{-# LANGUAGE NoImplicitPrelude #-}
{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE FlexibleInstances #-}
module Synthesizer.State.Analysis (
   volumeMaximum,
   volumeEuclidean,
   volumeEuclideanSqr,
   volumeSum,
   volumeVectorMaximum,
   volumeVectorEuclidean,
   volumeVectorEuclideanSqr,
   volumeVectorSum,
   bounds,
   histogramDiscreteArray,
   histogramLinearArray,
   histogramDiscreteIntMap,
   histogramLinearIntMap,
   histogramIntMap,
   directCurrentOffset,
   scalarProduct,
   centroid,
   centroidRecompute,
   firstMoment,
   average,
   averageRecompute,
   rectify,
   zeros,
   flipFlopHysteresis,
   chirpTransform,
   ) where

import qualified Synthesizer.Plain.Analysis as Ana
import qualified Synthesizer.State.Control as Ctrl
import qualified Synthesizer.State.Signal  as Sig

import qualified Algebra.Algebraic             as Algebraic
import qualified Algebra.RealField             as RealField
import qualified Algebra.Field                 as Field
import qualified Algebra.RealRing              as RealRing
import qualified Algebra.Absolute              as Absolute
import qualified Algebra.Ring                  as Ring
import qualified Algebra.Additive              as Additive

import qualified Algebra.NormedSpace.Maximum   as NormedMax
import qualified Algebra.NormedSpace.Euclidean as NormedEuc
import qualified Algebra.NormedSpace.Sum       as NormedSum

import qualified Data.IntMap as IntMap
import qualified Data.Array as Array

import Data.Array (accumArray)

import NumericPrelude.Numeric
import NumericPrelude.Base


{- * Notions of volume -}

{- |
Volume based on Manhattan norm.
-}
{-# INLINE volumeMaximum #-}
volumeMaximum :: (RealRing.C y) => Sig.T y -> y
volumeMaximum :: forall y. C y => T y -> y
volumeMaximum =
   forall acc x. (acc -> x -> acc) -> acc -> T x -> acc
Sig.foldL forall a. Ord a => a -> a -> a
max forall a. C a => a
zero forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall y. C y => T y -> T y
rectify
--   maximum . rectify

{- |
Volume based on Energy norm.
-}
{-# INLINE volumeEuclidean #-}
volumeEuclidean :: (Algebraic.C y) => Sig.T y -> y
volumeEuclidean :: forall y. C y => T y -> y
volumeEuclidean =
   forall a. C a => a -> a
Algebraic.sqrt forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall y. C y => T y -> y
volumeEuclideanSqr

{-# INLINE volumeEuclideanSqr #-}
volumeEuclideanSqr :: (Field.C y) => Sig.T y -> y
volumeEuclideanSqr :: forall y. C y => T y -> y
volumeEuclideanSqr =
   forall y. C y => T y -> y
average forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall a b. (a -> b) -> T a -> T b
Sig.map forall a. C a => a -> a
sqr

{- |
Volume based on Sum norm.
-}
{-# INLINE volumeSum #-}
volumeSum :: (Field.C y, Absolute.C y) => Sig.T y -> y
volumeSum :: forall y. (C y, C y) => T y -> y
volumeSum = forall y. C y => T y -> y
average forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall y. C y => T y -> T y
rectify



{- |
Volume based on Manhattan norm.
-}
{-# INLINE volumeVectorMaximum #-}
volumeVectorMaximum :: (NormedMax.C y yv, Ord y) => Sig.T yv -> y
volumeVectorMaximum :: forall y yv. (C y yv, Ord y) => T yv -> y
volumeVectorMaximum =
   forall acc x. (acc -> x -> acc) -> acc -> T x -> acc
Sig.foldL forall a. Ord a => a -> a -> a
max forall a. C a => a
zero forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall a b. (a -> b) -> T a -> T b
Sig.map forall a v. C a v => v -> a
NormedMax.norm
--   NormedMax.norm
--   maximum . Sig.map NormedMax.norm

{- |
Volume based on Energy norm.
-}
{-# INLINE volumeVectorEuclidean #-}
volumeVectorEuclidean :: (Algebraic.C y, NormedEuc.C y yv) => Sig.T yv -> y
volumeVectorEuclidean :: forall y yv. (C y, C y yv) => T yv -> y
volumeVectorEuclidean =
   forall a. C a => a -> a
Algebraic.sqrt forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall y yv. (C y, Sqr y yv) => T yv -> y
volumeVectorEuclideanSqr

{-# INLINE volumeVectorEuclideanSqr #-}
volumeVectorEuclideanSqr :: (Field.C y, NormedEuc.Sqr y yv) => Sig.T yv -> y
volumeVectorEuclideanSqr :: forall y yv. (C y, Sqr y yv) => T yv -> y
volumeVectorEuclideanSqr =
   forall y. C y => T y -> y
average forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall a b. (a -> b) -> T a -> T b
Sig.map forall a v. Sqr a v => v -> a
NormedEuc.normSqr

{- |
Volume based on Sum norm.
-}
{-# INLINE volumeVectorSum #-}
volumeVectorSum :: (NormedSum.C y yv, Field.C y) => Sig.T yv -> y
volumeVectorSum :: forall y yv. (C y yv, C y) => T yv -> y
volumeVectorSum =
   forall y. C y => T y -> y
average forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall a b. (a -> b) -> T a -> T b
Sig.map forall a v. C a v => v -> a
NormedSum.norm




{- |
Compute minimum and maximum value of the stream the efficient way.
Input list must be non-empty and finite.
-}
{-# INLINE bounds #-}
bounds :: (Ord y) => Sig.T y -> (y,y)
bounds :: forall y. Ord y => T y -> (y, y)
bounds =
   forall b a. b -> (a -> T a -> b) -> T a -> b
Sig.switchL
      (forall a. HasCallStack => [Char] -> a
error [Char]
"Analysis.bounds: List must contain at least one element.")
      (\y
x T y
xs ->
          forall acc x. (acc -> x -> acc) -> acc -> T x -> acc
Sig.foldL (\(y
minX,y
maxX) y
y -> (forall a. Ord a => a -> a -> a
min y
y y
minX, forall a. Ord a => a -> a -> a
max y
y y
maxX)) (y
x,y
x) T y
xs)



{- * Miscellaneous -}

{-
histogram:
    length x = sum (histogramDiscrete x)

    units:
    1) histogram (amplify k x) = timestretch k (amplify (1/k) (histogram x))
    2) histogram (timestretch k x) = amplify k (histogram x)
    timestretch: k -> (s -> V) -> (k*s -> V)
    amplify:     k -> (s -> V) -> (s -> k*V)
    histogram:   (a -> b) -> (a^ia*b^ib -> a^ja*b^jb)
    x:           (s -> V)
    1) => (s^ia*(k*V)^ib -> s^ja*(k*V)^jb)
              = (s^ia*V^ib*k -> s^ja*V^jb/k)
       => ib=1, jb=-1
    2) => ((k*s)^ia*V^ib -> (k*s)^ja*V^jb)
              = (s^ia*V^ib -> s^ja*V^jb*k)
       => ia=0, ja=1
    histogram:   (s -> V) -> (V -> s/V)
histogram':
    integral (histogram' x) = integral x
    histogram' (amplify k x) = timestretch k (histogram' x)
    histogram' (timestretch k x) = amplify k (histogram' x)
     -> this does only apply if we slice the area horizontally
        and sum the slice up at each level,
        we must also restrict to the positive values,
        this is not quite the usual histogram
-}

{- |
Input list must be finite.
List is scanned twice, but counting may be faster.
-}
{-# INLINE histogramDiscreteArray #-}
histogramDiscreteArray :: Sig.T Int -> (Int, Sig.T Int)
histogramDiscreteArray :: T Int -> (Int, T Int)
histogramDiscreteArray =
   forall y. [Char] -> (T y -> (Int, T y)) -> T y -> (Int, T y)
withAtLeast1 [Char]
"histogramDiscreteArray" forall a b. (a -> b) -> a -> b
$ \ T Int
x ->
   let hist :: Array Int Int
hist =
          forall i e a.
Ix i =>
(e -> a -> e) -> e -> (i, i) -> [(i, a)] -> Array i e
accumArray forall a. C a => a -> a -> a
(+) forall a. C a => a
zero
             (forall y. Ord y => T y -> (y, y)
bounds T Int
x) (forall i. T i -> [(i, Int)]
attachOne T Int
x)
   in  (forall a b. (a, b) -> a
fst (forall i e. Array i e -> (i, i)
Array.bounds Array Int Int
hist), forall y. [y] -> T y
Sig.fromList (forall i e. Array i e -> [e]
Array.elems Array Int Int
hist))


{- |
Input list must be finite.
If the input signal is empty, the offset is @undefined@.
List is scanned twice, but counting may be faster.
The sum of all histogram values is one less than the length of the signal.
-}
{-# INLINE histogramLinearArray #-}
histogramLinearArray :: RealField.C y => Sig.T y -> (Int, Sig.T y)
histogramLinearArray :: forall y. C y => T y -> (Int, T y)
histogramLinearArray =
   forall y. C y => [Char] -> (T y -> (Int, T y)) -> T y -> (Int, T y)
withAtLeast2 [Char]
"histogramLinearArray" forall a b. (a -> b) -> a -> b
$ \ T y
x ->
   let (y
xMin,y
xMax) = forall y. Ord y => T y -> (y, y)
bounds T y
x
       hist :: Array Int y
hist =
          forall i e a.
Ix i =>
(e -> a -> e) -> e -> (i, i) -> [(i, a)] -> Array i e
accumArray forall a. C a => a -> a -> a
(+) forall a. C a => a
zero
             (forall a b. (C a, C b) => a -> b
floor y
xMin, forall a b. (C a, C b) => a -> b
floor y
xMax)
             (forall y. C y => T y -> [(Int, y)]
meanValues T y
x)
   in  (forall a b. (a, b) -> a
fst (forall i e. Array i e -> (i, i)
Array.bounds Array Int y
hist), forall y. [y] -> T y
Sig.fromList (forall i e. Array i e -> [e]
Array.elems Array Int y
hist))

{- |
Input list must be finite.
If the input signal is empty, the offset is @undefined@.
List is scanned once, counting may be slower.
-}
{-# INLINE histogramDiscreteIntMap #-}
histogramDiscreteIntMap :: Sig.T Int -> (Int, Sig.T Int)
histogramDiscreteIntMap :: T Int -> (Int, T Int)
histogramDiscreteIntMap =
   forall y. [Char] -> (T y -> (Int, T y)) -> T y -> (Int, T y)
withAtLeast1 [Char]
"histogramDiscreteIntMap" forall a b. (a -> b) -> a -> b
$ \ T Int
x ->
   let hist :: IntMap Int
hist = forall a. (a -> a -> a) -> [(Int, a)] -> IntMap a
IntMap.fromListWith forall a. C a => a -> a -> a
(+) (forall i. T i -> [(i, Int)]
attachOne T Int
x)
   in  case forall a. IntMap a -> [(Int, a)]
IntMap.toAscList IntMap Int
hist of
          [] -> forall a. HasCallStack => [Char] -> a
error [Char]
"histogramDiscreteIntMap: the list was non-empty before processing ..."
          fAll :: [(Int, Int)]
fAll@((Int
fIndex,Int
fHead):[(Int, Int)]
fs) -> (Int
fIndex,
              forall y. [y] -> T y
Sig.fromList forall a b. (a -> b) -> a -> b
$
              Int
fHead forall a. a -> [a] -> [a]
:
              forall (t :: * -> *) a. Foldable t => t [a] -> [a]
concat (forall a b c. (a -> b -> c) -> [a] -> [b] -> [c]
zipWith
                 (\(Int
i0,Int
_) (Int
i1,Int
f1) -> forall a. Int -> a -> [a]
replicate (Int
i1forall a. C a => a -> a -> a
-Int
i0forall a. C a => a -> a -> a
-Int
1) forall a. C a => a
zero forall a. [a] -> [a] -> [a]
++ [Int
f1])
                 [(Int, Int)]
fAll [(Int, Int)]
fs))

{-# INLINE histogramLinearIntMap #-}
histogramLinearIntMap :: RealField.C y => Sig.T y -> (Int, Sig.T y)
histogramLinearIntMap :: forall y. C y => T y -> (Int, T y)
histogramLinearIntMap =
   forall y. C y => [Char] -> (T y -> (Int, T y)) -> T y -> (Int, T y)
withAtLeast2 [Char]
"histogramLinearIntMap" forall a b. (a -> b) -> a -> b
$ \ T y
x ->
   let hist :: IntMap y
hist = forall a. (a -> a -> a) -> [(Int, a)] -> IntMap a
IntMap.fromListWith forall a. C a => a -> a -> a
(+) (forall y. C y => T y -> [(Int, y)]
meanValues T y
x)
   -- we can rely on the fact that the keys are contiguous
       (Int
startKey:[Int]
_, [y]
elems) = forall a b. [(a, b)] -> ([a], [b])
unzip (forall a. IntMap a -> [(Int, a)]
IntMap.toAscList IntMap y
hist)
   in  (Int
startKey, forall y. [y] -> T y
Sig.fromList [y]
elems)
   -- This doesn't work, due to a bug in IntMap of GHC-6.4.1
   -- in  (head (IntMap.keys hist), IntMap.elems hist)

{-# INLINE withAtLeast1 #-}
withAtLeast1 ::
   String ->
   (Sig.T y -> (Int, Sig.T y)) ->
   Sig.T y ->
   (Int, Sig.T y)
withAtLeast1 :: forall y. [Char] -> (T y -> (Int, T y)) -> T y -> (Int, T y)
withAtLeast1 [Char]
name T y -> (Int, T y)
f T y
x =
   forall b a. b -> (a -> b) -> Maybe a -> b
maybe
      (forall a. HasCallStack => [Char] -> a
error ([Char]
name forall a. [a] -> [a] -> [a]
++ [Char]
": no bounds found"), forall a. T a
Sig.empty)
      (forall a b. a -> b -> a
const (T y -> (Int, T y)
f T y
x)) forall a b. (a -> b) -> a -> b
$
   forall a. T a -> Maybe (a, T a)
Sig.viewL T y
x

{-# INLINE withAtLeast2 #-}
withAtLeast2 :: (RealRing.C y) =>
   String ->
   (Sig.T y -> (Int, Sig.T y)) ->
   Sig.T y ->
   (Int, Sig.T y)
withAtLeast2 :: forall y. C y => [Char] -> (T y -> (Int, T y)) -> T y -> (Int, T y)
withAtLeast2 [Char]
name T y -> (Int, T y)
f T y
x =
   forall b a. b -> (a -> b) -> Maybe a -> b
maybe
      (forall a. HasCallStack => [Char] -> a
error ([Char]
name forall a. [a] -> [a] -> [a]
++ [Char]
": no bounds found"), forall a. T a
Sig.empty)
      (\(y
y,T y
ys) ->
           if forall a. T a -> Bool
Sig.null T y
ys
             then (forall a b. (C a, C b) => a -> b
floor y
y, forall a. T a
Sig.empty)
             else T y -> (Int, T y)
f T y
x) forall a b. (a -> b) -> a -> b
$
   forall a. T a -> Maybe (a, T a)
Sig.viewL T y
x

{-
The bug in IntMap GHC-6.4.1 is:

*Synthesizer.Plain.Analysis> IntMap.keys $ IntMap.fromList $ [(0,0),(-1,-1::Int)]
[0,-1]
*Synthesizer.Plain.Analysis> IntMap.elems $ IntMap.fromList $ [(0,0),(-1,-1::Int)]
[0,-1]
*Synthesizer.Plain.Analysis> IntMap.assocs $ IntMap.fromList $ [(0,0),(-1,-1::Int)]
[(0,0),(-1,-1)]

The bug has gone in IntMap as shipped with GHC-6.6.
-}

{-# INLINE histogramIntMap #-}
histogramIntMap :: (RealField.C y) => y -> Sig.T y -> (Int, Sig.T Int)
histogramIntMap :: forall y. C y => y -> T y -> (Int, T Int)
histogramIntMap y
binsPerUnit =
   T Int -> (Int, T Int)
histogramDiscreteIntMap forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall y. C y => y -> T y -> T Int
quantize y
binsPerUnit

{-# INLINE quantize #-}
quantize :: (RealRing.C y) => y -> Sig.T y -> Sig.T Int
quantize :: forall y. C y => y -> T y -> T Int
quantize y
binsPerUnit = forall a b. (a -> b) -> T a -> T b
Sig.map (forall a b. (C a, C b) => a -> b
floor forall b c a. (b -> c) -> (a -> b) -> a -> c
. (y
binsPerUnitforall a. C a => a -> a -> a
*))

{-# INLINE attachOne #-}
attachOne :: Sig.T i -> [(i,Int)]
attachOne :: forall i. T i -> [(i, Int)]
attachOne = forall y. T y -> [y]
Sig.toList forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall a b. (a -> b) -> T a -> T b
Sig.map (\i
i -> (i
i,forall a. C a => a
one))

{-# INLINE meanValues #-}
meanValues :: RealField.C y => Sig.T y -> [(Int,y)]
meanValues :: forall y. C y => T y -> [(Int, y)]
meanValues = forall (t :: * -> *) a b. Foldable t => (a -> [b]) -> t a -> [b]
concatMap forall y. C y => (y, y) -> [(Int, y)]
Ana.spread forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall y. T y -> [y]
Sig.toList forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall a b. (a -> a -> b) -> T a -> T b
Sig.mapAdjacent (,)

{- |
Requires finite length.
This is identical to the arithmetic mean.
-}
{-# INLINE directCurrentOffset #-}
directCurrentOffset :: Field.C y => Sig.T y -> y
directCurrentOffset :: forall y. C y => T y -> y
directCurrentOffset = forall y. C y => T y -> y
average


{-# INLINE scalarProduct #-}
scalarProduct :: Ring.C y => Sig.T y -> Sig.T y -> y
scalarProduct :: forall y. C y => T y -> T y -> y
scalarProduct T y
xs T y
ys =
   forall a. C a => T a -> a
Sig.sum (forall a b c. (a -> b -> c) -> T a -> T b -> T c
Sig.zipWith forall a. C a => a -> a -> a
(*) T y
xs T y
ys)

{- |
'directCurrentOffset' must be non-zero.
-}
{-# INLINE centroid #-}
centroid :: Field.C y => Sig.T y -> y
centroid :: forall y. C y => T y -> y
centroid =
   forall a b c. (a -> b -> c) -> (a, b) -> c
uncurry forall a. C a => a -> a -> a
(/) forall b c a. (b -> c) -> (a -> b) -> a -> c
.
   forall a. C a => T a -> a
Sig.sum forall b c a. (b -> c) -> (a -> b) -> a -> c
.
   forall a b c. (a -> b -> c) -> T a -> T b -> T c
Sig.zipWith
      (\y
k y
x -> (y
kforall a. C a => a -> a -> a
*y
x, y
x))
      (forall a. (a -> a) -> a -> T a
Sig.iterate (forall a. C a => a
oneforall a. C a => a -> a -> a
+) forall a. C a => a
zero)

centroidRecompute :: Field.C y => Sig.T y -> y
centroidRecompute :: forall y. C y => T y -> y
centroidRecompute T y
xs =
   forall y. C y => T y -> y
firstMoment T y
xs forall a. C a => a -> a -> a
/ forall a. C a => T a -> a
Sig.sum T y
xs

{-# INLINE firstMoment #-}
firstMoment :: Field.C y => Sig.T y -> y
firstMoment :: forall y. C y => T y -> y
firstMoment T y
xs =
   forall y. C y => T y -> T y -> y
scalarProduct (forall a. (a -> a) -> a -> T a
Sig.iterate (forall a. C a => a
oneforall a. C a => a -> a -> a
+) forall a. C a => a
zero) T y
xs


{-# INLINE average #-}
average :: Field.C y => Sig.T y -> y
average :: forall y. C y => T y -> y
average =
   forall a b c. (a -> b -> c) -> (a, b) -> c
uncurry forall a. C a => a -> a -> a
(/) forall b c a. (b -> c) -> (a -> b) -> a -> c
.
   forall a. C a => T a -> a
Sig.sum forall b c a. (b -> c) -> (a -> b) -> a -> c
.
   forall a b. (a -> b) -> T a -> T b
Sig.map (forall a b c. (a -> b -> c) -> b -> a -> c
flip (,) forall a. C a => a
one)

averageRecompute :: Field.C y => Sig.T y -> y
averageRecompute :: forall y. C y => T y -> y
averageRecompute T y
x =
   forall a. C a => T a -> a
Sig.sum T y
x forall a. C a => a -> a -> a
/ forall a b. (C a, C b) => a -> b
fromIntegral (forall a. T a -> Int
Sig.length T y
x)

{-# INLINE rectify #-}
rectify :: Absolute.C y => Sig.T y -> Sig.T y
rectify :: forall y. C y => T y -> T y
rectify = forall a b. (a -> b) -> T a -> T b
Sig.map forall a. C a => a -> a
abs

{- |
Detects zeros (sign changes) in a signal.
This can be used as a simple measure of the portion
of high frequencies or noise in the signal.
It ca be used as voiced\/unvoiced detector in a vocoder.

@zeros x !! n@ is @True@ if and only if
@(x !! n >= 0) \/= (x !! (n+1) >= 0)@.
The result will be one value shorter than the input.
-}
{-# INLINE zeros #-}
zeros :: (Ord y, Additive.C y) => Sig.T y -> Sig.T Bool
zeros :: forall y. (Ord y, C y) => T y -> T Bool
zeros =
   forall a b. (a -> a -> b) -> T a -> T b
Sig.mapAdjacent forall a. Eq a => a -> a -> Bool
(/=) forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall a b. (a -> b) -> T a -> T b
Sig.map (forall a. Ord a => a -> a -> Bool
>=forall a. C a => a
zero)



{- |
Detect thresholds with a hysteresis.
-}
{-# INLINE flipFlopHysteresis #-}
flipFlopHysteresis :: (Ord y) =>
   (y,y) -> Ana.BinaryLevel -> Sig.T y -> Sig.T Ana.BinaryLevel
flipFlopHysteresis :: forall y. Ord y => (y, y) -> BinaryLevel -> T y -> T BinaryLevel
flipFlopHysteresis (y, y)
bnds = forall acc x. (acc -> x -> acc) -> acc -> T x -> T acc
Sig.scanL (forall a. Ord a => (a, a) -> BinaryLevel -> a -> BinaryLevel
Ana.flipFlopHysteresisStep (y, y)
bnds)

{- |
Almost naive implementation of the chirp transform,
a generalization of the Fourier transform.

More sophisticated algorithms like Rader, Cooley-Tukey, Winograd, Prime-Factor may follow.
-}
{-# INLINE chirpTransform #-}
chirpTransform :: Ring.C y =>
   y -> Sig.T y -> Sig.T y
chirpTransform :: forall y. C y => y -> T y -> T y
chirpTransform y
z T y
xs =
   forall a b. (a -> b) -> T a -> T b
Sig.map (forall y. C y => T y -> T y -> y
scalarProduct T y
xs) forall a b. (a -> b) -> a -> b
$
   forall a b. (a -> b) -> T a -> T b
Sig.map (\y
zn -> forall y. (y -> y -> y) -> y -> y -> T y
Ctrl.curveMultiscaleNeutral forall a. C a => a -> a -> a
(*) y
zn forall a. C a => a
one) forall a b. (a -> b) -> a -> b
$
   forall y. (y -> y -> y) -> y -> y -> T y
Ctrl.curveMultiscaleNeutral forall a. C a => a -> a -> a
(*) y
z forall a. C a => a
one