{-|
Module: Numeric.Morpheus
Description: Low-level machine learning auxiliary functions
Copyright: (c) Alexander Ignatyev, 2017
License: BSD-3
Stability: experimental
Portability: POSIX


Purely functional interface to morpheus based on hmatrix. Morpheus library contains a bunch of cache line aware numerical algorithms suitable for using as a low-level primitives to build machine learning applications.

Naive implementations, which do not take into account cache lines, would suffer order of magnitude performance degradation if tried to traverse a row major matrix in column order.

The library functions take into account CPU cache and work well for both row major and column major matrices, as you can see from the benchmark below which measure time for finding indices of max elements for every column and every row in comparison with naive approach:

@
| Benchmark                           | Morheus   | Naive    |
+-------------------------------------+-----------+----------+
| max index in columns - row major    | 0.9077 ms | 12.93 ms |
+-------------------------------------+-----------+----------+
| max index in columns - column major | 0.8778 ms | 1.490 ms |
+-------------------------------------+-----------+----------+
| max index in rows - row major       | 0.8622 ms | 1.504 ms |
+-------------------------------------+-----------+----------+
| max index in rows - column major    | 0.8913 ms | 12.80 ms |
+-------------------------------------+-----------+----------+
@

== Examples

@
import Numeric.LinearAlgebra
import Numeric.Morpheus


a = matrix 5 [
  71, 11, 3,  -9, -7,
  21, -7,  -2,  23, 11,
  -11, 32, 53, -49, 37,
  1,  -24, 78, 90, 17
  ]


main :: IO ()
main = do
  putStrLn "\nNumeric.Morpheus.MatrixReduce functions: "

  putStr "sum of elements of rows: "
  print $ rowSum a

  putStr "product of elements of rows: "
  print $ rowPredicate (*) a

  putStr "max values of columns: "
  print $ fst $ columnMaxIndex a

  putStr "indices of max values of columns: "
  print $ snd $ columnMaxIndex a


  putStrLn "\n\nNumeric.Morpheus.Activation functions: "

  putStrLn "\nSigmoid:"
  disp 3 (sigmoid a)

  putStrLn "ReLu:"
  disp 3 (relu a)

  putStrLn "ReLu gradient:"
  disp 3 (reluGradient a)


  putStrLn "\n\nNumeric.Morpheus.Statistics functions: "

  putStrLn "\nColumn Means:"
  let colmeans = columnMean a
  print colmeans

  putStrLn "Column Standard Deviations: "
  print (columnStddev_m colmeans a)
@
-}

module Numeric.Morpheus
(
  module Numeric.Morpheus.Activation
  , module Numeric.Morpheus.MatrixReduce
  , module Numeric.Morpheus.Statistics
)

where

import Numeric.Morpheus.Activation
import Numeric.Morpheus.MatrixReduce
import Numeric.Morpheus.Statistics
