(WIP) BUG/CLN: Better timeseries plotting / refactoring tsplot
Must be revisited after #7717.
#6608 seems to be solved by following 4 fixes.
- [ ] `PeriodIndex` should support the same freqs as `DatetimeIndex` (Related to #7222, maybe solved by #5148)
- [ ] Better logic to find common divisor frequency (try to use `tsplot` as much)
- [x] When plotting with `x_compat` to the `ax` which already holds `tsplot` lines, `tsplot` lines must be redrawn on `x_compat` coordinates.
  - [ ] Check whether `to_timestamp(how='e')` always revert `PeriodIndex` back to original `DatetimeIndex`
- [x] If target ax already holds `x_compat` lines, continuous plot should be drawn on `x_compat` coordinates (current version already have a logic, but cannot work if `ax` once have `freq` property).

Other refactoring:
- [x] Do not re-plot every row in `tsplot`
- [x] Simplify `LinePlot` flow (separated as #7717)
- [x] Store plot_func for line and area mixed time-series plot  (separated as #7733)

Result using current PR (modified #6608 a little to show legend).

```
s1 = pd.Series([1, 2, 3], index=[datetime.datetime(1995, 12, 31),
                                 datetime.datetime(2000, 12, 31),
                                 datetime.datetime(2005, 12, 31)], name='idx1')
s2 = pd.Series([1, 2, 3], index=[datetime.datetime(1997, 12, 31),
                                 datetime.datetime(2003, 12, 31),
                                 datetime.datetime(2008, 12, 31)], name='idx2')

ax = s1.plot(legend=True)
ax = s2.plot(legend=True)
s1.plot(ax=ax, legend=True)
```

![figure_1](https://cloud.githubusercontent.com/assets/1696302/3486598/477df0e8-0445-11e4-873b-dc619adaa92a.png)

One question is whether `tsplot` is categorized as public function? If so, I'll prepare separate func.

@sinhrks status?
 @jreback As #5148 was once closed, I'll skip top 2 items and add a test for this in this weekend. Top 2 items are not required to solve the #6608.
 @sinhrks status on this?
 @sinhrks status?
 @TomAugspurger can you pick this up for 0.15? or can defer to 0.15.1
 Let me look at it today.
 This is an improvement (just a couple of fixups first). But still not entirely there.

The following two plots should be identical I think:

``` python
In [28]: import datetime

In [29]: pidx = pd.PeriodIndex(start='2010-01-01', freq='m', periods=5)

In [30]: didx = pd.DatetimeIndex(['2010-01-01', '2010-02-05', '2010-03-10', '2010-04-15', '2010-05-25'])

In [31]: x1 = pd.Series(np.arange(5), index=pidx)

In [32]: x2 = pd.Series(np.arange(5), index=didx)

In [33]: ax = x1.plot(marker='o')

In [34]: x2.plot(marker='^', ax=ax)
Out[34]: <matplotlib.axes._subplots.AxesSubplot at 0x11758ae80>

In [35]: ax.set_title("Period then DatetimeIndex")
Out[35]: <matplotlib.text.Text at 0x117b03160>

In [38]: plt.close()

In [39]: ax = x2.plot(marker='^')

In [40]: x1.plot(ax=ax, marker='o')
Out[40]: <matplotlib.axes._subplots.AxesSubplot at 0x117af5a58>

In [41]: ax.set_title("Datetime then PeriodIndex")
Out[41]: <matplotlib.text.Text at 0x117b88828>
```

![p1](https://cloud.githubusercontent.com/assets/1312546/4469338/0635aa80-4910-11e4-9b4d-9753adf10499.png)
![p2](https://cloud.githubusercontent.com/assets/1312546/4469337/063207c2-4910-11e4-8cc3-241762a60a24.png)
 @TomAugspurger push?
 @TomAugspurger status?
 @TomAugspurger what are we oing with this (and #6608) ?
 Push I think. Right now it's only fixed in one direction iirc. 
 @sinhrks, @TomAugspurger  what is status on this?
 I'm revisiting this, and want to change `tsplot` as below to make the fix simple:
- Allow to accept `DataFrame`.
- Remove legend handling.
- Change `_maybe_resample` to allow Period-DatetimeIndex roundtrip in a single rule.

Let me confirm `tsplot` is considered to be a public function. If so, direct-call of `tsplot` can be deprecated because now `Series.plot` should output the time series plotting?
 @TomAugspurger can you have a look
 Yeah, I'll see where we are at.
 I couldn't finish it yet because of the following (the same one as the @TomAugspurger  pointed): 

> Check whether to_timestamp(how='e') always revert PeriodIndex back to original DatetimeIndex

Based on the following code, there could be no single logic to revert converted `PeriodIndex` to original. Thus I think we should change the below logic to cover all the cases.

https://github.com/pydata/pandas/blob/master/pandas/tseries/plotting.py#L78

Though this PR cannot cover all the issues, it can fix original one. Thus, one option is move this forward once leaving above as it is.
 @sinhrks status?
 I couldn't investigate the detail above yet. Would like to finish #9814 first which also has tsplot related changes.
 @sinhrks want to update
 Revisiting this... I believe we have to clarify the plotting rules first. This should cause current behavior changes.
- Repeated time series plot should output the same result regardless of plotting order.
- `DatetimeIndex` should be regarded as `PeriodIndex` (and converted to `PeriodIndex`) if it has `freq/inferred_freq`
- `PeriodIndex` is regarded as "regular" time series. `DatetimeIndex` doesn't have `freq/inferred_freq` is regarded as "irregular" time series.
- If any of time sereis is "irregular", all the time series should be plotted based on absolute time stamp. No freq adjustment needed.
- If all the time series are "regular", period adjustment should be performed to take highest frequency.
- When `PeriodIndex` is resampled, the begining time of the "Period" should be taken. e.g. resampling monthly `Period` "2011-01" with daily freq should result in  "2011-01-01", not "2011-01-31".

Based on the rule, above @TomAugspurger 's example should result in latter(bottom) output in both cases.

I've created a demo on Gist, but not able to cover all conditions yet. 

https://gist.github.com/sinhrks/e12cc7caf753097a2ef0
 I think those all seem reasonable... 
 @sinhrks @TomAugspurger status of this?
 @sinhrks status?
 status?
 status?
 closing, but @sinhrks pls reopen if you want / can fix.