Grouping indices of unique elements in numpy

this can be solved via python pandas (python data analysis library) and a DataFrame.groupby call.

Consider the following

 a = np.array([1, 2, 6, 4, 2, 3, 2])

 import pandas as pd
 df = pd.DataFrame({'a':a})

 gg = df.groupby(by=df.a)
 gg.groups

output

 {1: [0], 2: [1, 4, 6], 3: [5], 4: [3], 6: [2]}

This is very similar to what was asked here, so what follows is an adaptation of my answer there. The simplest way to vectorize this is to use sorting. The following code borrows a lot from the implementation of np.unique for the upcoming version 1.9, which includes unique item counting functionality, see here:

>>> a = np.array([1, 2, 6, 4, 2, 3, 2])
>>> sort_idx = np.argsort(a)
>>> a_sorted = a[idx]
>>> unq_first = np.concatenate(([True], a_sorted[1:] != a_sorted[:-1]))
>>> unq_items = a_sorted[unq_first]
>>> unq_count = np.diff(np.nonzero(unq_first)[0])

and now:

>>> unq_items
array([1, 2, 3, 4, 6])
>>> unq_count
array([1, 3, 1, 1, 1], dtype=int64)

To get the positional indices for each values, we simply do:

>>> unq_idx = np.split(sort_idx, np.cumsum(unq_count))
>>> unq_idx
[array([0], dtype=int64), array([1, 4, 6], dtype=int64), array([5], dtype=int64),
 array([3], dtype=int64), array([2], dtype=int64)]

And you can now construct your dictionary zipping unq_items and unq_idx.

Note that unq_count doesn't count the occurrences of the last unique item, because that is not needed to split the index array. If you wanted to have all the values you could do:

>>> unq_count = np.diff(np.concatenate(np.nonzero(unq_first) + ([a.size],)))
>>> unq_idx = np.split(sort_idx, np.cumsum(unq_count[:-1]))

The numpy_indexed package (disclaimer: I am its author) implements a solution inspired by Jaime's; but with tests, a nice interface, and a lot of related functionality:

import numpy_indexed as npi
unique, idx_groups = npi.group_by(a, np.arange(len(a))