BUG: pd.to_datetime(infer_datetime_format=True) drops timezone
- [x] closes #41047
- [x] tests added / passed
- [x] Ensure all linting tests pass, see [here](https://pandas.pydata.org/pandas-docs/dev/development/contributing.html#code-standards) for how to run them
- [x] whatsnew entry

In this PR, I try to fix issue #41047.
I would appreciate it if you could review this PR.

## About the issue
In the UTC format, "Z" is used as a special timezone "+00:00".
But current `pd.to_datetime` function can not recognize the last "Z" when the `infer_datetime_format` is `True`.
Note that `pd.to_datetime` can properly interpret "Z" as "+00:00" when the `infer_datetime_format` is unspecified.

The problem happens in the following codes of datetimes.py:

```py
    if infer_datetime_format and format is None:
        format = _guess_datetime_format_for_array(arg, dayfirst=dayfirst)

    if format is not None:
        # There is a special fast-path for iso8601 formatted
        # datetime strings, so in those cases don't use the inferred
        # format because this path makes process slower in this
        # special case
        format_is_iso8601 = format_is_iso(format)
        if format_is_iso8601:
            require_iso8601 = not infer_datetime_format
            format = None

    if format is not None:
        res = _to_datetime_with_format(
            arg, orig_arg, name, tz, format, exact, errors, infer_datetime_format
        )
        if res is not None:
            return res

```

Here, the `_guess_datetime_format_for_array` returns a format string like '%Y-%m-%d %H:%M:%SZ' depending on the input strings.
The resulting format is estimated by `format_is_iso` function. 
This result is used to judge whether the function specialized for iso format is used or not.
But current `format_is_iso` can not recognize the last "Z" in a format string, so it returns `False` if the format has "Z" regardless the format is valid iso8601 format or not.
Because of this misjudgment, the wrong function (`_to_datetime_with_format`) is used for the iso string, and the timestamp that does not have timezone information is returned.

## About the fix

I fixed the format_is_iso function to recognize the last "Z" in the format string to solve this problem.
@mroeschke  I revised my PR based on the review comments.
Now `format_is_iso` function recognize "%z" and "%Z" format instead of "Z".
To fix the problem, I improved the `guess_datetime_format` to recognize some additional timezone patterns (see below).

ex.
```py
print(pd._libs.tslibs.parsing.guess_datetime_format('2020-05-01T18:04:03UTC'))
print(pd._libs.tslibs.parsing.guess_datetime_format('2020-05-01T18:04:03Z'))
print(pd._libs.tslibs.parsing.guess_datetime_format('2020-05-01T18:04:03+0000'))

# Before the fix
# %Y-%m-%dT%H:%M:%S%Z
# %Y-%m-%dT%H:%M:%SZ
# %Y-%m-%dT%H:%M:%S+%f

# After the fix
# %Y-%m-%dT%H:%M:%S%Z
# %Y-%m-%dT%H:%M:%S%z
# %Y-%m-%dT%H:%M:%S%z
```

In the fix of `guess_datetime_format`, I have tried to make the fix to be simple but there may be some tricky parts.
If you have any suggestions on how to implement it better, I would appreciate your advice.
 @mroeschke  Now the `guess_datetime_format` can parse “+hh:mm” type timezone offset.
For consistency, I added some patterns that may not be commonly used to make the function recognize timezone formats that can be parsed correctly by the default parser.
The following examples demonstrate parser results and inferred formats.

```py
import pandas as pd
from dateutil.parser import parse as du_parse

def try_parse(dt_str):
    try:
        print(f"{dt_str:<26}", "->", du_parse(dt_str), "->", pd._libs.tslibs.parsing.guess_datetime_format(dt_str))
    except Exception as e:
        print(type(e), e)
        print("->", pd._libs.tslibs.parsing.guess_datetime_format(dt_str))

try_parse("2011-12-30T00:00:00+9")
try_parse("2011-12-30T00:00:00+09")
try_parse("2011-12-30T00:00:00+0905")
try_parse("2011-12-30T00:00:00+9:5")
try_parse("2011-12-30T00:00:00+09:05")
try_parse("2011-12-30T00:00:00+9:005")
try_parse("2011-12-30T00:00:00+009:00")
try_parse("2011-12-30T00:00:00+090")
try_parse("2011-12-30T00:00:00+09:")

# Outputs:
#
# 2011-12-30T00:00:00+9      -> 2011-12-30 00:00:00+09:00 -> %Y-%m-%dT%H:%M:%S%z
# 2011-12-30T00:00:00+09     -> 2011-12-30 00:00:00+09:00 -> %Y-%m-%dT%H:%M:%S%z
# 2011-12-30T00:00:00+0905   -> 2011-12-30 00:00:00+09:05 -> %Y-%m-%dT%H:%M:%S%z
# 2011-12-30T00:00:00+9:5    -> 2011-12-30 00:00:00+09:05 -> %Y-%m-%dT%H:%M:%S%z
# 2011-12-30T00:00:00+09:05  -> 2011-12-30 00:00:00+09:05 -> %Y-%m-%dT%H:%M:%S%z
# 2011-12-30T00:00:00+9:005  -> 2011-12-30 00:00:00+09:05 -> %Y-%m-%dT%H:%M:%S%z
# 2011-12-30T00:00:00+009:00 -> 2011-12-30 00:00:00+09:00 -> %Y-%m-%dT%H:%M:%S%z
# <class 'dateutil.parser._parser.ParserError'> Unknown string format: 2011-12-30T00:00:00+090
# -> None
# <class 'dateutil.parser._parser.ParserError'> Unknown string format: 2011-12-30T00:00:00+09:
# -> None
```

I would appreciate it if you could review this. @mroeschke Thank you for your advice. I revised the PR. Any comments are welcome.
 @mroeschke @jreback  Thank you for your reviews.

> i appreciate that we have a bug, but this is WAY more complicated than before. can you simplify this at all

@jreback As you say, the current fix is complex rather than what I thought first.

Now I have no idea to simplify the fix of the "guess_datetime_format" without any downgrade of the functionality.

But the fix might be overkill for the original bug.
I think that the minimal fix for the function for this bug is returning `None` for the timezone offset.

Ex.

```py
    if parsed_datetime.tzinfo is not None:
        if (
            (len(tokens) > 0 and tokens[-1] == "Z")
            or (len(tokens) > 1 and tokens[-2] in ("+", "-"))
        ):
            return None
```


The only user of the `guess_datetime_format` is the `to_datetime` function. 
In the `to_datetime` function, if the `guess_datetime_format` correctly fails to parse and returns None, the input string is passed to the `object_to_datetime64ns` function. And then, the `object_to_datetime64ns` function can parse timezone.

Bugs will happen when the `guess_datetime_format` incorrectly parses and returns the wrong format.
So the strategy of returning None when the input has a timezone offset also works.

(In the above code, I excluded the condition `or (len(tokens) > 3 and tokens[-4] in ("+", "-"))` because this pattern correctly fails in the subsequent process.)

Is this acceptable as the alternative solution? @mroeschke @jreback I found a more straightforward way to handle timezone offset. 
I would appreciate it if you could review this revision. This pull request is stale because it has been open for thirty days with no activity. Please update or respond to this comment if you're still interested in working on this. This pull request is stale because it has been open for thirty days with no activity. Please update or respond to this comment if you're still interested in working on this. @i-aki-y can you merge master.

also can you run the to_datetime benchamarks to see if any change here Hi, @jreback @mroeschke I merged the current master branch.

> also can you run the to_datetime benchamarks to see if any change here

OK, but what benchmark should I do?
If you say about the benchmark of asv described at the following docs,

https://pandas.pydata.org/docs/dev/development/contributing_codebase.html?highlight=bench#running-the-performance-test-suite

I have run the `asv` command for the `inference.py` because the `asv_bench/inference.py` has some `to_datetime` benchmarks.

```
$ asv continuous -f 1.1 master fix-infer_datetime_format-drop-timezone -b inference
```

And I got the following results summary:

```
        before           after         ratio
     [02fdbde3]       [267b971f]
     <master>         <fix-infer_datetime_format-drop-timezone>
-        379±20μs         331±10μs     0.87  inference.ToDatetimeCacheSmallCount.time_unique_date_strings(False, 500)
-      2.97±0.2ms      2.58±0.03ms     0.87  inference.ToNumeric.time_from_numeric_str('coerce')
-     1.36±0.07ms      1.06±0.02ms     0.78  inference.ToNumericDowncast.time_downcast('datetime64', 'float')

SOME BENCHMARKS HAVE CHANGED SIGNIFICANTLY.
PERFORMANCE INCREASED.
```

Although some differences are reported, these are seem to be unrelated to the fix.

I also wrote the following benchmark code specific for the fixes. 

```py
import pandas as pd
rng = pd.date_range(start="1/1/2000", periods=20000, freq="H")
strings_tz_space = [
    x.strftime("%Y-%m-%d %H:%M:%S") + "Z" for x in rng
]
fmts = [
    "%Y-%m-%dT%H:%M:%S",
    "%Y-%m-%dT%H:%M:%S%z",
    "%Y-%m-%dT%H:%M:%S%Z",
    "%Y-%m-%dT%H:%M:%S.%f",
    "%Y-%m-%dT%H:%M:%S.%f%z",
    "%Y-%m-%dT%H:%M:%S.%f%Z",
]

## to_datetime
%timeit pd.to_datetime(strings_tz_space)
%timeit pd.to_datetime(strings_tz_space, infer_datetime_format=True)

## For functions used internally.
%timeit [pd._libs.tslibs.parsing.guess_datetime_format(ts) for ts in strings_tz_space[:500]]
%timeit [pd._libs.tslibs.parsing.format_is_iso(fmt) for fmt in fmts]
```

The results are here:

```
%timeit pd.to_datetime(strings_tz_space)
# master: 7.78 ms ± 119 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)
# PR    : 7.51 ms ± 130 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)
# ratio : 0.96

%timeit pd.to_datetime(strings_tz_space, infer_datetime_format=True)
# master: 60.1 ms ± 1.44 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)
# PR    : 8.77 ms ± 144 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)
# ratio : 0.14

%timeit [pd._libs.tslibs.parsing.guess_datetime_format(ts) for ts in strings_tz_space[:500]]
# master: 174 ms ± 11.9 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)
# PR    : 171 ms ± 4.52 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)
# ratio : 0.98

%timeit [pd._libs.tslibs.parsing.format_is_iso(fmt) for fmt in fmts]
# master: 59.1 µs ± 991 ns per loop (mean ± std. dev. of 7 runs, 10000 loops each)
# PR    : 298 µs ± 10.4 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)
# ratio : 5.04
```

The PR version of the `pd.to_datetime(..., infer_datetime_format=True)` looks much faster than the master version.
This seems because the fix of format inference makes select the optimal parse function internally.
The `format_is_iso` 5x slow down, but I think this impact will be limited because this still be fast and the function called once for each input list, not per list item.

If any other investigation is needed, let me know. @i-aki-y can you add the additional cases to the existing asv's (e.g. the ones you list here https://github.com/pandas-dev/pandas/pull/42068#issuecomment-917835632); we care about the `to_datetime` ones rather than the internal functions themselves.

ping on green. Hello @i-aki-y! Thanks for updating this PR. We checked the lines you've touched for [PEP 8](https://www.python.org/dev/peps/pep-0008) issues, and found:







There are currently no PEP 8 issues detected in this Pull Request. Cheers! :beers: 

##### Comment last updated at 2021-09-14 04:50:23 UTC @jreback I added a benchmark for `to_datetime(..., infer_datetime_format=True)` to the `asv_bench/inference.py`. thanks @i-aki-y very nice! keep em coming!