Allow grouping noisy arrays using tolerances

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Assessment

Difficulty
4/5
Estimated time
3-5 days
Newbie friendliness
35/100
Issue type
Feature
Clarity
Mostly clear
Activity status
Stale
Tech stack
numpy, python
Domain
data-engineering

Research direction

Start by locating the array groupby API and its grouping implementation. Compare the proposed groupby_isclose_argsort example with current grouping behavior, including the noted dask limitation. Done means tolerance parameters such as atol and rtol are supported through the groupby API and produce the intended groups for noisy arrays.

Written by the indexing model from the issue text.

Description

documentation

I find grouping data can be a little more intuitive when using tolerances.
This can be done for example like this:

def groupby_isclose_argsort(arr, atol=0, rtol=0.1):
    """
    Return a group idx of a noisy array.

    TODO: argsort not available in dask.

    Examples
    --------
    reps = 2
    y = np.array([72, 72, 100, 100, 300, 300, 500, 500])
    y = np.stack(reps*[y], 0)
    noise = lambda y : 1 + 0.1 * (np.random.rand(*y.shape) - 0.5)
    y = y * noise(y)
    groupby_isclose_argsort(y)
    array([[0, 0, 1, 1, 2, 2, 3, 3],
           [0, 0, 1, 1, 2, 2, 3, 3]], dtype=int32)
    """
    # Sort values to make sure values are monotonically increasing:
    a = arr.ravel()
    i = np.argsort(a)
    i_rev = np.empty(i.shape, dtype=np.intp, like=a)
    i_rev[i] = np.arange(len(a), like=a)
    a = a[i]

    # Calculate a monotonically increasing index that increase when the
    # difference between current and previous value changes:
    b = np.roll(a, 1)
    b[0] = a[0]
    by = np.cumsum(~np.isclose(a, b, atol=atol, rtol=rtol))
    # tolerance = atol + rtol * b
    # by = np.cumsum(np.abs(a - b) > tolerance)

    return by[i_rev].reshape(arr.shape)

So on a dataset the api would look something like this ds.groupby("arr", atol=0, rtol=0.1).

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