# Quantity¶

The `Quantity`

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

## Creating Quantity instances¶

`Quantity`

objects are created through multiplication or division with
`Unit`

objects. For example, to create a `Quantity`

to represent 15 m/s:

```
>>> import astropy.units as u
>>> 15 * u.m / u.s
<Quantity 15.0 m / s>
```

Note

`Quantity`

objects are converted to float by default.

As another example:

```
>>> 1.25 / u.s
<Quantity 1.25 1 / s>
```

You can also create instances using the `Quantity`

constructor directly, by
specifying a value and unit:

```
>>> u.Quantity(15, u.m / u.s)
<Quantity 15.0 m / s>
```

`Quantity`

objects can also be created automatically from Numpy arrays
or Python sequences:

```
>>> [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>
```

`Quantity`

objects can also be created from sequences of `Quantity`

objects, as long as all of their units are equivalent, and will
automatically convert to Numpy arrays:

```
>>> qlst = [60 * u.s, 1 * u.min]
>>> u.Quantity(qlst, u.minute)
<Quantity [ 1., 1.] min>
```

Finally, 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
```

## Converting to different units¶

`Quantity`

objects can be converted to different units using the
`to()`

method:

```
>>> 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 S.I. or c.g.s units:

```
>>> q = 2.4 * u.m / u.s
>>> q.si
<Quantity 2.4 m / s>
>>> q.cgs
<Quantity 240.0 cm / s>
```

## Arithmetic¶

### Addition and Subtraction¶

Addition or subtraction between `Quantity`

objects is supported when their
units are equivalent. When the units are equal, the resulting object has the
same unit:

```
>>> 11 * u.s + 30 * u.s
<Quantity 41.0 s>
>>> 30 * u.s - 11 * u.s
<Quantity 19.0 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 is not supported between `Quantity`

objects and basic
numeric types:

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

except for dimensionless quantities (see Dimensionless quantities).

### Multiplication and Division¶

Multiplication and division is 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**:

```
>>> 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 20.0 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 1.5433000000000001 m2>
>>> (1.1 * u.m * 140.3 * u.cm).to(u.cm**2)
<Quantity 15433.000000000002 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 0.3419509727792778 cm kg m / (ms s)>
>>> (15. * u.kg * 32. * u.cm * 15 * u.m / (11. * u.s * 1914.15 * u.ms)).decompose()
<Quantity 3.4195097277927777 kg m2 / s2>
```

## Numpy functions¶

`Quantity`

objects are actually full Numpy arrays (the `Quantity`

object class inherits from and extends the `numpy.ndarray`

class), and
we have tried to ensure that most 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 1.118033988749895 m / s>
```

including functions that only accept specific units such as angles:

```
>>> q = 30. * u.deg
>>> np.sin(q)
<Quantity 0.49999999999999994>
```

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 0.995212254618668>
```

(see Dimensionless quantities for more details).

## Dimensionless quantities¶

Dimensionless quantities have the characteristic that if they are
added 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 a non-quantity object, 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 0.995212254618668>
```

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

```
>>> nu = 3.e9 * u.Hz
>>> T = 30 * u.K
>>> np.exp(- h * nu / (k_B * T))
<Quantity 0.995212254618668>
```

## 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
```

Instead, 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 Accepting Quantities¶

Validation of quantity arguments to functions can lead to many repetitons
of the same checking code. A decorator is provided which verifies that certain
arguments to a function are `Quantity`

objects and that the units
are compatible with a desired unit.

The decorator does not convert the unit to the desired unit, say arcseconds
to degrees, it merely checks that such a conversion is possible, thus verifying
that the `Quantity`

argument can be used in calculations.

The decorator `quantity_input`

accepts keyword arguments to
spcifiy which arguments should be validated and what unit they are expected to
be compatible with:

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

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

Under Python 3 you can use the annotations syntax to provide the units:

```
>>> @u.quantity_input
... def myfunction(myarg: u.arcsec):
... return myarg.unit
```

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

## Known issues with conversion to numpy arrays¶

Since `Quantity`

objects are Numpy arrays, we are not able to ensure
that only dimensionless quantities are converted to Numpy arrays:

```
>>> np.array([1, 2, 3] * u.m)
array([ 1., 2., 3.])
```

Similarly, while most numpy functions work properly, a few have known
issues, either ignoring the unit (e.g., `np.dot`

) or
not reinitializing it properly (e.g., `np.hstack`

). This propagates to
more complex functions such as `np.linalg.norm`

and
`scipy.integrate.odeint`

.

## Subclassing Quantity¶

To subclass `Quantity`

, one generally proceeds as one would when subclassing
`ndarray`

, i.e., one typically needs to override `__new__`

(rather than `__init__`

) and uses the `numpy.ndarray.__array_finalize__`

method to update attributes. For details, see the numpy documentation on
subclassing. For
examples, one can look at `Quantity`

itself, where, e.g., 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, one 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, e.g., in
`Angle`

to return a `Quantity`

if a calculation
returns a unit other than an angular one.