Manipulating a field generally involves operating on its data array and making any necessary changes to the field’s domain to make it consistent with the new array.
A field’s data array may be converted to either an independent numpy masked array or a numpy masked array view (numpy.ndarray.view) with its varray and array attributes respectively:
>>> a = f.array
>>> print a
[[2 -- 4 -- 6]]
>>> a[0, 0] = 999
>>> print a
[[999 -- 4 -- 6]]
>>> print f.array
[[2 -- 4 -- 6]]
>>> va = f.varray
>>> va[0, 0] = 999
>>> print f.array
[[999 -- 4 -- 6]]
Note that changing the numpy array view in place will also change the field’s data array in-place.
A deep copy of a variable may be created with its copy method or equivalently with the copy.deepcopy function:
>>> g = f.copy()
>>> import copy
>>> g = copy.deepcopy(f)
Copying utilizes LAMA copying functionality.
Subspacing a field means subspacing its data array and its domain in a consistent manner.
A field may be subspaced via its subspace attribute. This attribute returns an object which may be indexed to select a subspace by dimension index values (f.subspace[indices]) or called to select a subspace by dimension coordinate array values (f.subspace(**coordinate_values)):
>>> g = f.subspace[0, ...]
>>> g = f.subspace(latitude=30, longitude=cf.wi(0, 90, 'degrees'))
The result of subspacing a field is a new, independent field whose data array and, crucially, any data arrays within the field’s metadata (such as coordinates, ancillary variables, transforms, etc.) are appropriate subspaces of their originals:
>>> print f
air_temperature field summary
-----------------------------
Data : air_temperature(time(12), latitude(73), longitude(96)) K
Cell methods : time: mean
Dimensions : time(12) = [1860-01-16 12:00:00, ..., 1860-12-16 12:00:00]
: latitude(73) = [-90, ..., 90] degrees_north
: longitude(96) = [0, ..., 356.25] degrees_east
: height(1) = [2] m
>>> g = f.subspace[-1, :, 48::-1]
>>> print g
air_temperature field summary
-----------------------------
Data : air_temperature(time(1), latitude(73), longitude(49)) K
Cell methods : time: mean
Dimensions : time(1) = [1860-12-16 12:00:00]
: latitude(73) = [-90, ..., 90] degrees_north
: longitude(49) = [180, ..., 0] degrees_east
: height(1) = [2] m
Subspacing utilizes LAMA subspacing functionality.
Subspacing by dimension indices uses an extended Python slicing syntax, which is similar to numpy array indexing:
>>> f.shape
(12, 73, 96)
>>> f.subspace[...].shape
(12, 73, 96)
>>> f.subspace[slice(0, 12), :, 10:0:-2].shape
(12, 73, 5)
>>> lon = f.coord('longitude').array
>>> f.subspace[..., lon<180]
There are two important extensions to the numpy indexing functionality:
Size 1 dimensions are never removed.
An integer index i takes the i-th element but does not reduce the rank of the output array by one:
>>> f.shape
(12, 73, 96)
>>> f.subspace[0, ...].shape
(1, 73, 96)
>>> f.subspace[3, slice(10, 0, -2), 95].shape
(1, 5, 1)
When advanced indexing is used on more than one dimension, the advanced indices work independently.
When more than one dimension’s slice is a 1-d boolean sequence or 1-d sequence of integers, then these indices work independently along each dimension (similar to the way vector subscripts work in Fortran), rather than by their elements:
>>> f.shape
(12, 73, 96)
>>> f.subspace[:, [0, 72], [5, 4, 3]].shape
(12, 2, 3)
Note that the indices of this example would raise an error when given to a numpy array.
Subspacing by values of 1-d coordinates allows a subspaced field to be defined via coordinate values of its domain. The benefits of subspacing in this fashion are:
Coordinate values are provided as keyword arguments to a call to the subspace attribute. Coordinates are identified by their identity or their dimension’s identifier in the field’s domain.
>>> f.subspace().shape
(12, 73, 96)
>>> f.subspace(latitude=0).shape
(12, 1, 96)
>>> f.subspace(latitude=cf.wi(-30, 30)).shape
(12, 25, 96)
>>> f.subspace(long=cf.ge(270, 'degrees_east'), lat=cf.set([0, 2.5, 10])).shape
(12, 3, 24)
>>> f.subspace(latitude=cf.lt(0, 'degrees_north'))
(12, 36, 96)
>>> f.subspace(latitude=[cf.lt(0, 'degrees_north'), 90])
(12, 37, 96)
>>> import math
>>> f.subspace(longitude=cf.lt(math.pi, 'radian'), height=2)
(12, 73, 48)
>>> f.subspace(height=cf.gt(3))
IndexError: No indices found for 'height' values gt 3
>>> f.subspace(dim2=3.75).shape
(12, 1, 96)
Note that if a comparison function (such as cf.wi) does not specify any units, then the units of the named coordinate are assumed.
Fields may be tested for matching given conditions with the match method and selected by matching given conditions with the select method. Both methods share the same interface. Conditions may be given on:
| Field conditions | Method keyword | Example |
|---|---|---|
| CF properties | prop | prop={'standard_name': '.*pressure.*'} |
| Other attributes | attr | attr=dict(ncvar='tas') |
| Coordinate values | coord | coord={'latitude': 0} |
| Coordinate cell sizes | cellsize | cellsize={'time': cf.wi(28, 31, 'days')} |
For example:
>>> f
[<CF Field: eastward_wind(grid_latitude(110), grid_longitude(106)) m s-1>,
<CF Field: air_temperature(time(12), latitude(73), longitude(96)) K>]
>>> f.match(prop={'standard_name': '.*temperature'})
[False, True]
>>> g = f.select(prop={'standard_name': '.*temperature'}, coord={'longitude': 0})
>>> g
[<CF Field: air_temperature(time(12), latitude(73), longitude(96)) K>]
Any of these keywords may also be used with cf.read to select on input:
>>> f = cf.read('file*.nc', prop={'standard_name': '.*temperature'},
... coord={'longitude': 0})
Selection may also be applied to a field, rather than a field list. In this case, the select method returns the field itself if there is a match:
>>> f
<CF Field: air_temperature(time(12), latitude(73), longitude(96)) K>
>>> f.match(prop=dict(standard_name=cf.eq('air_temperature'))
True
>>> g = f.select(prop=dict(standard_name=cf.eq('air_temperature'))
>>> g is f
True
Fields are aggregated into as few multidimensional fields as possible with the cf.aggregate function, which implements the CF aggregation rules.
>>> f
[<CF Field: eastward_wind(grid_latitude(110), grid_longitude(106)) m s-1>,
<CF Field: eastward_wind(grid_latitude(110), grid_longitude(106)) m s-1>,
<CF Field: eastward_wind(grid_latitude(110), grid_longitude(106)) m s-1>,
<CF Field: eastward_wind(grid_latitude(110), grid_longitude(106)) m s-1>,
<CF Field: eastward_wind(grid_latitude(110), grid_longitude(106)) m s-1>,
<CF Field: eastward_wind(grid_latitude(110), grid_longitude(106)) miles hour-1>,
<CF Field: air_temperature(time(12), latitude(73), longitude(96)) K>,
<CF Field: air_temperature(latitude(73), longitude(96)) K @ 273.15>]
>>> cf.aggregate(f)
>>> f
[<CF Field: eastward_wind(time(3), height(2), grid_latitude(110), grid_longitude(106)) m s-1>,
<CF Field: air_temperature(time(13), latitude(73), longitude(96)) K>]
By default, the fields returned by cf.read have been aggregated:
>>> f = cf.read('file*.nc')
>>> len(f)
1
>>> f = cf.read('file*.nc', aggregate=False)
>>> len(f)
12
Aggregation implements the CF aggregation rules.
The preferred way of changing elements of a field’s data array in place is with the field’s setitem method [1].
Assignment uses LAMA functionality, so it is possible to assign to subspaces which are larger than the available memory.
Array elements may be set from a field or logically scalar object, using the same broadcasting rules as for field arithmetic and comparison operations.
Set all values to 273.15:
>>> f.setitem(273.15)
Set all values to between 210 and 270 degrees longitude and -5 and 5 degrees latitude to 273.15:
>>> f.setitem(273.15, dict(longitude=cf.wi(210, 270, 'degrees_east'),
latitude=cf.wi(-5, 5, 'degrees_north'))
Set all values less the 10 Celcius to 10 Celcius:
>>> f.setitem(cf.Data(10, 'K @ 273.15'), condition=cf.lt(10, 'K @ 273.15'))
Set all unmasked values to 300:
>>> f.setitem(300, masked=False)
Arithmetic and comparison operations are defined on a field as element-wise array operations which yield a new cf.Field object or, for augmented arithmetic assignments, modify the field’s data array in-place.
Comparison operators
| __lt__ | The rich comparison operator < |
| __le__ | The rich comparison operator <= |
| __eq__ | The rich comparison operator == |
| __ne__ | The rich comparison operator != |
| __gt__ | The rich comparison operator > |
| __ge__ | The rich comparison operator >= |
Binary arithmetic operators
| __add__ | The binary arithmetic operation + |
| __sub__ | The binary arithmetic operation - |
| __mul__ | The binary arithmetic operation * |
| __div__ | The binary arithmetic operation / |
| __truediv__ | The binary arithmetic operation / (true division) |
| __floordiv__ | The binary arithmetic operation // |
| __pow__ | The binary arithmetic operations ** and pow |
| __and__ | The binary arithmetic operation & |
| __or__ | The binary arithmetic operation | |
| __xor__ | The binary arithmetic operation ^ |
Binary arithmetic operators with reflected (swapped) operands
| __radd__ | The binary arithmetic operation + with reflected operands |
| __rsub__ | The binary arithmetic operation - with reflected operands |
| __rmul__ | The binary arithmetic operation * with reflected operands |
| __rdiv__ | The binary arithmetic operation / with reflected operands |
| __rtruediv__ | The binary arithmetic operation / (true division) with reflected operands |
| __rfloordiv__ | The binary arithmetic operation // with reflected operands |
| __rpow__ | The binary arithmetic operations ** and pow with reflected operands |
| __rand__ | The binary arithmetic operation & with reflected operands |
| __ror__ | The binary arithmetic operation | with reflected operands |
| __rxor__ | The binary arithmetic operation ^ with reflected operands |
Augmented arithmetic assignments
| __iadd__ | The augmented arithmetic assignment += |
| __isub__ | The augmented arithmetic assignment -= |
| __imul__ | The augmented arithmetic assignment *=. |
| __idiv__ | The augmented arithmetic assignment /= |
| __itruediv__ | The augmented arithmetic assignment /= (true division) |
| __ifloordiv__ | The augmented arithmetic assignment //= |
| __ipow__ | The augmented arithmetic assignment **= |
| __iand__ | The augmented arithmetic assignment &= |
| __ior__ | The augmented arithmetic assignment |= |
| __ixor__ | The augmented arithmetic assignment ^= |
Unary arithmetic operators
| __neg__ | The unary arithmetic operation - |
| __pos__ | The unary arithmetic operation + |
| __abs__ | The unary arithmetic operation abs |
| __invert__ | The unary arithmetic operation ~ |
A field’s data array is modified in a very similar way to how a numpy array would be modified in the same operation, i.e. broadcasting ensures that the operands are compatible and the data array is modified element-wise.
Broadcasting is metadata-aware and will automatically account for arbitrary configurations, such as dimension order, but will not allow incompatible metadata to be combined, such as adding a field of height to one of temperature.
The resulting field’s metadata will be very similar to that of the operands which are also fields. Differences arise when the existing metadata can not correctly describe the newly created field. For example, when dividing a field with units of metres by one with units of seconds, the resulting field will have units of metres per second.
Arithmetic and comparison utilizes LAMA functionality so data arrays larger than the available physical memory may be operated on.
The term broadcasting describes how data arrays of the operands with different shapes are treated during arithmetic, comparison and assignment operations. Subject to certain constraints, the smaller array is “broadcast” across the larger array so that they have compatible shapes.
The general broadcasting rules are similar to the broadcasting rules implemented in numpy, the only difference occurring when both operands are fields, in which case the fields are temporarily conformed so that:
This restructuring of the field ensures that the matching dimensions are broadcast against each other.
Broadcasting is done without making needless copies of data and so is usually very efficient.
A field may be combined or compared with the following objects:
| Object | Description |
|---|---|
| int, long, float | The field’s data array is combined with the python scalar |
| Data with size 1 | The field’s data array is combined with the cf.Data object’s scalar value, taking into account:
|
| Field | The two field’s must satisfy the field combination rules. The fields’ data arrays and domains are combined taking into account:
|
A field may appear on the left or right hand side of an operator.
Warning
Combining a numpy array on the left with a field on the right does work, but will give generally unintended results – namely a numpy array of fields.
When creating a new field which has different physical properties to the input field(s) the units will also need to be changed:
>>> f.units
'K'
>>> f += 2
>>> f.units
'K'
>>> f.units
'K'
>>> f **= 2
>>> f.units
'K2'
>>> f.units, g.units
('m', 's')
>>> h = f / g
>>> h.units
'm s-1'
When creating a new field which has a different domain to the input fields, the new domain will in general contain the superset of dimensions from the two input fields, but may not have some of either input field’s auxiliary coordinates or size 1 dimension coordinates. Refer to the field combination rules for details.
A field has methods which manipulate the its data array. Many of these behave similarly to their numpy counterparts with the same name but always change the field’s data array in-place. New fields with the same changes may be created with equivalently named module functions.
| Field method | Description | Numpy counterpart | Function |
|---|---|---|---|
| clip | Clip (limit) the values in the data array | numpy.ma.clip | cf.clip |
| cos | Trigonometric cosine of the data array | numpy.ma.cos | cf.cos |
| expand_dims | Expand the shape of the data array | numpy.ma.expand_dims | cf.expand_dims |
| flip | Flip dimensions of the field | cf.flip | |
| sin | Trigonometric sine of the data array | numpy.ma.sin | cf.sin |
| squeeze | Remove size 1 dimensions from the field’s data array | numpy.ma.squeeze | cf.squeeze |
| transpose | Permute the dimensions of the data array | numpy.ma.transpose | cf.transpose |
| unsqueeze | Insert size 1 dimensions from the field’s domain into its data array | cf.unsqueeze |
A field is a subclass of cf.Variable, and that class and other subclasses of cf.Variable share generally similar behaviours and methods:
| Class | Description |
|---|---|
| cf.CellMeasure | A CF cell measure construct containing information that is needed about the size, shape or location of the field’s cells. |
| cf.Coordinate | A CF dimension or auxiliary coordinate construct. |
| cf.CoordinateBounds | A CF coordinate’s bounds object containing cell boundaries or intervals of climatological time. |
| cf.Variable | Base class for storing a data array with metadata. |
In general, different dimension identities, different dimension orders and different dimension directions are not considered, since these objects do not contain a coordinate system required to define these properties (unlike a field).
Coordinates are a special case as they may contain a data array for their coordinate bounds which needs to be treated consistently with the main coordinate array. If a coordinate has bounds then all coordinate methods also operate on the bounds in a consistent manner:
>>> c
<CF Coordinate: latitude(73, 96)>
>>> c.bounds
<CF CoordinateBounds: (73, 96, 4)>
>>> d = c.subspace[0:10]
>>> d.shape
(10, 96)
>>> d.bounds.shape
(10, 96, 4)
>>> d.transpose([1, 0])
>>> d.shape
(96, 10)
>>> d.bounds.shape
(96, 10, 4)
Note
If the coordinate bounds are operated on independently, care should be taken not to break consistency with the parent coordinate.
Footnotes
| [1] | Other methods are available. See cf.Field.setitem for details. |