# Reshaping and reorganizing data

Reshaping and reorganizing data refers to the process of changing the structure or organization of data by modifying dimensions, array shapes, order of values, or indexes. Xarray provides several methods to accomplish these tasks.

These methods are particularly useful for reshaping xarray objects for use in machine learning packages, such as scikit-learn, that usually require two-dimensional numpy arrays as inputs. Reshaping can also be required before passing data to external visualization tools, for example geospatial data might expect input organized into a particular format corresponding to stacks of satellite images.

## Importing the library

## Reordering dimensions

To reorder dimensions on a `DataArray` or across all variables on a `Dataset`, use `transpose()`. An ellipsis (…) can be used to represent all other dimensions:

    In [1]: ds = xr.Dataset({"foo": (("x", "y", "z"), [[[42]]]), "bar": (("y", "z"), [[24]])})

    In [2]: ds.transpose("y", "z", "x")
    Out[2]:
    <xarray.Dataset> Size: 16B
    Dimensions:  (x: 1, y: 1, z: 1)
    Dimensions without coordinates: x, y, z
    Data variables:
        foo      (y, z, x) int64 8B 42
        bar      (y, z) int64 8B 24

    In [3]: ds.transpose(..., "x")  # equivalent
    Out[3]:
    <xarray.Dataset> Size: 16B
    Dimensions:  (x: 1, y: 1, z: 1)
    Dimensions without coordinates: x, y, z
    Data variables:
        foo      (y, z, x) int64 8B 42
        bar      (y, z) int64 8B 24

    In [4]: ds.transpose()  # reverses all dimensions
    Out[4]:
    <xarray.Dataset> Size: 16B
    Dimensions:  (x: 1, y: 1, z: 1)
    Dimensions without coordinates: x, y, z
    Data variables:
        foo      (z, y, x) int64 8B 42
        bar      (z, y) int64 8B 24

## Expand and squeeze dimensions

To expand a `DataArray` or all variables on a `Dataset` along a new dimension, use `expand_dims()`

    In [5]: expanded = ds.expand_dims("w")

    In [6]: expanded
    Out[6]:
    <xarray.Dataset> Size: 16B
    Dimensions:  (w: 1, x: 1, y: 1, z: 1)
    Dimensions without coordinates: w, x, y, z
    Data variables:
        foo      (w, x, y, z) int64 8B 42
        bar      (w, y, z) int64 8B 24

This method attaches a new dimension with size 1 to all data variables.

To remove such a size-1 dimension from the `DataArray` or `Dataset`, use `squeeze()`

    In [7]: expanded.squeeze("w")
    Out[7]:
    <xarray.Dataset> Size: 16B
    Dimensions:  (x: 1, y: 1, z: 1)
    Dimensions without coordinates: x, y, z
    Data variables:
        foo      (x, y, z) int64 8B 42
        bar      (y, z) int64 8B 24

## Converting between datasets and arrays

To convert from a Dataset to a DataArray, use `to_dataarray()`:

    In [8]: arr = ds.to_dataarray()

    In [9]: arr
    Out[9]:
    <xarray.DataArray (variable: 2, x: 1, y: 1, z: 1)> Size: 16B
    array([[[[42]]],

           [[[24]]]])
    Coordinates:
      * variable  (variable) object 16B 'foo' 'bar'
    Dimensions without coordinates: x, y, z

This method broadcasts all data variables in the dataset against each other, then concatenates them along a new dimension into a new array while preserving coordinates.

To convert back from a DataArray to a Dataset, use `to_dataset()`:

    In [10]: arr.to_dataset(dim="variable")
    Out[10]:
    <xarray.Dataset> Size: 16B
    Dimensions:  (x: 1, y: 1, z: 1)
    Dimensions without coordinates: x, y, z
    Data variables:
        foo      (x, y, z) int64 8B 42
        bar      (x, y, z) int64 8B 24

The broadcasting behavior of `to_dataarray` means that the resulting array includes the union of data variable dimensions:

    In [11]: ds2 = xr.Dataset({"a": 0, "b": ("x", [3, 4, 5])})

    # the input dataset has 4 elements
    In [12]: ds2
    Out[12]:
    <xarray.Dataset> Size: 32B
    Dimensions:  (x: 3)
    Dimensions without coordinates: x
    Data variables:
        a        int64 8B 0
        b        (x) int64 24B 3 4 5

    # the resulting array has 6 elements
    In [13]: ds2.to_dataarray()
    Out[13]:
    <xarray.DataArray (variable: 2, x: 3)> Size: 48B
    array([[0, 0, 0],
           [3, 4, 5]])
    Coordinates:
      * variable  (variable) object 16B 'a' 'b'
    Dimensions without coordinates: x

Otherwise, the result could not be represented as an orthogonal array.

If you use `to_dataset` without supplying the `dim` argument, the DataArray will be converted into a Dataset of one variable:

    In [14]: arr.to_dataset(name="combined")
    Out[14]:
    <xarray.Dataset> Size: 32B
    Dimensions:   (variable: 2, x: 1, y: 1, z: 1)
    Coordinates:
      * variable  (variable) object 16B 'foo' 'bar'
    Dimensions without coordinates: x, y, z
    Data variables:
        combined  (variable, x, y, z) int64 16B 42 24

## Stack and unstack

As part of xarray’s nascent support for `pandas.MultiIndex`, we have implemented `stack()` and `unstack()` method, for combining or splitting dimensions:

    In [15]: array = xr.DataArray(
       ....:     np.random.randn(2, 3), coords=[("x", ["a", "b"]), ("y", [0, 1, 2])]
       ....: )
       ....:

    In [16]: stacked = array.stack(z=("x", "y"))

    In [17]: stacked
    Out[17]:
    <xarray.DataArray (z: 6)> Size: 48B
    array([ 0.469, -0.283, -1.509, -1.136,  1.212, -0.173])
    Coordinates:
      * z        (z) object 48B MultiIndex
      * x        (z) <U1 24B 'a' 'a' 'a' 'b' 'b' 'b'
      * y        (z) int64 48B 0 1 2 0 1 2

    In [18]: stacked.unstack("z")
    Out[18]:
    <xarray.DataArray (x: 2, y: 3)> Size: 48B
    array([[ 0.469, -0.283, -1.509],
           [-1.136,  1.212, -0.173]])
    Coordinates:
      * x        (x) <U1 8B 'a' 'b'
      * y        (y) int64 24B 0 1 2

As elsewhere in xarray, an ellipsis (…) can be used to represent all unlisted dimensions:

    In [19]: stacked = array.stack(z=[..., "x"])

    In [20]: stacked
    Out[20]:
    <xarray.DataArray (z: 6)> Size: 48B
    array([ 0.469, -1.136, -0.283,  1.212, -1.509, -0.173])
    Coordinates:
      * z        (z) object 48B MultiIndex
      * y        (z) int64 48B 0 0 1 1 2 2
      * x        (z) <U1 24B 'a' 'b' 'a' 'b' 'a' 'b'

These methods are modeled on the `pandas.DataFrame` methods of the same name, although in xarray they always create new dimensions rather than adding to the existing index or columns.

Like `DataFrame.unstack`, xarray’s `unstack` always succeeds, even if the multi-index being unstacked does not contain all possible levels. Missing levels are filled in with `NaN` in the resulting object:

    In [21]: stacked2 = stacked[::2]

    In [22]: stacked2
    Out[22]:
    <xarray.DataArray (z: 3)> Size: 24B
    array([ 0.469, -0.283, -1.509])
    Coordinates:
      * z        (z) object 24B MultiIndex
      * y        (z) int64 24B 0 1 2
      * x        (z) <U1 12B 'a' 'a' 'a'

    In [23]: stacked2.unstack("z")
    Out[23]:
    <xarray.DataArray (y: 3, x: 1)> Size: 24B
    array([[ 0.469],
           [-0.283],
           [-1.509]])
    Coordinates:
      * y        (y) int64 24B 0 1 2
      * x        (x) <U1 4B 'a'

However, xarray’s `stack` has an important difference from pandas: unlike pandas, it does not automatically drop missing values. Compare:

    In [24]: array = xr.DataArray([[np.nan, 1], [2, 3]], dims=["x", "y"])

    In [25]: array.stack(z=("x", "y"))
    Out[25]:
    <xarray.DataArray (z: 4)> Size: 32B
    array([nan,  1.,  2.,  3.])
    Coordinates:
      * z        (z) object 32B MultiIndex
      * x        (z) int64 32B 0 0 1 1
      * y        (z) int64 32B 0 1 0 1

    In [26]: array.to_pandas().stack()
    Out[26]:
    x  y
    0  1    1.0
    1  0    2.0
       1    3.0
    dtype: float64

We departed from pandas’s behavior here because predictable shapes for new array dimensions is necessary for Parallel Computing with Dask.

### Stacking different variables together

These stacking and unstacking operations are particularly useful for reshaping xarray objects for use in machine learning packages, such as scikit-learn, that usually require two-dimensional numpy arrays as inputs. For datasets with only one variable, we only need `stack` and `unstack`, but combining multiple variables in a `xarray.Dataset` is more complicated. If the variables in the dataset have matching numbers of dimensions, we can call `to_dataarray()` and then stack along the the new coordinate. But `to_dataarray()` will broadcast the dataarrays together, which will effectively tile the lower dimensional variable along the missing dimensions. The method `xarray.Dataset.to_stacked_array()` allows combining variables of differing dimensions without this wasteful copying while `xarray.DataArray.to_unstacked_dataset()` reverses this operation. Just as with `xarray.Dataset.stack()` the stacked coordinate is represented by a `pandas.MultiIndex` object. These methods are used like this:

    In [27]: data = xr.Dataset(
       ....:     data_vars={"a": (("x", "y"), [[0, 1, 2], [3, 4, 5]]), "b": ("x", [6, 7])},
       ....:     coords={"y": ["u", "v", "w"]},
       ....: )
       ....:

    In [28]: data
    Out[28]:
    <xarray.Dataset> Size: 76B
    Dimensions:  (x: 2, y: 3)
    Coordinates:
      * y        (y) <U1 12B 'u' 'v' 'w'
    Dimensions without coordinates: x
    Data variables:
        a        (x, y) int64 48B 0 1 2 3 4 5
        b        (x) int64 16B 6 7

    In [29]: stacked = data.to_stacked_array("z", sample_dims=["x"])

    In [30]: stacked
    Out[30]:
    <xarray.DataArray 'a' (x: 2, z: 4)> Size: 64B
    array([[0, 1, 2, 6],
           [3, 4, 5, 7]])
    Coordinates:
      * z         (z) object 32B MultiIndex
      * variable  (z) <U1 16B 'a' 'a' 'a' 'b'
      * y         (z) object 32B 'u' 'v' 'w' nan
    Dimensions without coordinates: x

    In [31]: unstacked = stacked.to_unstacked_dataset("z")

    In [32]: unstacked
    Out[32]:
    <xarray.Dataset> Size: 88B
    Dimensions:  (y: 3, x: 2)
    Coordinates:
      * y        (y) object 24B 'u' 'v' 'w'
    Dimensions without coordinates: x
    Data variables:
        a        (x, y) int64 48B 0 1 2 3 4 5
        b        (x) int64 16B 6 7

In this example, `stacked` is a two dimensional array that we can easily pass to a scikit-learn or another generic numerical method.

Note

Unlike with `stack`, in `to_stacked_array`, the user specifies the dimensions they do not want stacked. For a machine learning task, these unstacked dimensions can be interpreted as the dimensions over which samples are drawn, whereas the stacked coordinates are the features. Naturally, all variables should possess these sampling dimensions.

## Set and reset index

Complementary to stack / unstack, xarray’s `.set_index`, `.reset_index` and `.reorder_levels` allow easy manipulation of `DataArray` or `Dataset` multi-indexes without modifying the data and its dimensions.

You can create a multi-index from several 1-dimensional variables and/or coordinates using `set_index()`:

    In [33]: da = xr.DataArray(
       ....:     np.random.rand(4),
       ....:     coords={
       ....:         "band": ("x", ["a", "a", "b", "b"]),
       ....:         "wavenumber": ("x", np.linspace(200, 400, 4)),
       ....:     },
       ....:     dims="x",
       ....: )
       ....:

    In [34]: da
    Out[34]:
    <xarray.DataArray (x: 4)> Size: 32B
    array([0.123, 0.543, 0.373, 0.448])
    Coordinates:
        band        (x) <U1 16B 'a' 'a' 'b' 'b'
        wavenumber  (x) float64 32B 200.0 266.7 333.3 400.0
    Dimensions without coordinates: x

    In [35]: mda = da.set_index(x=["band", "wavenumber"])

    In [36]: mda
    Out[36]:
    <xarray.DataArray (x: 4)> Size: 32B
    array([0.123, 0.543, 0.373, 0.448])
    Coordinates:
      * x           (x) object 32B MultiIndex
      * band        (x) <U1 16B 'a' 'a' 'b' 'b'
      * wavenumber  (x) float64 32B 200.0 266.7 333.3 400.0

These coordinates can now be used for indexing, e.g.,

    In [37]: mda.sel(band="a")
    Out[37]:
    <xarray.DataArray (wavenumber: 2)> Size: 16B
    array([0.123, 0.543])
    Coordinates:
      * wavenumber  (wavenumber) float64 16B 200.0 266.7
        band        <U1 4B 'a'

Conversely, you can use `reset_index()` to extract multi-index levels as coordinates (this is mainly useful for serialization):

    In [38]: mda.reset_index("x")
    Out[38]:
    <xarray.DataArray (x: 4)> Size: 32B
    array([0.123, 0.543, 0.373, 0.448])
    Coordinates:
        band        (x) <U1 16B 'a' 'a' 'b' 'b'
        wavenumber  (x) float64 32B 200.0 266.7 333.3 400.0
    Dimensions without coordinates: x

`reorder_levels()` allows changing the order of multi-index levels:

    In [39]: mda.reorder_levels(x=["wavenumber", "band"])
    Out[39]:
    <xarray.DataArray (x: 4)> Size: 32B
    array([0.123, 0.543, 0.373, 0.448])
    Coordinates:
      * x           (x) object 32B MultiIndex
      * wavenumber  (x) float64 32B 200.0 266.7 333.3 400.0
      * band        (x) <U1 16B 'a' 'a' 'b' 'b'

As of xarray v0.9 coordinate labels for each dimension are optional. You can also use `.set_index` / `.reset_index` to add / remove labels for one or several dimensions:

    In [40]: array = xr.DataArray([1, 2, 3], dims="x")

    In [41]: array
    Out[41]:
    <xarray.DataArray (x: 3)> Size: 24B
    array([1, 2, 3])
    Dimensions without coordinates: x

    In [42]: array["c"] = ("x", ["a", "b", "c"])

    In [43]: array.set_index(x="c")
    Out[43]:
    <xarray.DataArray (x: 3)> Size: 24B
    array([1, 2, 3])
    Coordinates:
      * x        (x) <U1 12B 'a' 'b' 'c'

    In [44]: array = array.set_index(x="c")

    In [45]: array = array.reset_index("x", drop=True)

## Shift and roll

To adjust coordinate labels, you can use the `shift()` and `roll()` methods:

    In [46]: array = xr.DataArray([1, 2, 3, 4], dims="x")

    In [47]: array.shift(x=2)
    Out[47]:
    <xarray.DataArray (x: 4)> Size: 32B
    array([nan, nan,  1.,  2.])
    Dimensions without coordinates: x

    In [48]: array.roll(x=2, roll_coords=True)
    Out[48]:
    <xarray.DataArray (x: 4)> Size: 32B
    array([3, 4, 1, 2])
    Dimensions without coordinates: x

## Sort

One may sort a DataArray/Dataset via `sortby()` and `sortby()`. The input can be an individual or list of 1D `DataArray` objects:

    In [49]: ds = xr.Dataset(
       ....:     {
       ....:         "A": (("x", "y"), [[1, 2], [3, 4]]),
       ....:         "B": (("x", "y"), [[5, 6], [7, 8]]),
       ....:     },
       ....:     coords={"x": ["b", "a"], "y": [1, 0]},
       ....: )
       ....:

    In [50]: dax = xr.DataArray([100, 99], [("x", [0, 1])])

    In [51]: day = xr.DataArray([90, 80], [("y", [0, 1])])

    In [52]: ds.sortby([day, dax])
    Out[52]:
    <xarray.Dataset> Size: 88B
    Dimensions:  (x: 2, y: 2)
    Coordinates:
      * x        (x) <U1 8B 'b' 'a'
      * y        (y) int64 16B 1 0
    Data variables:
        A        (x, y) int64 32B 1 2 3 4
        B        (x, y) int64 32B 5 6 7 8

As a shortcut, you can refer to existing coordinates by name:

    In [53]: ds.sortby("x")
    Out[53]:
    <xarray.Dataset> Size: 88B
    Dimensions:  (x: 2, y: 2)
    Coordinates:
      * x        (x) <U1 8B 'a' 'b'
      * y        (y) int64 16B 1 0
    Data variables:
        A        (x, y) int64 32B 3 4 1 2
        B        (x, y) int64 32B 7 8 5 6

    In [54]: ds.sortby(["y", "x"])
    Out[54]:
    <xarray.Dataset> Size: 88B
    Dimensions:  (x: 2, y: 2)
    Coordinates:
      * x        (x) <U1 8B 'a' 'b'
      * y        (y) int64 16B 0 1
    Data variables:
        A        (x, y) int64 32B 4 3 2 1
        B        (x, y) int64 32B 8 7 6 5

    In [55]: ds.sortby(["y", "x"], ascending=False)
    Out[55]:
    <xarray.Dataset> Size: 88B
    Dimensions:  (x: 2, y: 2)
    Coordinates:
      * x        (x) <U1 8B 'b' 'a'
      * y        (y) int64 16B 1 0
    Data variables:
        A        (x, y) int64 32B 1 2 3 4
        B        (x, y) int64 32B 5 6 7 8

## Reshaping via coarsen

Whilst `coarsen` is normally used for reducing your data’s resolution by applying a reduction function (see the page on computation), it can also be used to reorganise your data without applying a computation via `construct()`.

Taking our example tutorial air temperature dataset over the Northern US

    In [56]: air = xr.tutorial.open_dataset("air_temperature")["air"]
    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 0x7ff7bef0a210>: Failed to resolve 'github.com' ([Errno -2] Name or service not known)"))

    In [57]: air.isel(time=0).plot(x="lon", y="lat")
    NameError: name 'air' is not defined

we can split this up into sub-regions of size `(9, 18)` points using `construct()`:

    In [58]: regions = air.coarsen(lat=9, lon=18, boundary="pad").construct(
       ....:     lon=("x_coarse", "x_fine"), lat=("y_coarse", "y_fine")
       ....: )
       ....:
    NameError: name 'air' is not defined

    In [59]: regions
    NameError: name 'regions' is not defined

9 new regions have been created, each of size 9 by 18 points. The `boundary="pad"` kwarg ensured that all regions are the same size even though the data does not evenly divide into these sizes.

By plotting these 9 regions together via faceting we can see how they relate to the original data.

    In [60]: regions.isel(time=0).plot(
       ....:     x="x_fine", y="y_fine", col="x_coarse", row="y_coarse", yincrease=False
       ....: )
       ....:
    NameError: name 'regions' is not defined

We are now free to easily apply any custom computation to each coarsened region of our new dataarray. This would involve specifying that applied functions should act over the `"x_fine"` and `"y_fine"` dimensions, but broadcast over the `"x_coarse"` and `"y_coarse"` dimensions.