# Subsetting a Cube#

The Loading Iris Cubes section of the user guide showed how to load data into multidimensional Iris cubes. However it is often necessary to reduce the dimensionality of a cube down to something more appropriate and/or manageable.

Iris provides several ways of reducing both the amount of data and/or the number of dimensions in your cube depending on the circumstance.
In all cases **the subset of a valid cube is itself a valid cube**.

## Cube Extraction#

A subset of a cube can be “extracted” from a multi-dimensional cube in order to reduce its dimensionality:

```
>>> import iris
>>> filename = iris.sample_data_path('space_weather.nc')
>>> cube = iris.load_cube(filename, 'electron density')
>>> equator_slice = cube.extract(iris.Constraint(grid_latitude=0))
>>> print(equator_slice)
electron density / (1E11 e/m^3) (height: 29; grid_longitude: 31)
Dimension coordinates:
height x -
grid_longitude - x
Auxiliary coordinates:
latitude - x
longitude - x
Scalar coordinates:
grid_latitude 0.0 degrees
Attributes:
Conventions 'CF-1.5'
```

In this example we start with a 3 dimensional cube, with dimensions of `height`

, `grid_latitude`

and `grid_longitude`

,
and use `iris.Constraint`

to extract every point where the latitude is 0, resulting in a 2d cube with axes of `height`

and `grid_longitude`

.

Warning

Caution is required when using equality constraints with floating point coordinates such as `grid_latitude`

.
Printing the points of a coordinate does not necessarily show the full precision of the underlying number and it
is very easy to return no matches to a constraint when one was expected.
This can be avoided by using a function as the argument to the constraint:

```
def near_zero(cell):
"""Returns true if the cell is between -0.1 and 0.1."""
return -0.1 < cell < 0.1
equator_constraint = iris.Constraint(grid_latitude=near_zero)
```

Often you will see this construct in shorthand using a lambda function definition:

```
equator_constraint = iris.Constraint(grid_latitude=lambda cell: -0.1 < cell < 0.1)
```

The extract method could be applied again to the *equator_slice* cube to get a further subset.

For example to get a `height`

of 9000 metres at the equator the following line extends the previous example:

```
equator_height_9km_slice = equator_slice.extract(iris.Constraint(height=9000))
print(equator_height_9km_slice)
```

The two steps required to get `height`

of 9000 m at the equator can be simplified into a single constraint:

```
equator_height_9km_slice = cube.extract(iris.Constraint(grid_latitude=0, height=9000))
print(equator_height_9km_slice)
```

Alternatively, constraints can be combined using `&`

:

```
cube = iris.load_cube(filename, 'electron density')
equator_constraint = iris.Constraint(grid_latitude=0)
height_constraint = iris.Constraint(height=9000)
equator_height_9km_slice = cube.extract(equator_constraint & height_constraint)
```

Note

Whilst `&`

is supported, the `|`

that might reasonably be expected is
not. Explanation as to why is in the `iris.Constraint`

reference
documentation.

For an example of constraining to multiple ranges of the same coordinate to
generate one cube, see the `iris.Constraint`

reference documentation.

A common requirement is to limit the value of a coordinate to a specific range, this can be achieved by passing the constraint a function:

```
def below_9km(cell):
# return True or False as to whether the cell in question should be kept
return cell <= 9000
cube = iris.load_cube(filename, 'electron density')
height_below_9km = iris.Constraint(height=below_9km)
below_9km_slice = cube.extract(height_below_9km)
```

As we saw in Loading Iris Cubes the result of `iris.load()`

is a `CubeList`

.
The `extract`

method also exists on a `CubeList`

and behaves in exactly the
same way as loading with constraints:

```
>>> import iris
>>> air_temp_and_fp_6 = iris.Constraint('air_potential_temperature', forecast_period=6)
>>> level_10 = iris.Constraint(model_level_number=10)
>>> filename = iris.sample_data_path('uk_hires.pp')
>>> cubes = iris.load(filename).extract(air_temp_and_fp_6 & level_10)
>>> print(cubes)
0: air_potential_temperature / (K) (grid_latitude: 204; grid_longitude: 187)
>>> print(cubes[0])
air_potential_temperature / (K) (grid_latitude: 204; grid_longitude: 187)
Dimension coordinates:
grid_latitude x -
grid_longitude - x
Auxiliary coordinates:
surface_altitude x x
Derived coordinates:
altitude x x
Scalar coordinates:
forecast_period 6.0 hours
forecast_reference_time 2009-11-19 04:00:00
level_height 395.0 m, bound=(360.0, 433.3332) m
model_level_number 10
sigma 0.9549927, bound=(0.9589389, 0.95068014)
time 2009-11-19 10:00:00
Attributes:
STASH m01s00i004
source 'Data from Met Office Unified Model'
um_version '7.3'
```

Cube attributes can also be part of the constraint criteria. Supposing a
cube attribute of `STASH`

existed, as is the case when loading `PP`

files,
then specific STASH codes can be filtered:

```
filename = iris.sample_data_path('uk_hires.pp')
level_10_with_stash = iris.AttributeConstraint(STASH='m01s00i004') & iris.Constraint(model_level_number=10)
cubes = iris.load(filename).extract(level_10_with_stash)
```

See also

For advanced usage there are further examples in the
`iris.Constraint`

reference documentation.

### Constraining a Circular Coordinate Across its Boundary#

Occasionally you may need to constrain your cube with a region that crosses the boundary of a circular coordinate (this is often the meridian or the dateline / antimeridian). An example use-case of this is to extract the entire Pacific Ocean from a cube whose longitudes are bounded by the dateline.

This functionality cannot be provided reliably using constraints. Instead you should use the
functionality provided by `cube.intersection`

to extract this region.

### Constraining on Time#

Iris follows NetCDF-CF rules in representing time coordinate values as normalised, purely numeric, values which are normalised by the calendar specified in the coordinate’s units (e.g. “days since 1970-01-01”). However, when constraining by time we usually want to test calendar-related aspects such as hours of the day or months of the year, so Iris provides special features to facilitate this.

Firstly, when Iris evaluates `iris.Constraint`

expressions, it will convert
time-coordinate values (points and bounds) from numbers into `datetime`

-like
objects for ease of calendar-based testing.

```
>>> filename = iris.sample_data_path('uk_hires.pp')
>>> cube_all = iris.load_cube(filename, 'air_potential_temperature')
>>> print('All times :\n' + str(cube_all.coord('time')))
All times :
DimCoord : time / (hours since 1970-01-01 00:00:00, gregorian calendar)
points: [2009-11-19 10:00:00, 2009-11-19 11:00:00, 2009-11-19 12:00:00]
shape: (3,)
dtype: float64
standard_name: 'time'
>>> # Define a function which accepts a datetime as its argument (this is simplified in later examples).
>>> hour_11 = iris.Constraint(time=lambda cell: cell.point.hour == 11)
>>> cube_11 = cube_all.extract(hour_11)
>>> print('Selected times :\n' + str(cube_11.coord('time')))
Selected times :
DimCoord : time / (hours since 1970-01-01 00:00:00, gregorian calendar)
points: [2009-11-19 11:00:00]
shape: (1,)
dtype: float64
standard_name: 'time'
```

Secondly, the `iris.time`

module provides flexible time comparison
facilities. An `iris.time.PartialDateTime`

object can be compared to
objects such as `datetime.datetime`

instances, and this comparison will
then test only those ‘aspects’ which the PartialDateTime instance defines:

```
>>> import datetime
>>> from iris.time import PartialDateTime
>>> dt = datetime.datetime(2011, 3, 7)
>>> print(dt > PartialDateTime(year=2010, month=6))
True
>>> print(dt > PartialDateTime(month=6))
False
```

These two facilities can be combined to provide straightforward calendar-based time selections when loading or extracting data.

The previous constraint example can now be written as:

```
>>> the_11th_hour = iris.Constraint(time=iris.time.PartialDateTime(hour=11))
>>> print(iris.load_cube(
... iris.sample_data_path('uk_hires.pp'),
... 'air_potential_temperature' & the_11th_hour).coord('time'))
DimCoord : time / (hours since 1970-01-01 00:00:00, gregorian calendar)
points: [2009-11-19 11:00:00]
shape: (1,)
dtype: float64
standard_name: 'time'
```

It is common that a cube will need to be constrained between two given dates. In the following example we construct a time sequence representing the first day of every week for many years:

```
>>> print(long_ts.coord('time'))
DimCoord : time / (days since 2007-04-09, gregorian calendar)
points: [
2007-04-09 00:00:00, 2007-04-16 00:00:00, ...,
2010-02-08 00:00:00, 2010-02-15 00:00:00]
shape: (150,)
dtype: int64
standard_name: 'time'
```

Given two dates in datetime format, we can select all points between them.
Instead of constraining at loaded time, we already have the time coord so
we constrain that coord using `iris.cube.Cube.extract`

```
>>> d1 = datetime.datetime.strptime('20070715T0000Z', '%Y%m%dT%H%MZ')
>>> d2 = datetime.datetime.strptime('20070825T0000Z', '%Y%m%dT%H%MZ')
>>> st_swithuns_daterange_07 = iris.Constraint(
... time=lambda cell: d1 <= cell.point < d2)
>>> within_st_swithuns_07 = long_ts.extract(st_swithuns_daterange_07)
>>> print(within_st_swithuns_07.coord('time'))
DimCoord : time / (days since 2007-04-09, gregorian calendar)
points: [
2007-07-16 00:00:00, 2007-07-23 00:00:00, 2007-07-30 00:00:00,
2007-08-06 00:00:00, 2007-08-13 00:00:00, 2007-08-20 00:00:00]
shape: (6,)
dtype: int64
standard_name: 'time'
```

Alternatively, we may rewrite this using `iris.time.PartialDateTime`

objects.

```
>>> pdt1 = PartialDateTime(year=2007, month=7, day=15)
>>> pdt2 = PartialDateTime(year=2007, month=8, day=25)
>>> st_swithuns_daterange_07 = iris.Constraint(
... time=lambda cell: pdt1 <= cell.point < pdt2)
>>> within_st_swithuns_07 = long_ts.extract(st_swithuns_daterange_07)
>>> print(within_st_swithuns_07.coord('time'))
DimCoord : time / (days since 2007-04-09, gregorian calendar)
points: [
2007-07-16 00:00:00, 2007-07-23 00:00:00, 2007-07-30 00:00:00,
2007-08-06 00:00:00, 2007-08-13 00:00:00, 2007-08-20 00:00:00]
shape: (6,)
dtype: int64
standard_name: 'time'
```

A more complex example might require selecting points over an annually repeating date range. We can select points within a certain part of the year, in this case between the 15th of July through to the 25th of August. By making use of PartialDateTime this becomes simple:

```
>>> st_swithuns_daterange = iris.Constraint(
... time=lambda cell: PartialDateTime(month=7, day=15) <= cell.point < PartialDateTime(month=8, day=25))
>>> within_st_swithuns = long_ts.extract(st_swithuns_daterange)
...
>>> # Note: using summary(max_values) to show more of the points
>>> print(within_st_swithuns.coord('time').summary(max_values=100))
DimCoord : time / (days since 2007-04-09, gregorian calendar)
points: [
2007-07-16 00:00:00, 2007-07-23 00:00:00, 2007-07-30 00:00:00,
2007-08-06 00:00:00, 2007-08-13 00:00:00, 2007-08-20 00:00:00,
2008-07-21 00:00:00, 2008-07-28 00:00:00, 2008-08-04 00:00:00,
2008-08-11 00:00:00, 2008-08-18 00:00:00, 2009-07-20 00:00:00,
2009-07-27 00:00:00, 2009-08-03 00:00:00, 2009-08-10 00:00:00,
2009-08-17 00:00:00, 2009-08-24 00:00:00]
shape: (17,)
dtype: int64
standard_name: 'time'
```

Notice how the dates printed are between the range specified in the `st_swithuns_daterange`

and that they span multiple years.

The above examples involve constraining on the points of the time coordinate. Constraining on bounds can be done in the following way:

```
filename = iris.sample_data_path('ostia_monthly.nc')
cube = iris.load_cube(filename, 'surface_temperature')
dtmin = datetime.datetime(2008, 1, 1)
cube.extract(iris.Constraint(time = lambda cell: any(bound > dtmin for bound in cell.bound)))
```

The above example constrains to cells where either the upper or lower bound occur after 1st January 2008.

## Cube Iteration#

It is not possible to directly iterate over an Iris cube. That is, you cannot use code such as
`for x in cube:`

. However, you can iterate over cube slices, as this section details.

A useful way of dealing with a Cube in its **entirety** is by iterating over its layers or slices.
For example, to deal with a 3 dimensional cube (z,y,x) you could iterate over all 2 dimensional slices in y and x
which make up the full 3d cube.:

```
import iris
filename = iris.sample_data_path('hybrid_height.nc')
cube = iris.load_cube(filename)
print(cube)
for yx_slice in cube.slices(['grid_latitude', 'grid_longitude']):
print(repr(yx_slice))
```

As the original cube had the shape (15, 100, 100) there were 15 latitude longitude slices and hence the
line `print(repr(yx_slice))`

was run 15 times.

Note

The order of latitude and longitude in the list is important; had they been swapped the resultant cube slices would have been transposed.

For further information see `Cube.slices`

.

This method can handle n-dimensional slices by providing more or fewer coordinate names in the list to **slices**:

```
import iris
filename = iris.sample_data_path('hybrid_height.nc')
cube = iris.load_cube(filename)
print(cube)
for i, x_slice in enumerate(cube.slices(['grid_longitude'])):
print(i, repr(x_slice))
```

The Python function `enumerate()`

is used in this example to provide an incrementing variable **i** which is
printed with the summary of each cube slice. Note that there were 1500 1d longitude cubes as a result of
slicing the 3 dimensional cube (15, 100, 100) by longitude (i starts at 0 and 1500 = 15 * 100).

Hint

It is often useful to get a single 2d slice from a multidimensional cube in order to develop a 2d plot function, for example.
This can be achieved by using the `next()`

function on the result of
slices:

```
first_slice = next(cube.slices(['grid_latitude', 'grid_longitude']))
```

Once the your code can handle a 2d slice, it is then an easy step to loop over **all** 2d slices within the bigger
cube using the slices method.

## Cube Indexing#

In the same way that you would expect a numeric multidimensional array to be **indexed** to take a subset of your
original array, you can **index** a Cube for the same purpose.

Here are some examples of array indexing in `numpy`

:

```
import numpy as np
# create an array of 12 consecutive integers starting from 0
a = np.arange(12)
print(a)
print(a[0]) # first element of the array
print(a[-1]) # last element of the array
print(a[0:4]) # first four elements of the array (the same as a[:4])
print(a[-4:]) # last four elements of the array
print(a[::-1]) # gives all of the array, but backwards
# Make a 2d array by reshaping a
b = a.reshape(3, 4)
print(b)
print(b[0, 0]) # first element of the first and second dimensions
print(b[0]) # first element of the first dimension (+ every other dimension)
# get the second element of the first dimension and all of the second dimension
# in reverse, by steps of two.
print(b[1, ::-2])
```

Similarly, Iris cubes have indexing capability:

```
import iris
filename = iris.sample_data_path('hybrid_height.nc')
cube = iris.load_cube(filename)
print(cube)
# get the first element of the first dimension (+ every other dimension)
print(cube[0])
# get the last element of the first dimension (+ every other dimension)
print(cube[-1])
# get the first 4 elements of the first dimension (+ every other dimension)
print(cube[0:4])
# Get the first element of the first and third dimension (+ every other dimension)
print(cube[0, :, 0])
# Get the second element of the first dimension and all of the second dimension
# in reverse, by steps of two.
print(cube[1, ::-2])
```