The labels associated with :py:class:`~xarray.DataArray` and :py:class:`~xarray.Dataset` objects enables some powerful shortcuts for computation, notably including aggregation and broadcasting by dimension names.
Arithmetic operations with a single DataArray automatically vectorize (like numpy) over all array values:
.. ipython:: python
:suppress:
import numpy as np
import pandas as pd
import xarray as xr
np.random.seed(123456)
.. ipython:: python
arr = xr.DataArray(np.random.RandomState(0).randn(2, 3),
[('x', ['a', 'b']), ('y', [10, 20, 30])])
arr - 3
abs(arr)
You can also use any of numpy's or scipy's many ufunc functions directly on a DataArray:
.. ipython:: python
np.sin(arr)
Use :py:func:`~xarray.where` to conditionally switch between values:
.. ipython:: python
xr.where(arr > 0, 'positive', 'negative')
Data arrays also implement many :py:class:`numpy.ndarray` methods:
.. ipython:: python
arr.round(2)
arr.T
xarray objects borrow the :py:meth:`~xarray.DataArray.isnull`, :py:meth:`~xarray.DataArray.notnull`, :py:meth:`~xarray.DataArray.count`, :py:meth:`~xarray.DataArray.dropna`, :py:meth:`~xarray.DataArray.fillna`, :py:meth:`~xarray.DataArray.ffill`, and :py:meth:`~xarray.DataArray.bfill` methods for working with missing data from pandas:
.. ipython:: python
x = xr.DataArray([0, 1, np.nan, np.nan, 2], dims=['x'])
x.isnull()
x.notnull()
x.count()
x.dropna(dim='x')
x.fillna(-1)
x.ffill('x')
x.bfill('x')
Like pandas, xarray uses the float value np.nan (not-a-number) to represent
missing values.
xarray objects also have an :py:meth:`~xarray.DataArray.interpolate_na` method for filling missing values via 1D interpolation.
.. ipython:: python
x = xr.DataArray([0, 1, np.nan, np.nan, 2], dims=['x'],
coords={'xx': xr.Variable('x', [0, 1, 1.1, 1.9, 3])})
x.interpolate_na(dim='x', method='linear', use_coordinate='xx')
Note that xarray slightly diverges from the pandas interpolate syntax by
providing the use_coordinate keyword which facilitates a clear specification
of which values to use as the index in the interpolation.
Aggregation methods have been updated to take a dim argument instead of axis. This allows for very intuitive syntax for aggregation methods that are applied along particular dimension(s):
.. ipython:: python
arr.sum(dim='x')
arr.std(['x', 'y'])
arr.min()
If you need to figure out the axis number for a dimension yourself (say, for wrapping code designed to work with numpy arrays), you can use the :py:meth:`~xarray.DataArray.get_axis_num` method:
.. ipython:: python
arr.get_axis_num('y')
These operations automatically skip missing values, like in pandas:
.. ipython:: python
xr.DataArray([1, 2, np.nan, 3]).mean()
If desired, you can disable this behavior by invoking the aggregation method
with skipna=False.
DataArray objects include a :py:meth:`~xarray.DataArray.rolling` method. This
method supports rolling window aggregation:
.. ipython:: python
arr = xr.DataArray(np.arange(0, 7.5, 0.5).reshape(3, 5),
dims=('x', 'y'))
arr
:py:meth:`~xarray.DataArray.rolling` is applied along one dimension using the
name of the dimension as a key (e.g. y) and the window size as the value
(e.g. 3). We get back a Rolling object:
.. ipython:: python
arr.rolling(y=3)
The label position and minimum number of periods in the rolling window are
controlled by the center and min_periods arguments:
.. ipython:: python
arr.rolling(y=3, min_periods=2, center=True)
Aggregation and summary methods can be applied directly to the Rolling object:
.. ipython:: python
r = arr.rolling(y=3)
r.mean()
r.reduce(np.std)
Note that rolling window aggregations are faster when bottleneck is installed.
We can also manually iterate through Rolling objects:
.. ipython:: python
@verbatim
for label, arr_window in r:
# arr_window is a view of x
Finally, the rolling object has a construct method which returns a
view of the original DataArray with the windowed dimension in
the last position.
You can use this for more advanced rolling operations such as strided rolling,
windowed rolling, convolution, short-time FFT etc.
.. ipython:: python
# rolling with 2-point stride
rolling_da = r.construct('window_dim', stride=2)
rolling_da
rolling_da.mean('window_dim', skipna=False)
Because the DataArray given by r.construct('window_dim') is a view
of the original array, it is memory efficient.
You can also use construct to compute a weighted rolling sum:
.. ipython:: python
weight = xr.DataArray([0.25, 0.5, 0.25], dims=['window'])
arr.rolling(y=3).construct('window').dot(weight)
Note
numpy's Nan-aggregation functions such as nansum copy the original array.
In xarray, we internally use these functions in our aggregation methods
(such as .sum()) if skipna argument is not specified or set to True.
This means rolling_da.mean('window_dim') is memory inefficient.
To avoid this, use skipna=False as the above example.
DataArray objects are automatically align themselves ("broadcasting" in
the numpy parlance) by dimension name instead of axis order. With xarray, you
do not need to transpose arrays or insert dimensions of length 1 to get array
operations to work, as commonly done in numpy with :py:func:`np.reshape` or
:py:const:`np.newaxis`.
This is best illustrated by a few examples. Consider two one-dimensional arrays with different sizes aligned along different dimensions:
.. ipython:: python
a = xr.DataArray([1, 2], [('x', ['a', 'b'])])
a
b = xr.DataArray([-1, -2, -3], [('y', [10, 20, 30])])
b
With xarray, we can apply binary mathematical operations to these arrays, and their dimensions are expanded automatically:
.. ipython:: python
a * b
Moreover, dimensions are always reordered to the order in which they first appeared:
.. ipython:: python
c = xr.DataArray(np.arange(6).reshape(3, 2), [b['y'], a['x']])
c
a + c
This means, for example, that you always subtract an array from its transpose:
.. ipython:: python
c - c.T
You can explicitly broadcast xaray data structures by using the :py:func:`~xarray.broadcast` function:
.. ipython:: python
a2, b2 = xr.broadcast(a, b)
a2
b2
xarray enforces alignment between index :ref:`coordinates` (that is,
coordinates with the same name as a dimension, marked by *) on objects used
in binary operations.
Similarly to pandas, this alignment is automatic for arithmetic on binary operations. The default result of a binary operation is by the intersection (not the union) of coordinate labels:
.. ipython:: python
arr = xr.DataArray(np.arange(3), [('x', range(3))])
arr + arr[:-1]
If coordinate values for a dimension are missing on either argument, all matching dimensions must have the same size:
.. ipython:: python
@verbatim
In [1]: arr + xr.DataArray([1, 2], dims='x')
ValueError: arguments without labels along dimension 'x' cannot be aligned because they have different dimension size(s) {2} than the size of the aligned dimension labels: 3
However, one can explicitly change this default automatic alignment type ("inner") via :py:func:`~xarray.set_options()` in context manager:
.. ipython:: python
with xr.set_options(arithmetic_join="outer"):
arr + arr[:1]
arr + arr[:1]
Before loops or performance critical code, it's a good idea to align arrays explicitly (e.g., by putting them in the same Dataset or using :py:func:`~xarray.align`) to avoid the overhead of repeated alignment with each operation. See :ref:`align and reindex` for more details.
Note
There is no automatic alignment between arguments when performing in-place
arithmetic operations such as +=. You will need to use
:ref:`manual alignment<align and reindex>`. This ensures in-place
arithmetic never needs to modify data types.
Although index coordinates are aligned, other coordinates are not, and if their values conflict, they will be dropped. This is necessary, for example, because indexing turns 1D coordinates into scalar coordinates:
.. ipython:: python
arr[0]
arr[1]
# notice that the scalar coordinate 'x' is silently dropped
arr[1] - arr[0]
Still, xarray will persist other coordinates in arithmetic, as long as there are no conflicting values:
.. ipython:: python
# only one argument has the 'x' coordinate
arr[0] + 1
# both arguments have the same 'x' coordinate
arr[0] - arr[0]
Datasets support arithmetic operations by automatically looping over all data variables:
.. ipython:: python
ds = xr.Dataset({'x_and_y': (('x', 'y'), np.random.randn(3, 5)),
'x_only': ('x', np.random.randn(3))},
coords=arr.coords)
ds > 0
Datasets support most of the same methods found on data arrays:
.. ipython:: python
ds.mean(dim='x')
abs(ds)
Datasets also support NumPy ufuncs (requires NumPy v1.13 or newer), or alternatively you can use :py:meth:`~xarray.Dataset.apply` to apply a function to each variable in a dataset:
.. ipython:: python
np.sin(ds)
ds.apply(np.sin)
Datasets also use looping over variables for broadcasting in binary
arithmetic. You can do arithmetic between any DataArray and a dataset:
.. ipython:: python
ds + arr
Arithmetic between two datasets matches data variables of the same name:
.. ipython:: python
ds2 = xr.Dataset({'x_and_y': 0, 'x_only': 100})
ds - ds2
Similarly to index based alignment, the result has the intersection of all matching data variables.
It doesn't always make sense to do computation directly with xarray objects:
- In the inner loop of performance limited code, using xarray can add considerable overhead compared to using NumPy or native Python types. This is particularly true when working with scalars or small arrays (less than ~1e6 elements). Keeping track of labels and ensuring their consistency adds overhead, and xarray's core itself is not especially fast, because it's written in Python rather than a compiled language like C. Also, xarray's high level label-based APIs removes low-level control over how operations are implemented.
- Even if speed doesn't matter, it can be important to wrap existing code, or to support alternative interfaces that don't use xarray objects.
For these reasons, it is often well-advised to write low-level routines that work with NumPy arrays, and to wrap these routines to work with xarray objects. However, adding support for labels on both :py:class:`~xarray.Dataset` and :py:class:`~xarray.DataArray` can be a bit of a chore.
To make this easier, xarray supplies the :py:func:`~xarray.apply_ufunc` helper
function, designed for wrapping functions that support broadcasting and
vectorization on unlabeled arrays in the style of a NumPy
universal function ("ufunc" for short).
apply_ufunc takes care of everything needed for an idiomatic xarray wrapper,
including alignment, broadcasting, looping over Dataset variables (if
needed), and merging of coordinates. In fact, many internal xarray
functions/methods are written using apply_ufunc.
Simple functions that act independently on each value should work without any additional arguments:
.. ipython:: python
squared_error = lambda x, y: (x - y) ** 2
arr1 = xr.DataArray([0, 1, 2, 3], dims='x')
xr.apply_ufunc(squared_error, arr1, 1)
For using more complex operations that consider some array values collectively,
it's important to understand the idea of "core dimensions" from NumPy's
generalized ufuncs. Core dimensions are defined as dimensions
that should not be broadcast over. Usually, they correspond to the fundamental
dimensions over which an operation is defined, e.g., the summed axis in
np.sum. A good clue that core dimensions are needed is the presence of an
axis argument on the corresponding NumPy function.
With apply_ufunc, core dimensions are recognized by name, and then moved to
the last dimension of any input arguments before applying the given function.
This means that for functions that accept an axis argument, you usually need
to set axis=-1. As an example, here is how we would wrap
:py:func:`numpy.linalg.norm` to calculate the vector norm:
def vector_norm(x, dim, ord=None):
return xr.apply_ufunc(np.linalg.norm, x,
input_core_dims=[[dim]],
kwargs={'ord': ord, 'axis': -1}).. ipython:: python
:suppress:
def vector_norm(x, dim, ord=None):
return xr.apply_ufunc(np.linalg.norm, x,
input_core_dims=[[dim]],
kwargs={'ord': ord, 'axis': -1})
.. ipython:: python
vector_norm(arr1, dim='x')
Because apply_ufunc follows a standard convention for ufuncs, it plays
nicely with tools for building vectorized functions, like
:func:`numpy.broadcast_arrays` and :func:`numpy.vectorize`. For high performance
needs, consider using Numba's :doc:`vectorize and guvectorize <numba:user/vectorize>`.
In addition to wrapping functions, apply_ufunc can automatically parallelize
many functions when using dask by setting dask='parallelized'. See
:ref:`dask.automatic-parallelization` for details.
:py:func:`~xarray.apply_ufunc` also supports some advanced options for controlling alignment of variables and the form of the result. See the docstring for full details and more examples.