Should the (field) equality operation be noncommutative? #133
Description
There are cases where a.equals(b) evaluates differently to b.equals(a), at least with a and b being fields as I recently noticed during the work towards append mode (#69), namely for cases where the fields in question are the same except for one having a component missing. In other words, our equals method appears to not be commutative/symmetric for certain operands.
See below for details of the particular case which I observed to give different results (confirmed on the master) depending on the order of fields as class upon which the method acts or the parameter.
This raises some questions for me, because I found the difference in output of a * b and b * a confusing given equality in a logical sense should, to me (e.g. it's certainly the case in a mathematical sense), imply commutative behaviour. The relevant parts of the documentation did not seem to provide any information or clues as to whether the equality method should be symmetric or not, but I thought:
Equality is strict by default.
suggests it should, though perhaps (my emphasis):
Any type of object may be tested but, in general, equality is only possible with another object of the same type, or a subclass of one
could be relevant?
My questions are:
- Is a difference in result for
a.equals(b)andb.equals(a)something that should be possible, particularly in cases such as that outlined below, or is it a bug we should fix? - In either case, I think we should add a few lines to the documentation to explicitly outline whether these cases are possible and for what inputs and what constructs the
equalsmethod is bound to, so there is no ambiguity. - If it is a bug and we ensure symmetrical behaviour, could we and should we make it configurable so a field and another that is the same but reduced can be treated as equal if users desire in some context, e.g. with a kwarg called something like
accept_subset?
Example case
Note this example with one field a and a field b that is the same but missing a time dimension coordinate:
...
>>> a.dump()
------------------------------------------------------------------
Field: air_potential_temperature (ncvar%air_potential_temperature)
------------------------------------------------------------------
Conventions = 'CF-1.8'
standard_name = 'air_potential_temperature'
units = 'K'
Data(time(36), latitude(5), longitude(8)) = [[[210.7, ..., 286.6]]] K
Cell Method: area: mean
Domain Axis: air_pressure(1)
Domain Axis: latitude(5)
Domain Axis: longitude(8)
Domain Axis: time(36)
Dimension coordinate: time
standard_name = 'time'
units = 'days since 1959-01-01'
Data(time(36)) = [1959-12-16 12:00:00, ..., 1962-11-16 00:00:00]
Bounds:Data(time(36), 2) = [[1959-12-01 00:00:00, ..., 1962-12-01 00:00:00]]
Dimension coordinate: latitude
standard_name = 'latitude'
units = 'degrees_north'
Data(latitude(5)) = [-75.0, ..., 75.0] degrees_north
Bounds:Data(latitude(5), 2) = [[-90.0, ..., 90.0]] degrees_north
Dimension coordinate: longitude
standard_name = 'longitude'
units = 'degrees_east'
Data(longitude(8)) = [22.5, ..., 337.5] degrees_east
Bounds:Data(longitude(8), 2) = [[0.0, ..., 360.0]] degrees_east
Dimension coordinate: air_pressure
standard_name = 'air_pressure'
units = 'hPa'
Data(air_pressure(1)) = [850.0] hPa
>>> b.dump()
--------------------------------------------------------------------
Field: air_potential_temperature (ncvar%air_potential_temperature_1)
--------------------------------------------------------------------
Conventions = 'CF-1.8'
standard_name = 'air_potential_temperature'
units = 'K'
Data(ncdim%time_1(36), latitude(5), longitude(8)) = [[[210.7, ..., 286.6]]] K
Cell Method: area: mean
Domain Axis: air_pressure(1)
Domain Axis: latitude(5)
Domain Axis: longitude(8)
Domain Axis: ncdim%time_1(36)
Dimension coordinate: latitude
standard_name = 'latitude'
units = 'degrees_north'
Data(latitude(5)) = [-75.0, ..., 75.0] degrees_north
Bounds:Data(latitude(5), 2) = [[-90.0, ..., 90.0]] degrees_north
Dimension coordinate: longitude
standard_name = 'longitude'
units = 'degrees_east'
Data(longitude(8)) = [22.5, ..., 337.5] degrees_east
Bounds:Data(longitude(8), 2) = [[0.0, ..., 360.0]] degrees_east
Dimension coordinate: air_pressure
standard_name = 'air_pressure'
units = 'hPa'
Data(air_pressure(1)) = [850.0] hPa
>>> a.equals(b)
False
>>> b.equals(a)
True
>>> a.equals(b, verbose=-1)
Constructs: Comparing <DimensionCoordinate: time(36) days since 1959-01-01 >, <DimensionCoordinate: latitude(5) degrees_north>:
Constructs: Can't match constructs spanning axes ['time']
Constructs: Can't match <DimensionCoordinate: time(36) days since 1959-01-01 >
Constructs: Can't match <DimensionCoordinate: time(36) days since 1959-01-01 >
Constructs: Can't match <DimensionCoordinate: time(36) days since 1959-01-01 >
Field: Different metadata constructs
False