.. _quantity:

Quantity
********

.. |quantity| replace:: :class:`~astropy.units.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
:class:`~astropy.units.Unit` objects. For example, to create a |quantity|
to represent 15 m/s:

    >>> import astropy.units as u
    >>> 15 * u.m / u.s  # doctest: +FLOAT_CMP
    <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  # doctest: +FLOAT_CMP
    <Quantity [1., 2., 3.] m>
    >>> import numpy as np
    >>> np.array([1, 2, 3]) * u.m  # doctest: +FLOAT_CMP
    <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)  # doctest: +FLOAT_CMP
    <Quantity 15. m / s>

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

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

The current unit and value can be accessed via the
`~astropy.units.quantity.Quantity.unit` and
`~astropy.units.quantity.Quantity.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 :ref:`further below
	  <astropy-units-quantity-no-copy>`.  one can instead obtain a
	  `~numpy.ndarray.view` by passing ``copy=False`` to |quantity| or use
	  the ``<<`` operator.

Converting to different units
=============================

|quantity| objects can be converted to different units using the
:meth:`~astropy.units.quantity.Quantity.to` method:

    >>> q = 2.3 * u.m / u.s
    >>> q.to(u.km / u.h)  # doctest: +FLOAT_CMP
    <Quantity 8.28 km / h>

For convenience, the `~astropy.units.quantity.Quantity.si` and
`~astropy.units.quantity.Quantity.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  # doctest: +FLOAT_CMP
    <Quantity 2.4 m / s>
    >>> q.cgs  # doctest: +FLOAT_CMP
    <Quantity 240. cm / s>

If you want the value of the quantity in a different unit, you can use
:meth:`~astropy.units.Quantity.to_value` as a short-cut:

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

.. note:: You could get the value in ``cm`` also using ``q.to(u.cm).value``.
          The difference is that :meth:`~astropy.units.Quantity.to_value` does
          no conversion if the unit is already the correct one, instead just
          returning an :meth:`~numpy.ndarray.view` of the data (just as if you
          had done ``q.value``).  In contrast,
          :meth:`~astropy.units.Quantity.to` always returns a copy (which also
          means it is slower for the case where no conversion is necessary).
          As discussed :ref:`further below <astropy-units-quantity-no-copy>`,
          one can avoid the copy if the unit is already correct by using the
          ``<<`` operator.

Comparing quantities
====================

|quantity| objects can be compared as follows:

    >>> from astropy import units as u
    >>> u.allclose([1, 2] * u.m, [100, 200] * u.cm)
    True
    >>> u.isclose([1, 2] * u.m, [100, 20] * u.cm)  # doctest: +SKIP
    array([ True, False])

.. _plotting-quantities:

Plotting quantities
===================

|quantity| objects can be conveniently plotted using matplotlib.  This
feature needs to be explicitly turned on:

.. doctest-requires:: matplotlib

    >>> from astropy.visualization import quantity_support
    >>> quantity_support()  # doctest: +IGNORE_OUTPUT
    <astropy.visualization.units.MplQuantityConverter ...>

Then |quantity| objects can be passed to matplotlib plotting
functions.  The axis labels are automatically labeled with the unit of
the quantity:

.. doctest-requires:: matplotlib

    >>> from matplotlib import pyplot as plt
    >>> plt.figure(figsize=(5,3))
    <...>
    >>> plt.plot([1, 2, 3] * u.m)
    [...]

.. plot::

    from astropy import units as u
    from astropy.visualization import quantity_support
    quantity_support()
    from matplotlib import pyplot as plt
    plt.figure(figsize=(5,3))
    plt.plot([1, 2, 3] * u.m)

Quantities are automatically converted to the first unit set on a
particular axis, so in the following, the y-axis remains in ``m`` even
though the second line is given in ``cm``:

.. doctest-requires:: matplotlib

    >>> plt.plot([1, 2, 3] * u.cm)
    [...]

.. plot::

    from astropy import units as u
    from astropy.visualization import quantity_support
    quantity_support()
    from matplotlib import pyplot as plt
    plt.figure(figsize=(5,3))
    plt.plot([1, 2, 3] * u.m)
    plt.plot([1, 2, 3] * u.cm)

Plotting a quantity with an incompatible unit will raise an exception:

.. doctest-requires:: matplotlib

    >>> plt.plot([1, 2, 3] * u.kg)  # doctest: +IGNORE_EXCEPTION_DETAIL
    Traceback (most recent call last):
    ...
    UnitConversionError: 'kg' (mass) and 'm' (length) are not convertible
    >>> plt.clf()

To make sure unit support is turned off afterward, you can use
`~astropy.visualization.quantity_support` with a ``with`` statement:

.. doctest-requires:: matplotlib

    >>> from astropy.visualization import quantity_support
    >>> from matplotlib import pyplot as plt
    >>> with quantity_support():
    ...     plt.figure(figsize=(5,3))
    ...     plt.plot([1, 2, 3] * u.m)
    <...>
    [...]

.. plot::

    from astropy import units as u
    from astropy.visualization import quantity_support
    from matplotlib import pyplot as plt
    with quantity_support():
        plt.figure(figsize=(5,3))
        plt.plot([1, 2, 3] * u.m)

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  # doctest: +FLOAT_CMP
    <Quantity 41. s>
    >>> 30 * u.s - 11 * u.s  # doctest: +FLOAT_CMP
    <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  # doctest: +FLOAT_CMP
    <Quantity 14.6001 km>
    >>> 1100.1 * u.m - 13.5 * u.km
    <Quantity -12399.9 m>
    >>> 13.5 * u.km - 1100.1 * u.m  # doctest: +FLOAT_CMP
    <Quantity 12.3999 km>

Addition and subtraction are not supported between |quantity| objects and basic
numeric types:

    >>> 13.5 * u.km + 19.412  # doctest: +IGNORE_EXCEPTION_DETAIL
    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 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**:

    >>> 1.1 * u.m * 140.3 * u.cm  # doctest: +FLOAT_CMP
    <Quantity 154.33 cm m>
    >>> 140.3 * u.cm * 1.1 * u.m  # doctest: +FLOAT_CMP
    <Quantity 154.33 cm m>
    >>> 1. * u.m / (20. * u.cm)  # doctest: +FLOAT_CMP
    <Quantity 0.05 m / cm>
    >>> 20. * u.cm / (1. * u.m)  # doctest: +FLOAT_CMP
    <Quantity 20. cm / m>

For multiplication, you can change how to represent the resulting object by
using the :meth:`~astropy.units.quantity.Quantity.to` method:

    >>> (1.1 * u.m * 140.3 * u.cm).to(u.m**2)  # doctest: +FLOAT_CMP
    <Quantity 1.5433 m2>
    >>> (1.1 * u.m * 140.3 * u.cm).to(u.cm**2)  # doctest: +FLOAT_CMP
    <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
:meth:`~astropy.units.quantity.Quantity.decompose()` method:

    >>> (20. * u.cm / (1. * u.m)).decompose()  # doctest: +FLOAT_CMP
    <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)  # doctest: +FLOAT_CMP
    <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()  # doctest: +FLOAT_CMP
    <Quantity 3.41950973 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)  # doctest: +FLOAT_CMP
    <Quantity 1.11803399 m / s>

including functions that only accept specific units such as angles:

    >>> q = 30. * u.deg
    >>> np.sin(q)  # doctest: +FLOAT_CMP
    <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))  # doctest: +FLOAT_CMP
    <Quantity 0.99521225>

(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 `~numpy.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  # doctest: +FLOAT_CMP
    <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))  # doctest: +FLOAT_CMP
    <Quantity 0.99521225>

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))  # doctest: +FLOAT_CMP
    <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

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 that accept Quantities
================================

Validation of quantity arguments to functions can lead to many repetitions
of the same checking code. A decorator is provided which verifies that certain
arguments to a function are `~astropy.units.Quantity` objects and that the units
are compatible with a desired unit or physical type.

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 `~astropy.units.Quantity`
argument can be used in calculations.

The decorator `~astropy.units.quantity_input` accepts keyword arguments to
specify 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")

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)  # doctest: +FLOAT_CMP
    (<Quantity 1. km>, None)
    >>> myfunction(1.*u.km, 1*u.deg)  # doctest: +FLOAT_CMP
    (<Quantity 1. km>, <Quantity 1. deg>)

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

    >>> @u.quantity_input  # doctest: +SKIP
    ... def myfunction(myarg: u.arcsec):
    ...     return myarg.unit

    >>> myfunction(100*u.arcsec)  # doctest: +SKIP
    Unit("arcsec")

Also under Python 3 only you can define a return decoration, to which the return
value will be converted, i.e.::

    >>> @u.quantity_input  # doctest: +SKIP
    ... def myfunction(myarg: u.arcsec) -> u.deg:
    ...     return myarg*1000

    >>> myfunction(100*u.arcsec)  # doctest: +SKIP
    <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.

The decorator also supports specifying a list of valid equivalent units or
physical types 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, one can use instead the representations underlying coordinates, which
allow one to use representations other than cartesian (such as spherical or
cylindrical), as well as simple vector arithmetic.  For details, see
:ref:`astropy-coordinates-representations`.

.. _astropy-units-quantity-no-copy:

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::

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

This may be particularly useful in functions which do not change their input;
it also ensures that if a user passes in a |quantity| with units of length,
it will be converted to meters.

As a shortcut, one can "shift" to the requested unit using the ``<<``
operator::

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

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

    >>> q << u.cm  # doctest: +FLOAT_CMP
    <Quantity [-100.,  100.,  200.,  300.,  400.] cm>

It can also be used for in-place conversion::

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

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)  # doctest: +FLOAT_CMP
    array([1., 2., 3.])

Similarly, while most numpy functions work properly, a few have :ref:`known
issues <quantity_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
:class:`~numpy.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
<https://docs.scipy.org/doc/numpy/user/basics.subclassing.html>`__.  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 :class:`~astropy.coordinates.Angle`, where strings are parsed
as angles in the ``astropy.coordinates.Angle.__new__`` method and at
:class:`~astropy.coordinates.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
:class:`~astropy.coordinates.Angle` to return a |quantity| if a calculation
returns a unit other than an angular one.
