Use align_method in comp_method_FRAME
Closes #20090

<b>update</b> Since #23000 was merged, some of the discussion is out of date.  The bottom line remains unchanged: This PR makes DataFrame _comparison_ ops behave like DataFrame _arithmetic_ ops currently do.  Also fixes some bugs e.g. #20090
<b> end update</b>

This is a much nicer alternative to the implementation in #22751.  The problem is that two tests still fail with this implementation.  We need to pin down the design spec more explicitly regardless.

core.ops has three functions for defining DataFrame ops: _arith_method_FRAME, _flex_comp_method_FRAME, _comp_method_FRAME.  The first two both call `_align_method_FRAME`, with `_comp_method_FRAME` being the outlier.  This PR just adds that alignment call.

The two tests that currently fail:

```
df = DataFrame(np.arange(6).reshape((3, 2)))
b_r = np.atleast_2d([2, 2])
l = (2, 2, 2)
expected = DataFrame([[False, False], [False, True], [True, True]])
result = df > l   # <-- raises ValueError under this PR because it has the wrong shape
assert_frame_equal(result, expected)

result = df > b_r   # <-- raises ValueError under this PR because it has the wrong shape
assert_frame_equal(result, expected)
```

```
df = pd.DataFrame(np.arange(6).reshape((3, 2)))
with pytest.raises(ValueError):  # <-- doesnt raise
           df == (2, 2)
```

I understand why the behavior tested by the first test makes sense, but don't see the logic behind having `df == (2, 2)` raise (maybe #4576 holds the answer, will look at that more closely)
Hello @jbrockmendel! Thanks for submitting the PR.

 - There are no PEP8 issues in the file [`pandas/core/frame.py`](https://github.com/jbrockmendel/pandas/blob/b6e3ed99fcee1024250001d9e026af0847c427f6/pandas/core/frame.py) !

 - There are no PEP8 issues in the file [`pandas/core/ops.py`](https://github.com/jbrockmendel/pandas/blob/b6e3ed99fcee1024250001d9e026af0847c427f6/pandas/core/ops.py) !

 - There are no PEP8 issues in the file [`pandas/tests/frame/test_operators.py`](https://github.com/jbrockmendel/pandas/blob/b6e3ed99fcee1024250001d9e026af0847c427f6/pandas/tests/frame/test_operators.py) !

 Related: #22355. @jorisvandenbossche this is the "pretty" alternative to #22751, needs attention despite not being green.  Any thoughts on desired behavior? @pandas-dev/pandas-core this now contains a non-trivial API change, should make sure there is consensus before moving forward.

TL;DR: broadcasting/alignment on DataFrame comparison ops behaves differently from arithmetic ops (#22355).  Both behave differently from numpy convention (#22686).  This PR changes the comparison behavior to match the arithmetic behavior, with the numpy part saved for the next round.

Demonstration (based on tests.frame.test_operators test_boolean_comparison in master):
```
df = pd.DataFrame(np.arange(6).reshape((3, 2)))
b = np.array([2, 2])
b_r = np.atleast_2d([2, 2])
b_c = b_r.T
l = (2, 2, 2)
tup = tuple(l)

cmp_expected = pd.DataFrame([[False, False], [False, True], [True, True]])
arith_expected = pd.DataFrame([[2, 3], [4, 5], [6, 7]])

# For the 1-D array `b`, comparison and arithmetic broadcast the same way
result = df > b
tm.assert_frame_equal(result, cmp_expected)
result = df.values > b
tm.assert_numpy_array_equal(result, cmp_expected.values)
result = df + b
tm.assert_frame_equal(result, arith_expected)
result = df.values + b
tm.assert_numpy_array_equal(result, arith_expected.values)

# In the 2-D case, the broadcasting behavior is different
result = df > b_r
tm.assert_frame_equal(result, cmp_expected)
result = df.values > b_r
tm.assert_numpy_array_equal(result, cmp_expected.values)

result = df.values + b_r
tm.assert_numpy_array_equal(result, arith_expected.values)

with pytest.raises(ValueError):  # we DONT want this to raise
    # ValueError: Unable to coerce to DataFrame, shape must be (3, 2): given (1, 2)
    result = df + b_r


# ditto for tuple/list
result = df > tup  # doesn't match numpy or arithmetic behavior
tm.assert_frame_equal(result, cmp_expected)

with pytest.raises(ValueError):
     # numpy behavior
     result = df.values > tup

with pytest.raises(ValueError):
     # numpy behavior
    result = df.values + tup

with pytest.raises(ValueError):
    # ValueError: Unable to coerce to Series, length must be 2: given 3
    result = df + tup
``` Just to make sure I understand, the changes would be

- DataFrame + 2-d ndarray with matching trailing dimension: Previously raised, now broadcasts
- DataFrame + non-ndarray iterable with matching first dimension: Previously broadcast, now raises

Did I miss any? > DataFrame + 2-d ndarray with matching trailing dimension: Previously raised, now broadcasts

<s>np.ndarray with shape (1, df.shape[1]): previously broadcasts, now raises </s> Broadcasts following #23000

> DataFrame + non-ndarray iterable with matching first dimension: Previously broadcast, now raises

list or tuple with len == df.shape[0] != df.shape[1]: previously broadcasts, now raises <-- AFAICT this behavior is not currently tested

list or tuple with len == df.shape[1]: previously raises, now broadcasts


\* In a separate PR I would like to change the behavior when operating with ndarray with shape (nrows, 1) or (1, ncols) so that both of these broadcast identically to numpy (ATM the (nrows, 1) case raises for both arithmetic and comparison ops).  This change would be for both arithmetic and comparison ops (whereas this PR just changes comparison ops to behave like arithmetic ops) Update: In a different branch I edited the alignment code so that 2d arrays of (nrows, 1) or (1, ncols) both broadcast for arithmetic ops.  This did not cause any test failures.  So AFAICT this particular behavior may be unintentional.

<b>update^2</b> #23000 has now implemented this behavior for arithmetic ops # [Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/22880?src=pr&el=h1) Report
> Merging [#22880](https://codecov.io/gh/pandas-dev/pandas/pull/22880?src=pr&el=desc) into [master](https://codecov.io/gh/pandas-dev/pandas/commit/e4b67ca725db373afe8f4565672eb16e1e8e3b31?src=pr&el=desc) will **increase** coverage by `0.03%`.
> The diff coverage is `100%`.

[![Impacted file tree graph](https://codecov.io/gh/pandas-dev/pandas/pull/22880/graphs/tree.svg?width=650&token=eZ4WkYLtcO&height=150&src=pr)](https://codecov.io/gh/pandas-dev/pandas/pull/22880?src=pr&el=tree)

```diff
@@            Coverage Diff             @@
##           master   #22880      +/-   ##
==========================================
+ Coverage   92.21%   92.24%   +0.03%     
==========================================
  Files         169      169              
  Lines       50884    50814      -70     
==========================================
- Hits        46922    46874      -48     
+ Misses       3962     3940      -22
```

| Flag | Coverage Δ | |
|---|---|---|
| #multiple | `90.66% <100%> (+0.03%)` | :arrow_up: |
| #single | `42.3% <100%> (+0.05%)` | :arrow_up: |

| [Impacted Files](https://codecov.io/gh/pandas-dev/pandas/pull/22880?src=pr&el=tree) | Coverage Δ | |
|---|---|---|
| [pandas/core/internals/managers.py](https://codecov.io/gh/pandas-dev/pandas/pull/22880/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvaW50ZXJuYWxzL21hbmFnZXJzLnB5) | `96.64% <ø> (-0.02%)` | :arrow_down: |
| [pandas/core/internals/blocks.py](https://codecov.io/gh/pandas-dev/pandas/pull/22880/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvaW50ZXJuYWxzL2Jsb2Nrcy5weQ==) | `94.62% <ø> (+1.14%)` | :arrow_up: |
| [pandas/core/ops.py](https://codecov.io/gh/pandas-dev/pandas/pull/22880/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvb3BzLnB5) | `97.19% <100%> (ø)` | :arrow_up: |
| [pandas/core/frame.py](https://codecov.io/gh/pandas-dev/pandas/pull/22880/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvZnJhbWUucHk=) | `97.11% <100%> (-0.01%)` | :arrow_down: |
| [pandas/io/formats/csvs.py](https://codecov.io/gh/pandas-dev/pandas/pull/22880/diff?src=pr&el=tree#diff-cGFuZGFzL2lvL2Zvcm1hdHMvY3N2cy5weQ==) | `98.21% <0%> (ø)` | :arrow_up: |

------

[Continue to review full report at Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/22880?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/22880?src=pr&el=footer). Last update [e4b67ca...826f2c7](https://codecov.io/gh/pandas-dev/pandas/pull/22880?src=pr&el=lastupdated). Read the [comment docs](https://docs.codecov.io/docs/pull-request-comments).
 you refernced https://github.com/pandas-dev/pandas/issues/4576 which is indeed behavior we patched in the past, but doesn't necessary make sense for a DataFrame, while for a homogenous ndarray does a bit more.

Have to look at your changes in some detail.. > Have to look at your changes in some detail..

Sure.  The succinct version is my favorite: "Make DataFrame comparison ops behave like DataFrame arithmetic ops".  That change is enabled entirely by the 1 line added in `core.ops`. Extra benefit: After we get rid of Block.eval, it looks like _try_coerce_args can be simplified. >  .eval dispatched to numexpr, 

I'm pretty sure this is not accurate. @jbrockmendel 

> .eval dispatched to numexpr,


hmm memory is failing, ok then. @jbrockmendel did you do a check of the performance to be sure there is no implication? > did you do a check of the performance to be sure there is no implication?

There does appear to be a performance hit in the relevant case, but a) there is room for subsequent optimization and b) the bugs this avoids are much more important than the performance  impact.

```
In [3]: arr = np.arange(600).reshape(30, 20)
In [4]: df = pd.DataFrame(arr)
In [5] %timeit arr == arr[[0], :]    # calibrate based on numpy timings
10000 loops, best of 3: 82.9 µs per loop   <-- master
10000 loops, best of 3: 84 µs per loop      <-- PR

In [6]: ser = pd.Series(arr[0, :])
In [7]: l = list(ser)

In [8]: %timeit df == arr[[0], :]
100 loops, best of 3: 4.42 ms per loop   # <-- master
10 loops, best of 3: 87.5 ms per loop    # <-- PR

In [9]: %timeit df == ser
10 loops, best of 3: 83 ms per loop       <-- master
10 loops, best of 3: 86.9 ms per loop    <-- PR

In [10]: %timeit df == l
ValueError: Invalid broadcasting comparison       <-- master
10 loops, best of 3: 82.4 ms per loop    <-- PR

In [11]: df[1] = df[1].astype('f8')
    ...: df[3] = df[3].astype('uint8')
    ...: df[5] = df[5].view('m8[ns]')
    ...: df[7] = df[7].view('M8[ns]')
    ...: df[9] = df[9].astype('f4')
    ...:
In [12]: %timeit df == arr[[0], :]
ValueError: cannot broadcast shape [(30, 15)] with block values [(1, 20)]   <-- master, BUG
TypeError: cannot compare a TimedeltaIndex with type int64   <-- PR, BUG (in TimedeltaIndex.__eq__; just opened #23063)

In [13]: df[5] = df[5].view('i8').astype('i4')
In [14]: %timeit df == arr[[0], :]
ValueError: cannot broadcast shape [(30, 15)] with block values [(1, 20)]  <-- master, BUG
10 loops, best of 3: 86.7 ms per loop  <-- PR

In [14]: %timeit df == arr[0, :]
ValueError: Invalid broadcasting comparison [array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19])] with block values  <-- master
10 loops, best of 3: 80.9 ms per loop  <-- PR

``` gentle ping.  If this (or #23031) goes through the follow-ups will keep me busy in places orthogonal to PeriodArray constructors Quick general feedback: for the cases that worked before but will raise now, I think we should go through a deprecation cycle.

(looking now more in detail on your explanation of the changes above) > In [8]: %timeit df == arr[[0], :]
100 loops, best of 3: 4.42 ms per loop   # <-- master
10 loops, best of 3: 87.5 ms per loop    # <-- PR

How do you see this performance difference? I though this would now raise an error on this PR?

---

So if I understand correctly, some cases that now work, will raise after this PR, but you plan to let them work again in a later PR? 
That makes it a bit difficult to assess what the overall changes for users would be (eg if a deprecation warning would be needed, see my previous post)

(it's not possible to for example first align arithmetic ops with numpy, and then comparison ops with arithmeric/numpy, so you don't have this back and forth?)

---

Something else to consider: for Index we actually deliberately disabled comparing with a length 1 array. See also the recently opened issue https://github.com/pandas-dev/pandas/issues/23078 where we were planning to actually raise instead of broadcast
 > How do you see this performance difference?

If you drill down into this, it is driven by poor performance of cmp(DataFrame, Series), which I think can be improved on a subsequent pass.  In the interim I see this as a uncommon corner case and the performance hit as being less important than internal consistency and bugfixes (just noticed this clsoes #20090)

> I though this would now raise an error on this PR?

That was the case when this PR was opened, but since then #22355 changed the behavior of op(DataFrame, ndarray[ndim=2]) to match numpy broadcasting behavior.

> (it's not possible to for example first align arithmetic ops with numpy, and then comparison ops with arithmeric/numpy, so you don't have this back and forth?)

If I understand correctly, this is similar to what I have in mind for optimizing the DataFrame vs Series op.  

> So if I understand correctly, some cases that now work, will raise after this PR, but you plan to let them work again in a later PR?

I think the only case that falls into this category is a list/tuple (_not_ ndarray or Series) with `length(obj) == len(df) != len(df.columns)`.  Those comparisons currently "work" and this PR causes them to raise (matching arithmetic ops behavior).

I would be open to subsequently changing the behavior of both arithmetic+comparisons to do something like:

```
if len(obj) == len(df.columns):
    [behave like arithmetic ops currently do]
elif len(obj) == len(df):
    [behave like comparison ops currently do]
```

but only if this is made consistent across arithmetic/comparison ops. > > I though this would now raise an error on this PR?

> That was the case when this PR was opened, but since then #22355 changed the behavior of op(DataFrame, ndarray[ndim=2]) to match numpy broadcasting behavior.

But then the whatsnew addition you have in this PR is not up to date anymore? As that still mentions that this case will now raise an error > But then the whatsnew addition you have in this PR is not up to date anymore

Will update. Can you please give a new summary of what this PR does / changes etc, as I am rather lost now. The comment above about "non-trivial API change" is also not relevant any more? (and update the top post) > Can you please give a new summary of what this PR does / changes etc, as I am rather lost now.

Updated above.

Bottom line: This PR makes DataFrame comparison ops broadcasting consistent with DataFrame arithmetic ops. > update Since #22355 was merged,

That's an open issue, not a merged PR? Updated, #23000 ping @gfyoung sorry, but Brock and me were still actively discussing this. @jreback I think it was clear that was the case, so please don't say "ping on green" in such a case OK, so I simply reverted the merge. That seemed the easiest way to continue the discussion. It's a bit annoying, but @jbrockmendel you will need to open a new PR since this one cannot be re-opened ..