# Manipulating `cf.Field` objects

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.

## Data array

### Conversion to a numpy array

A field’s data array may be converted to either an independent numpy array or a numpy array view (`numpy.ndarray.view`) with its `array` and `varray` 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]]

Changing the numpy array view in place will also change the field’s data array in-place:

    >>> v = f.varray
    >>> print v
    [[2 -- 4 -- 6]]
    >>> v[0, 0] = 999
    >>> print f.array
    [[999 -- 4 -- 6]]

A field exposes the numpy array interface and so may be used as input to any of the numpy array creation functions:

    >>> print f.array
    [[2 -- 4 -- 6]]
    >>> numpy.all(f.array)
    True
    >>> numpy.all(f)
    True

Note

The numpy array created by the `varray` or `array` attributes forces all of the data to be read into memory at the same time, which may not be possible for very large arrays.

### Data mask

A copy of a field’s missing data mask is returned by its `mask` attribute.

This mask is an independent field in its own right, and so changes to it will not be seen by the field which generated it. See the assignment section for details on how to edit the field’s mask in place.

## Copying

A deep copy of a field may be created with its `copy` method, which is functionally equivalent to, but faster than, using the `copy.deepcopy` function:

    >>> g = f.copy()
    >>> import copy
    >>> g = copy.deepcopy(f)

Copying utilizes LAMA copying functionality.

## Subspacing

Subspacing a field means subspacing its data array and its domain in a consistent manner.

A field may be subspaced in “index-space” or “domain-space”. In index-space, a subspace is defined by specifying indices of the data array, whilst in domain-space a subspace is defined as the part of the data array corresponds to given domain item values (e.g. particular coordinate values)

Subspacing utilizes LAMA subspacing functionality.

### Indexing

Subspacing by axis indices is done with the use of square brackets ([]) on a field and uses an extended Python slicing syntax which is similar to numpy array indexing:

    >>> f.shape
    (12, 73, 96)
    >>> f[...].shape
    (12, 73, 96)
    >>> f[slice(0, 12), :, 10:0:-2].shape
    (12, 73, 5)
    >>> f[..., f.coord('longitude')<180].shape
    (12, 73, 48)

There are three extensions to the numpy indexing functionality:

- Size 1 axes 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[0].shape
      (1, 73, 96)
      >>> f[3, slice(10, 0, -2), 95:93:-1].shape
      (1, 5, 2)

- The indices for each axis work independently.

  When more than one axis’s slice is a 1-d boolean sequence or 1-d sequence of integers, then these indices work independently along each axis (similar to the way vector subscripts work in Fortran), rather than by their elements:

      >>> f.shape
      (12, 73, 96)
      >>> f[:, [0, 72], [5, 4, 3]].shape
      (12, 2, 3)

  Note that the indices of the last example would raise an error when given to a numpy array.

- Boolean indices may be any object which exposes the numpy array interface, such as the field’s coordinate objects:

      >>> f[:, f.coord('latitude')<0].shape
      (12, 36, 96)

Alternatively, the indices may be applied by indexing `Field.subspace`. For example:

    >>> f[..., 2:34:-2, [2, 4, 5]]

is exactly equivalent to

    >>> f.subspace[..., 2:34:-2, [2, 4, 5]]

### Domain values

Subspacing by values of domain items (coordinates or cell measures) allows a subspaced field to be defined via metadata values of its domain. The benefits of subspacing in this fashion are:

- The axes to be subspaced may identified by name.
- The position in the data array of each axis need not be known and the axes to be subspaced may be given in any order.
- Axes for which no subspacing is required need not be specified.
- Size 1 axes of the domain which are not spanned by the data array may be specified.

Coordinate values are provided as keyword arguments to a call to `subspace`. Coordinates are identified by their `identity` or their axis’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('exact', 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)
    >>> f.subspace(time=cf.le(cf.dt('1860-06-16 12:00:00')).shape
    (6, 73, 96)
    >>> f.subspace(time=cf.gt(cf.dt(1860, 7)),shape
    (5, 73, 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.

## Cyclic axes

    >>> f[..., -10, 10]
    (12, 25, 96)
    >>> f.subspace(longitude=cf.wi(-30, 30))
    (12, 3, 24)
    >>> f.subspace(long=cf.ge(270, 'degrees_east'), lat=cf.set([0, 2.5, 10])).shape
    (12, 3, 24)

## Assignment

Elements of a field’s data array may be changed by assigning values directly to an indexed subspace the field or by using the `where` method.

Assignment uses LAMA functionality, so it is possible to assign to fields which are larger than the available memory.

Array elements may be set from a field or logically scalar object, using the same metadata-aware broadcasting rules as for field arithmetic and comparison operations. In the `subspace` case, the object attribute must be broadcastable to the defined subspace, whilst in the `where` case the object must be broadcastable to the field itself.

The treatment of missing data elements depends on the value of field’s `hardmask` attribute. If it is True then masked elements will not unmasked, otherwise masked elements may be set to any value. In either case, unmasked elements may be set to any value (including missing data).

Set all values to 273.15:

    >>> f[...] = 273.15

or equivalently:

    >>> f.where(True, 273.15, None, i=True)

Set all negative data array values to zero and leave all other elements unchanged:

    >>> g = f.where(f<0, 0)

Double the values in the northern hemisphere:

    >>> index = f.indices(longitude=cf.ge(0))
    >>> f[index] *= 2

See `cf.Field.where` for more examples.

## Selection

### Field selection

Fields from field lists may be selected according to conditions on their metadata with the `cf.FieldList.select` method (as well as the `cf.Field.select` method). Conditions may be given on attributes and CF properties, domain items of the field (dimension coordinate, auxiliary coordinate, cell measure or coordinate reference objects), the number of field domain axes and the number of field data array axes. 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.select('air_temperature')
    <CF Field: air_temperature(time(12), latitude(73), longitude(96)) K>]

    >>>  f.select('air_temperature', rank=2)
    []
    >>>  f.select('air_temperature', items={'latitude': cf.gt(0)}, rank=cf.ge(3))
    <CF Field: air_temperature(time(12), latitude(73), longitude(96)) K>

Any of the `select` arguments may also be used with `cf.read` to select fields when reading from files:

    >>> f = cf.read('file*.nc', select='air_temperature')
    >>> f = cf.read('file*.nc', select_options={'rank': cf.gt(2)})
    >>> f = cf.read('file*.nc', select='air_temperature', select_options={'rank': cf.gt(2)})

This may be faster than reading all fields and then selecting afterwards.

### Domain item selection

Domain items may be retrieved with a variety of methods, some specific to each item type (such as `cf.Field.dim`) and some more generic (such as `cf.Field.coords` and `cf.Field.item`):

Item | Field retrieval methods
--- | ---
Dimension coordinate object | `dim`, `dims`, `coord`, `coords` `item`, `items`
Auxiliary coordinate object | `aux`, `auxs`, `coord`, `coords` `item`, `items`
Cell measure object | `measure`, `measures`, `item`, `items`
Coordinate reference object | `ref`, `refs`, `item`, `items`

In each case the singular method form (such as `aux`) returns an actual domain item whereas the plural method form (such as `auxs`) returns a dictionary whose keys are the domain item identifiers with corresponding values of the items themselves.

For example, to retrieve a unique dimension coordinate object with a standard name of “time”:

    >>> f.dim('time')
    <CF DimensionCoordinate: time(12) noleap>

To retrieve all coordinate objects and their domain identifiers:

    >>> f.coords()
    {'dim0': <CF DimensionCoordinate: time(12) noleap>,
     'dim1': <CF DimensionCoordinate: latitude(64) degrees_north>,
     'dim2': <CF DimensionCoordinate: longitude(128) degrees_east>,
     'dim3': <CF DimensionCoordinate: height(1) m>}

To retrieve all domain items and their domain identifiers:

    >>> f.items()
    {'dim0': <CF DimensionCoordinate: time(12) noleap>,
     'dim1': <CF DimensionCoordinate: latitude(64) degrees_north>,
     'dim2': <CF DimensionCoordinate: longitude(128) degrees_east>,
     'dim3': <CF DimensionCoordinate: height(1) m>}

In this example, all of the items happen to be coordinates.

## Aggregation

Fields are aggregated into as few multidimensional fields as possible with the `cf.aggregate` function, which implements the CF aggregation rules.

    >>> f
    [<CF Field: air_temperature(time(12), latitude(73), longitude(96)) K>,
     <CF Field: air_temperature(latitude(73), longitude(96)) K @ 273.15>]
    >>> print f
    Field: air_temperature (ncvar%temp)
    -----------------------------------
    Data           : air_temperature(time(12), latitude(73), longitude(96)) K
    Cell methods   : time: mean
    AXes           : 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
    Field: air_temperature (ncvar%temperature)
    ------------------------------------------
    Data           : air_temperature(latitude(73), longitude(96)) K @ 273.15
    Cell methods   : time: mean
    Axes           : time(12) = [1859-12-16 12:00:00]
                   : longitude(96) = [356.25, ..., 0] degrees_east
                   : latitude(73) = [-90, ..., 90] degrees_north
                   : height(1) = [2] m
    ...
    >>> g = cf.aggregate(f)
    >>> g
    [<CF Field: air_temperature(time(13), latitude(73), longitude(96)) K>]
    >>> print g
    Field: air_temperature (ncvar%temperature)
    ------------------------------------------
    Data           : air_temperature(time(13), latitude(73), longitude(96)) K
    Cell methods   : time: mean
    Axes           : time(13) = [1859-12-16 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

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

## Arithmetic and comparison

Arithmetic, bitwise and comparison operations are defined on a field as element-wise operations on its data array which yield a new `cf.Field` object or, for augmented assignments, modify the field’s data array in-place.

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 axis order, but will not allow fields with 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.

### Broadcasting

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:

- The fields have matching units.
- Axes are aligned according to their coordinates’ metadata to ensure that matching axes are broadcast against each other.
- Common axes have matching axis directions.

This restructuring of the field ensures that the matching axes are broadcast against each other.

Broadcasting is done without making needless copies of data and so is usually very efficient.

### Valid operands

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
`cf.Data` with size 1 | The field’s data array is combined with the `cf.Data` object’s scalar value, taking into account: Different but equivalent units
`cf.Field` | The two field’s must satisfy the field combination rules. The fields’ data arrays and domains are combined taking into account: Axis identities Array units Axis orders Axis directions Missing data values

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.

### Resulting metadata

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 the axes of 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.

### Floating point errors

It is possible to set the action to take when an arithmetic operation produces one of the following floating-point errors:

Error | Description
--- | ---
Division by zero | Infinite result obtained from finite numbers.
Overflow | Result too large to be expressed.
Invalid operation | Result is not an expressible number, typically indicates that a NaN was produced.
Underflow | Result so close to zero that some precision was lost.

For each type of error, one of the following actions may be chosen:

- Take no action. Allows invalid values to occur in the result data array.
- Print a `RuntimeWarning` (via the Python `warnings` module). Allows invalid values to occur in the result data array.
- Raise a `FloatingPointError` exception.

The treatment of floating-point errors is set with `cf.Data.seterr`. Converting invalid numbers to masked values after an arithmetic operation may be done with the `cf.Field.mask_invalid` method. It is also possible to mask invalid numbers during arithmetic operations (see `cf.Data.mask_fpe`).

Note that these setting apply to all data array arithmetic within the `cf` package.

### Operations on field components

Operating on a field component works in much the same was as operating on the field itself:

    >>> a = f.field_anc('air_temperature standard_error')
    >>> a.data
    <CF Data: [[[1.2, ..., 5.6]]] K>
    >>> a += 2
    >>> a.data
    <CF Data: [[[3.2, ..., 7.6]]] K>

If the component has bounds, however, the bounds are operated on with the same operand as for the variable’s data array:

    >>> x = f.coord('X')
    >>> x.dump()
    Dimension Coordinate: longitude
        standard_name = 'longitude'
        Data(128) = [0.0, ..., 357.1875] degrees_east
        Bounds(128, 2) = [[-1.40625, ..., 358.59375]] degrees_east
    >>> (x + 2).dump()
    Dimension Coordinate: longitude
        standard_name = 'longitude'
        Data(128) = [2.0, ..., 359.1875] degrees_east
        Bounds(128, 2) = [[0.59375, ..., 360.59375]] degrees_east
    >>> (x + x).dump()
    Dimension Coordinate: longitude
        axis = 'X'
        long_name = 'longitude'
        standard_name = 'longitude'
        Data(128) = [0.0, ..., 714.375] degrees_east
        Bounds(128, 2) = [[-1.40625, ..., 715.78125]] degrees_east

This means that cells do not change size when undergoing simple relocation. For example, of a coordinate of 0.5 with cell bounds of [-1, 1] has 2 added to it, the the coordinate becomes 2.5 with cell bounds [1, 3].

## Statistical operations

Axes of a field may be collapsed by statistical methods with the `cf.Field.collapse` method. Collapsing an axis involves reducing its size with a given (typically statistical) method.

By default all axes with size greater than 1 are collapsed completely with the given method. For example, to find the minumum of the data array:

    >>> g = f.collapse('min')

By default the calculations of means, standard deviations and variances use a combination of volume, area and linear weights based on the field’s metadata. For example to find the mean of the data array, weighted where possible:

    >>> g = f.collapse('mean')

Specific weights may be forced with the weights parameter. For example to find the variance of the data array, weighting the X and Y axes by cell area, the T axis linearly and leaving all other axes unweighted:

    >>> g = f.collapse('variance', weights=['area', 'T'])

A subset of the axes may be collapsed. For example, to find the mean over the time axis:

    >>> f
    <CF Field: air_temperature(time(12), latitude(73), longitude(96) K>
    >>> g = f.collapse('T: mean')
    >>> g
    <CF Field: air_temperature(time(1), latitude(73), longitude(96) K>

For example, to find the maximum over the time and height axes:

    >>> g = f.collapse('T: Z: max')

or, equivalently:

    >>> g = f.collapse('max', axes=['T', 'Z'])

An ordered sequence of collapses over different (or the same) subsets of the axes may be specified. For example, to first find the mean over the time axis and subequently the standard deviation over the latitude and longitude axes:

    >>> g = f.collapse('T: mean area: sd')

or, equivalently, in two steps:

    >>> g = f.collapse('mean', axes='T').collapse('sd', axes='area')

Grouped collapses are possible, whereby groups of elements along an axis are defined and each group is collapsed independently. The collapsed groups are concatenated so that the collapsed axis in the output field has a size equal to the number of groups. For example, to find the variance along the longitude axis within each group of size 10 degrees:

    >>> g = f.collapse('longitude: variance', group=cf.Data(10, 'degrees'))

Climatological statistics (a type of grouped collapse) as defined by the CF conventions may be specified. For example, to collapse a time axis into multiannual means of calendar monthly minima:

    >>> g = f.collapse('time: minimum within years T: mean over years',
    ...                 within_years=cf.M())

In all collapses, missing data array elements are accounted for in the calculation.

The following collapse methods are available, over any subset of the axes:

Method | Notes
--- | ---
Maximum | The maximum of the values.
Minimum | The minimum of the values.
Sum | The sum of the values.
Mid-range | The average of the maximum and the minimum of the values.
Range | The absolute difference between the maximum and the minimum of the values.
Mean | The unweighted mean, \(m\), of \(N\) values \(x_i\) is \[m=\frac{1}{N}\sum_{i=1}^{N} x_i\] The weighted mean, \(\tilde{m}\), of \(N\) values \(x_i\) with corresponding weights \(w_i\) is \[\tilde{m}=\frac{1}{\sum_{i=1}^{N} w_i} \sum_{i=1}^{N} w_i x_i\]
Standard deviation | The unweighted standard deviation, \(s\), of \(N\) values \(x_i\) with mean \(m\) and with \(N-ddof\) degrees of freedom (\(ddof\ge0\)) is \[s=\sqrt{\frac{1}{N-ddof} \sum_{i=1}^{N} (x_i - m)^2}\] The weighted standard deviation, \(\tilde{s}_N\), of \(N\) values \(x_i\) with corresponding weights \(w_i\), weighted mean \(\tilde{m}\) and with \(N\) degrees of freedom is \[\tilde{s}_N=\sqrt{\frac{1} {\sum_{i=1}^{N} w_i} \sum_{i=1}^{N} w_i(x_i - \tilde{m})^2}\] The weighted standard deviation, \(\tilde{s}\), of \(N\) values \(x_i\) with corresponding weights \(w_i\) and with \(N-ddof\) degrees of freedom \((ddof>0)\) is \[\tilde{s}=\sqrt{ \frac{a \sum_{i=1}^{N} w_i}{a \sum_{i=1}^{N} w_i - ddof}} \tilde{s}_N\] where \(a\) is the smallest positive number whose product with each weight is an integer. \(a \sum_{i=1}^{N} w_i\) is the size of a new sample created by each \(x_i\) having \(aw_i\) repeats. In practice, \(a\) may not exist or may be difficult to calculate, so \(a\) is either set to a predetermined value or an approximate value is calculated (see `cf.Field.collapse` for details).
Variance | The variance is the square of the standard deviation.
Sample size | The sample size, \(N\), as would be used for other statistical calculations.
Sum of weights | The sum of sample weights, \(\sum_{i=1}^{N} w_i\), as would be used for other statistical calculations.
Sum of squares of weights | The sum of squares of sample weights, \(\sum_{i=1}^{N} {w_i}^{2}\), as would be used for other statistical calculations.

Any collapse method that involves a calculation (such as calculating a mean), as opposed to just selecting a value (such as finding a maximum), will return a field containing double precision floating point numbers or, if all of the input data are integers, double precision integers. If this is not desired, then the datatype can be reset after the collapse:

    >>> g = f.collapse('T: mean')
    >>> g.dtype = f.dtype
    >>> h = f.collapse('area: variance')
    >>> h.dtype = 'float32'

See `cf.Field.collapse` for more details.

## Regridding operations

A field may be regridded onto a new latitude-longitude grid:

    >>> f
    <CF Field: air_temperature(time(12), latitude(73), longitude(96) K>
    >>> g
    <CF Field: precipitation(time(24), longitude(128), latitude(64)) kg m-2 s-1>
    >>> h = f.regrids(g)
    >>> h
    <CF Field: air_temperature(time(12), longitude(128), latitude(64) K>

By default the interpolation is first-order conservative, but bilinear interpolation is also possible. The missing data masks of the field and the new grid are aslo taken into account.

See `cf.Field.regrids` for more details.

## Units

A field (as well as any other object which inherits from `cf.Variable`) always contains a `cf.Units` object which gives the physical units of the values contained in its data array.

The `cf.Units` object is stored in the field’s `Units` attribute but may also be accessed through the field’s `units` and `calendar` CF properties, which may take any value allowed by the CF conventions. In particular, the value of the `units` CF property is a string that can be recognized by UNIDATA’s Udunits-2 package, with a few exceptions for greater consistency with CF. These are detailed by the `cf.Units` object.

### Assignment

The Field’s units may be assigned directly to its `cf.Units` object:

    >>> f.Units.units = 'days since 1-1-1'
    >>> f.Units.calendar = 'noleap'

    >>> f.Units = cf.Units('metre')

But the same result is achieved by assigning to the field’s `units` and `calendar` CF properties:

    >>> f.units = 'days since 1-1-1'
    >>> f.calendar = 'noleap'
    >>> f.Units
    <CF Units: days since 1-1-1 calendar=noleap>
    >>> f.units
    'days since 1-1-1'
    >>> f.calendar
    'noleap'

### Time units

Time units may be given as durations of time or as an amount of time since a reference time:

    >>> f.units = 'day'
    >>> f.units = 'seconds since 1992-10-8 15:15:42.5 -6:00'

Note

It is recommended that the units `'year'` and `'month'` be used with caution, as explained in the following excerpt from the CF conventions: “The Udunits package defines a year to be exactly 365.242198781 days (the interval between 2 successive passages of the sun through vernal equinox). It is not a calendar year. Udunits includes the following definitions for years: a common_year is 365 days, a leap_year is 366 days, a Julian_year is 365.25 days, and a Gregorian_year is 365.2425 days. For similar reasons the unit `'month'`, which is defined to be exactly year/12, should also be used with caution.”

The date given in reference time units is always associated with one of the calendars recognized by the CF conventions and may be set with the calendar CF property (on the field or Units object).

If the calendar is not set then, as in the CF conventions, for the purposes of calculation and comparison, it defaults to the mixed Gregorian/Julian calendar as defined by Udunits:

    >>> f.units = 'days since 2000-1-1'
    >>> f.calendar
    AttributeError: Can't get 'Field' attribute 'calendar'
    >>> g.units = 'days since 2000-1-1'
    >>> g.calendar = 'gregorian'
    >>> g.Units.equals(f.Units)
    True

The calendar is ignored for units other than reference time units.

### Changing units

Changing units to equivalent units causes the variable’s data array values to be modified in place (if required) when they are next accessed, and not before:

    >>> f.units
    'metre'
    >>> f.array
    array([    0.,  1000.,  2000.,  3000.,  4000.])
    >>> f.units = 'kilometre'
    >>> f.units
    'kilometre'
    >>> f.array
    array([ 0.,  1.,  2.,  3.,  4.])

    >>> f.units
    'hours since 2000-1-1'
    >>> f.array
    array([-1227192., -1227168., -1227144.])
    >>> f.units = 'days since 1860-1-1'
    >>> f.array
    array([ 1.,  2.,  3.])

The `cf.Units` object may be operated on with augmented arithmetic assignments and binary arithmetic operations:

    >>> f.units
    'kelvin'
    >>> f.array
    array([ 273.15,  274.15,  275.15,  276.15,  277.15])

    >>> f.Units -= 273.15
    >>> f.units
    'K @ 273.15'
    >>> f.array
    array([ 0.,  1.,  2.,  3.,  4.])

    >>> f.Units = f.Units + 273.15
    >>> f.units
    'K'
    >>> f.array
    array([ 273.15,  274.15,  275.15,  276.15,  277.15])

    >>> f.units = 'K @ 237.15'
    'K @ 273.15'
    >>> f.array
    array([ 0.,  1.,  2.,  3.,  4.])

If the field has a data array and its units are changed to non-equivalent units then a `TypeError` will be raised when the data are next accessed:

    >>> f.units
    'm s-1'
    >>> f.units = 'K'
    >>> f.array
    TypeError: Units are not convertible: <CF Units: m s-1>, <CF Units: K>

### Overriding units

If the units are incorrect, either due to a data manipulation or an incorrect encoding, it is possible to replace the existing units with new units, which don’t have to be equivalent, without altering the data values:

    >>> f.units
    'mm/day'
    >>> f.mean()
    <CF Data: 3.3455467 mm/day>
    >>> g = f.override_units('kg m-2 s-1')
    >>> g.mean()
    <CF Data: 3.3455467 kg m-2 s-1>
    >>> g.override_units('watts m-2', i=True)
    >>> g.mean()
    <CF Data: 3.3455467 watts m-2>

Overriding the calendar of reference time units is done in a similar manner:

    >>> f.calendar
    '360_day'
    >>> f.array.min()
    59.0
    >>> f.min()
    <CF Data: 1960-02-30 00:00:00 360_day>
    >>> g = f.override_calandar('gregorian')
    >>> g.array.min()
    59.0
    >>> g.min()
    <CF Data: 1960-02-29 00:00:00 gregorian>

Note that in this case the data values have remained unchanged, but their date-time interpretation has been redefined.

See `cf.Field.override_units` and `cf.Field.override_calendar` for details.

### Equality and equivalence of units

The `cf.Units` object has methods for assessing whether two units are equivalent or equal, regardless of their exact string representations.

Two units are equivalent if and only if numeric values in one unit are convertible to numeric values in the other unit (such as `'kilometres'` and `'metres'`). Two units are equal if and only if they are equivalent and their conversion is a scale factor of 1 (such as `'kilometres'` and `'1000 metres'`). Note that equivalence and equality are based on internally stored binary representations of the units, rather than their string representations.

    >>> f.units = 'm/s'

    >>> g.units = 'm s-1'
    >>> f.Units == g.Units
    True
    >>> f.Units.equals(g.Units)
    True

    >>> g.units = 'km s-1'
    >>> f.Units.equivalent(g.Units)
    False

    >>> f.units = 'days since 1987-12-3'
    >>> g.units = 'hours since 2000-12-1'
    >>> f.Units == g.Units
    False
    >>> f.Units.equivalent(g.Units)
    True

### Bounds units

The units of variables with cell bounds (i.e. coordinates and domain ancillaries) are always the same as the coordinate itself, and the units of the bounds automatically change when a variable’s units are changed:

    >>> c.units
    'degrees'
    >>> c.bounds.units
    'degrees'
    >>> print c.bounds.array
    [  0.  90.]
    >>> c.units = 'radians'
    >>> c.bounds.units
    'radians'
    >>> print c.bounds.array
    [ 0.  1.57079633]

## Manipulating other variables

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.AuxiliaryCoordinate` | A CF auxiliary coordinate construct.
`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` | Base class for storing a coordinate.
`cf.DimensionCoordinate` | A CF dimension coordinate construct.
`cf.Variable` | Base class for storing a data array with metadata.

In general, different axis identities, different axis orders and different axis directions are not considered, since these objects do not contain a coordinate system required to define these properties (unlike a field).

### Coordinates

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 Bounds: (73, 96, 4)>
    >>> d = c[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.