Fix bugs in IntervalIndex.is_non_overlapping_monotonic
State: closed

- [X] closes #17237
- [X] closes #16560
- [X] tests added / passed
- [X] passes `git diff upstream/master -u -- "*.py" | flake8 --diff`
- [X] whatsnew entry

I had to modify one of the existing tests, which used an `IntervalIndex` that was overlapping at endpoints but was assumed to be non-overlapping.  The test failed due to an intermediate check against `is_non_overlapping_monotonic`, which is now fixed and properly returns that the index in question is in fact overlapping.  The test was modified to use an index which is similar with `closed='both'` but non-overlapping.

Note that #16588 also fixes #16560, but the PR appears to have gone stale, as there hasn't been an update in over two months.  Both #17237 and #16560 involve making changes to the same block of code, so it seemed easiest to fix both simultaneously.  

Labels:
name: Bug
name: Interval
description: Interval data type

Comments:
# [Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/17238?src=pr&el=h1) Report
> Merging [#17238](https://codecov.io/gh/pandas-dev/pandas/pull/17238?src=pr&el=desc) into [master](https://codecov.io/gh/pandas-dev/pandas/commit/133a2087d038da035a57ab90aad557a328b3d60b?src=pr&el=desc) will **decrease** coverage by `0.01%`.
> The diff coverage is `100%`.

[![Impacted file tree graph](https://codecov.io/gh/pandas-dev/pandas/pull/17238/graphs/tree.svg?height=150&token=eZ4WkYLtcO&width=650&src=pr)](https://codecov.io/gh/pandas-dev/pandas/pull/17238?src=pr&el=tree)

```diff
@@            Coverage Diff             @@
##           master   #17238      +/-   ##
==========================================
- Coverage   91.01%   90.99%   -0.02%     
==========================================
  Files         162      162              
  Lines       49535    49537       +2     
==========================================
- Hits        45082    45075       -7     
- Misses       4453     4462       +9
```

| Flag | Coverage Δ | |
|---|---|---|
| #multiple | `88.77% <100%> (ø)` | :arrow_up: |
| #single | `40.25% <0%> (-0.07%)` | :arrow_down: |

| [Impacted Files](https://codecov.io/gh/pandas-dev/pandas/pull/17238?src=pr&el=tree) | Coverage Δ | |
|---|---|---|
| [pandas/core/indexes/interval.py](https://codecov.io/gh/pandas-dev/pandas/pull/17238?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvaW5kZXhlcy9pbnRlcnZhbC5weQ==) | `92.61% <100%> (+0.02%)` | :arrow_up: |
| [pandas/io/gbq.py](https://codecov.io/gh/pandas-dev/pandas/pull/17238?src=pr&el=tree#diff-cGFuZGFzL2lvL2dicS5weQ==) | `25% <0%> (-58.34%)` | :arrow_down: |
| [pandas/core/frame.py](https://codecov.io/gh/pandas-dev/pandas/pull/17238?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvZnJhbWUucHk=) | `97.72% <0%> (-0.1%)` | :arrow_down: |

------

[Continue to review full report at Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/17238?src=pr&el=continue).
> **Legend** - [Click here to learn more](https://docs.codecov.io/docs/codecov-delta)
> `Δ = absolute <relative> (impact)`, `ø = not affected`, `? = missing data`
> Powered by [Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/17238?src=pr&el=footer). Last update [133a208...d7fb080](https://codecov.io/gh/pandas-dev/pandas/pull/17238?src=pr&el=lastupdated). Read the [comment docs](https://docs.codecov.io/docs/pull-request-comments).

thanks @jschendel