Indexing and selecting data¶
Similarly to pandas objects, xarray objects support both integer and label based lookups along each dimension. However, xarray objects also have named dimensions, so you can optionally use dimension names instead of relying on the positional ordering of dimensions.
Thus in total, xarray supports four different kinds of indexing, as described below and summarized in this table:
Dimension lookup | Index lookup | DataArray syntax |
Dataset syntax |
---|---|---|---|
Positional | By integer | arr[:, 0] |
not available |
Positional | By label | arr.loc[:, 'IA'] |
not available |
By name | By integer | arr.isel(space=0) or arr[dict(space=0)] |
ds.isel(space=0) or ds[dict(space=0)] |
By name | By label | arr.sel(space='IA') or arr.loc[dict(space='IA')] |
ds.sel(space='IA') or ds.loc[dict(space='IA')] |
Positional indexing¶
Indexing a DataArray
directly works (mostly) just like it
does for numpy arrays, except that the returned object is always another
DataArray:
In [1]: arr = xr.DataArray(np.random.rand(4, 3),
...: [('time', pd.date_range('2000-01-01', periods=4)),
...: ('space', ['IA', 'IL', 'IN'])])
...:
In [2]: arr[:2]
Out[2]:
<xarray.DataArray (time: 2, space: 3)>
array([[ 0.127, 0.967, 0.26 ],
[ 0.897, 0.377, 0.336]])
Coordinates:
* time (time) datetime64[ns] 2000-01-01 2000-01-02
* space (space) |S2 'IA' 'IL' 'IN'
In [3]: arr[0, 0]
Out[3]:
<xarray.DataArray ()>
array(0.12696983303810094)
Coordinates:
time datetime64[ns] 2000-01-01
space |S2 'IA'
In [4]: arr[:, [2, 1]]
Out[4]:
<xarray.DataArray (time: 4, space: 2)>
array([[ 0.26 , 0.967],
[ 0.336, 0.377],
[ 0.123, 0.84 ],
[ 0.448, 0.373]])
Coordinates:
* time (time) datetime64[ns] 2000-01-01 2000-01-02 2000-01-03 2000-01-04
* space (space) |S2 'IN' 'IL'
Attributes are persisted in all indexing operations.
Warning
Positional indexing deviates from the NumPy when indexing with multiple
arrays like arr[[0, 1], [0, 1]]
, as described in Orthogonal (outer) vs. vectorized indexing.
See Pointwise indexing for how to achieve this functionality in
xarray.
xarray also supports label-based indexing, just like pandas. Because
we use a pandas.Index
under the hood, label based indexing is very
fast. To do label based indexing, use the loc
attribute:
In [5]: arr.loc['2000-01-01':'2000-01-02', 'IA']
Out[5]:
<xarray.DataArray (time: 2)>
array([ 0.127, 0.897])
Coordinates:
* time (time) datetime64[ns] 2000-01-01 2000-01-02
space |S2 'IA'
You can perform any of the label indexing operations supported by pandas, including indexing with individual, slices and arrays of labels, as well as indexing with boolean arrays. Like pandas, label based indexing in xarray is inclusive of both the start and stop bounds.
Setting values with label based indexing is also supported:
In [6]: arr.loc['2000-01-01', ['IL', 'IN']] = -10
In [7]: arr
Out[7]:
<xarray.DataArray (time: 4, space: 3)>
array([[ 0.127, -10. , -10. ],
[ 0.897, 0.377, 0.336],
[ 0.451, 0.84 , 0.123],
[ 0.543, 0.373, 0.448]])
Coordinates:
* time (time) datetime64[ns] 2000-01-01 2000-01-02 2000-01-03 2000-01-04
* space (space) |S2 'IA' 'IL' 'IN'
Indexing with labeled dimensions¶
With labeled dimensions, we do not have to rely on dimension order and can use them explicitly to slice data. There are two ways to do this:
Use a dictionary as the argument for array positional or label based array indexing:
# index by integer array indices In [8]: arr[dict(space=0, time=slice(None, 2))] Out[8]: <xarray.DataArray (time: 2)> array([ 0.127, 0.897]) Coordinates: * time (time) datetime64[ns] 2000-01-01 2000-01-02 space |S2 'IA' # index by dimension coordinate labels In [9]: arr.loc[dict(time=slice('2000-01-01', '2000-01-02'))] Out[9]: <xarray.DataArray (time: 2, space: 3)> array([[ 0.127, -10. , -10. ], [ 0.897, 0.377, 0.336]]) Coordinates: * time (time) datetime64[ns] 2000-01-01 2000-01-02 * space (space) |S2 'IA' 'IL' 'IN'
Use the
sel()
andisel()
convenience methods:# index by integer array indices In [10]: arr.isel(space=0, time=slice(None, 2)) Out[10]: <xarray.DataArray (time: 2)> array([ 0.127, 0.897]) Coordinates: * time (time) datetime64[ns] 2000-01-01 2000-01-02 space |S2 'IA' # index by dimension coordinate labels In [11]: arr.sel(time=slice('2000-01-01', '2000-01-02')) Out[11]: <xarray.DataArray (time: 2, space: 3)> array([[ 0.127, -10. , -10. ], [ 0.897, 0.377, 0.336]]) Coordinates: * time (time) datetime64[ns] 2000-01-01 2000-01-02 * space (space) |S2 'IA' 'IL' 'IN'
The arguments to these methods can be any objects that could index the array
along the dimension given by the keyword, e.g., labels for an individual value,
Python slice()
objects or 1-dimensional arrays.
Note
We would love to be able to do indexing with labeled dimension names inside
brackets, but unfortunately, Python does yet not support indexing with
keyword arguments like arr[space=0]
Warning
Do not try to assign values when using any of the indexing methods isel
,
isel_points
, sel
or sel_points
:
# DO NOT do this
arr.isel(space=0) = 0
Depending on whether the underlying numpy indexing returns a copy or a view, the method will fail, and when it fails, it will fail silently. Instead, you should use normal index assignment:
# this is safe
arr[dict(space=0)] = 0
Pointwise indexing¶
xarray pointwise indexing supports the indexing along multiple labeled dimensions
using list-like objects. While isel()
performs
orthogonal indexing, the isel_points()
method
provides similar numpy indexing behavior as if you were using multiple
lists to index an array (e.g. arr[[0, 1], [0, 1]]
):
# index by integer array indices
In [12]: da = xr.DataArray(np.arange(56).reshape((7, 8)), dims=['x', 'y'])
In [13]: da
Out[13]:
<xarray.DataArray (x: 7, y: 8)>
array([[ 0, 1, 2, ..., 5, 6, 7],
[ 8, 9, 10, ..., 13, 14, 15],
[16, 17, 18, ..., 21, 22, 23],
...,
[32, 33, 34, ..., 37, 38, 39],
[40, 41, 42, ..., 45, 46, 47],
[48, 49, 50, ..., 53, 54, 55]])
Coordinates:
* x (x) int64 0 1 2 3 4 5 6
* y (y) int64 0 1 2 3 4 5 6 7
In [14]: da.isel_points(x=[0, 1, 6], y=[0, 1, 0])
Out[14]:
<xarray.DataArray (points: 3)>
array([ 0, 9, 48])
Coordinates:
y (points) int64 0 1 0
x (points) int64 0 1 6
* points (points) int64 0 1 2
There is also sel_points()
, which analogously
allows you to do point-wise indexing by label:
In [15]: times = pd.to_datetime(['2000-01-03', '2000-01-02', '2000-01-01'])
In [16]: arr.sel_points(space=['IA', 'IL', 'IN'], time=times)
Out[16]:
<xarray.DataArray (points: 3)>
array([ 0.451, 0.377, -10. ])
Coordinates:
time (points) datetime64[ns] 2000-01-03 2000-01-02 2000-01-01
space (points) |S2 'IA' 'IL' 'IN'
* points (points) int64 0 1 2
The equivalent pandas method to sel_points
is
lookup()
.
Dataset indexing¶
We can also use these methods to index all variables in a dataset simultaneously, returning a new dataset:
In [17]: ds = arr.to_dataset(name='foo')
In [18]: ds.isel(space=[0], time=[0])
Out[18]:
<xarray.Dataset>
Dimensions: (space: 1, time: 1)
Coordinates:
* time (time) datetime64[ns] 2000-01-01
* space (space) |S2 'IA'
Data variables:
foo (time, space) float64 0.127
In [19]: ds.sel(time='2000-01-01')
Out[19]:
<xarray.Dataset>
Dimensions: (space: 3)
Coordinates:
time datetime64[ns] 2000-01-01
* space (space) |S2 'IA' 'IL' 'IN'
Data variables:
foo (space) float64 0.127 -10.0 -10.0
In [20]: ds2 = da.to_dataset(name='bar')
In [21]: ds2.isel_points(x=[0, 1, 6], y=[0, 1, 0], dim='points')
Out[21]:
<xarray.Dataset>
Dimensions: (points: 3)
Coordinates:
y (points) int64 0 1 0
x (points) int64 0 1 6
* points (points) int64 0 1 2
Data variables:
bar (points) int64 0 9 48
Positional indexing on a dataset is not supported because the ordering of dimensions in a dataset is somewhat ambiguous (it can vary between different arrays). However, you can do normal indexing with labeled dimensions:
In [22]: ds[dict(space=[0], time=[0])]
Out[22]:
<xarray.Dataset>
Dimensions: (space: 1, time: 1)
Coordinates:
* time (time) datetime64[ns] 2000-01-01
* space (space) |S2 'IA'
Data variables:
foo (time, space) float64 0.127
In [23]: ds.loc[dict(time='2000-01-01')]
Out[23]:
<xarray.Dataset>
Dimensions: (space: 3)
Coordinates:
time datetime64[ns] 2000-01-01
* space (space) |S2 'IA' 'IL' 'IN'
Data variables:
foo (space) float64 0.127 -10.0 -10.0
Using indexing to assign values to a subset of dataset (e.g.,
ds[dict(space=0)] = 1
) is not yet supported.
Dropping labels¶
The drop()
method returns a new object with the listed
index labels along a dimension dropped:
In [24]: ds.drop(['IN', 'IL'], dim='space')
Out[24]:
<xarray.Dataset>
Dimensions: (space: 1, time: 4)
Coordinates:
* time (time) datetime64[ns] 2000-01-01 2000-01-02 2000-01-03 2000-01-04
* space (space) |S2 'IA'
Data variables:
foo (time, space) float64 0.127 0.8972 0.4514 0.543
drop
is both a Dataset
and DataArray
method.
Nearest neighbor lookups¶
The label based selection methods sel()
,
reindex()
and reindex_like()
all
support method
and tolerance
keyword argument. The method parameter allows for
enabling nearest neighbor (inexact) lookups by use of the methods 'pad'
,
'backfill'
or 'nearest'
:
In [25]: data = xr.DataArray([1, 2, 3], dims='x')
In [26]: data.sel(x=[1.1, 1.9], method='nearest')
Out[26]:
<xarray.DataArray (x: 2)>
array([2, 3])
Coordinates:
* x (x) int64 1 2
In [27]: data.sel(x=0.1, method='backfill')
Out[27]:
<xarray.DataArray ()>
array(2)
Coordinates:
x int64 1
In [28]: data.reindex(x=[0.5, 1, 1.5, 2, 2.5], method='pad')
Out[28]:
<xarray.DataArray (x: 5)>
array([1, 2, 2, 3, 3])
Coordinates:
* x (x) float64 0.5 1.0 1.5 2.0 2.5
Tolerance limits the maximum distance for valid matches with an inexact lookup:
In [29]: data.reindex(x=[1.1, 1.5], method='nearest', tolerance=0.2)
Out[29]:
<xarray.DataArray (x: 2)>
array([ 2., nan])
Coordinates:
* x (x) float64 1.1 1.5
Using method='nearest'
or a scalar argument with .sel()
requires pandas
version 0.16 or newer. Using tolerance
requries pandas version 0.17 or newer.
The method parameter is not yet supported if any of the arguments
to .sel()
is a slice
object:
In [30]: data.sel(x=slice(1, 3), method='nearest')
NotImplementedError
However, you don’t need to use method
to do inexact slicing. Slicing
already returns all values inside the range (inclusive), as long as the index
labels are monotonic increasing:
In [31]: data.sel(x=slice(0.9, 3.1))
Out[31]:
<xarray.DataArray (x: 2)>
array([2, 3])
Coordinates:
* x (x) int64 1 2
Indexing axes with monotonic decreasing labels also works, as long as the
slice
or .loc
arguments are also decreasing:
In [32]: reversed_data = data[::-1]
In [33]: reversed_data.loc[3.1:0.9]
Out[33]:
<xarray.DataArray (x: 2)>
array([3, 2])
Coordinates:
* x (x) int64 2 1
Masking with where
¶
Indexing methods on xarray objects generally return a subset of the original data.
However, it is sometimes useful to select an object with the same shape as the
original data, but with some elements masked. To do this type of selection in
xarray, use where()
:
In [34]: arr2 = xr.DataArray(np.arange(16).reshape(4, 4), dims=['x', 'y'])
In [35]: arr2.where(arr2.x + arr2.y < 4)
Out[35]:
<xarray.DataArray (x: 4, y: 4)>
array([[ 0., 1., 2., 3.],
[ 4., 5., 6., nan],
[ 8., 9., nan, nan],
[ 12., nan, nan, nan]])
Coordinates:
* x (x) int64 0 1 2 3
* y (y) int64 0 1 2 3
This is particularly useful for ragged indexing of multi-dimensional data,
e.g., to apply a 2D mask to an image. Note that where
follows all the
usual xarray broadcasting and alignment rules for binary operations (e.g.,
+
) between the object being indexed and the condition, as described in
Computation:
In [36]: arr2.where(arr2.y < 2)
Out[36]:
<xarray.DataArray (x: 4, y: 4)>
array([[ 0., 1., nan, nan],
[ 4., 5., nan, nan],
[ 8., 9., nan, nan],
[ 12., 13., nan, nan]])
Coordinates:
* x (x) int64 0 1 2 3
* y (y) int64 0 1 2 3
By default where
maintains the original size of the data. For cases
where the selected data size is much smaller than the original data,
use of the option drop=True
clips coordinate
elements that are fully masked:
In [37]: arr2.where(arr2.y < 2, drop=True)
Out[37]:
<xarray.DataArray (x: 4, y: 2)>
array([[ 0., 1.],
[ 4., 5.],
[ 8., 9.],
[ 12., 13.]])
Coordinates:
* x (x) int64 0 1 2 3
* y (y) int64 0 1
Multi-level indexing¶
Just like pandas, advanced indexing on multi-level indexes is possible with
loc
and sel
. You can slice a multi-index by providing multiple indexers,
i.e., a tuple of slices, labels, list of labels, or any selector allowed by
pandas:
In [38]: midx = pd.MultiIndex.from_product([list('abc'), [0, 1]],
....: names=('one', 'two'))
....:
In [39]: mda = xr.DataArray(np.random.rand(6, 3),
....: [('x', midx), ('y', range(3))])
....:
In [40]: mda
Out[40]:
<xarray.DataArray (x: 6, y: 3)>
array([[ 0.129, 0.86 , 0.82 ],
[ 0.352, 0.229, 0.777],
[ 0.595, 0.138, 0.853],
[ 0.236, 0.146, 0.59 ],
[ 0.574, 0.061, 0.59 ],
[ 0.245, 0.34 , 0.985]])
Coordinates:
* x (x) object ('a', 0) ('a', 1) ('b', 0) ('b', 1) ('c', 0) ('c', 1)
* y (y) int64 0 1 2
In [41]: mda.sel(x=(list('ab'), [0]))
Out[41]:
<xarray.DataArray (x: 2, y: 3)>
array([[ 0.129, 0.86 , 0.82 ],
[ 0.595, 0.138, 0.853]])
Coordinates:
* x (x) object ('a', 0) ('b', 0)
* y (y) int64 0 1 2
You can also select multiple elements by providing a list of labels or tuples or a slice of tuples:
In [42]: mda.sel(x=[('a', 0), ('b', 1)])
Out[42]:
<xarray.DataArray (x: 2, y: 3)>
array([[ 0.129, 0.86 , 0.82 ],
[ 0.236, 0.146, 0.59 ]])
Coordinates:
* x (x) object ('a', 0) ('b', 1)
* y (y) int64 0 1 2
Additionally, xarray supports dictionaries:
In [43]: mda.sel(x={'one': 'a', 'two': 0})
Out[43]:
<xarray.DataArray (y: 3)>
array([ 0.129, 0.86 , 0.82 ])
Coordinates:
x object ('a', 0)
* y (y) int64 0 1 2
In [44]: mda.loc[{'one': 'a'}, ...]
Out[44]:
<xarray.DataArray (two: 2, y: 3)>
array([[ 0.129, 0.86 , 0.82 ],
[ 0.352, 0.229, 0.777]])
Coordinates:
* two (two) int64 0 1
* y (y) int64 0 1 2
Like pandas, xarray handles partial selection on multi-index (level drop). As shown in the last example above, it also renames the dimension / coordinate when the multi-index is reduced to a single index.
Unlike pandas, xarray does not guess whether you provide index levels or
dimensions when using loc
in some ambiguous cases. For example, for
mda.loc[{'one': 'a', 'two': 0}]
and mda.loc['a', 0]
xarray
always interprets (‘one’, ‘two’) and (‘a’, 0) as the names and
labels of the 1st and 2nd dimension, respectively. You must specify all
dimensions or use the ellipsis in the loc
specifier, e.g. in the example
above, mda.loc[{'one': 'a', 'two': 0}, :]
or mda.loc[('a', 0), ...]
.
Multi-dimensional indexing¶
xarray does not yet support efficient routines for generalized multi-dimensional indexing or regridding. However, we are definitely interested in adding support for this in the future (see GH475 for the ongoing discussion).
Copies vs. views¶
Whether array indexing returns a view or a copy of the underlying data depends on the nature of the labels. For positional (integer) indexing, xarray follows the same rules as NumPy:
- Positional indexing with only integers and slices returns a view.
- Positional indexing with arrays or lists returns a copy.
The rules for label based indexing are more complex:
- Label-based indexing with only slices returns a view.
- Label-based indexing with arrays returns a copy.
- Label-based indexing with scalars returns a view or a copy, depending upon if the corresponding positional indexer can be represented as an integer or a slice object. The exact rules are determined by pandas.
Whether data is a copy or a view is more predictable in xarray than in pandas, so unlike pandas, xarray does not produce SettingWithCopy warnings. However, you should still avoid assignment with chained indexing.
Orthogonal (outer) vs. vectorized indexing¶
Indexing with xarray objects has one important difference from indexing numpy arrays: you can only use one-dimensional arrays to index xarray objects, and each indexer is applied “orthogonally” along independent axes, instead of using numpy’s broadcasting rules to vectorize indexers. This means you can do indexing like this, which would require slightly more awkward syntax with numpy arrays:
In [45]: arr[arr['time.day'] > 1, arr['space'] != 'IL']
Out[45]:
<xarray.DataArray (time: 3, space: 2)>
array([[ 0.897, 0.336],
[ 0.451, 0.123],
[ 0.543, 0.448]])
Coordinates:
* time (time) datetime64[ns] 2000-01-02 2000-01-03 2000-01-04
* space (space) |S2 'IA' 'IN'
This is a much simpler model than numpy’s advanced indexing. If you would like to do advanced-style array indexing in xarray, you have several options:
- Pointwise indexing
- Masking with where
- Index the underlying NumPy array directly using
.values
, e.g.,
In [46]: arr.values[arr.values > 0.5]
Out[46]: array([ 0.897, 0.84 , 0.543])
Align and reindex¶
xarray’s reindex
, reindex_like
and align
impose a DataArray
or
Dataset
onto a new set of coordinates corresponding to dimensions. The
original values are subset to the index labels still found in the new labels,
and values corresponding to new labels not found in the original object are
in-filled with NaN.
xarray operations that combine multiple objects generally automatically align their arguments to share the same indexes. However, manual alignment can be useful for greater control and for increased performance.
To reindex a particular dimension, use reindex()
:
In [47]: arr.reindex(space=['IA', 'CA'])
Out[47]:
<xarray.DataArray (time: 4, space: 2)>
array([[ 0.127, nan],
[ 0.897, nan],
[ 0.451, nan],
[ 0.543, nan]])
Coordinates:
* time (time) datetime64[ns] 2000-01-01 2000-01-02 2000-01-03 2000-01-04
* space (space) |S2 'IA' 'CA'
The reindex_like()
method is a useful shortcut.
To demonstrate, we will make a subset DataArray with new values:
In [48]: foo = arr.rename('foo')
In [49]: baz = (10 * arr[:2, :2]).rename('baz')
In [50]: baz
Out[50]:
<xarray.DataArray 'baz' (time: 2, space: 2)>
array([[ 1.27 , -100. ],
[ 8.972, 3.767]])
Coordinates:
* time (time) datetime64[ns] 2000-01-01 2000-01-02
* space (space) |S2 'IA' 'IL'
Reindexing foo
with baz
selects out the first two values along each
dimension:
In [51]: foo.reindex_like(baz)
Out[51]:
<xarray.DataArray 'foo' (time: 2, space: 2)>
array([[ 0.127, -10. ],
[ 0.897, 0.377]])
Coordinates:
* time (time) datetime64[ns] 2000-01-01 2000-01-02
* space (space) object 'IA' 'IL'
The opposite operation asks us to reindex to a larger shape, so we fill in the missing values with NaN:
In [52]: baz.reindex_like(foo)
Out[52]:
<xarray.DataArray 'baz' (time: 4, space: 3)>
array([[ 1.27 , -100. , nan],
[ 8.972, 3.767, nan],
[ nan, nan, nan],
[ nan, nan, nan]])
Coordinates:
* time (time) datetime64[ns] 2000-01-01 2000-01-02 2000-01-03 2000-01-04
* space (space) object 'IA' 'IL' 'IN'
The align()
function lets us perform more flexible database-like
'inner'
, 'outer'
, 'left'
and 'right'
joins:
In [53]: xr.align(foo, baz, join='inner')
Out[53]:
(<xarray.DataArray 'foo' (time: 2, space: 2)>
array([[ 0.127, -10. ],
[ 0.897, 0.377]])
Coordinates:
* time (time) datetime64[ns] 2000-01-01 2000-01-02
* space (space) object 'IA' 'IL',
<xarray.DataArray 'baz' (time: 2, space: 2)>
array([[ 1.27 , -100. ],
[ 8.972, 3.767]])
Coordinates:
* time (time) datetime64[ns] 2000-01-01 2000-01-02
* space (space) object 'IA' 'IL')
In [54]: xr.align(foo, baz, join='outer')
Out[54]:
(<xarray.DataArray 'foo' (time: 4, space: 3)>
array([[ 0.127, -10. , -10. ],
[ 0.897, 0.377, 0.336],
[ 0.451, 0.84 , 0.123],
[ 0.543, 0.373, 0.448]])
Coordinates:
* time (time) datetime64[ns] 2000-01-01 2000-01-02 2000-01-03 2000-01-04
* space (space) object 'IA' 'IL' 'IN',
<xarray.DataArray 'baz' (time: 4, space: 3)>
array([[ 1.27 , -100. , nan],
[ 8.972, 3.767, nan],
[ nan, nan, nan],
[ nan, nan, nan]])
Coordinates:
* time (time) datetime64[ns] 2000-01-01 2000-01-02 2000-01-03 2000-01-04
* space (space) object 'IA' 'IL' 'IN')
Both reindex_like
and align
work interchangeably between
DataArray
and Dataset
objects, and with any number of matching dimension names:
In [55]: ds
Out[55]:
<xarray.Dataset>
Dimensions: (space: 3, time: 4)
Coordinates:
* time (time) datetime64[ns] 2000-01-01 2000-01-02 2000-01-03 2000-01-04
* space (space) |S2 'IA' 'IL' 'IN'
Data variables:
foo (time, space) float64 0.127 -10.0 -10.0 0.8972 0.3767 0.3362 ...
In [56]: ds.reindex_like(baz)
Out[56]:
<xarray.Dataset>
Dimensions: (space: 2, time: 2)
Coordinates:
* time (time) datetime64[ns] 2000-01-01 2000-01-02
* space (space) object 'IA' 'IL'
Data variables:
foo (time, space) float64 0.127 -10.0 0.8972 0.3767
In [57]: other = xr.DataArray(['a', 'b', 'c'], dims='other')
# this is a no-op, because there are no shared dimension names
In [58]: ds.reindex_like(other)
Out[58]:
<xarray.Dataset>
Dimensions: (space: 3, time: 4)
Coordinates:
* time (time) datetime64[ns] 2000-01-01 2000-01-02 2000-01-03 2000-01-04
* space (space) |S2 'IA' 'IL' 'IN'
Data variables:
foo (time, space) float64 0.127 -10.0 -10.0 0.8972 0.3767 0.3362 ...