Decomposing and Composing Units

Reducing a Unit to Its Irreducible Parts

A unit or quantity can be decomposed into its irreducible parts using the Unit.decompose() or Quantity.decompose() methods.

Examples

To decompose a unit with 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 bases and 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 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")

Automatically Composing a Unit into More Complex Units

Conversely, a unit may be recomposed back into more complex units using the compose() method. Since there may be multiple equally good results, a list is always returned.

Examples

To recompose a unit with compose():

>>> x = u.Ry.decompose()
>>> x.compose()
[Unit("Ry"),
 Unit("2.17987e-18 J"),
 Unit("2.17987e-11 erg"),
 Unit("13.6057 eV")]

Some other interesting examples:

>>> (u.s ** -1).compose()  
[Unit("Bq"), Unit("Hz"), Unit("2.7027e-11 Ci")]

Composition can be combined with Equivalencies:

>>> (u.s ** -1).compose(equivalencies=u.spectral())  
[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")]

Converting Between Systems

Built on top of this functionality is a convenience method to convert between unit systems.

Examples

To convert between unit systems:

>>> u.Pa.to_system(u.cgs)
[Unit("10 P / s"), Unit("10 Ba")]

There is also a shorthand for this which only returns the first of many possible matches:

>>> u.Pa.cgs
Unit("10 P / s")

This is equivalent to decomposing into the new system and then composing into the most complex units possible, though to_system() adds some extra logic to return the results sorted in the most useful order:

>>> u.Pa.decompose(bases=u.cgs.bases)
Unit("10 g / (cm s2)")
>>> _.compose(units=u.cgs)
[Unit("10 Ba"), Unit("10 P / s")]