Computation¶
The labels associated with DataArray
and
Dataset
objects enables some powerful shortcuts for
computation, notably including aggregation and broadcasting by dimension
names.
Basic array math¶
Arithmetic operations with a single DataArray automatically vectorize (like numpy) over all array values:
In [1]: arr = xr.DataArray(np.random.randn(2, 3),
...: [('x', ['a', 'b']), ('y', [10, 20, 30])])
...:
In [2]: arr - 3
Out[2]:
<xarray.DataArray (x: 2, y: 3)>
array([[-2.5308877 , -3.28286334, -4.5090585 ],
[-4.13563237, -1.78788797, -3.17321465]])
Coordinates:
* x (x) |S1 'a' 'b'
* y (y) int64 10 20 30
In [3]: abs(arr)
Out[3]:
<xarray.DataArray (x: 2, y: 3)>
array([[ 0.4691123 , 0.28286334, 1.5090585 ],
[ 1.13563237, 1.21211203, 0.17321465]])
Coordinates:
* x (x) |S1 'a' 'b'
* y (y) int64 10 20 30
You can also use any of numpy’s or scipy’s many ufunc functions directly on a DataArray:
In [4]: np.sin(arr)
Out[4]:
<xarray.DataArray (x: 2, y: 3)>
array([[ 0.45209466, -0.27910634, -0.99809483],
[-0.90680094, 0.9363595 , -0.17234978]])
Coordinates:
* x (x) |S1 'a' 'b'
* y (y) int64 10 20 30
Data arrays also implement many numpy.ndarray
methods:
In [5]: arr.round(2)
Out[5]:
<xarray.DataArray (x: 2, y: 3)>
array([[ 0.47, -0.28, -1.51],
[-1.14, 1.21, -0.17]])
Coordinates:
* x (x) |S1 'a' 'b'
* y (y) int64 10 20 30
In [6]: arr.T
Out[6]:
<xarray.DataArray (y: 3, x: 2)>
array([[ 0.4691123 , -1.13563237],
[-0.28286334, 1.21211203],
[-1.5090585 , -0.17321465]])
Coordinates:
* x (x) |S1 'a' 'b'
* y (y) int64 10 20 30
Missing values¶
xarray objects borrow the isnull()
,
notnull()
, count()
,
dropna()
and fillna()
methods
for working with missing data from pandas:
In [7]: x = xr.DataArray([0, 1, np.nan, np.nan, 2], dims=['x'])
In [8]: x.isnull()
Out[8]:
<xarray.DataArray (x: 5)>
array([False, False, True, True, False], dtype=bool)
Coordinates:
* x (x) int64 0 1 2 3 4
In [9]: x.notnull()
Out[9]:
<xarray.DataArray (x: 5)>
array([ True, True, False, False, True], dtype=bool)
Coordinates:
* x (x) int64 0 1 2 3 4
In [10]: x.count()
Out[10]:
<xarray.DataArray ()>
array(3)
In [11]: x.dropna(dim='x')
Out[11]:
<xarray.DataArray (x: 3)>
array([ 0., 1., 2.])
Coordinates:
* x (x) int64 0 1 4
In [12]: x.fillna(-1)
Out[12]:
<xarray.DataArray (x: 5)>
array([ 0., 1., -1., -1., 2.])
Coordinates:
* x (x) int64 0 1 2 3 4
Like pandas, xarray uses the float value np.nan
(not-a-number) to represent
missing values.
Aggregation¶
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):
In [13]: arr.sum(dim='x')
Out[13]:
<xarray.DataArray (y: 3)>
array([-0.66652007, 0.92924868, -1.68227315])
Coordinates:
* y (y) int64 10 20 30
In [14]: arr.std(['x', 'y'])
Out[14]:
<xarray.DataArray ()>
array(0.9156385956757354)
In [15]: arr.min()
Out[15]:
<xarray.DataArray ()>
array(-1.5090585031735124)
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
get_axis_num()
method:
In [16]: arr.get_axis_num('y')
Out[16]: 1
These operations automatically skip missing values, like in pandas:
In [17]: xr.DataArray([1, 2, np.nan, 3]).mean()
Out[17]:
<xarray.DataArray ()>
array(2.0)
If desired, you can disable this behavior by invoking the aggregation method
with skipna=False
.
Rolling window operations¶
DataArray
objects include a rolling()
method. This
method supports rolling window aggregation:
In [18]: arr = xr.DataArray(np.arange(0, 7.5, 0.5).reshape(3, 5),
....: dims=('x', 'y'))
....:
In [19]: arr
Out[19]:
<xarray.DataArray (x: 3, y: 5)>
array([[ 0. , 0.5, 1. , 1.5, 2. ],
[ 2.5, 3. , 3.5, 4. , 4.5],
[ 5. , 5.5, 6. , 6.5, 7. ]])
Coordinates:
* x (x) int64 0 1 2
* y (y) int64 0 1 2 3 4
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:
In [20]: arr.rolling(y=3)
Out[20]: DataArrayRolling [window->3,center->False,dim->y]
The label position and minimum number of periods in the rolling window are
controlled by the center
and min_periods
arguments:
In [21]: arr.rolling(y=3, min_periods=2, center=True)
Out[21]: DataArrayRolling [window->3,min_periods->2,center->True,dim->y]
Aggregation and summary methods can be applied directly to the Rolling
object:
In [22]: r = arr.rolling(y=3)
In [23]: r.mean()
Out[23]:
<xarray.DataArray (y: 5, x: 3)>
array([[ nan, nan, nan],
[ nan, nan, nan],
[ 0.5, 3. , 5.5],
[ 1. , 3.5, 6. ],
[ 1.5, 4. , 6.5]])
Coordinates:
* x (x) int64 0 1 2
* y (y) int64 0 1 2 3 4
In [24]: r.reduce(np.std)
Out[24]:
<xarray.DataArray (y: 5, x: 3)>
array([[ nan, nan, nan],
[ nan, nan, nan],
[ 0.40824829, 0.40824829, 0.40824829],
[ 0.40824829, 0.40824829, 0.40824829],
[ 0.40824829, 0.40824829, 0.40824829]])
Coordinates:
* x (x) int64 0 1 2
* y (y) int64 0 1 2 3 4
Note that rolling window aggregations are much faster (both asymptotically and because they avoid a loop in Python) when bottleneck is installed. Otherwise, we fall back to a slower, pure Python implementation.
Finally, we can manually iterate through Rolling
objects:
In [25]: for label, arr_window in r:
# arr_window is a view of x
Broadcasting by dimension name¶
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 np.reshape()
or
np.newaxis
.
This is best illustrated by a few examples. Consider two one-dimensional arrays with different sizes aligned along different dimensions:
In [26]: a = xr.DataArray([1, 2], [('x', ['a', 'b'])])
In [27]: a
Out[27]:
<xarray.DataArray (x: 2)>
array([1, 2])
Coordinates:
* x (x) |S1 'a' 'b'
In [28]: b = xr.DataArray([-1, -2, -3], [('y', [10, 20, 30])])
In [29]: b
Out[29]:
<xarray.DataArray (y: 3)>
array([-1, -2, -3])
Coordinates:
* y (y) int64 10 20 30
With xarray, we can apply binary mathematical operations to these arrays, and their dimensions are expanded automatically:
In [30]: a * b
Out[30]:
<xarray.DataArray (x: 2, y: 3)>
array([[-1, -2, -3],
[-2, -4, -6]])
Coordinates:
* x (x) |S1 'a' 'b'
* y (y) int64 10 20 30
Moreover, dimensions are always reordered to the order in which they first appeared:
In [31]: c = xr.DataArray(np.arange(6).reshape(3, 2), [b['y'], a['x']])
In [32]: c
Out[32]:
<xarray.DataArray (y: 3, x: 2)>
array([[0, 1],
[2, 3],
[4, 5]])
Coordinates:
* y (y) int64 10 20 30
* x (x) |S1 'a' 'b'
In [33]: a + c
Out[33]:
<xarray.DataArray (x: 2, y: 3)>
array([[1, 3, 5],
[3, 5, 7]])
Coordinates:
* x (x) |S1 'a' 'b'
* y (y) int64 10 20 30
This means, for example, that you always subtract an array from its transpose:
In [34]: c - c.T
Out[34]:
<xarray.DataArray (y: 3, x: 2)>
array([[0, 0],
[0, 0],
[0, 0]])
Coordinates:
* y (y) int64 10 20 30
* x (x) |S1 'a' 'b'
You can explicitly broadcast xaray data structures by using the
broadcast()
function:
a2, b2 = xr.broadcast(a, b2) a2 b2
Automatic alignment¶
xarray enforces alignment between index 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. Note that unlike pandas, this the result of a binary operation is by the intersection (not the union) of coordinate labels:
In [35]: arr + arr[:1]
Out[35]:
<xarray.DataArray (x: 1, y: 5)>
array([[ 0., 1., 2., 3., 4.]])
Coordinates:
* x (x) int64 0
* y (y) int64 0 1 2 3 4
If the result would be empty, an error is raised instead:
In [36]: arr[:2] + arr[2:]
ValueError: no overlapping labels for some dimensions: ['x']
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
align()
) to avoid the overhead of repeated alignment with each
operation. See 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
manual alignment. This ensures in-place
arithmetic never needs to modify data types.
Coordinates¶
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:
In [37]: arr[0]
Out[37]:
<xarray.DataArray (y: 5)>
array([ 0. , 0.5, 1. , 1.5, 2. ])
Coordinates:
x int64 0
* y (y) int64 0 1 2 3 4
In [38]: arr[1]
Out[38]:
<xarray.DataArray (y: 5)>
array([ 2.5, 3. , 3.5, 4. , 4.5])
Coordinates:
x int64 1
* y (y) int64 0 1 2 3 4
# notice that the scalar coordinate 'x' is silently dropped
In [39]: arr[1] - arr[0]
Out[39]:
<xarray.DataArray (y: 5)>
array([ 2.5, 2.5, 2.5, 2.5, 2.5])
Coordinates:
* y (y) int64 0 1 2 3 4
Still, xarray will persist other coordinates in arithmetic, as long as there are no conflicting values:
# only one argument has the 'x' coordinate
In [40]: arr[0] + 1
Out[40]:
<xarray.DataArray (y: 5)>
array([ 1. , 1.5, 2. , 2.5, 3. ])
Coordinates:
x int64 0
* y (y) int64 0 1 2 3 4
# both arguments have the same 'x' coordinate
In [41]: arr[0] - arr[0]
Out[41]:
<xarray.DataArray (y: 5)>
array([ 0., 0., 0., 0., 0.])
Coordinates:
x int64 0
* y (y) int64 0 1 2 3 4
Math with datasets¶
Datasets support arithmetic operations by automatically looping over all data variables:
In [42]: ds = xr.Dataset({'x_and_y': (('x', 'y'), np.random.randn(3, 5)),
....: 'x_only': ('x', np.random.randn(3))},
....: coords=arr.coords)
....:
In [43]: ds > 0
Out[43]:
<xarray.Dataset>
Dimensions: (x: 3, y: 5)
Coordinates:
* y (y) int64 0 1 2 3 4
* x (x) int64 0 1 2
Data variables:
x_only (x) bool True False True
x_and_y (x, y) bool True False False False False True True False False ...
Datasets support most of the same methods found on data arrays:
In [44]: ds.mean(dim='x')
Out[44]:
<xarray.Dataset>
Dimensions: (y: 5)
Coordinates:
* y (y) int64 0 1 2 3 4
Data variables:
x_only float64 -0.2799
x_and_y (y) float64 0.2553 0.08145 -0.4308 -1.411 -0.2989
In [45]: abs(ds)
Out[45]:
<xarray.Dataset>
Dimensions: (x: 3, y: 5)
Coordinates:
* y (y) int64 0 1 2 3 4
* x (x) int64 0 1 2
Data variables:
x_only (x) float64 0.1136 1.478 0.525
x_and_y (x, y) float64 0.1192 1.044 0.8618 2.105 0.4949 1.072 0.7216 ...
Unfortunately, a limitation of the current version of numpy means that we
cannot override ufuncs for datasets, because datasets cannot be written as
a single array [1]. apply()
works around this
limitation, by applying the given function to each variable in the dataset:
In [46]: ds.apply(np.sin)
Out[46]:
<xarray.Dataset>
Dimensions: (x: 3, y: 5)
Coordinates:
* x (x) int64 0 1 2
* y (y) int64 0 1 2 3 4
Data variables:
x_only (x) float64 0.1134 -0.9957 0.5012
x_and_y (x, y) float64 0.1189 -0.8645 -0.759 -0.8609 -0.475 0.8781 ...
Datasets also use looping over variables for broadcasting in binary
arithmetic. You can do arithmetic between any DataArray
and a dataset:
In [47]: ds + arr
Out[47]:
<xarray.Dataset>
Dimensions: (x: 3, y: 5)
Coordinates:
* x (x) int64 0 1 2
* y (y) int64 0 1 2 3 4
Data variables:
x_only (x, y) float64 0.1136 0.6136 1.114 1.614 2.114 1.022 1.522 ...
x_and_y (x, y) float64 0.1192 -0.5442 0.1382 -0.6046 1.505 3.572 3.722 ...
Arithmetic between two datasets matches data variables of the same name:
In [48]: ds2 = xr.Dataset({'x_and_y': 0, 'x_only': 100})
In [49]: ds - ds2
Out[49]:
<xarray.Dataset>
Dimensions: (x: 3, y: 5)
Coordinates:
* x (x) int64 0 1 2
* y (y) int64 0 1 2 3 4
Data variables:
x_only (x) float64 -99.89 -101.5 -99.48
x_and_y (x, y) float64 0.1192 -1.044 -0.8618 -2.105 -0.4949 1.072 ...
Similarly to index based alignment, the result has the intersection of all
matching variables, and ValueError
is raised if the result would be empty.
[1] | In some future version of NumPy, we should be able to override ufuncs for
datasets by making use of __numpy_ufunc__ . |