{-# 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
{-# 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
{-# 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
{-# 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
{-# 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
{-# 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
{-# 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
{-# 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)
{-# 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))
{-# 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))
{-# 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)
(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)
{-# 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
{-# 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 (,)
{-# 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)
{-# 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
{-# 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)
{-# 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)
{-# 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