# Indexing and selecting data

Xarray offers extremely flexible indexing routines that combine the best features of NumPy and pandas for data selection.

The most basic way to access elements of a `DataArray` object is to use Python’s `[]` syntax, such as `array[i, j]`, where `i` and `j` are both integers. As xarray objects can store coordinates corresponding to each dimension of an array, label-based indexing similar to `pandas.DataFrame.loc` is also possible. In label-based indexing, the element position `i` is automatically looked-up from the coordinate values.

Dimensions of xarray objects have names, so you can also lookup the dimensions by name, instead of remembering their positional order.

## Quick overview

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 | `da[:, 0]` | not available
Positional | By label | `da.loc[:, 'IA']` | not available
By name | By integer | `da.isel(space=0)` or `da[dict(space=0)]` | `ds.isel(space=0)` or `ds[dict(space=0)]`
By name | By label | `da.sel(space='IA')` or `da.loc[dict(space='IA')]` | `ds.sel(space='IA')` or `ds.loc[dict(space='IA')]`

More advanced indexing is also possible for all the methods by supplying `DataArray` objects as indexer. See Vectorized Indexing for the details.

## 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]: da = xr.DataArray(
       ...:     np.random.rand(4, 3),
       ...:     [
       ...:         ("time", pd.date_range("2000-01-01", periods=4)),
       ...:         ("space", ["IA", "IL", "IN"]),
       ...:     ],
       ...: )
       ...:

    In [2]: da[:2]
    Out[2]:
    <xarray.DataArray (time: 2, space: 3)> Size: 48B
    array([[0.127, 0.967, 0.26 ],
           [0.897, 0.377, 0.336]])
    Coordinates:
      * time     (time) datetime64[ns] 16B 2000-01-01 2000-01-02
      * space    (space) <U2 24B 'IA' 'IL' 'IN'

    In [3]: da[0, 0]
    Out[3]:
    <xarray.DataArray ()> Size: 8B
    array(0.127)
    Coordinates:
        time     datetime64[ns] 8B 2000-01-01
        space    <U2 8B 'IA'

    In [4]: da[:, [2, 1]]
    Out[4]:
    <xarray.DataArray (time: 4, space: 2)> Size: 64B
    array([[0.26 , 0.967],
           [0.336, 0.377],
           [0.123, 0.84 ],
           [0.448, 0.373]])
    Coordinates:
      * time     (time) datetime64[ns] 32B 2000-01-01 2000-01-02 ... 2000-01-04
      * space    (space) <U2 16B 'IN' 'IL'

Attributes are persisted in all indexing operations.

Warning

Positional indexing deviates from the NumPy when indexing with multiple arrays like `da[[0, 1], [0, 1]]`, as described in Vectorized Indexing.

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]: da.loc["2000-01-01":"2000-01-02", "IA"]
    Out[5]:
    <xarray.DataArray (time: 2)> Size: 16B
    array([0.127, 0.897])
    Coordinates:
      * time     (time) datetime64[ns] 16B 2000-01-01 2000-01-02
        space    <U2 8B 'IA'

In this example, the selected is a subpart of the array in the range ‘2000-01-01’:’2000-01-02’ along the first coordinate `time` and with ‘IA’ value from the second coordinate `space`.

You can perform any of the label indexing operations supported by pandas, including indexing with individual, slices and lists/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]: da.loc["2000-01-01", ["IL", "IN"]] = -10

    In [7]: da
    Out[7]:
    <xarray.DataArray (time: 4, space: 3)> Size: 96B
    array([[  0.127, -10.   , -10.   ],
           [  0.897,   0.377,   0.336],
           [  0.451,   0.84 ,   0.123],
           [  0.543,   0.373,   0.448]], shape=(4, 3))
    Coordinates:
      * time     (time) datetime64[ns] 32B 2000-01-01 2000-01-02 ... 2000-01-04
      * space    (space) <U2 24B 'IA' 'IL' 'IN'

## Indexing with dimension names

With the dimension names, we do not have to rely on dimension order and can use them explicitly to slice data. There are two ways to do this:

1. Use the `sel()` and `isel()` convenience methods:

   >     # index by integer array indices
   >     In [8]: da.isel(space=0, time=slice(None, 2))
   >     Out[8]:
   >     <xarray.DataArray (time: 2)> Size: 16B
   >     array([0.127, 0.897])
   >     Coordinates:
   >       * time     (time) datetime64[ns] 16B 2000-01-01 2000-01-02
   >         space    <U2 8B 'IA'

   >     # index by dimension coordinate labels
   >     In [9]: da.sel(time=slice("2000-01-01", "2000-01-02"))
   >     Out[9]:
   >     <xarray.DataArray (time: 2, space: 3)> Size: 48B
   >     array([[  0.127, -10.   , -10.   ],
   >            [  0.897,   0.377,   0.336]])
   >     Coordinates:
   >       * time     (time) datetime64[ns] 16B 2000-01-01 2000-01-02
   >       * space    (space) <U2 24B 'IA' 'IL' 'IN'

2. Use a dictionary as the argument for array positional or label based array indexing:

   >     # index by integer array indices
   >     In [10]: da[dict(space=0, time=slice(None, 2))]
   >     Out[10]:
   >     <xarray.DataArray (time: 2)> Size: 16B
   >     array([0.127, 0.897])
   >     Coordinates:
   >       * time     (time) datetime64[ns] 16B 2000-01-01 2000-01-02
   >         space    <U2 8B 'IA'

   >     # index by dimension coordinate labels
   >     In [11]: da.loc[dict(time=slice("2000-01-01", "2000-01-02"))]
   >     Out[11]:
   >     <xarray.DataArray (time: 2, space: 3)> Size: 48B
   >     array([[  0.127, -10.   , -10.   ],
   >            [  0.897,   0.377,   0.336]])
   >     Coordinates:
   >       * time     (time) datetime64[ns] 16B 2000-01-01 2000-01-02
   >       * space    (space) <U2 24B '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 not yet support indexing with keyword arguments like `da[space=0]`

## 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 [12]: da = xr.DataArray([1, 2, 3], [("x", [0, 1, 2])])

    In [13]: da.sel(x=[1.1, 1.9], method="nearest")
    Out[13]:
    <xarray.DataArray (x: 2)> Size: 16B
    array([2, 3])
    Coordinates:
      * x        (x) int64 16B 1 2

    In [14]: da.sel(x=0.1, method="backfill")
    Out[14]:
    <xarray.DataArray ()> Size: 8B
    array(2)
    Coordinates:
        x        int64 8B 1

    In [15]: da.reindex(x=[0.5, 1, 1.5, 2, 2.5], method="pad")
    Out[15]:
    <xarray.DataArray (x: 5)> Size: 40B
    array([1, 2, 2, 3, 3])
    Coordinates:
      * x        (x) float64 40B 0.5 1.0 1.5 2.0 2.5

Tolerance limits the maximum distance for valid matches with an inexact lookup:

    In [16]: da.reindex(x=[1.1, 1.5], method="nearest", tolerance=0.2)
    Out[16]:
    <xarray.DataArray (x: 2)> Size: 16B
    array([ 2., nan])
    Coordinates:
      * x        (x) float64 16B 1.1 1.5

The method parameter is not yet supported if any of the arguments to `.sel()` is a `slice` object:

    In [17]: da.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 [18]: da.sel(x=slice(0.9, 3.1))
    Out[18]:
    <xarray.DataArray (x: 2)> Size: 16B
    array([2, 3])
    Coordinates:
      * x        (x) int64 16B 1 2

Indexing axes with monotonic decreasing labels also works, as long as the `slice` or `.loc` arguments are also decreasing:

    In [19]: reversed_da = da[::-1]

    In [20]: reversed_da.loc[3.1:0.9]
    Out[20]:
    <xarray.DataArray (x: 2)> Size: 16B
    array([3, 2])
    Coordinates:
      * x        (x) int64 16B 2 1

Note

If you want to interpolate along coordinates rather than looking up the nearest neighbors, use `interp()` and `interp_like()`. See interpolation for the details.

## Dataset indexing

We can also use these methods to index all variables in a dataset simultaneously, returning a new dataset:

    In [21]: da = xr.DataArray(
       ....:     np.random.rand(4, 3),
       ....:     [
       ....:         ("time", pd.date_range("2000-01-01", periods=4)),
       ....:         ("space", ["IA", "IL", "IN"]),
       ....:     ],
       ....: )
       ....:

    In [22]: ds = da.to_dataset(name="foo")

    In [23]: ds.isel(space=[0], time=[0])
    Out[23]:
    <xarray.Dataset> Size: 24B
    Dimensions:  (time: 1, space: 1)
    Coordinates:
      * time     (time) datetime64[ns] 8B 2000-01-01
      * space    (space) <U2 8B 'IA'
    Data variables:
        foo      (time, space) float64 8B 0.1294

    In [24]: ds.sel(time="2000-01-01")
    Out[24]:
    <xarray.Dataset> Size: 56B
    Dimensions:  (space: 3)
    Coordinates:
        time     datetime64[ns] 8B 2000-01-01
      * space    (space) <U2 24B 'IA' 'IL' 'IN'
    Data variables:
        foo      (space) float64 24B 0.1294 0.8599 0.8204

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 dimension names:

    In [25]: ds[dict(space=[0], time=[0])]
    Out[25]:
    <xarray.Dataset> Size: 24B
    Dimensions:  (time: 1, space: 1)
    Coordinates:
      * time     (time) datetime64[ns] 8B 2000-01-01
      * space    (space) <U2 8B 'IA'
    Data variables:
        foo      (time, space) float64 8B 0.1294

    In [26]: ds.loc[dict(time="2000-01-01")]
    Out[26]:
    <xarray.Dataset> Size: 56B
    Dimensions:  (space: 3)
    Coordinates:
        time     datetime64[ns] 8B 2000-01-01
      * space    (space) <U2 24B 'IA' 'IL' 'IN'
    Data variables:
        foo      (space) float64 24B 0.1294 0.8599 0.8204

## Dropping labels and dimensions

The `drop_sel()` method returns a new object with the listed index labels along a dimension dropped:

    In [27]: ds.drop_sel(space=["IN", "IL"])
    Out[27]:
    <xarray.Dataset> Size: 72B
    Dimensions:  (time: 4, space: 1)
    Coordinates:
      * time     (time) datetime64[ns] 32B 2000-01-01 2000-01-02 ... 2000-01-04
      * space    (space) <U2 8B 'IA'
    Data variables:
        foo      (time, space) float64 32B 0.1294 0.3521 0.5948 0.2355

`drop_sel` is both a `Dataset` and `DataArray` method.

Use `drop_dims()` to drop a full dimension from a Dataset. Any variables with these dimensions are also dropped:

    In [28]: ds.drop_dims("time")
    Out[28]:
    <xarray.Dataset> Size: 24B
    Dimensions:  (space: 3)
    Coordinates:
      * space    (space) <U2 24B 'IA' 'IL' 'IN'
    Data variables:
        *empty*

## 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 [29]: da = xr.DataArray(np.arange(16).reshape(4, 4), dims=["x", "y"])

    In [30]: da.where(da.x + da.y < 4)
    Out[30]:
    <xarray.DataArray (x: 4, y: 4)> Size: 128B
    array([[ 0.,  1.,  2.,  3.],
           [ 4.,  5.,  6., nan],
           [ 8.,  9., nan, nan],
           [12., nan, nan, nan]], shape=(4, 4))
    Dimensions without coordinates: x, y

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 [31]: da.where(da.y < 2)
    Out[31]:
    <xarray.DataArray (x: 4, y: 4)> Size: 128B
    array([[ 0.,  1., nan, nan],
           [ 4.,  5., nan, nan],
           [ 8.,  9., nan, nan],
           [12., 13., nan, nan]], shape=(4, 4))
    Dimensions without coordinates: x, y

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 [32]: da.where(da.y < 2, drop=True)
    Out[32]:
    <xarray.DataArray (x: 4, y: 2)> Size: 64B
    array([[ 0.,  1.],
           [ 4.,  5.],
           [ 8.,  9.],
           [12., 13.]])
    Dimensions without coordinates: x, y

## Selecting values with `isin`

To check whether elements of an xarray object contain a single object, you can compare with the equality operator `==` (e.g., `arr == 3`). To check multiple values, use `isin()`:

    In [33]: da = xr.DataArray([1, 2, 3, 4, 5], dims=["x"])

    In [34]: da.isin([2, 4])
    Out[34]:
    <xarray.DataArray (x: 5)> Size: 5B
    array([False,  True, False,  True, False])
    Dimensions without coordinates: x

`isin()` works particularly well with `where()` to support indexing by arrays that are not already labels of an array:

    In [35]: lookup = xr.DataArray([-1, -2, -3, -4, -5], dims=["x"])

    In [36]: da.where(lookup.isin([-2, -4]), drop=True)
    Out[36]:
    <xarray.DataArray (x: 2)> Size: 16B
    array([2., 4.])
    Dimensions without coordinates: x

However, some caution is in order: when done repeatedly, this type of indexing is significantly slower than using `sel()`.

## Vectorized Indexing

Like numpy and pandas, xarray supports indexing many array elements at once in a vectorized manner.

If you only provide integers, slices, or unlabeled arrays (array without dimension names, such as `np.ndarray`, `list`, but not `DataArray()` or `Variable()`) indexing can be understood as orthogonally. Each indexer component selects independently along the corresponding dimension, similar to how vector indexing works in Fortran or MATLAB, or after using the `numpy.ix_()` helper:

    In [37]: da = xr.DataArray(
       ....:     np.arange(12).reshape((3, 4)),
       ....:     dims=["x", "y"],
       ....:     coords={"x": [0, 1, 2], "y": ["a", "b", "c", "d"]},
       ....: )
       ....:

    In [38]: da
    Out[38]:
    <xarray.DataArray (x: 3, y: 4)> Size: 96B
    array([[ 0,  1,  2,  3],
           [ 4,  5,  6,  7],
           [ 8,  9, 10, 11]], shape=(3, 4))
    Coordinates:
      * x        (x) int64 24B 0 1 2
      * y        (y) <U1 16B 'a' 'b' 'c' 'd'

    In [39]: da[[0, 2, 2], [1, 3]]
    Out[39]:
    <xarray.DataArray (x: 3, y: 2)> Size: 48B
    array([[ 1,  3],
           [ 9, 11],
           [ 9, 11]])
    Coordinates:
      * x        (x) int64 24B 0 2 2
      * y        (y) <U1 8B 'b' 'd'

For more flexibility, you can supply `DataArray()` objects as indexers. Dimensions on resultant arrays are given by the ordered union of the indexers’ dimensions:

    In [40]: ind_x = xr.DataArray([0, 1], dims=["x"])

    In [41]: ind_y = xr.DataArray([0, 1], dims=["y"])

    In [42]: da[ind_x, ind_y]  # orthogonal indexing
    Out[42]:
    <xarray.DataArray (x: 2, y: 2)> Size: 32B
    array([[0, 1],
           [4, 5]])
    Coordinates:
      * x        (x) int64 16B 0 1
      * y        (y) <U1 8B 'a' 'b'

Slices or sequences/arrays without named-dimensions are treated as if they have the same dimension which is indexed along:

    # Because [0, 1] is used to index along dimension 'x',
    # it is assumed to have dimension 'x'
    In [43]: da[[0, 1], ind_x]
    Out[43]:
    <xarray.DataArray (x: 2)> Size: 16B
    array([0, 5])
    Coordinates:
      * x        (x) int64 16B 0 1
        y        (x) <U1 8B 'a' 'b'

Furthermore, you can use multi-dimensional `DataArray()` as indexers, where the resultant array dimension is also determined by indexers’ dimension:

    In [44]: ind = xr.DataArray([[0, 1], [0, 1]], dims=["a", "b"])

    In [45]: da[ind]
    Out[45]:
    <xarray.DataArray (a: 2, b: 2, y: 4)> Size: 128B
    array([[[0, 1, 2, 3],
            [4, 5, 6, 7]],

           [[0, 1, 2, 3],
            [4, 5, 6, 7]]], shape=(2, 2, 4))
    Coordinates:
        x        (a, b) int64 32B 0 1 0 1
      * y        (y) <U1 16B 'a' 'b' 'c' 'd'
    Dimensions without coordinates: a, b

Similar to how NumPy’s advanced indexing works, vectorized indexing for xarray is based on our broadcasting rules. See Indexing rules for the complete specification.

Vectorized indexing also works with `isel`, `loc`, and `sel`:

    In [46]: ind = xr.DataArray([[0, 1], [0, 1]], dims=["a", "b"])

    In [47]: da.isel(y=ind)  # same as da[:, ind]
    Out[47]:
    <xarray.DataArray (x: 3, a: 2, b: 2)> Size: 96B
    array([[[0, 1],
            [0, 1]],

           [[4, 5],
            [4, 5]],

           [[8, 9],
            [8, 9]]], shape=(3, 2, 2))
    Coordinates:
      * x        (x) int64 24B 0 1 2
        y        (a, b) <U1 16B 'a' 'b' 'a' 'b'
    Dimensions without coordinates: a, b

    In [48]: ind = xr.DataArray([["a", "b"], ["b", "a"]], dims=["a", "b"])

    In [49]: da.loc[:, ind]  # same as da.sel(y=ind)
    Out[49]:
    <xarray.DataArray (x: 3, a: 2, b: 2)> Size: 96B
    array([[[0, 1],
            [1, 0]],

           [[4, 5],
            [5, 4]],

           [[8, 9],
            [9, 8]]], shape=(3, 2, 2))
    Coordinates:
      * x        (x) int64 24B 0 1 2
        y        (a, b) <U1 16B 'a' 'b' 'b' 'a'
    Dimensions without coordinates: a, b

These methods may also be applied to `Dataset` objects

    In [50]: ds = da.to_dataset(name="bar")

    In [51]: ds.isel(x=xr.DataArray([0, 1, 2], dims=["points"]))
    Out[51]:
    <xarray.Dataset> Size: 136B
    Dimensions:  (points: 3, y: 4)
    Coordinates:
        x        (points) int64 24B 0 1 2
      * y        (y) <U1 16B 'a' 'b' 'c' 'd'
    Dimensions without coordinates: points
    Data variables:
        bar      (points, y) int64 96B 0 1 2 3 4 5 6 7 8 9 10 11

Vectorized indexing may be used to extract information from the nearest grid cells of interest, for example, the nearest climate model grid cells to a collection specified weather station latitudes and longitudes. To trigger vectorized indexing behavior you will need to provide the selection dimensions with a new shared output dimension name. In the example below, the selections of the closest latitude and longitude are renamed to an output dimension named “points”:

    In [52]: ds = xr.tutorial.open_dataset("air_temperature")
    ConnectionError: HTTPSConnectionPool(host='github.com', port=443): Max retries exceeded with url: /pydata/xarray-data/raw/master/air_temperature.nc (Caused by NameResolutionError("<urllib3.connection.HTTPSConnection object at 0x7ff7c0a78a50>: Failed to resolve 'github.com' ([Errno -2] Name or service not known)"))

    # Define target latitude and longitude (where weather stations might be)
    In [53]: target_lon = xr.DataArray([200, 201, 202, 205], dims="points")

    In [54]: target_lat = xr.DataArray([31, 41, 42, 42], dims="points")

    # Retrieve data at the grid cells nearest to the target latitudes and longitudes
    In [55]: da = ds["air"].sel(lon=target_lon, lat=target_lat, method="nearest")
    KeyError: "No variable named 'air'. Did you mean one of ('bar',)?"

    In [56]: da
    Out[56]:
    <xarray.DataArray (x: 3, y: 4)> Size: 96B
    array([[ 0,  1,  2,  3],
           [ 4,  5,  6,  7],
           [ 8,  9, 10, 11]], shape=(3, 4))
    Coordinates:
      * x        (x) int64 24B 0 1 2
      * y        (y) <U1 16B 'a' 'b' 'c' 'd'

Tip

If you are lazily loading your data from disk, not every form of vectorized indexing is supported (or if supported, may not be supported efficiently). You may find increased performance by loading your data into memory first, e.g., with `load()`.

Note

If an indexer is a `DataArray()`, its coordinates should not conflict with the selected subpart of the target array (except for the explicitly indexed dimensions with `.loc`/`.sel`). Otherwise, `IndexError` will be raised.

## Assigning values with indexing

To select and assign values to a portion of a `DataArray()` you can use indexing with `.loc` :

    In [57]: ds = xr.tutorial.open_dataset("air_temperature")
    ConnectionError: HTTPSConnectionPool(host='github.com', port=443): Max retries exceeded with url: /pydata/xarray-data/raw/master/air_temperature.nc (Caused by NameResolutionError("<urllib3.connection.HTTPSConnection object at 0x7ff7c0a7b250>: Failed to resolve 'github.com' ([Errno -2] Name or service not known)"))

    # add an empty 2D dataarray
    In [58]: ds["empty"] = xr.full_like(ds.air.mean("time"), fill_value=0)
    AttributeError: 'Dataset' object has no attribute 'air'

    # modify one grid point using loc()
    In [59]: ds["empty"].loc[dict(lon=260, lat=30)] = 100
    KeyError: "No variable named 'empty'. Variables on the dataset include ['x', 'y', 'bar']"

    # modify a 2D region using loc()
    In [60]: lc = ds.coords["lon"]
    KeyError: "No variable named 'lon'. Variables on the dataset include ['x', 'y', 'bar']"

    In [61]: la = ds.coords["lat"]
    KeyError: "No variable named 'lat'. Variables on the dataset include ['x', 'y', 'bar']"

    In [62]: ds["empty"].loc[
       ....:     dict(lon=lc[(lc > 220) & (lc < 260)], lat=la[(la > 20) & (la < 60)])
       ....: ] = 100
       ....:
    KeyError: "No variable named 'empty'. Variables on the dataset include ['x', 'y', 'bar']"

or `where()`:

    # modify one grid point using xr.where()
    In [63]: ds["empty"] = xr.where(
       ....:     (ds.coords["lat"] == 20) & (ds.coords["lon"] == 260), 100, ds["empty"]
       ....: )
       ....:
    KeyError: "No variable named 'lat'. Variables on the dataset include ['x', 'y', 'bar']"

    # or modify a 2D region using xr.where()
    In [64]: mask = (
       ....:     (ds.coords["lat"] > 20)
       ....:     & (ds.coords["lat"] < 60)
       ....:     & (ds.coords["lon"] > 220)
       ....:     & (ds.coords["lon"] < 260)
       ....: )
       ....:
    KeyError: "No variable named 'lat'. Variables on the dataset include ['x', 'y', 'bar']"

    In [65]: ds["empty"] = xr.where(mask, 100, ds["empty"])
    NameError: name 'mask' is not defined

Vectorized indexing can also be used to assign values to xarray object.

    In [66]: da = xr.DataArray(
       ....:     np.arange(12).reshape((3, 4)),
       ....:     dims=["x", "y"],
       ....:     coords={"x": [0, 1, 2], "y": ["a", "b", "c", "d"]},
       ....: )
       ....:

    In [67]: da
    Out[67]:
    <xarray.DataArray (x: 3, y: 4)> Size: 96B
    array([[ 0,  1,  2,  3],
           [ 4,  5,  6,  7],
           [ 8,  9, 10, 11]], shape=(3, 4))
    Coordinates:
      * x        (x) int64 24B 0 1 2
      * y        (y) <U1 16B 'a' 'b' 'c' 'd'

    In [68]: da[0] = -1  # assignment with broadcasting

    In [69]: da
    Out[69]:
    <xarray.DataArray (x: 3, y: 4)> Size: 96B
    array([[-1, -1, -1, -1],
           [ 4,  5,  6,  7],
           [ 8,  9, 10, 11]], shape=(3, 4))
    Coordinates:
      * x        (x) int64 24B 0 1 2
      * y        (y) <U1 16B 'a' 'b' 'c' 'd'

    In [70]: ind_x = xr.DataArray([0, 1], dims=["x"])

    In [71]: ind_y = xr.DataArray([0, 1], dims=["y"])

    In [72]: da[ind_x, ind_y] = -2  # assign -2 to (ix, iy) = (0, 0) and (1, 1)

    In [73]: da
    Out[73]:
    <xarray.DataArray (x: 3, y: 4)> Size: 96B
    array([[-2, -2, -1, -1],
           [-2, -2,  6,  7],
           [ 8,  9, 10, 11]], shape=(3, 4))
    Coordinates:
      * x        (x) int64 24B 0 1 2
      * y        (y) <U1 16B 'a' 'b' 'c' 'd'

    In [74]: da[ind_x, ind_y] += 100  # increment is also possible

    In [75]: da
    Out[75]:
    <xarray.DataArray (x: 3, y: 4)> Size: 96B
    array([[98, 98, -1, -1],
           [98, 98,  6,  7],
           [ 8,  9, 10, 11]], shape=(3, 4))
    Coordinates:
      * x        (x) int64 24B 0 1 2
      * y        (y) <U1 16B 'a' 'b' 'c' 'd'

Like `numpy.ndarray`, value assignment sometimes works differently from what one may expect.

    In [76]: da = xr.DataArray([0, 1, 2, 3], dims=["x"])

    In [77]: ind = xr.DataArray([0, 0, 0], dims=["x"])

    In [78]: da[ind] -= 1

    In [79]: da
    Out[79]:
    <xarray.DataArray (x: 4)> Size: 32B
    array([-1,  1,  2,  3])
    Dimensions without coordinates: x

Where the 0th element will be subtracted 1 only once. This is because `v[0] = v[0] - 1` is called three times, rather than `v[0] = v[0] - 1 - 1 - 1`. See Assigning values to indexed arrays for the details.

Note

Dask array does not support value assignment (see Parallel Computing with Dask for the details).

Note

Coordinates in both the left- and right-hand-side arrays should not conflict with each other. Otherwise, `IndexError` will be raised.

Warning

Do not try to assign values when using any of the indexing methods `isel` or `sel`:

    # DO NOT do this
    da.isel(space=0) = 0

Instead, values can be assigned using dictionary-based indexing:

    da[dict(space=0)] = 0

Assigning values with the chained indexing using `.sel` or `.isel` fails silently.

    In [80]: da = xr.DataArray([0, 1, 2, 3], dims=["x"])

    # DO NOT do this
    In [81]: da.isel(x=[0, 1, 2])[1] = -1

    In [82]: da
    Out[82]:
    <xarray.DataArray (x: 4)> Size: 32B
    array([0, 1, 2, 3])
    Dimensions without coordinates: x

You can also assign values to all variables of a `Dataset` at once:

    In [83]: ds_org = xr.tutorial.open_dataset("eraint_uvz").isel(
       ....:     latitude=slice(56, 59), longitude=slice(255, 258), level=0
       ....: )
       ....:
    ConnectionError: HTTPSConnectionPool(host='github.com', port=443): Max retries exceeded with url: /pydata/xarray-data/raw/master/eraint_uvz.nc (Caused by NameResolutionError("<urllib3.connection.HTTPSConnection object at 0x7ff7c0a7b250>: Failed to resolve 'github.com' ([Errno -2] Name or service not known)"))

    # set all values to 0
    In [84]: ds = xr.zeros_like(ds_org)
    NameError: name 'ds_org' is not defined

    In [85]: ds
    Out[85]:
    <xarray.Dataset> Size: 136B
    Dimensions:  (x: 3, y: 4)
    Coordinates:
      * x        (x) int64 24B 0 1 2
      * y        (y) <U1 16B 'a' 'b' 'c' 'd'
    Data variables:
        bar      (x, y) int64 96B 0 1 2 3 4 5 6 7 8 9 10 11

    # by integer
    In [86]: ds[dict(latitude=2, longitude=2)] = 1
    ValueError: Variable 'bar': indexer {'latitude': 2, 'longitude': 2} not available

    In [87]: ds["u"]
    KeyError: "No variable named 'u'. Variables on the dataset include ['x', 'y', 'bar']"

    In [88]: ds["v"]
    KeyError: "No variable named 'v'. Variables on the dataset include ['x', 'y', 'bar']"

    # by label
    In [89]: ds.loc[dict(latitude=47.25, longitude=[11.25, 12])] = 100
    KeyError: "'latitude' is not a valid dimension or coordinate for Dataset with dimensions FrozenMappingWarningOnValuesAccess({'x': 3, 'y': 4})"

    In [90]: ds["u"]
    KeyError: "No variable named 'u'. Variables on the dataset include ['x', 'y', 'bar']"

    # dataset as new values
    In [91]: new_dat = ds_org.loc[dict(latitude=48, longitude=[11.25, 12])]
    NameError: name 'ds_org' is not defined

    In [92]: new_dat
    NameError: name 'new_dat' is not defined

    In [93]: ds.loc[dict(latitude=47.25, longitude=[11.25, 12])] = new_dat
    NameError: name 'new_dat' is not defined

    In [94]: ds["u"]
    KeyError: "No variable named 'u'. Variables on the dataset include ['x', 'y', 'bar']"

The dimensions can differ between the variables in the dataset, but all variables need to have at least the dimensions specified in the indexer dictionary. The new values must be either a scalar, a `DataArray` or a `Dataset` itself that contains all variables that also appear in the dataset to be modified.

## More advanced indexing

The use of `DataArray()` objects as indexers enables very flexible indexing. The following is an example of the pointwise indexing:

    In [95]: da = xr.DataArray(np.arange(56).reshape((7, 8)), dims=["x", "y"])

    In [96]: da
    Out[96]:
    <xarray.DataArray (x: 7, y: 8)> Size: 448B
    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]], shape=(7, 8))
    Dimensions without coordinates: x, y

    In [97]: da.isel(x=xr.DataArray([0, 1, 6], dims="z"), y=xr.DataArray([0, 1, 0], dims="z"))
    Out[97]:
    <xarray.DataArray (z: 3)> Size: 24B
    array([ 0,  9, 48])
    Dimensions without coordinates: z

where three elements at `(ix, iy) = ((0, 0), (1, 1), (6, 0))` are selected and mapped along a new dimension `z`.

If you want to add a coordinate to the new dimension `z`, you can supply a `DataArray` with a coordinate,

    In [98]: da.isel(
       ....:     x=xr.DataArray([0, 1, 6], dims="z", coords={"z": ["a", "b", "c"]}),
       ....:     y=xr.DataArray([0, 1, 0], dims="z"),
       ....: )
       ....:
    Out[98]:
    <xarray.DataArray (z: 3)> Size: 24B
    array([ 0,  9, 48])
    Coordinates:
      * z        (z) <U1 12B 'a' 'b' 'c'

Analogously, label-based pointwise-indexing is also possible by the `.sel` method:

    In [99]: da = xr.DataArray(
       ....:     np.random.rand(4, 3),
       ....:     [
       ....:         ("time", pd.date_range("2000-01-01", periods=4)),
       ....:         ("space", ["IA", "IL", "IN"]),
       ....:     ],
       ....: )
       ....:

    In [100]: times = xr.DataArray(
       .....:     pd.to_datetime(["2000-01-03", "2000-01-02", "2000-01-01"]), dims="new_time"
       .....: )
       .....:

    In [101]: da.sel(space=xr.DataArray(["IA", "IL", "IN"], dims=["new_time"]), time=times)
    Out[101]:
    <xarray.DataArray (new_time: 3)> Size: 24B
    array([0.92, 0.34, 0.59])
    Coordinates:
        time      (new_time) datetime64[ns] 24B 2000-01-03 2000-01-02 2000-01-01
        space     (new_time) <U2 24B 'IA' 'IL' 'IN'
      * new_time  (new_time) datetime64[ns] 24B 2000-01-03 2000-01-02 2000-01-01

## 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 [102]: da.reindex(space=["IA", "CA"])
    Out[102]:
    <xarray.DataArray (time: 4, space: 2)> Size: 64B
    array([[0.574,   nan],
           [0.245,   nan],
           [0.92 ,   nan],
           [0.754,   nan]])
    Coordinates:
      * time     (time) datetime64[ns] 32B 2000-01-01 2000-01-02 ... 2000-01-04
      * space    (space) <U2 16B 'IA' 'CA'

The `reindex_like()` method is a useful shortcut. To demonstrate, we will make a subset DataArray with new values:

    In [103]: foo = da.rename("foo")

    In [104]: baz = (10 * da[:2, :2]).rename("baz")

    In [105]: baz
    Out[105]:
    <xarray.DataArray 'baz' (time: 2, space: 2)> Size: 32B
    array([[5.74 , 0.613],
           [2.453, 3.404]])
    Coordinates:
      * time     (time) datetime64[ns] 16B 2000-01-01 2000-01-02
      * space    (space) <U2 16B 'IA' 'IL'

Reindexing `foo` with `baz` selects out the first two values along each dimension:

    In [106]: foo.reindex_like(baz)
    Out[106]:
    <xarray.DataArray 'foo' (time: 2, space: 2)> Size: 32B
    array([[0.574, 0.061],
           [0.245, 0.34 ]])
    Coordinates:
      * time     (time) datetime64[ns] 16B 2000-01-01 2000-01-02
      * space    (space) <U2 16B 'IA' 'IL'

The opposite operation asks us to reindex to a larger shape, so we fill in the missing values with `NaN`:

    In [107]: baz.reindex_like(foo)
    Out[107]:
    <xarray.DataArray 'baz' (time: 4, space: 3)> Size: 96B
    array([[5.74 , 0.613,   nan],
           [2.453, 3.404,   nan],
           [  nan,   nan,   nan],
           [  nan,   nan,   nan]], shape=(4, 3))
    Coordinates:
      * time     (time) datetime64[ns] 32B 2000-01-01 2000-01-02 ... 2000-01-04
      * space    (space) <U2 24B 'IA' 'IL' 'IN'

The `align()` function lets us perform more flexible database-like `'inner'`, `'outer'`, `'left'` and `'right'` joins:

    In [108]: xr.align(foo, baz, join="inner")
    Out[108]:
    (<xarray.DataArray 'foo' (time: 2, space: 2)> Size: 32B
     array([[0.574, 0.061],
            [0.245, 0.34 ]])
     Coordinates:
       * time     (time) datetime64[ns] 16B 2000-01-01 2000-01-02
       * space    (space) <U2 16B 'IA' 'IL',
     <xarray.DataArray 'baz' (time: 2, space: 2)> Size: 32B
     array([[5.74 , 0.613],
            [2.453, 3.404]])
     Coordinates:
       * time     (time) datetime64[ns] 16B 2000-01-01 2000-01-02
       * space    (space) <U2 16B 'IA' 'IL')

    In [109]: xr.align(foo, baz, join="outer")
    Out[109]:
    (<xarray.DataArray 'foo' (time: 4, space: 3)> Size: 96B
     array([[0.574, 0.061, 0.59 ],
            [0.245, 0.34 , 0.985],
            [0.92 , 0.038, 0.862],
            [0.754, 0.405, 0.344]], shape=(4, 3))
     Coordinates:
       * time     (time) datetime64[ns] 32B 2000-01-01 2000-01-02 ... 2000-01-04
       * space    (space) <U2 24B 'IA' 'IL' 'IN',
     <xarray.DataArray 'baz' (time: 4, space: 3)> Size: 96B
     array([[5.74 , 0.613,   nan],
            [2.453, 3.404,   nan],
            [  nan,   nan,   nan],
            [  nan,   nan,   nan]], shape=(4, 3))
     Coordinates:
       * time     (time) datetime64[ns] 32B 2000-01-01 2000-01-02 ... 2000-01-04
       * space    (space) <U2 24B 'IA' 'IL' 'IN')

Both `reindex_like` and `align` work interchangeably between `DataArray` and `Dataset` objects, and with any number of matching dimension names:

    In [110]: ds
    Out[110]:
    <xarray.Dataset> Size: 136B
    Dimensions:  (x: 3, y: 4)
    Coordinates:
      * x        (x) int64 24B 0 1 2
      * y        (y) <U1 16B 'a' 'b' 'c' 'd'
    Data variables:
        bar      (x, y) int64 96B 0 1 2 3 4 5 6 7 8 9 10 11

    In [111]: ds.reindex_like(baz)
    Out[111]:
    <xarray.Dataset> Size: 136B
    Dimensions:  (x: 3, y: 4)
    Coordinates:
      * x        (x) int64 24B 0 1 2
      * y        (y) <U1 16B 'a' 'b' 'c' 'd'
    Data variables:
        bar      (x, y) int64 96B 0 1 2 3 4 5 6 7 8 9 10 11

    In [112]: other = xr.DataArray(["a", "b", "c"], dims="other")

    # this is a no-op, because there are no shared dimension names
    In [113]: ds.reindex_like(other)
    Out[113]:
    <xarray.Dataset> Size: 136B
    Dimensions:  (x: 3, y: 4)
    Coordinates:
      * x        (x) int64 24B 0 1 2
      * y        (y) <U1 16B 'a' 'b' 'c' 'd'
    Data variables:
        bar      (x, y) int64 96B 0 1 2 3 4 5 6 7 8 9 10 11

## Missing coordinate labels

Coordinate labels for each dimension are optional (as of xarray v0.9). Label based indexing with `.sel` and `.loc` uses standard positional, integer-based indexing as a fallback for dimensions without a coordinate label:

    In [114]: da = xr.DataArray([1, 2, 3], dims="x")

    In [115]: da.sel(x=[0, -1])
    Out[115]:
    <xarray.DataArray (x: 2)> Size: 16B
    array([1, 3])
    Dimensions without coordinates: x

Alignment between xarray objects where one or both do not have coordinate labels succeeds only if all dimensions of the same name have the same length. Otherwise, it raises an informative error:

    In [116]: xr.align(da, da[:2])
    ValueError: arguments without labels along dimension 'x' cannot be aligned because they have different dimension sizes: {2, 3}

## Underlying Indexes

Xarray uses the `pandas.Index` internally to perform indexing operations. If you need to access the underlying indexes, they are available through the `indexes` attribute.

    In [117]: da = xr.DataArray(
       .....:     np.random.rand(4, 3),
       .....:     [
       .....:         ("time", pd.date_range("2000-01-01", periods=4)),
       .....:         ("space", ["IA", "IL", "IN"]),
       .....:     ],
       .....: )
       .....:

    In [118]: da
    Out[118]:
    <xarray.DataArray (time: 4, space: 3)> Size: 96B
    array([[0.171, 0.395, 0.642],
           [0.275, 0.462, 0.871],
           [0.401, 0.611, 0.118],
           [0.702, 0.414, 0.342]], shape=(4, 3))
    Coordinates:
      * time     (time) datetime64[ns] 32B 2000-01-01 2000-01-02 ... 2000-01-04
      * space    (space) <U2 24B 'IA' 'IL' 'IN'

    In [119]: da.indexes
    Out[119]:
    Indexes:
        time     DatetimeIndex(['2000-01-01', '2000-01-02', '2000-01-03', '2000-01-04'], dtype='datetime64[ns]', name='time', freq='D')
        space    Index(['IA', 'IL', 'IN'], dtype='object', name='space')

    In [120]: da.indexes["time"]
    Out[120]: DatetimeIndex(['2000-01-01', '2000-01-02', '2000-01-03', '2000-01-04'], dtype='datetime64[ns]', name='time', freq='D')

Use `get_index()` to get an index for a dimension, falling back to a default `pandas.RangeIndex` if it has no coordinate labels:

    In [121]: da = xr.DataArray([1, 2, 3], dims="x")

    In [122]: da
    Out[122]:
    <xarray.DataArray (x: 3)> Size: 24B
    array([1, 2, 3])
    Dimensions without coordinates: x

    In [123]: da.get_index("x")
    Out[123]: RangeIndex(start=0, stop=3, step=1, name='x')

## 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.

Note that other operations (such as `values()`) may also return views rather than copies.

## 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 [124]: midx = pd.MultiIndex.from_product([list("abc"), [0, 1]], names=("one", "two"))

    In [125]: mda = xr.DataArray(np.random.rand(6, 3), [("x", midx), ("y", range(3))])

    In [126]: mda
    Out[126]:
    <xarray.DataArray (x: 6, y: 3)> Size: 144B
    array([[0.596, 0.2  , 0.1  ],
           [0.735, 0.017, 0.481],
           [0.096, 0.497, 0.839],
           [0.897, 0.733, 0.759],
           [0.561, 0.471, 0.139],
           [0.094, 0.942, 0.134]], shape=(6, 3))
    Coordinates:
      * x        (x) object 48B MultiIndex
      * one      (x) object 48B 'a' 'a' 'b' 'b' 'c' 'c'
      * two      (x) int64 48B 0 1 0 1 0 1
      * y        (y) int64 24B 0 1 2

    In [127]: mda.sel(x=(list("ab"), [0]))
    Out[127]:
    <xarray.DataArray (x: 2, y: 3)> Size: 48B
    array([[0.596, 0.2  , 0.1  ],
           [0.096, 0.497, 0.839]])
    Coordinates:
      * x        (x) object 16B MultiIndex
      * one      (x) object 16B 'a' 'b'
      * two      (x) int64 16B 0 0
      * y        (y) int64 24B 0 1 2

You can also select multiple elements by providing a list of labels or tuples or a slice of tuples:

    In [128]: mda.sel(x=[("a", 0), ("b", 1)])
    Out[128]:
    <xarray.DataArray (x: 2, y: 3)> Size: 48B
    array([[0.596, 0.2  , 0.1  ],
           [0.897, 0.733, 0.759]])
    Coordinates:
      * x        (x) object 16B MultiIndex
      * one      (x) object 16B 'a' 'b'
      * two      (x) int64 16B 0 1
      * y        (y) int64 24B 0 1 2

Additionally, xarray supports dictionaries:

    In [129]: mda.sel(x={"one": "a", "two": 0})
    Out[129]:
    <xarray.DataArray (y: 3)> Size: 24B
    array([0.596, 0.2  , 0.1  ])
    Coordinates:
        x        object 8B ('a', np.int64(0))
        one      <U1 4B 'a'
        two      int64 8B 0
      * y        (y) int64 24B 0 1 2

For convenience, `sel` also accepts multi-index levels directly as keyword arguments:

    In [130]: mda.sel(one="a", two=0)
    Out[130]:
    <xarray.DataArray (y: 3)> Size: 24B
    array([0.596, 0.2  , 0.1  ])
    Coordinates:
        x        object 8B ('a', np.int64(0))
        one      <U1 4B 'a'
        two      int64 8B 0
      * y        (y) int64 24B 0 1 2

Note that using `sel` it is not possible to mix a dimension indexer with level indexers for that dimension (e.g., `mda.sel(x={'one': 'a'}, two=0)` will raise a `ValueError`).

Like pandas, xarray handles partial selection on multi-index (level drop). As shown below, it also renames the dimension / coordinate when the multi-index is reduced to a single index.

    In [131]: mda.loc[{"one": "a"}, ...]
    Out[131]:
    <xarray.DataArray (two: 2, y: 3)> Size: 48B
    array([[0.596, 0.2  , 0.1  ],
           [0.735, 0.017, 0.481]])
    Coordinates:
      * two      (two) int64 16B 0 1
      * y        (y) int64 24B 0 1 2
        one      <U1 4B 'a'

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), ...]`.

## Indexing rules

Here we describe the full rules xarray uses for vectorized indexing. Note that this is for the purposes of explanation: for the sake of efficiency and to support various backends, the actual implementation is different.

0. (Only for label based indexing.) Look up positional indexes along each dimension from the corresponding `pandas.Index`.

1. A full slice object `:` is inserted for each dimension without an indexer.

2. `slice` objects are converted into arrays, given by `np.arange(*slice.indices(...))`.

3. Assume dimension names for array indexers without dimensions, such as `np.ndarray` and `list`, from the dimensions to be indexed along. For example, `v.isel(x=[0, 1])` is understood as `v.isel(x=xr.DataArray([0, 1], dims=['x']))`.

4. For each variable in a `Dataset` or `DataArray` (the array and its coordinates):

   1. Broadcast all relevant indexers based on their dimension names (see Broadcasting by dimension name for full details).

   2. Index the underling array by the broadcast indexers, using NumPy’s advanced indexing rules.

5. If any indexer DataArray has coordinates and no coordinate with the same name exists, attach them to the indexed object.

Note

Only 1-dimensional boolean arrays can be used as indexers.