Synthesizer.Interpolation.Class

See NumericPrelude.AffineSpace for design discussion.

Documentation

class C a => C a v where

Given that scale zero v == Additive.zero this type class is equivalent to Module in the following way:

scaleAndAccumulate (a,x) =
   let ax = a *> x
   in  (ax, (ax+))

(see implementation of scaleAndAccumulateModule) and

x+y = scaleAccumulate one y $ scale one x
zero = scale zero x
s*>x = scale s x

But this redundancy is only because of a lack of the type system or lack of my imagination how to solve it better. Use this type class for all kinds of interpolation, that is where addition and scaling alone make no sense.

I intended to name this class AffineSpace, because all interpolations should be affine combinations. This property is equivalent to interpolations that preserve constant functions. However, I cannot easily assert this property and I'm not entirely sure that all reasonable interpolations are actually affine.

Early versions had a zero method, but this is against the idea of interpolation. For implementing zero we needed a Maybe wrapper for interpolation of StorableVectors. Btw. having zero instead of scale is also inefficient, since every sum must include a zero summand, which works well only when the optimizer simplifies addition with a constant.

We use only one class method that contains actually two methods: scale and scaleAccumulate. We expect that instances are always defined on record types lifting interpolations from scalars to records. This should be done using makeMac and friends or the MAC type and the Applicative interface for records with many elements.

Minimal complete definition

scaleAndAccumulate

Methods

scaleAndAccumulate :: (a, v) -> (v, v -> v)

Instances

C Double Double

Methods

scaleAndAccumulate :: (Double, Double) -> (Double, Double -> Double)

C Float Float

Methods

scaleAndAccumulate :: (Float, Float) -> (Float, Float -> Float)

C a v => C a (T v)

Methods

scaleAndAccumulate :: (a, T v) -> (T v, T v -> T v)

C a v => C a (T v)

Methods

scaleAndAccumulate :: (a, T v) -> (T v, T v -> T v)

C a v => C a (Parameter v)

Methods

scaleAndAccumulate :: (a, Parameter v) -> (Parameter v, Parameter v -> Parameter v)

C a v => C a (Parameter v)

Methods

scaleAndAccumulate :: (a, Parameter v) -> (Parameter v, Parameter v -> Parameter v)

(C a v, Storable v) => C a (Parameter v)

Methods

scaleAndAccumulate :: (a, Parameter v) -> (Parameter v, Parameter v -> Parameter v)

C a v => C a (Parameter v)

Methods

scaleAndAccumulate :: (a, Parameter v) -> (Parameter v, Parameter v -> Parameter v)

C a v => C a (Parameter v)

Methods

scaleAndAccumulate :: (a, Parameter v) -> (Parameter v, Parameter v -> Parameter v)

C a v => C a (Parameter v)

Methods

scaleAndAccumulate :: (a, Parameter v) -> (Parameter v, Parameter v -> Parameter v)

C a v => C a (Parameter v)

Methods

scaleAndAccumulate :: (a, Parameter v) -> (Parameter v, Parameter v -> Parameter v)

(C a v, C a w) => C a (v, w)

Methods

scaleAndAccumulate :: (a, (v, w)) -> ((v, w), (v, w) -> (v, w))

(C a v, C a w, C a u) => C a (v, w, u)

Methods

scaleAndAccumulate :: (a, (v, w, u)) -> ((v, w, u), (v, w, u) -> (v, w, u))

C a => C (T a) (T a)

Methods

scaleAndAccumulate :: (T a, T a) -> (T a, T a -> T a)

scale :: C a v => (a, v) -> v

scaleAccumulate :: C a v => (a, v) -> v -> v

(+.*) :: C a v => v -> (a, v) -> v infixl 6

Infix variant of scaleAccumulate.

combine2 :: C a v => a -> (v, v) -> v

combineMany :: C a v => (a, T a) -> (v, T v) -> v

convenience functions for defining scaleAndAccumulate

scaleAndAccumulateRing :: C a => (a, a) -> (a, a -> a)

scaleAndAccumulateModule :: C a v => (a, v) -> (v, v -> v)

scaleAndAccumulateApplicative :: (C a v, Applicative f) => (a, f v) -> (f v, f v -> f v)

scaleAndAccumulateRingApplicative :: (C a, Applicative f) => (a, f a) -> (f a, f a -> f a)

scaleAndAccumulateModuleApplicative :: (C a v, Applicative f) => (a, f v) -> (f v, f v -> f v)

newtype MAC a v x

A special reader monad.

Constructors

MAC

Fields

• runMac :: (a, v) -> (x, v -> x)

Instances

Functor (MAC a v)

Methods

fmap :: (a -> b) -> MAC a v a -> MAC a v b

(<$) :: a -> MAC a v b -> MAC a v a

Applicative (MAC a v)

Methods

pure :: a -> MAC a v a

(<*>) :: MAC a v (a -> b) -> MAC a v a -> MAC a v b

liftA2 :: (a -> b -> c) -> MAC a v a -> MAC a v b -> MAC a v c

(*>) :: MAC a v a -> MAC a v b -> MAC a v b

(<*) :: MAC a v a -> MAC a v b -> MAC a v a

element :: C a x => (v -> x) -> MAC a v x

makeMac :: C a x => (x -> v) -> (v -> x) -> (a, v) -> (v, v -> v)

makeMac2 :: (C a x, C a y) => (x -> y -> v) -> (v -> x) -> (v -> y) -> (a, v) -> (v, v -> v)

makeMac3 :: (C a x, C a y, C a z) => (x -> y -> z -> v) -> (v -> x) -> (v -> y) -> (v -> z) -> (a, v) -> (v, v -> v)