Numeric.LazySplines

This module consists of source code to accompany the draft paper: "Declarative Equations, Compositional Strategies: Solving Differential Systems with Lazy Splines" at http://gbaz.github.io/slides/ode-draft-2009.pdf.

See the paper for a description of how the system works, and the source of the Examples module for usage.

Some slides from a more recent description of the core mechanism are at http://gbaz.github.io/slides/integration.html.

Documentation

class Sampleable a where

Something that can be sampled.

Methods

at :: a -> Double -> Double

Instances

Sampleable Spline

Sampleable PolySegment

Sampleable Poly

Sampleable [Poly]

type Poly = [Double]

type PolySegment = (Double, Poly)

type Spline = [PolySegment]

type SplinePredicate = Double -> Double -> Poly -> Double

duration :: Spline -> Double

maxDuration :: Double

liftS :: Double -> Spline

deriveSpline :: Spline -> Spline

integrateSpline :: Spline -> Spline

inSpline2 :: (Poly -> Poly -> Poly) -> Spline -> Spline -> Spline

shiftBy :: Double -> Poly -> Poly

mapSpline :: Bool -> (Double -> Double -> Poly -> Poly) -> Spline -> Spline

match :: a -> [a] -> [a]

matchScale :: Double -> Double -> [Double] -> [Double]

trimmingTo :: Spline -> Int -> Spline infixl 1

extrapForward :: Spline -> Double -> Spline infixl 1

scaleRest :: Poly -> Double -> Poly

satisfying :: Spline -> (Double, SplinePredicate) -> Spline infixl 1

splitWhen :: Spline -> (Double, Double, SplinePredicate) -> Spline infixl 1

extendWhen :: Spline -> (Double, Double, SplinePredicate) -> Spline infixl 1

lastDef :: t -> [t] -> t

trimSmart :: Spline -> SplinePredicate -> Spline infixl 1

headDef :: t -> [t] -> t

(#) :: (Num [a], Num a, Eq a) => [a] -> [a] -> [a] infixr 9

integ :: [Double] -> [Double]

diff :: Num c => [c] -> [c]

countFrom :: Num a => a -> [a]

dropZeros :: [Double] -> [Double]

newton :: Double -> (Double -> Double) -> [Double]

pickValue :: Double -> (a -> Double) -> [a] -> a

findValue :: Double -> (a -> Double) -> (Double -> a) -> a