How can I identify consecutive regions of empty intervals using NumPy?

Below is one approach using NumPy and a short Python loop to group consecutive empty intervals (i.e. intervals where

  start == (end_excl - 1)

) that share the same start and end indices:

PYTHONCopied
import numpy as np

# Input arrays
interval_start_idxs    = np.array([0, 3, 3, 3, 6, 7])
interval_end_excl_idxs = np.array([2, 4, 4, 4, 7, 9])

# Boolean mask for empty intervals
empty_mask = (interval_start_idxs == interval_end_excl_idxs - 1)
empty_idxs = np.nonzero(empty_mask)[0]  # indices in the original arrays that are empty

# Group consecutive empty indices if they share the same interval boundaries
empty_interval_starts = []      # will store the starting index (inclusive) of each group
empty_intervals_ends_excl = []  # will store the ending index (excluded) of each group

if empty_idxs.size > 0:
    # Initialize first group
    group_start = empty_idxs[0]
    group_end = empty_idxs[0]
    
    for idx in empty_idxs[1:]:
        # Check if this empty interval has the same start/end values as the previous one
        same_boundary = (interval_start_idxs[idx] == interval_start_idxs[group_end] and
                         interval_end_excl_idxs[idx] == interval_end_excl_idxs[group_end])
        # Check if idx is consecutive (optional, as intervals come sorted)
        if same_boundary and idx == group_end + 1:
            # same group
            group_end = idx
        else:
            # finish current group and start a new group
            empty_interval_starts.append(group_start)
            empty_intervals_ends_excl.append(group_end + 1)  # region is defined as [start, group_end+1)
            group_start = idx
            group_end = idx

    # Append final group
    empty_interval_starts.append(group_start)
    empty_intervals_ends_excl.append(group_end + 1)

print("empty_interval_starts     =", empty_interval_starts)
print("empty_intervals_ends_excl =", empty_intervals_ends_excl)

Explanation

1. We first compute a Boolean mask empty_mask that flags the intervals which are empty (i.e. where
     interval_start_idxs[i] == interval_end_excl_idxs[i] - 1).

2. We then get the indices of empty intervals with np.nonzero(empty_mask)[0].

3. We iterate through these indices. For each index, we check two things:

   • If it has the same start and end as the current group.
   • If it is immediately consecutive (i.e., the index equals the previous index + 1).

   If both hold true, we extend the current group; otherwise, we finish the current group and start a new one.

4. Finally, we print out the start indices of each region and the end (excluded) indices of these regions. For the given example, the expected output is:

   empty_interval_starts = [1, 4]
   empty_intervals_ends_excl = [4, 5]

This way you identify regions of empty intervals correctly based on your criteria.