[BUG] Concat duplicates errors (or lack there of)
- [ ] closes #6963
- [ ]  xref #36263, #36290
- [ ] tests added / passed
- [ ] passes `black pandas`
- [ ] passes `git diff upstream/master -u -- "*.py" | flake8 --diff`
- [ ] whatsnew entry

@jreback

So here is a basic proposal for making `concat` throw a more useful error when there are duplicate values on the index not being concatenated along. Below are some examples of how this error message is improved. I'm including a comparison to 1.2.0rc1, since it includes a pr which was supposed to change some of these errors to working cases, but those cases are extremely limited. That's why the first commit of this PR reverts that change.

I haven't gone too far with this since it a) reverts a merged PR and b) affects the release candidate, so should be conservative. I would like to get feedback on whether I should proceed with this approach.

My thinking right now is that a better error and revert should go into 1.2 – no behaviour change from 1.1, just better errors. A question of whether `pd.concat(..., join="inner")` means an intersection of indices (the current [and documented](https://pandas.pydata.org/docs/user_guide/merging.html#concatenating-objects) behaviour) or an actual inner join seems like something that could benefit from more discussion.

If they are set operations, it should probably error on duplicates. If they are relational algebra operations, they should work with duplicates. It would probably also be useful to then add more arguments to `concat`, like `merge`s `validate`.

# One dataframe has repeated column names (str)

```python
pd.concat([
    pd.DataFrame(np.ones((4, 4)), columns=list("aabc")),
    pd.DataFrame(np.ones((4, 3)), columns=list("abc")),
])
```

This PR

```pytb
InvalidIndexError: Reindexing only valid with uniquely valued Index objects
```

Pandas v1.1.5

```pytb
ValueError: Plan shapes are not aligned
```

pandas 1.2.0rc1

```pytb
ValueError: Plan shapes are not aligned
```

-------------------------

# One dataframe has repeated column names (int)

```python
pd.concat([  # One dataframe has repeated column names
    pd.DataFrame(np.ones((4, 4)), columns=[1, 1, 2, 3]),
    pd.DataFrame(np.ones((4, 3)), columns=[1, 2, 3]),
)
```

This PR

```pytb
InvalidIndexError: Reindexing only valid with uniquely valued Index objects
```

Pandas v1.1.5

```pytb
ValueError: Plan shapes are not aligned
```

pandas 1.2.0rc1

```pytb
ValueError: Plan shapes are not aligned
```


--------------------------

# Repeated columns (same amount) different column ordering

```python
pd.concat([
    pd.DataFrame(np.ones((2, 4)), columns=list("aabc")),
    pd.DataFrame(np.ones((2, 4)), columns=list("abca")),
])
``` 

This PR:

```pytb
InvalidIndexError: Reindexing only valid with uniquely valued Index objects
```

In pandas v1.15

```pytb
AssertionError: Number of manager items must equal union of block items
# manager items: 3, # tot_items: 4
```

In pandas v1.2.0rc1

```pytb
AssertionError: Number of manager items must equal union of block items
# manager items: 3, # tot_items: 4
```

----------------------------

# Repeated columns of different values in each

This point is what the reverted PR was trying to fix. This demonstrates that it didn't seem to fix what it set out to, and that the intended fix introduced strange behaviour anyways. To do this, I'll use the reverted test case.

```python
# Test case from previous PR
a_int = pd.DataFrame([1, 2, 3, 4], index=[0, 1, 1, 4], columns=["a"])
b_int = pd.DataFrame([6, 7, 8, 9], index=[0, 0, 1, 3], columns=["b"])

# Same, but with string indexes
a_str = a_int.set_index(letters[a_int.index])
b_str = b_int.set_index(letters[b_int.index])
```

## Int index

```python
pd.concat([a_int, b_int], axis=1)
```

This PR

```pytb
InvalidIndexError: Reindexing only valid with uniquely valued Index objects
```

Pandas v1.1.5

```pytb
ValueError: Shape of passed values is (8, 2), indices imply (6, 2)
```

pandas 1.2.0rc1

```pytb
     a    b
0  1.0  6.0
0  1.0  7.0
1  2.0  8.0
1  3.0  8.0
3  NaN  9.0
4  4.0  NaN
```

<details>
<summary> This behaviour is a bit strange </summary>

First, the `concat` documentation [defines the options here as set operations, like intersect and union](https://pandas.pydata.org/docs/user_guide/merging.html#concatenating-objects). Is this a union, or is this an outer join?

If these are joins, then inner joins only seem to work when they are equivalent to intersections:

```python
>>> pd.concat([a_int, b_int], axis=1, join="inner")
...
ValueError: Shape of passed values is (3, 2), indices imply (2, 2)

>>> pd.merge(a_int, b_int, how="inner", left_index=True, right_index=True)
   a  b
0  1  6
0  1  7
1  2  8
1  3  8
```

</details>


## str index

This is mostly just to show the behaviour in 1.2.0rc1 is different for string and int indices

```python
pd.concat([a_str, b_str], axis=1)
```

This PR

```pytb
InvalidIndexError: Reindexing only valid with uniquely valued Index objects
```

Pandas v1.1.5

```pytb
ValueError: Shape of passed values is (5, 2), indices imply (4, 2)
```

pandas 1.2.0rc1

```pytb
ValueError: Shape of passed values is (5, 2), indices imply (4, 2)
```

wow let me have a closer look

cc @jbrockmendel  cc @jorisvandenbossche  cc @phofl I think i want to merge this for 1.2 @ivirshup can you add some tests cases here (we could merge w/o those). cc @simonjayhawkins  We should document that concat does not support duplicates and close all related issues. 
there is at least one more open  > We should document that concat does not support duplicates and close all related issues.
> there is at least one more open

yes abolutely. @ivirshup can you update this with some tests that assert this. ok i am going to merge this. @ivirshup pls open a new one and we can add tests. @meeseeksdev backport 1.2.x Ah, sorry, took the weekend off for the holiday! I'll get on those tests.

Just a point to make on this, I had left the case where dataframes have equal indexes, even with duplicates. E.g:

```python
pd.concat([
    pd.DataFrame(np.ones((3, 3)), columns=list("aab")),
    pd.DataFrame(np.ones((3, 3)), columns=list("aab"))
])
```

I believe this has worked for a while. It's more obvious what a user intended in this case – even if it's not quite a set or join operation. If this were to be disallowed, I think it could use a deprecation first. Indeed, that case has always worked (I assume because the indexes are equal, we don't attempt any reindexing). *If* we wanted to change that, it would indeed need a deprecation cycle, so let's keep that as a separate issue/PR (but personally I think I am fine with keeping it working as is). I would like to ask a question about this behavior on connection with the effect (or lack thereof) of `verify_integrity`. The situation in which I found this issue was combining two dataframes of timestamped values where some timestamps are repeated within the initial frames.

Here is a test case:

```
def test_concat(temp1,temp2):
    [display(frame) for frame in [temp1, temp2]]
    frames = [temp1, temp2]
    temp3 = pd.concat(frames,
                      axis = 1,
                      sort = True,
                      verify_integrity = False)
    display(temp3)
    
print('Case 1')
# Two frames with unique timestamps
test_concat(temp1 = pd.DataFrame(data = [[1,2],[3,4]], columns = ['A', 'B'], index = pd.to_datetime(['2020-01-01 10:00','2020-01-01 10:01'])),
            temp2 = pd.DataFrame(data = [[5,6],[7,8]], columns = ['C', 'D'], index = pd.to_datetime(['2020-01-01 10:00','2020-01-01 10:01'])))

print('Case 2')
# Same as case 1, except the first frame has identical timestamps on both rows
test_concat(temp1 = pd.DataFrame(data = [[1,2],[3,4]], columns = ['A', 'B'], index = pd.to_datetime(['2020-01-01 10:00','2020-01-01 10:00'])),
            temp2 = pd.DataFrame(data = [[5,6],[7,8]], columns = ['C', 'D'], index = pd.to_datetime(['2020-01-01 10:00','2020-01-01 10:01'])))
```

This returns the following output:

```Case 1
  | A | B
-- | -- | --
2020-01-01 10:00:00 | 1 | 2
2020-01-01 10:01:00 | 3 | 4


  | C | D
-- | -- | --
2020-01-01 10:00:00 | 5 | 6
2020-01-01 10:01:00 | 7 | 8


  | A | B | C | D
-- | -- | -- | -- | --
2020-01-01 10:00:00 | 1 | 2 | 5 | 6
2020-01-01 10:01:00 | 3 | 4 | 7 | 8

Case 2

  | A | B
-- | -- | --
2020-01-01 10:00:00 | 1 | 2
2020-01-01 10:00:00 | 3 | 4


  | C | D
-- | -- | --
2020-01-01 10:00:00 | 5 | 6
2020-01-01 10:01:00 | 7 | 8

ValueError                                Traceback (most recent call last)
<ipython-input-6-8812ae5e1d27> in <module>
     13 print('Case 2')
     14 test_concat(temp1 = pd.DataFrame(data = [[1,2],[3,4]], columns = ['A', 'B'], index = pd.to_datetime(['2020-01-01 10:00','2020-01-01 10:00'])),
---> 15             temp2 = pd.DataFrame(data = [[5,6],[7,8]], columns = ['C', 'D'], index = pd.to_datetime(['2020-01-01 10:00','2020-01-01 10:01'])))

<ipython-input-6-8812ae5e1d27> in test_concat(temp1, temp2)
      5                       axis = 1,
      6                       sort = True,
----> 7                       verify_integrity = False)
      8     display(temp3)
      9 

~/<path>/lib/python3.6/site-packages/pandas/core/reshape/concat.py in concat(objs, axis, join, ignore_index, keys, levels, names, verify_integrity, sort, copy)
    285     )
    286 
--> 287     return op.get_result()
    288 
    289 

~/<path>/lib/python3.6/site-packages/pandas/core/reshape/concat.py in get_result(self)
    501 
    502             new_data = concatenate_block_managers(
--> 503                 mgrs_indexers, self.new_axes, concat_axis=self.bm_axis, copy=self.copy,
    504             )
    505             if not self.copy:

~/<path>/lib/python3.6/site-packages/pandas/core/internals/concat.py in concatenate_block_managers(mgrs_indexers, axes, concat_axis, copy)
     82         blocks.append(b)
     83 
---> 84     return BlockManager(blocks, axes)
     85 
     86 

~/<path>/lib/python3.6/site-packages/pandas/core/internals/managers.py in __init__(self, blocks, axes, do_integrity_check)
    147 
    148         if do_integrity_check:
--> 149             self._verify_integrity()
    150 
    151         # Populate known_consolidate, blknos, and blklocs lazily

~/<path>/lib/python3.6/site-packages/pandas/core/internals/managers.py in _verify_integrity(self)
    327         for block in self.blocks:
    328             if block.shape[1:] != mgr_shape[1:]:
--> 329                 raise construction_error(tot_items, block.shape[1:], self.axes)
    330         if len(self.items) != tot_items:
    331             raise AssertionError(

ValueError: Shape of passed values is (5, 4), indices imply (3, 4)
```

It appears to me that `concat` is not respecting `verify_integrity = False`. The [User Guide](https://pandas.pydata.org/pandas-docs/stable/user_guide/merging.html#concatenating-objects) states `verify_integrity : boolean, default False. Check whether the new concatenated axis contains duplicates.` My interpretation of that is "when `verify_integrity = False`, `concat` should return all the supplied index values, even when there are duplicates." In pandas 1.1.5, however, the code above behaves identically with `verify_integrity = False` and `verify_integrity = True`. Is that the intended behavior? If so, I submit that the User Guide is misleading. 