# 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 : arr = xray.DataArray(np.random.randn(2, 3),
...:                      [('x', ['a', 'b']), ('y', [10, 20, 30])])
...:

In : arr - 3
Out:
<xray.DataArray (x: 2, y: 3)>
array([[-2.5308877 , -3.28286334, -4.5090585 ],
[-4.13563237, -1.78788797, -3.17321465]])
Coordinates:
* y        (y) int64 10 20 30
* x        (x) |S1 'a' 'b'

In : abs(arr)
Out:
<xray.DataArray (x: 2, y: 3)>
array([[ 0.4691123 ,  0.28286334,  1.5090585 ],
[ 1.13563237,  1.21211203,  0.17321465]])
Coordinates:
* y        (y) int64 10 20 30
* x        (x) |S1 'a' 'b'
```

You can also use any of numpy’s or scipy’s many ufunc functions directly on a DataArray:

```In : np.sin(arr)
Out:
<xray.DataArray (x: 2, y: 3)>
array([[ 0.45209466, -0.27910634, -0.99809483],
[-0.90680094,  0.9363595 , -0.17234978]])
Coordinates:
* y        (y) int64 10 20 30
* x        (x) |S1 'a' 'b'
```

Data arrays also implement many numpy.ndarray methods:

```In : arr.round(2)
Out:
<xray.DataArray (x: 2, y: 3)>
array([[ 0.47, -0.28, -1.51],
[-1.14,  1.21, -0.17]])
Coordinates:
* y        (y) int64 10 20 30
* x        (x) |S1 'a' 'b'

In : arr.T
Out:
<xray.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¶

xray objects borrow the isnull(), notnull(), count() and dropna() methods for working with missing data from pandas:

```In : x = xray.DataArray([0, 1, np.nan, np.nan, 2], dims=['x'])

In : x.isnull()
Out:
<xray.DataArray (x: 5)>
array([False, False,  True,  True, False], dtype=bool)
Coordinates:
* x        (x) int64 0 1 2 3 4

In : x.notnull()
Out:
<xray.DataArray (x: 5)>
array([ True,  True, False, False,  True], dtype=bool)
Coordinates:
* x        (x) int64 0 1 2 3 4

In : x.count()
Out:
<xray.DataArray ()>
array(3)

In : x.dropna(dim='x')
Out:
<xray.DataArray (x: 3)>
array([ 0.,  1.,  2.])
Coordinates:
* x        (x) int64 0 1 4
```

Like pandas, xray 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 : arr.sum(dim='x')
Out:
<xray.DataArray (y: 3)>
array([-0.66652007,  0.92924868, -1.68227315])
Coordinates:
* y        (y) int64 10 20 30

In : arr.std(['x', 'y'])
Out:
<xray.DataArray ()>
array(0.9156385956757354)

In : arr.min()
Out:
<xray.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 : arr.get_axis_num('y')
Out: 1
```

These operations automatically skip missing values, like in pandas:

```In : xray.DataArray([1, 2, np.nan, 3]).mean()
Out:
<xray.DataArray ()>
array(2.0)
```

If desired, you can disable this behavior by invoking the aggregation method with skipna=False.

## Broadcasting by dimension name¶

DataArray objects are automatically align themselves (“broadcasting” in the numpy parlance) by dimension name instead of axis order. With xray, 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 : a = xray.DataArray([1, 2], [('x', ['a', 'b'])])

In : a
Out:
<xray.DataArray (x: 2)>
array([1, 2])
Coordinates:
* x        (x) |S1 'a' 'b'

In : b = xray.DataArray([-1, -2, -3], [('y', [10, 20, 30])])

In : b
Out:
<xray.DataArray (y: 3)>
array([-1, -2, -3])
Coordinates:
* y        (y) int64 10 20 30
```

With xray, we can apply binary mathematical operations to these arrays, and their dimensions are expanded automatically:

```In : a * b
Out:
<xray.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 : c = xray.DataArray(np.arange(6).reshape(3, 2), [b['y'], a['x']])

In : c
Out:
<xray.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 : a + c
Out:
<xray.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 : c - c.T
Out:
<xray.DataArray (y: 3, x: 2)>
array([[0, 0],
[0, 0],
[0, 0]])
Coordinates:
* y        (y) int64 10 20 30
* x        (x) |S1 'a' 'b'
```

## Automatic alignment¶

xray 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 : arr + arr[:1]
Out:
<xray.DataArray (x: 1, y: 3)>
array([[ 0.9382246 , -0.56572669, -3.01811701]])
Coordinates:
* y        (y) int64 10 20 30
* x        (x) object 'a'
```

If the result would be empty, an error is raised instead:

```In : 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 : arr
Out:
<xray.DataArray (y: 3)>
array([ 0.4691123 , -0.28286334, -1.5090585 ])
Coordinates:
x        |S1 'a'
* y        (y) int64 10 20 30

In : arr
Out:
<xray.DataArray (y: 3)>
array([-1.13563237,  1.21211203, -0.17321465])
Coordinates:
x        |S1 'b'
* y        (y) int64 10 20 30

# notice that the scalar coordinate 'x' is silently dropped
In : arr - arr
Out:
<xray.DataArray (y: 3)>
array([-1.60474467,  1.49497537,  1.33584385])
Coordinates:
* y        (y) int64 10 20 30
```

Still, xray will persist other coordinates in arithmetic, as long as there are no conflicting values:

```# only one argument has the 'x' coordinate
In : arr + 1
Out:
<xray.DataArray (y: 3)>
array([ 1.4691123 ,  0.71713666, -0.5090585 ])
Coordinates:
* y        (y) int64 10 20 30
x        |S1 'a'

# both arguments have the same 'x' coordinate
In : arr - arr
Out:
<xray.DataArray (y: 3)>
array([ 0.,  0.,  0.])
Coordinates:
* y        (y) int64 10 20 30
x        |S1 'a'
```

## Math with Datasets¶

Datasets support arithmetic operations by automatically looping over all data variables:

```In : ds = xray.Dataset({'x_and_y': (('x', 'y'), np.random.randn(2, 3)),
....:                    'x_only': ('x', np.random.randn(2))},
....:                    coords=arr.coords)
....:

In : ds > 0
Out:
<xray.Dataset>
Dimensions:  (x: 2, y: 3)
Coordinates:
* y        (y) int64 10 20 30
* x        (x) |S1 'a' 'b'
Data variables:
x_only   (x) bool True False
x_and_y  (x, y) bool True False False False False True
```

Datasets support most of the same methods found on data arrays:

```In : ds.mean(dim='x')
Out:
<xray.Dataset>
Dimensions:  (y: 3)
Coordinates:
* y        (y) int64 10 20 30
Data variables:
x_only   float64 0.007392
x_and_y  (y) float64 -0.9927 -0.7696 0.105

In : abs(ds)
Out:
<xray.Dataset>
Dimensions:  (x: 2, y: 3)
Coordinates:
* y        (y) int64 10 20 30
* x        (x) |S1 'a' 'b'
Data variables:
x_only   (x) float64 0.7216 0.7068
x_and_y  (x, y) float64 0.1192 1.044 0.8618 2.105 0.4949 1.072
```

transpose() can also be used to reorder dimensions on all variables:

```In : ds.transpose('y', 'x')
Out:
<xray.Dataset>
Dimensions:  (x: 2, y: 3)
Coordinates:
* x        (x) |S1 'a' 'b'
* y        (y) int64 10 20 30
Data variables:
x_only   (x) float64 0.7216 -0.7068
x_and_y  (y, x) float64 0.1192 -2.105 -1.044 -0.4949 -0.8618 1.072
```

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 . apply() works around this limitation, by applying the given function to each variable in the dataset:

```In : ds.apply(np.sin)
Out:
<xray.Dataset>
Dimensions:  (x: 2, y: 3)
Coordinates:
* x        (x) |S1 'a' 'b'
* y        (y) int64 10 20 30
Data variables:
x_only   (x) float64 0.6606 -0.6494
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 : ds + arr
Out:
<xray.Dataset>
Dimensions:  (x: 2, y: 3)
Coordinates:
* y        (y) int64 10 20 30
* x        (x) |S1 'a' 'b'
Data variables:
x_only   (x, y) float64 1.191 0.4387 -0.7875 -1.842 0.5053 -0.88
x_and_y  (x, y) float64 0.5883 -1.327 -2.371 -3.24 0.7172 0.8986
```

Arithmetic between two datasets matches data variables of the same name:

```In : ds2 = xray.Dataset({'x_and_y': 0, 'x_only': 100})

In : ds - ds2
Out:
<xray.Dataset>
Dimensions:  (x: 2, y: 3)
Coordinates:
* y        (y) int64 10 20 30
* x        (x) |S1 'a' 'b'
Data variables:
x_only   (x) float64 -99.28 -100.7
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.

  When numpy 1.10 is released, we should be able to override ufuncs for datasets by making use of __numpy_ufunc__.