+17 Ry"),
Unit("6.24151e+18 eV")]
A name does not exist for every arbitrary derived unit
imaginable. In that case, the system will do its best to reduce the
unit to the fewest possible symbols::
>>> (u.cd * u.sr * u.V * u.s).compose()
[Unit("Wb lm"), Unit("1e+08 Mx lm")]
.. EXAMPLE END
Converting Between Systems
==========================
Built on top of this functionality is a convenience method to convert
between unit systems.
Examples
--------
.. EXAMPLE START: Converting Between Unit Systems
To convert between unit systems::
>>> u.Pa.to_system(u.cgs)
[Unit("10 Ba"), Unit("10 P / s")]
There is also a shorthand for this which only returns the first of
many possible matches::
>>> u.Pa.cgs
Unit("10 Ba")
This is equivalent to decomposing into the new system and then
composing into the simplest units possible in that system, though
:meth:`~astropy.units.core.UnitBase.to_system` adds some extra logic to
return the results sorted such that if a simple combination of base
units exists, it will be put sorted to the front::
>>> unit = u.m**2 / u.s
>>> unit.decompose(bases=u.cgs.bases)
Unit("10000 cm2 / s")
>>> _.compose(units=u.cgs)
[Unit("10000 St"), Unit("10000 cm2 / s")]
>>> unit.to_system(u.cgs)
[Unit("10000 cm2 / s"), Unit("10000 St")]
.. EXAMPLE END
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