pg_median_utils 0.0.7
=====================


An extension for PostgreSQL >= 9.6 containing some median-related utilities.

At this time, provides five window functions:
 - `median_filter` which behaves the same as SciPy's [medfilt](https://docs.scipy.org/doc/scipy-0.14.0/reference/generated/scipy.signal.medfilt.html)
 - `iterated_median_filter`, which applies the median filter iteratively until it converges (no change greater than some small value).
 - `rolling_median`, which calculates the median over the preceding `n` rows and returns `NULL` for the first `n` rows
 - `backfilled_rolling_median`, which calculates the median over the preceding `n` rows and backfills the first `n` rows with the median over them (returns `NULL` if there are less rows than the window size).
 - `rolling_median_impute`:
    1. Calculates the rolling median over all _non-null_ rows with window size `n`
    1. Backfills the first `n` rows with the first median over a complete window
    1. _Forward_-fills any null row with the nearest rolling median value

Usage
-----

### Median filters

Use with any double precision column, for example:


    SELECT v,  median_filter(v::double precision, 5) over() FROM generate_series(1, 10) as t(v);
     v  | median_filter 
    ----+---------------
      1 |             1
      2 |             2
      3 |             3
      4 |             4
      5 |             5
      6 |             6
      7 |             7
      8 |             8
      9 |             8
     10 |             8
    (10 rows)


Or for an iterated version:


    SELECT v,  iterated_median_filter(v, 3) over() FROM (VALUES (1), (1.1), (0.9), (1.1), (0.95), (2.1), (1.95), (2.0), (2.05), (3.11), (2.99), (3.05), (3.0)) as t(v);
      v   | iterated_median_filter 
    ------+------------------------
        1 |                      1
      1.1 |                      1
      0.9 |                      1
      1.1 |                    1.1
     0.95 |                    1.1
      2.1 |                   1.95
     1.95 |                      2
      2.0 |                      2
     2.05 |                   2.05
     3.11 |                   2.99
     2.99 |                      3
     3.05 |                      3
      3.0 |                      3
    (13 rows)


Comparing the two:


    SELECT median_filter(v, 3) over(), iterated_median_filter(v, 3, 0.0000001) over() FROM (VALUES (1), (1.1), (0.9), (1.1), (0.95), (2.1), (1.95), (2.0), (2.05), (3.11), (2.99), (3.05), (3.0)) as t(v);
    
    median_filter | iterated_median_filter 
    ---------------+------------------------
                 1 |                      1
                 1 |                      1
               1.1 |                      1
              0.95 |                    1.1
               1.1 |                    1.1
              1.95 |                   1.95
                 2 |                      2
                 2 |                      2
              2.05 |                   2.05
              2.99 |                   2.99
              3.05 |                      3
                 3 |                      3
                 3 |                      3
    (13 rows)

    
### Rolling medians

Usage of the rolling median functions is similar to the filters:


    SELECT v,  rolling_median(v::double precision, 5) over() FROM generate_series(1, 10) as t(v);
     v  | rolling_median 
    ----+----------------
      1 |               
      2 |               
      3 |               
      4 |               
      5 |              3
      6 |              4
      7 |              5
      8 |              6
      9 |              7
     10 |              8
    (10 rows)


Or for the backfilled equivalent:


    SELECT v,  backfilled_rolling_median(v::double precision, 5) over() FROM generate_series(1, 10) as t(v);
     v  | backfilled_rolling_median 
    ----+---------------------------
      1 |                         3
      2 |                         3
      3 |                         3
      4 |                         3
      5 |                         3
      6 |                         4
      7 |                         5
      8 |                         6
      9 |                         7
     10 |                         8
    (10 rows)


Imputation
----------


    SELECT v, rolling_median_impute(v, 3) over() FROM (VALUES (1), (1.1), (0.9), (NULL), (NULL), (2.1), (NULL), (2.0), (2.05), (3.11), (2.99), (3.05), (NULL)) as t(v);
     rolling_median_impute 
    -----------------------
                         1
                       1.1
                       0.9
                       1.1
                       1.1
                       2.1
                         2
                         2
                      2.05
                      3.11
                      2.99
                      3.05
                      2.99
    (13 rows)


Support
-------

This library is stored in an open
[GitHub repository](https://github.com/theory/pg-semver). Feel free to fork
and contribute! Please file bug reports via
[GitHub Issues](https://github.com/theory/pg-semver/issues/).

Authors
-------

* [Jono Gray](https://github.com/greenape)

Copyright and License
---------------------

MIT License

Copyright (c) 2019 Jono Gray

Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
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