Shekel.hs

{-# LANGUAGE MonoLocalBinds #-}
{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE OverloadedLabels #-}
{-# LANGUAGE RebindableSyntax #-}
{-# LANGUAGE NegativeLiterals #-}
{-# OPTIONS_GHC -fno-warn-orphans #-}
{-# OPTIONS_GHC -fno-warn-incomplete-patterns #-}

-- | Function with a tricky shape useful for testing.
--
-- See <https://en.wikipedia.org/wiki/Shekel_function>
--
module Ephemeral.Shekel
  ( shekel,
    shekelp,
  ) where

import NumHask.Prelude as P
import NumHask.Space

-- $setup
--
-- >>> :set -XOverloadedStrings
-- >>> :set -XOverloadedLabels
-- >>> import NumHask.Prelude as P

-- underlying shekel function constants
sa :: [[Double]]
sa =
  [ [9.681, 0.667, 4.783, 9.095, 3.517, 9.325, 6.544, 0.211, 5.122, 2.020],
    [9.400, 2.041, 3.788, 7.931, 2.882, 2.672, 3.568, 1.284, 7.033, 7.374],
    [8.025, 9.152, 5.114, 7.621, 4.564, 4.711, 2.996, 6.126, 0.734, 4.982],
    [2.196, 0.415, 5.649, 6.979, 9.510, 9.166, 6.304, 6.054, 9.377, 1.426],
    [8.074, 8.777, 3.467, 1.863, 6.708, 6.349, 4.534, 0.276, 7.633, 1.567],
    [7.650, 5.658, 0.720, 2.764, 3.278, 5.283, 7.474, 6.274, 1.409, 8.208],
    [1.256, 3.605, 8.623, 6.905, 0.584, 8.133, 6.071, 6.888, 4.187, 5.448],
    [8.314, 2.261, 4.224, 1.781, 4.124, 0.932, 8.129, 8.658, 1.208, 5.762],
    [0.226, 8.858, 1.420, 0.945, 1.622, 4.698, 6.228, 9.096, 0.972, 7.637],
    [7.305, 2.228, 1.242, 5.928, 9.133, 1.826, 4.060, 5.204, 8.713, 8.247],
    [0.652, 7.027, 0.508, 4.876, 8.807, 4.632, 5.808, 6.937, 3.291, 7.016],
    [2.699, 3.516, 5.874, 4.119, 4.461, 7.496, 8.817, 0.690, 6.593, 9.789],
    [8.327, 3.897, 2.017, 9.570, 9.825, 1.150, 1.395, 3.885, 6.354, 0.109],
    [2.132, 7.006, 7.136, 2.641, 1.882, 5.943, 7.273, 7.691, 2.880, 0.564],
    [4.707, 5.579, 4.080, 0.581, 9.698, 8.542, 8.077, 8.515, 9.231, 4.670],
    [8.304, 7.559, 8.567, 0.322, 7.128, 8.392, 1.472, 8.524, 2.277, 7.826],
    [8.632, 4.409, 4.832, 5.768, 7.050, 6.715, 1.711, 4.323, 4.405, 4.591],
    [4.887, 9.112, 0.170, 8.967, 9.693, 9.867, 7.508, 7.770, 8.382, 6.740],
    [2.440, 6.686, 4.299, 1.007, 7.008, 1.427, 9.398, 8.480, 9.950, 1.675],
    [6.306, 8.583, 6.084, 1.138, 4.350, 3.134, 7.853, 6.061, 7.457, 2.258],
    [0.652, 2.343, 1.370, 0.821, 1.310, 1.063, 0.689, 8.819, 8.833, 9.070],
    [5.558, 1.272, 5.756, 9.857, 2.279, 2.764, 1.284, 1.677, 1.244, 1.234],
    [3.352, 7.549, 9.817, 9.437, 8.687, 4.167, 2.570, 6.540, 0.228, 0.027],
    [8.798, 0.880, 2.370, 0.168, 1.701, 3.680, 1.231, 2.390, 2.499, 0.064],
    [1.460, 8.057, 1.336, 7.217, 7.914, 3.615, 9.981, 9.198, 5.292, 1.224],
    [0.432, 8.645, 8.774, 0.249, 8.081, 7.461, 4.416, 0.652, 4.002, 4.644],
    [0.679, 2.800, 5.523, 3.049, 2.968, 7.225, 6.730, 4.199, 9.614, 9.229],
    [4.263, 1.074, 7.286, 5.599, 8.291, 5.200, 9.214, 8.272, 4.398, 4.506],
    [9.496, 4.830, 3.150, 8.270, 5.079, 1.231, 5.731, 9.494, 1.883, 9.732],
    [4.138, 2.562, 2.532, 9.661, 5.611, 5.500, 6.886, 2.341, 9.699, 6.500]
  ]

sc :: [Double]
sc =
  [ 0.806,
    0.517,
    0.1,
    0.908,
    0.965,
    0.669,
    0.524,
    0.902,
    0.531,
    0.876,
    0.462,
    0.491,
    0.463,
    0.714,
    0.352,
    0.869,
    0.813,
    0.811,
    0.828,
    0.964,
    0.789,
    0.360,
    0.369,
    0.992,
    0.332,
    0.817,
    0.632,
    0.883,
    0.608,
    0.326
  ]

sdiff :: [Double] -> [Double]
sdiff xs = fmap ((sum . fmap (**2)) . zipWith (-) xs) sa

sinv :: [Double] -> Double
sinv xs = sum $ fmap (** -1) (zipWith (+) xs sc)

-- | The shekel function applied to a list and roughly normalised to Range (-0.5) 0.5
--
-- >>> shekel [0.302, 0.412, 0.5]
-- 0.614769661738902
--
shekel :: [Double] -> Double
shekel = sinv . sdiff

-- | The shekel function applied to a Point and roughly normalised to a Rect.unit
--
-- >>> shekelp (Point 0.302 0.412)
-- 1.1945742676096427
--
shekelp :: Point Double -> Double
shekelp (Point x y) = sinv . sdiff $ [x,y]