Quantity

The Quantity object is meant to represent a value that has some unit associated with the number.

Creating Quantity Instances

Quantity objects are normally created through multiplication with Unit objects.

Examples

To create a Quantity to represent 15 m/s:

>>> import astropy.units as u
>>> 15 * u.m / u.s  
<Quantity 15. m / s>

This extends as expected to division by a unit, or using numpy arrays or Python sequences:

>>> 1.25 / u.s
<Quantity 1.25 1 / s>
>>> [1, 2, 3] * u.m  
<Quantity [1., 2., 3.] m>
>>> import numpy as np
>>> np.array([1, 2, 3]) * u.m  
<Quantity [1., 2., 3.] m>

You can also create instances using the Quantity constructor directly, by specifying a value and unit:

>>> u.Quantity(15, u.m / u.s)  
<Quantity 15. m / s>

The constructor gives a few more options. In particular, it allows you to merge sequences of Quantity objects (as long as all of their units are equivalent), and to parse simple strings (which may help, for example, to parse configuration files, etc.):

>>> qlst = [60 * u.s, 1 * u.min]
>>> u.Quantity(qlst, u.minute)  
<Quantity [1.,  1.] min>
>>> u.Quantity('15 m/s')  
<Quantity 15. m / s>

The current unit and value can be accessed via the unit and value attributes:

>>> q = 2.5 * u.m / u.s
>>> q.unit
Unit("m / s")
>>> q.value
2.5

Note

Quantity objects are converted to float by default. Furthermore, any data passed in are copied, which for large arrays may not be optimal. As discussed further below, you can instead obtain a view by passing copy=False to Quantity or by using the << operator.

Converting to Different Units

Quantity objects can be converted to different units using the to() method.

Examples

To convert Quantity objects to different units:

>>> q = 2.3 * u.m / u.s
>>> q.to(u.km / u.h)  
<Quantity 8.28 km / h>

For convenience, the si and cgs attributes can be used to convert the Quantity to base SI or CGS units:

>>> q = 2.4 * u.m / u.s
>>> q.si  
<Quantity 2.4 m / s>
>>> q.cgs  
<Quantity 240. cm / s>

If you want the value of the quantity in a different unit, you can use to_value() as a shortcut:

>>> q = 2.5 * u.m
>>> q.to_value(u.cm)
250.0

Note

You could get the value in cm also by using q.to(u.cm).value. The difference is that to_value() does no copying if the unit is already the correct one, instead returning a view of the data (just as if you had done q.value). In contrast, to() always returns a copy (which also means it is slower for the case where no conversion is necessary). As discussed further below, you can avoid the copying by using the << operator.

Comparing Quantities

The equality of Quantity objects is best tested using the allclose() and isclose() functions, which are unit-aware analogues of the numpy functions with the same name:

>>> u.allclose([1, 2] * u.m, [100, 200] * u.cm)
True
>>> u.isclose([1, 2] * u.m, [100, 20] * u.cm)
array([ True, False])

The use of Python comparison operators is also supported:

>>> 1*u.m < 50*u.cm
False

Plotting Quantities

Quantity objects can be conveniently plotted using Matplotlib — see Plotting quantities for more details.

Arithmetic

Addition and Subtraction

Addition or subtraction between Quantity objects is supported when their units are equivalent.

Examples

When the units are equal, the resulting object has the same unit:

>>> 11 * u.s + 30 * u.s  
<Quantity 41. s>
>>> 30 * u.s - 11 * u.s  
<Quantity 19. s>

If the units are equivalent, but not equal (e.g., kilometer and meter), the resulting object has units of the object on the left:

>>> 1100.1 * u.m + 13.5 * u.km
<Quantity 14600.1 m>
>>> 13.5 * u.km + 1100.1 * u.m  
<Quantity 14.6001 km>
>>> 1100.1 * u.m - 13.5 * u.km
<Quantity -12399.9 m>
>>> 13.5 * u.km - 1100.1 * u.m  
<Quantity 12.3999 km>

Addition and subtraction are not supported between Quantity objects and basic numeric types, except for dimensionless quantities (see Dimensionless Quantities) or special values like zero and infinity:

>>> 13.5 * u.km + 19.412  
Traceback (most recent call last):
  ...
UnitConversionError: Can only apply 'add' function to dimensionless
quantities when other argument is not a quantity (unless the
latter is all zero/infinity/nan)

Multiplication and Division

Multiplication and division are supported between Quantity objects with any units, and with numeric types. For these operations between objects with equivalent units, the resulting object has composite units.

Examples

To perform these operations on Quantity objects:

>>> 1.1 * u.m * 140.3 * u.cm  
<Quantity 154.33 cm m>
>>> 140.3 * u.cm * 1.1 * u.m  
<Quantity 154.33 cm m>
>>> 1. * u.m / (20. * u.cm)  
<Quantity 0.05 m / cm>
>>> 20. * u.cm / (1. * u.m)  
<Quantity 20. cm / m>

For multiplication, you can change how to represent the resulting object by using the to() method:

>>> (1.1 * u.m * 140.3 * u.cm).to(u.m**2)  
<Quantity 1.5433 m2>
>>> (1.1 * u.m * 140.3 * u.cm).to(u.cm**2)  
<Quantity 15433. cm2>

For division, if the units are equivalent, you may want to make the resulting object dimensionless by reducing the units. To do this, use the decompose() method:

>>> (20. * u.cm / (1. * u.m)).decompose()  
<Quantity 0.2>

This method is also useful for more complicated arithmetic:

>>> 15. * u.kg * 32. * u.cm * 15 * u.m / (11. * u.s * 1914.15 * u.ms)  
<Quantity 0.34195097 cm kg m / (ms s)>
>>> (15. * u.kg * 32. * u.cm * 15 * u.m / (11. * u.s * 1914.15 * u.ms)).decompose()  
<Quantity 3.41950973 kg m2 / s2>

NumPy Functions

Quantity objects are actually full numpy arrays (the Quantity class inherits from and extends numpy.ndarray), and we have tried to ensure that numpy functions behave properly with quantities:

>>> q = np.array([1., 2., 3., 4.]) * u.m / u.s
>>> np.mean(q)
<Quantity 2.5 m / s>
>>> np.std(q)  
<Quantity 1.11803399 m / s>

This includes functions that only accept specific units such as angles:

>>> q = 30. * u.deg
>>> np.sin(q)  
<Quantity 0.5>

Or Dimensionless Quantities:

>>> from astropy.constants import h, k_B
>>> nu = 3 * u.GHz
>>> T = 30 * u.K
>>> np.exp(-h * nu / (k_B * T))  
<Quantity 0.99521225>

Note

Support for functions from other packages, such as scipy, is more incomplete (contributions to improve this are welcomed!).

Dimensionless Quantities

Dimensionless quantities have the characteristic that if they are added to or subtracted from a Python scalar or unitless ndarray, or if they are passed to a numpy function that takes dimensionless quantities, the units are simplified so that the quantity is dimensionless and scale-free. For example:

>>> 1. + 1. * u.m / u.km  
<Quantity 1.001>

Which is different from:

>>> 1. + (1. * u.m / u.km).value
2.0

In the latter case, the result is 2.0 because the unit of (1. * u.m / u.km) is not scale-free by default:

>>> q = (1. * u.m / u.km)
>>> q.unit
Unit("m / km")
>>> q.unit.decompose()
Unit(dimensionless with a scale of 0.001)

However, when combining with an object that is not a Quantity, the unit is automatically decomposed to be scale-free, giving the expected result.

This also occurs when passing dimensionless quantities to functions that take dimensionless quantities:

>>> nu = 3 * u.GHz
>>> T = 30 * u.K
>>> np.exp(- h * nu / (k_B * T))  
<Quantity 0.99521225>

The result is independent from the units in which the different quantities were specified:

>>> nu = 3.e9 * u.Hz
>>> T = 30 * u.K
>>> np.exp(- h * nu / (k_B * T))  
<Quantity 0.99521225>

Converting to Plain Python Scalars

Converting Quantity objects does not work for non-dimensionless quantities:

>>> float(3. * u.m)
Traceback (most recent call last):
  ...
TypeError: only dimensionless scalar quantities can be converted
to Python scalars

Only dimensionless values can be converted to plain Python scalars:

>>> float(3. * u.m / (4. * u.m))
0.75
>>> float(3. * u.km / (4. * u.m))
750.0
>>> int(6. * u.km / (2. * u.m))
3000

Functions that Accept Quantities

If a function accepts a Quantity as an argument then it can be a good idea to check that the provided Quantity belongs to one of the expected Physical Types. This can be done with the decorator quantity_input().

The decorator does not convert the input Quantity to the desired unit, say arcseconds to degrees in the example below, it merely checks that such a conversion is possible, thus verifying that the Quantity argument can be used in calculations.

Keyword arguments to quantity_input() specify which arguments should be validated and what unit they are expected to be compatible with.

Examples

To verify if a Quantity argument can be used in calculations:

>>> @u.quantity_input(myarg=u.deg)
... def myfunction(myarg):
...     return myarg.unit

>>> myfunction(100*u.arcsec)
Unit("arcsec")
>>> myfunction(2*u.m)  
Traceback (most recent call last):
...
UnitsError: Argument 'myarg' to function 'myfunction' must be in units
convertible to 'deg'.

It is also possible to instead specify the physical type of the desired unit:

>>> @u.quantity_input(myarg='angle')
... def myfunction(myarg):
...     return myarg.unit

>>> myfunction(100*u.arcsec)
Unit("arcsec")

Optionally, None keyword arguments are also supported; for such cases, the input is only checked when a value other than None is passed:

>>> @u.quantity_input(a='length', b='angle')
... def myfunction(a, b=None):
...     return a, b

>>> myfunction(1.*u.km)  
(<Quantity 1. km>, None)
>>> myfunction(1.*u.km, 1*u.deg)  
(<Quantity 1. km>, <Quantity 1. deg>)

Alternatively, you can use the annotations syntax to provide the units. While the raw unit or string can be used, the preferred method is with the unit-aware Quantity-annotation syntax. This requires Python 3.9 or the package typing_extensions.

Quantity[unit or "string", metadata, ...] .. doctest-skip:

>>> @u.quantity_input
... def myfunction(myarg: u.Quantity[u.arcsec]):
...     return myarg.unit
>>>
>>> myfunction(100*u.arcsec)
Unit("arcsec")

You can also annotate for different types in non-unit expecting arguments: .. doctest-skip:

>>> @u.quantity_input
... def myfunction(myarg: u.Quantity[u.arcsec], nice_string: str):
...     return myarg.unit, nice_string
>>> myfunction(100*u.arcsec, "a nice string")
(Unit("arcsec"), 'a nice string')

The output can be specified to have a desired unit with a function annotation, for example .. doctest-skip:

>>> @u.quantity_input
... def myfunction(myarg: u.Quantity[u.arcsec]) -> u.deg:
...     return myarg*1000
>>>
>>> myfunction(100*u.arcsec)  
<Quantity 27.77777778 deg>

This both checks that the return value of your function is consistent with what you expect and makes it much neater to display the results of the function.

Specifying a list of valid equivalent units or Physical Types is supported for functions that should accept inputs with multiple valid units:

>>> @u.quantity_input(a=['length', 'speed'])
... def myfunction(a):
...     return a.unit
>>> myfunction(1.*u.km)
Unit("km")
>>> myfunction(1.*u.km/u.s)
Unit("km / s")

Representing Vectors with Units

Quantity objects can, like numpy arrays, be used to represent vectors or matrices by assigning specific dimensions to represent the coordinates or matrix elements, but that implies tracking those dimensions carefully. For vectors Using and Designing Coordinate Representations can be more convenient as doing so allows you to use representations other than Cartesian (such as spherical or cylindrical), as well as simple vector arithmetic.

Creating and Converting Quantities without Copies

When creating a Quantity using multiplication with a unit, a copy of the underlying data is made. This can be avoided by passing on copy=False in the initializer.

Examples

To avoid duplication using copy=False:

>>> a = np.arange(5.)
>>> q = u.Quantity(a, u.m, copy=False)
>>> q  
<Quantity [0., 1., 2., 3., 4.] m>
>>> np.may_share_memory(a, q)
True
>>> a[0] = -1.
>>> q  
<Quantity [-1.,  1.,  2.,  3.,  4.] m>

This may be particularly useful in functions which do not change their input while ensuring that if a user passes in a Quantity then it will be converted to the desired unit.

As a shortcut, you can “shift” to the requested unit using the << operator:

>>> q = a << u.m
>>> np.may_share_memory(a, q)
True
>>> q  
<Quantity [-1.,  1.,  2.,  3.,  4.] m>

The operator works identically to the initialization with copy=False mentioned above:

>>> q << u.cm  
<Quantity [-100.,  100.,  200.,  300.,  400.] cm>

It can also be used for in-place conversion:

>>> q <<= u.cm
>>> q  
<Quantity [-100.,  100.,  200.,  300.,  400.] cm>
>>> a  
array([-100.,  100.,  200.,  300.,  400.])

QTable

It is possible to use Quantity objects as columns in astropy.table. See Quantity and QTable for more details.

Subclassing Quantity

To subclass Quantity, you generally proceed as you would when subclassing numpy.ndarray (i.e., you typically need to override __new__(), rather than __init__(), and use the numpy.ndarray.__array_finalize__() method to update attributes). For details, see the NumPy documentation on subclassing. To get a sense of what is involved, have a look at Quantity itself, where, for example, the astropy.units.Quantity.__array_finalize__() method is used to pass on the unit, at Angle, where strings are parsed as angles in the astropy.coordinates.Angle.__new__() method and at Longitude, where the astropy.coordinates.Longitude.__array_finalize__() method is used to pass on the angle at which longitudes wrap.

Another method that is meant to be overridden by subclasses, specific to Quantity, is astropy.units.Quantity.__quantity_subclass__(). This is called to decide which type of subclass to return, based on the unit of the Quantity that is to be created. It is used, for example, in Angle to return a Quantity if a calculation returns a unit other than an angular one. The implementation of this is via SpecificTypeQuantity, which more generally allows users to construct Quantity subclasses that have methods that are useful only for a specific physical type.