PVI update to match Investopedia definition

[Rossco8]

There are 2 PVI indicators on TradingView.

One calculates PVI using

pvi := na(pvi[1]) ? initial : (change(volume) > 0 ? pvi[1] * close / close[1] : pvi[1])

The other uses

nRes = iff(volume > volume[1], nz(nRes[1], 0) + xROC, nz(nRes[1], 0))

Both of them are different, and neither of them follow the logic outlined on most websites, e.g.

https://www.investopedia.com/terms/p/pvi.asp
https://www.kotaksecurities.com/share-market/what-is-positive-volume-index/
https://www.barchart.com/education/technical-indicators/positive_volume_index
https://www.angelone.in/knowledge-center/share-market/pvi

Which all show the formula as

Yesterday’s PVI + [[(Close – Yesterday’s Close) / Yesterday’s Close] * Yesterday’s PVI

There are other definitions of the formula available online, the authors of the TV indicators may have used

The source code referenced in issue #625 at the voice32 repo uses

pvi = prev_pvi + (row[close_col] - prev_close / prev_close * prev_pvi)

Which is almost the Investopedia version, if it had (row[close_col] - prev_close) in parentheses

So I have raised a PR and implemented the following - NOTE: This is a breaking change as the new PVI() returns a DataFrame rather than a Series

1. Loop through arrays rather than DF rows for performance improvements
2. initial value set to 100 rather than 1000 which seems to be the norm amongst the other implementations
3. Default length parameter set to 255 to match the other implementation
4. added mamode with a default of EMA
5. returns a DataFrame rather than a Series

Performance of the new PVI implementation is roughly twice as fast than previous version

3275 function calls (3214 primitive calls) in 0.012 seconds

   Ordered by: internal time

   ncalls  tottime  percall  cumtime  percall filename:lineno(function)
        1    0.001    0.001    0.001    0.001 datetimes.py:545(_box_func)
        1    0.001    0.001    0.011    0.011 pvi.py:77(pvi_new_vect)
        1    0.001    0.001    0.001    0.001 rolling.py:601(calc)
        1    0.001    0.001    0.001    0.001 sre_parse.py:494(_parse)
        2    0.000    0.000    0.002    0.001 indexing.py:1176(__getitem__)
  565/564    0.000    0.000    0.000    0.000 {built-in method builtins.isinstance}
        6    0.000    0.000    0.002    0.000 frame.py:3971(_ixs)
        4    0.000    0.000    0.001    0.000 base.py:475(__new__)
        3    0.000    0.000    0.001    0.000 base.py:6956(insert)
        5    0.000    0.000    0.001    0.000 frame.py:4050(__getitem__)
        3    0.000    0.000    0.003    0.001 managers.py:1347(insert)

Performance of the original PVI implementation

5088 function calls (4995 primitive calls) in 0.020 seconds

   Ordered by: internal time

   ncalls  tottime  percall  cumtime  percall filename:lineno(function)
        2    0.003    0.001    0.003    0.002 algorithms.py:1339(diff)
        1    0.001    0.001    0.001    0.001 base.py:411(_outer_indexer)
        3    0.001    0.000    0.001    0.000 datetimelike.py:388(_get_getitem_freq)
        1    0.000    0.000    0.020    0.020 <string>:1(<module>)
       12    0.000    0.000    0.002    0.000 series.py:389(__init__)
  996/979    0.000    0.000    0.001    0.000 {built-in method builtins.isinstance}
        2    0.000    0.000    0.002    0.001 frame.py:4050(__getitem__)
        1    0.000    0.000    0.018    0.018 pvi.py:169(pvi)
        2    0.000    0.000    0.004    0.002 generic.py:10612(_where)
       26    0.000    0.000    0.000    0.000 generic.py:6233(__finalize__)
        1    0.000    0.000    0.020    0.020 {built-in method builtins.exec}
       16    0.000    0.000    0.002    0.000 managers.py:317(apply)
        2    0.000    0.000    0.004    0.002 series.py:3026(diff)
  352/337    0.000    0.000    0.000    0.000 {built-in method builtins.getattr} 

[Rossco8]

Needs more work - dataframe extension failed