{-# LANGUAGE Strict #-}

module Currycarbon.Calibration.Calibration
    ( -- * Calibration functions
      --
      -- $calibration
      --
      -- This module provides an interface to the calibration logic
        getRelevantCalCurveSegment
      , prepareCalCurveSegment
      , makeCalCurveMatrix
      , uncalToPDF
      , calibrateDate
      , calibrateDates
      , refineCalDates
      , refineCalDate
      , CalibrateDatesConf (..)
      , defaultCalConf
    ) where

import Currycarbon.Calibration.Utils
import Currycarbon.Calibration.Bchron
import Currycarbon.Calibration.MatrixMult
import Currycarbon.Types
import Currycarbon.Utils

import Data.List (sort, sortBy, groupBy, elemIndex)
import Data.Maybe (fromJust)
import qualified Data.Vector.Unboxed as VU

-- | A data type to cover the configuration options of the calibrateDates function
data CalibrateDatesConf = CalibrateDatesConf {
      -- | The calibration algorithm that should be used  
        CalibrateDatesConf -> CalibrationMethod
_calConfMethod :: CalibrationMethod
      -- | Allow calibration to run outside of the range of the calibration curve
      , CalibrateDatesConf -> Bool
_calConfAllowOutside :: Bool
      -- | Interpolate the calibration curve before calibration.
      -- This is a simple linear interpolation only to increase the output
      -- resolution for earlier time periods, where the typical calibration
      -- curves are less dense by default. With the interpolation, the output
      -- will be a per-year density. The mechanism is inspired by the 
      -- [implementation in the Bchron R package](https://github.com/andrewcparnell/Bchron/blob/b202d18550319b488e676a8b542aba55853f6fa3/R/BchronCalibrate.R#L118-L119)
      , CalibrateDatesConf -> Bool
_calConfInterpolateCalCurve :: Bool 
    } deriving (Int -> CalibrateDatesConf -> ShowS
[CalibrateDatesConf] -> ShowS
CalibrateDatesConf -> String
(Int -> CalibrateDatesConf -> ShowS)
-> (CalibrateDatesConf -> String)
-> ([CalibrateDatesConf] -> ShowS)
-> Show CalibrateDatesConf
forall a.
(Int -> a -> ShowS) -> (a -> String) -> ([a] -> ShowS) -> Show a
showList :: [CalibrateDatesConf] -> ShowS
$cshowList :: [CalibrateDatesConf] -> ShowS
show :: CalibrateDatesConf -> String
$cshow :: CalibrateDatesConf -> String
showsPrec :: Int -> CalibrateDatesConf -> ShowS
$cshowsPrec :: Int -> CalibrateDatesConf -> ShowS
Show, CalibrateDatesConf -> CalibrateDatesConf -> Bool
(CalibrateDatesConf -> CalibrateDatesConf -> Bool)
-> (CalibrateDatesConf -> CalibrateDatesConf -> Bool)
-> Eq CalibrateDatesConf
forall a. (a -> a -> Bool) -> (a -> a -> Bool) -> Eq a
/= :: CalibrateDatesConf -> CalibrateDatesConf -> Bool
$c/= :: CalibrateDatesConf -> CalibrateDatesConf -> Bool
== :: CalibrateDatesConf -> CalibrateDatesConf -> Bool
$c== :: CalibrateDatesConf -> CalibrateDatesConf -> Bool
Eq)

-- | A default configuration that should yield almost identical calibration results 
-- to the [Bchron R package](https://github.com/andrewcparnell/Bchron)
defaultCalConf :: CalibrateDatesConf
defaultCalConf :: CalibrateDatesConf
defaultCalConf = CalibrateDatesConf :: CalibrationMethod -> Bool -> Bool -> CalibrateDatesConf
CalibrateDatesConf {
        _calConfMethod :: CalibrationMethod
_calConfMethod = Bchron :: CalibrationDistribution -> CalibrationMethod
Bchron { distribution :: CalibrationDistribution
distribution = Double -> CalibrationDistribution
StudentTDist Double
100 }
      , _calConfAllowOutside :: Bool
_calConfAllowOutside = Bool
False 
      , _calConfInterpolateCalCurve :: Bool
_calConfInterpolateCalCurve = Bool
True
    }

-- | Calibrates a list of dates with the provided calibration curve
calibrateDates :: CalibrateDatesConf -- ^ Configuration options to consider
                  -> CalCurveBP -- ^ A calibration curve
                  -> [UncalC14] -- ^ A list of uncalibrated radiocarbon dates  
                  -> [Either CurrycarbonException CalPDF] -- ^ The function returns a list for each input date, with
                                                          -- either an exception if the calibration failed for some
                                                          -- reason, or a 'CalPDF'
calibrateDates :: CalibrateDatesConf
-> CalCurveBP -> [UncalC14] -> [Either CurrycarbonException CalPDF]
calibrateDates CalibrateDatesConf
_ CalCurveBP
_ [] = []
calibrateDates (CalibrateDatesConf CalibrationMethod
MatrixMultiplication Bool
allowOutside Bool
interpolate) CalCurveBP
calCurve [UncalC14]
uncalDates =
    (UncalC14 -> Either CurrycarbonException CalPDF)
-> [UncalC14] -> [Either CurrycarbonException CalPDF]
forall a b. (a -> b) -> [a] -> [b]
map (Bool
-> Bool
-> CalCurveBP
-> UncalC14
-> Either CurrycarbonException CalPDF
calibrateDateMatrixMult Bool
allowOutside Bool
interpolate CalCurveBP
calCurve) [UncalC14]
uncalDates
calibrateDates (CalibrateDatesConf Bchron{distribution :: CalibrationMethod -> CalibrationDistribution
distribution=CalibrationDistribution
distr} Bool
allowOutside Bool
interpolate) CalCurveBP
calCurve [UncalC14]
uncalDates =
    (UncalC14 -> Either CurrycarbonException CalPDF)
-> [UncalC14] -> [Either CurrycarbonException CalPDF]
forall a b. (a -> b) -> [a] -> [b]
map (CalibrationDistribution
-> Bool
-> Bool
-> CalCurveBP
-> UncalC14
-> Either CurrycarbonException CalPDF
calibrateDateBchron CalibrationDistribution
distr Bool
allowOutside Bool
interpolate CalCurveBP
calCurve) [UncalC14]
uncalDates

-- | Calibrates a date with the provided calibration curve
calibrateDate :: CalibrateDatesConf -- ^ Configuration options to consider
                 -> CalCurveBP -- ^ A calibration curve
                 -> UncalC14 -- ^ An uncalibrated radiocarbon date
                 -> Either CurrycarbonException CalPDF -- ^ The function returns either an exception if the 
                                                        -- calibration failed for some reason, or a 'CalPDF'
calibrateDate :: CalibrateDatesConf
-> CalCurveBP -> UncalC14 -> Either CurrycarbonException CalPDF
calibrateDate (CalibrateDatesConf CalibrationMethod
MatrixMultiplication Bool
allowOutside Bool
interpolate) CalCurveBP
calCurve UncalC14
uncalDate =
    Bool
-> Bool
-> CalCurveBP
-> UncalC14
-> Either CurrycarbonException CalPDF
calibrateDateMatrixMult Bool
allowOutside Bool
interpolate CalCurveBP
calCurve UncalC14
uncalDate
calibrateDate (CalibrateDatesConf Bchron{distribution :: CalibrationMethod -> CalibrationDistribution
distribution=CalibrationDistribution
distr} Bool
allowOutside Bool
interpolate) CalCurveBP
calCurve UncalC14
uncalDate =
    CalibrationDistribution
-> Bool
-> Bool
-> CalCurveBP
-> UncalC14
-> Either CurrycarbonException CalPDF
calibrateDateBchron CalibrationDistribution
distr Bool
allowOutside Bool
interpolate CalCurveBP
calCurve UncalC14
uncalDate

-- | Transforms the raw, calibrated probability density table to a meaningful representation of a
-- calibrated radiocarbon date
refineCalDates :: [CalPDF] -> [Maybe CalC14]
refineCalDates :: [CalPDF] -> [Maybe CalC14]
refineCalDates = (CalPDF -> Maybe CalC14) -> [CalPDF] -> [Maybe CalC14]
forall a b. (a -> b) -> [a] -> [b]
map CalPDF -> Maybe CalC14
refineCalDate

refineCalDate :: CalPDF -> Maybe CalC14
refineCalDate :: CalPDF -> Maybe CalC14
refineCalDate (CalPDF String
name Vector Int
cals Vector Float
dens) =
    if Vector Float -> Float
forall a. (Unbox a, Num a) => Vector a -> a
VU.sum Vector Float
dens Float -> Float -> Bool
forall a. Eq a => a -> a -> Bool
== Float
0 Bool -> Bool -> Bool
|| Vector Float -> Int
forall a. Unbox a => Vector a -> Int
VU.length ((Float -> Bool) -> Vector Float -> Vector Float
forall a. Unbox a => (a -> Bool) -> Vector a -> Vector a
VU.filter (Float -> Float -> Bool
forall a. Ord a => a -> a -> Bool
>= Float
1.0) Vector Float
dens) Int -> Int -> Bool
forall a. Eq a => a -> a -> Bool
== Int
1 -- don't calculate CalC14, if it's not meaningful
    then Maybe CalC14
forall a. Maybe a
Nothing
    else CalC14 -> Maybe CalC14
forall a. a -> Maybe a
Just (CalC14 -> Maybe CalC14) -> CalC14 -> Maybe CalC14
forall a b. (a -> b) -> a -> b
$ CalC14 :: String -> CalRangeSummary -> [HDR] -> [HDR] -> CalC14
CalC14 {
          _calC14id :: String
_calC14id           = String
name
        , _calC14RangeSummary :: CalRangeSummary
_calC14RangeSummary = CalRangeSummary :: Int -> Int -> Int -> Int -> Int -> CalRangeSummary
CalRangeSummary {
              _calRangeStartTwoSigma :: Int
_calRangeStartTwoSigma = HDR -> Int
_hdrstart (HDR -> Int) -> HDR -> Int
forall a b. (a -> b) -> a -> b
$ [HDR] -> HDR
forall a. [a] -> a
head [HDR]
hdrs95
            , _calRangeStartOneSigma :: Int
_calRangeStartOneSigma = HDR -> Int
_hdrstart (HDR -> Int) -> HDR -> Int
forall a b. (a -> b) -> a -> b
$ [HDR] -> HDR
forall a. [a] -> a
head [HDR]
hdrs68
            , _calRangeMedian :: Int
_calRangeMedian        = Maybe Int -> Int
forall a. HasCallStack => Maybe a -> a
fromJust (Maybe Int -> Int) -> Maybe Int -> Int
forall a b. (a -> b) -> a -> b
$ Vector Int
cals Vector Int -> Maybe Int -> Maybe Int
forall a. Unbox a => Vector a -> Maybe Int -> Maybe a
`indexVU` Float -> [Float] -> Maybe Int
forall a. Eq a => a -> [a] -> Maybe Int
elemIndex ([Float] -> Float
forall (t :: * -> *) a. (Foldable t, Ord a) => t a -> a
minimum [Float]
distanceTo05) [Float]
distanceTo05
            , _calRangeStopOneSigma :: Int
_calRangeStopOneSigma  = HDR -> Int
_hdrstop  (HDR -> Int) -> HDR -> Int
forall a b. (a -> b) -> a -> b
$ [HDR] -> HDR
forall a. [a] -> a
last [HDR]
hdrs68
            , _calRangeStopTwoSigma :: Int
_calRangeStopTwoSigma  = HDR -> Int
_hdrstop  (HDR -> Int) -> HDR -> Int
forall a b. (a -> b) -> a -> b
$ [HDR] -> HDR
forall a. [a] -> a
last [HDR]
hdrs95
            }
        , _calC14HDROneSigma :: [HDR]
_calC14HDROneSigma  = [HDR]
hdrs68
        , _calC14HDRTwoSigma :: [HDR]
_calC14HDRTwoSigma  = [HDR]
hdrs95
    }
    where
        -- simple density cumsum for median age
        cumsumDensities :: [Float]
cumsumDensities = [(Int, Float)] -> [Float]
cumsumDens (Vector (Int, Float) -> [(Int, Float)]
forall a. Unbox a => Vector a -> [a]
VU.toList (Vector (Int, Float) -> [(Int, Float)])
-> Vector (Int, Float) -> [(Int, Float)]
forall a b. (a -> b) -> a -> b
$ Vector Int -> Vector Float -> Vector (Int, Float)
forall a b.
(Unbox a, Unbox b) =>
Vector a -> Vector b -> Vector (a, b)
VU.zip Vector Int
cals Vector Float
dens)
        distanceTo05 :: [Float]
distanceTo05 = (Float -> Float) -> [Float] -> [Float]
forall a b. (a -> b) -> [a] -> [b]
map (\Float
x -> Float -> Float
forall a. Num a => a -> a
abs (Float -> Float) -> Float -> Float
forall a b. (a -> b) -> a -> b
$ (Float
x Float -> Float -> Float
forall a. Num a => a -> a -> a
- Float
0.5)) [Float]
cumsumDensities
        -- sorted density cumsum for hdrs
        sortedDensities :: [(Int, Float)]
sortedDensities = ((Int, Float) -> (Int, Float) -> Ordering)
-> [(Int, Float)] -> [(Int, Float)]
forall a. (a -> a -> Ordering) -> [a] -> [a]
sortBy (((Int, Float) -> (Int, Float) -> Ordering)
-> (Int, Float) -> (Int, Float) -> Ordering
forall a b c. (a -> b -> c) -> b -> a -> c
flip (\ (Int
_, Float
dens1) (Int
_, Float
dens2) -> Float -> Float -> Ordering
forall a. Ord a => a -> a -> Ordering
compare Float
dens1 Float
dens2)) (Vector (Int, Float) -> [(Int, Float)]
forall a. Unbox a => Vector a -> [a]
VU.toList (Vector (Int, Float) -> [(Int, Float)])
-> Vector (Int, Float) -> [(Int, Float)]
forall a b. (a -> b) -> a -> b
$ Vector Int -> Vector Float -> Vector (Int, Float)
forall a b.
(Unbox a, Unbox b) =>
Vector a -> Vector b -> Vector (a, b)
VU.zip Vector Int
cals Vector Float
dens)
        cumsumSortedDensities :: [Float]
cumsumSortedDensities = [(Int, Float)] -> [Float]
cumsumDens [(Int, Float)]
sortedDensities
        isIn68 :: [Bool]
isIn68 = (Float -> Bool) -> [Float] -> [Bool]
forall a b. (a -> b) -> [a] -> [b]
map (Float -> Float -> Bool
forall a. Ord a => a -> a -> Bool
< Float
0.683) [Float]
cumsumSortedDensities
        isIn95 :: [Bool]
isIn95 = (Float -> Bool) -> [Float] -> [Bool]
forall a b. (a -> b) -> [a] -> [b]
map (Float -> Float -> Bool
forall a. Ord a => a -> a -> Bool
< Float
0.954) [Float]
cumsumSortedDensities
        contextualizedDensities :: [(Int, Float, Bool, Bool)]
contextualizedDensities = [(Int, Float, Bool, Bool)] -> [(Int, Float, Bool, Bool)]
forall a. Ord a => [a] -> [a]
sort ([(Int, Float, Bool, Bool)] -> [(Int, Float, Bool, Bool)])
-> [(Int, Float, Bool, Bool)] -> [(Int, Float, Bool, Bool)]
forall a b. (a -> b) -> a -> b
$ ((Int, Float) -> Bool -> Bool -> (Int, Float, Bool, Bool))
-> [(Int, Float)] -> [Bool] -> [Bool] -> [(Int, Float, Bool, Bool)]
forall a b c d. (a -> b -> c -> d) -> [a] -> [b] -> [c] -> [d]
zipWith3 (\(Int
y,Float
d) Bool
in68 Bool
in95 -> (Int
y,Float
d,Bool
in68,Bool
in95)) [(Int, Float)]
sortedDensities [Bool]
isIn68 [Bool]
isIn95
        hdrs68 :: [HDR]
hdrs68 = [(Int, Float, Bool, Bool)] -> [HDR]
densities2HDR68 [(Int, Float, Bool, Bool)]
contextualizedDensities
        hdrs95 :: [HDR]
hdrs95 = [(Int, Float, Bool, Bool)] -> [HDR]
densities2HDR95 [(Int, Float, Bool, Bool)]
contextualizedDensities
        -- helper functions
        indexVU :: Vector a -> Maybe Int -> Maybe a
indexVU Vector a
_ Maybe Int
Nothing = Maybe a
forall a. Maybe a
Nothing
        indexVU Vector a
x (Just Int
i) = Vector a
x Vector a -> Int -> Maybe a
forall a. Unbox a => Vector a -> Int -> Maybe a
VU.!? Int
i
        cumsumDens :: [(YearBCAD, Float)] -> [Float]
        cumsumDens :: [(Int, Float)] -> [Float]
cumsumDens [(Int, Float)]
x = (Float -> Float -> Float) -> [Float] -> [Float]
forall a. (a -> a -> a) -> [a] -> [a]
scanl1 Float -> Float -> Float
forall a. Num a => a -> a -> a
(+) ([Float] -> [Float]) -> [Float] -> [Float]
forall a b. (a -> b) -> a -> b
$ ((Int, Float) -> Float) -> [(Int, Float)] -> [Float]
forall a b. (a -> b) -> [a] -> [b]
map (Int, Float) -> Float
forall a b. (a, b) -> b
snd [(Int, Float)]
x
        densities2HDR68 :: [(Int, Float, Bool, Bool)] -> [HDR]
        densities2HDR68 :: [(Int, Float, Bool, Bool)] -> [HDR]
densities2HDR68 [(Int, Float, Bool, Bool)]
cDensities = 
            let highDensityGroups :: [[(Int, Float, Bool, Bool)]]
highDensityGroups = ((Int, Float, Bool, Bool) -> (Int, Float, Bool, Bool) -> Bool)
-> [(Int, Float, Bool, Bool)] -> [[(Int, Float, Bool, Bool)]]
forall a. (a -> a -> Bool) -> [a] -> [[a]]
groupBy (\(Int
_,Float
_,Bool
in681,Bool
_) (Int
_,Float
_,Bool
in682,Bool
_) -> Bool
in681 Bool -> Bool -> Bool
forall a. Eq a => a -> a -> Bool
== Bool
in682) [(Int, Float, Bool, Bool)]
cDensities
                filteredDensityGroups :: [[(Int, Float, Bool, Bool)]]
filteredDensityGroups = ([(Int, Float, Bool, Bool)] -> Bool)
-> [[(Int, Float, Bool, Bool)]] -> [[(Int, Float, Bool, Bool)]]
forall a. (a -> Bool) -> [a] -> [a]
filter (((Int, Float, Bool, Bool) -> Bool)
-> [(Int, Float, Bool, Bool)] -> Bool
forall (t :: * -> *) a. Foldable t => (a -> Bool) -> t a -> Bool
all (Int, Float, Bool, Bool) -> Bool
getIn68) [[(Int, Float, Bool, Bool)]]
highDensityGroups
            in ([(Int, Float, Bool, Bool)] -> HDR)
-> [[(Int, Float, Bool, Bool)]] -> [HDR]
forall a b. (a -> b) -> [a] -> [b]
map (\[(Int, Float, Bool, Bool)]
xs -> let yearRange :: [Int]
yearRange = ((Int, Float, Bool, Bool) -> Int)
-> [(Int, Float, Bool, Bool)] -> [Int]
forall a b. (a -> b) -> [a] -> [b]
map (Int, Float, Bool, Bool) -> Int
getYear [(Int, Float, Bool, Bool)]
xs in Int -> Int -> HDR
HDR ([Int] -> Int
forall a. [a] -> a
head [Int]
yearRange) ([Int] -> Int
forall a. [a] -> a
last [Int]
yearRange)) [[(Int, Float, Bool, Bool)]]
filteredDensityGroups
        densities2HDR95 :: [(Int, Float, Bool, Bool)] -> [HDR]
        densities2HDR95 :: [(Int, Float, Bool, Bool)] -> [HDR]
densities2HDR95 [(Int, Float, Bool, Bool)]
cDensities = 
            let highDensityGroups :: [[(Int, Float, Bool, Bool)]]
highDensityGroups = ((Int, Float, Bool, Bool) -> (Int, Float, Bool, Bool) -> Bool)
-> [(Int, Float, Bool, Bool)] -> [[(Int, Float, Bool, Bool)]]
forall a. (a -> a -> Bool) -> [a] -> [[a]]
groupBy (\(Int
_,Float
_,Bool
_,Bool
in951) (Int
_,Float
_,Bool
_,Bool
in952) -> Bool
in951 Bool -> Bool -> Bool
forall a. Eq a => a -> a -> Bool
== Bool
in952) [(Int, Float, Bool, Bool)]
cDensities
                filteredDensityGroups :: [[(Int, Float, Bool, Bool)]]
filteredDensityGroups = ([(Int, Float, Bool, Bool)] -> Bool)
-> [[(Int, Float, Bool, Bool)]] -> [[(Int, Float, Bool, Bool)]]
forall a. (a -> Bool) -> [a] -> [a]
filter (((Int, Float, Bool, Bool) -> Bool)
-> [(Int, Float, Bool, Bool)] -> Bool
forall (t :: * -> *) a. Foldable t => (a -> Bool) -> t a -> Bool
all (Int, Float, Bool, Bool) -> Bool
getIn95) [[(Int, Float, Bool, Bool)]]
highDensityGroups
            in ([(Int, Float, Bool, Bool)] -> HDR)
-> [[(Int, Float, Bool, Bool)]] -> [HDR]
forall a b. (a -> b) -> [a] -> [b]
map (\[(Int, Float, Bool, Bool)]
xs -> let yearRange :: [Int]
yearRange = ((Int, Float, Bool, Bool) -> Int)
-> [(Int, Float, Bool, Bool)] -> [Int]
forall a b. (a -> b) -> [a] -> [b]
map (Int, Float, Bool, Bool) -> Int
getYear [(Int, Float, Bool, Bool)]
xs in Int -> Int -> HDR
HDR ([Int] -> Int
forall a. [a] -> a
head [Int]
yearRange) ([Int] -> Int
forall a. [a] -> a
last [Int]
yearRange)) [[(Int, Float, Bool, Bool)]]
filteredDensityGroups
        getIn68 :: (Int, Float, Bool, Bool) -> Bool
        getIn68 :: (Int, Float, Bool, Bool) -> Bool
getIn68 (Int
_,Float
_,Bool
x,Bool
_) = Bool
x
        getIn95 :: (Int, Float, Bool, Bool) -> Bool
        getIn95 :: (Int, Float, Bool, Bool) -> Bool
getIn95 (Int
_,Float
_,Bool
_,Bool
x) = Bool
x
        getYear :: (Int, Float, Bool, Bool) -> Int
        getYear :: (Int, Float, Bool, Bool) -> Int
getYear (Int
year,Float
_,Bool
_,Bool
_) = Int
year