issue_comments

I have created a PR for my work-in-progress: pandas-dev/pandas#22043

Do we want to dive straight to that? Or, would it make more sense to first submit some PRs piping the support for a tolerance kwarg through more of the API? Or perhaps we should propose that a "tolerance" attribute should be an optional attribute that methods like get_indexer() and such could always check for? Not being a pandas dev, I am not sure how piecemeal we should approach this.

In addition, we are likely going to have to implement a decent chunk of code ourselves for compatibility's sake, I think.

I am not concerned about the non-commutativeness of the indexer itself. There is no way around that. At some point, you have to choose values, whether it is done by an indexer or done by some particular set operation.

As for the different sizes, that happens when the tolerance is greater than half the smallest delta. I figure a final implementation would enforce such a constraint on the tolerance.

On Fri, Jun 22, 2018 at 5:56 PM, Stephan Hoyer notifications@github.com wrote:

@WeatherGod https://github.com/WeatherGod One problem with your definition of tolerance is that it isn't commutative, even if both indexes have the same tolerance:

a = ImpreciseIndex([0.1, 0.2, 0.3, 0.4]) a.tolerance = 0.1 b = ImpreciseIndex([0.301, 0.401, 0.501, 0.601]) b.tolerance = 0.1print(a.union(b)) # ImpreciseIndex([0.1, 0.2, 0.3, 0.4, 0.501, 0.601], dtype='float64')print(b.union(a)) # ImpreciseIndex([0.1, 0.2, 0.301, 0.401, 0.501, 0.601], dtype='float64')

If you try a little harder, you could even have cases where the result has a different size, e.g.,

a = ImpreciseIndex([1, 2, 3]) a.tolerance = 0.5 b = ImpreciseIndex([1, 1.9, 2.1, 3]) b.tolerance = 0.5print(a.union(b)) # ImpreciseIndex([1.0, 2.0, 3.0], dtype='float64')print(b.union(a)) # ImpreciseIndex([1.0, 1.9, 2.1, 3.0], dtype='float64')

Maybe these aren't really problems in practice, but it's at least a little strange/surprising.

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Actually, I disagree. Pandas's set operations methods are mostly index-based. For union and intersection, they have an optimization that dives down into some c-code when the Indexes are monotonic, but everywhere else, it all works off of results from get_indexer(). I have made a quick toy demo code that seems to work. Note, I didn't know how to properly make a constructor for a subclassed Index, so I added the tolerance attribute after construction just for the purposes of this demo.

``` python from future import print_function import warnings from pandas import Index import numpy as np

from pandas.indexes.base import is_object_dtype, algos, is_dtype_equal from pandas.indexes.base import _ensure_index, _concat, _values_from_object, _unsortable_types from pandas.indexes.numeric import Float64Index

def _choose_tolerance(this, that, tolerance): if tolerance is None: tolerance = max(this.tolerance, getattr(that, 'tolerance', 0.0)) return tolerance

class ImpreciseIndex(Float64Index): def astype(self, dtype, copy=True): return ImpreciseIndex(self.values.astype(dtype=dtype, copy=copy), name=self.name, dtype=dtype)

@property
def tolerance(self):
    return self._tolerance

@tolerance.setter
def tolerance(self, tolerance):
    self._tolerance = self._convert_tolerance(tolerance)

def union(self, other, tolerance=None):
    self._assert_can_do_setop(other)
    other = _ensure_index(other)

    if len(other) == 0 or self.equals(other, tolerance=tolerance):
        return self._get_consensus_name(other)

    if len(self) == 0:
        return other._get_consensus_name(self)

    if not is_dtype_equal(self.dtype, other.dtype):
        this = self.astype('O')
        other = other.astype('O')
        return this.union(other, tolerance=tolerance)

    tolerance = _choose_tolerance(self, other, tolerance)

    indexer = self.get_indexer(other, tolerance=tolerance)
    indexer, = (indexer == -1).nonzero()

    if len(indexer) > 0:
        other_diff = algos.take_nd(other._values, indexer,
                                   allow_fill=False)
        result = _concat._concat_compat((self._values, other_diff))

        try:
            self._values[0] < other_diff[0]
        except TypeError as e:
            warnings.warn("%s, sort order is undefined for "
                          "incomparable objects" % e, RuntimeWarning,
                          stacklevel=3)
        else:
            types = frozenset((self.inferred_type,
                               other.inferred_type))
            if not types & _unsortable_types:
                result.sort()
   else:
        result = self._values

        try:
            result = np.sort(result)
        except TypeError as e:
            warnings.warn("%s, sort order is undefined for "
                          "incomparable objects" % e, RuntimeWarning,
                          stacklevel=3)

    # for subclasses
    return self._wrap_union_result(other, result)


def equals(self, other, tolerance=None):
    if self.is_(other):
        return True

    if not isinstance(other, Index):
        return False

    if is_object_dtype(self) and not is_object_dtype(other):
        # if other is not object, use other's logic for coercion
        if isinstance(other, ImpreciseIndex):
            return other.equals(self, tolerance=tolerance)
        else:
            return other.equals(self)

    if len(self) != len(other):
        return False

    tolerance = _choose_tolerance(self, other, tolerance)
    diff = np.abs(_values_from_object(self) -
                  _values_from_object(other))
    return np.all(diff < tolerance)

def intersection(self, other, tolerance=None):
    self._assert_can_do_setop(other)
    other = _ensure_index(other)

    if self.equals(other, tolerance=tolerance):
        return self._get_consensus_name(other)

    if not is_dtype_equal(self.dtype, other.dtype):
        this = self.astype('O')
        other = other.astype('O')
        return this.intersection(other, tolerance=tolerance)

    tolerance = _choose_tolerance(self, other, tolerance)
    try:
        indexer = self.get_indexer(other._values, tolerance=tolerance)
        indexer = indexer.take((indexer != -1).nonzero()[0])
    except:
        # duplicates
        # FIXME: get_indexer_non_unique() doesn't take a tolerance argument
        indexer = Index(self._values).get_indexer_non_unique(
            other._values)[0].unique()
        indexer = indexer[indexer != -1]

    taken = self.take(indexer)
    if self.name != other.name:
        taken.name = None
    return taken

# TODO: Do I need to re-implement _get_unique_index()?

def get_loc(self, key, method=None, tolerance=None):
    if tolerance is None:
        tolerance = self.tolerance
    if tolerance > 0 and method is None:
        method = 'nearest'
    return super(ImpreciseIndex, self).get_loc(key, method, tolerance)

def get_indexer(self, target, method=None, limit=None, tolerance=None):
    if tolerance is None:
        tolerance = self.tolerance
    if tolerance > 0 and method is None:
        method = 'nearest'
    return super(ImpreciseIndex, self).get_indexer(target, method, limit, tolerance)

if name == 'main': a = ImpreciseIndex([0.1, 0.2, 0.3, 0.4]) a.tolerance = 0.01 b = ImpreciseIndex([0.301, 0.401, 0.501, 0.601]) b.tolerance = 0.025 print(a, b) print("a | b :", a.union(b)) print("a & b :", a.intersection(b)) print("a.get_indexer(b):", a.get_indexer(b)) print("b.get_indexer(a):", b.get_indexer(a)) ```

Run this and get the following results: ImpreciseIndex([0.1, 0.2, 0.3, 0.4], dtype='float64') ImpreciseIndex([0.301, 0.401, 0.501, 0.601], dtype='float64') a | b : ImpreciseIndex([0.1, 0.2, 0.3, 0.4, 0.501, 0.601], dtype='float64') a & b : ImpreciseIndex([0.3, 0.4], dtype='float64') a.get_indexer(b): [ 2 3 -1 -1] b.get_indexer(a): [-1 -1 0 1]

This is mostly lifted from the Index base class methods, just with me taking out the monotonic optimization path, and supplying the tolerance argument to the respective calls to get_indexer. The choice of tolerance for a given operation is that unless provided as a keyword argument, then use the larger tolerance of the two objects being compared (with a failback if the other isn't an ImpreciseIndex).

Ok, I see how you implemented it for pandas's reindex. You essentially inserted an inexact filter within .get_indexer(). And the intersection() and union() uses these methods, so, in theory, one could pipe a tolerance argument through them (as well as for the other set operations). The work needs to be expanded a bit, though, as get_indexer_non_unique() needs the tolerance parameter, too, I think.

For xarray, though, I think we can work around backwards compatibility by having Dataset hold specialized subclasses of Index for floating-point data types that would have the needed changes to the Index class. We can have this specialized class have some default tolerance (say 100*finfo(dtype).resolution?), and it would have its methods use the stored tolerance by default, so it should be completely transparent to the end-user (hopefully). This way, xr.open_mfdataset() would "just work".

@shoyer, I am thinking your original intuition was right about needing to introduce improve the Index classes to perhaps work with an optional epsilon argument to its constructor. How receptive do you think pandas would be to that? And even if they would accept such a feature, we probably would need to implement it a bit ourselves in situations where older pandas versions are used.

Well, I need this to work for join='outer', so, it is gonna happen one way or another...

One concept I was toying with today was a distinction between aligning coords (which is what it does now) and aligning bounding boxes.

To be clear, my use-case would not be solved by join='override' (isn't that just join='left'?). I have moving nests of coordinates that can have some floating-point noise in them, but are otherwise identical.

I was just pointed to this issue yesterday, and I have an immediate need for this feature in xarray for a work project. I'll take responsibility to implement this feature tomorrow.