Numeric.Tools.Interpolation

Function interpolation.

Sine interpolation using cubic splines:

>>> let tbl = cubicSpline $ tabulateFun (uniformMesh (0,10) 100) sin
>>> tbl `at` 1.786
0.9769239849844867

Type class

class (IndexVal (interp mesh) ~ (Double, Double), Indexable (interp mesh), IndexVal mesh ~ Double, Mesh mesh) => Interpolation interp mesh where

Type class for Interpolation algorithms. Since some algorithms require some particular mesh type it's present as type class parameter. Every algorithms should be instance of Indexable as well. Indexing should return pair (x,y) for u'th mesh node.

Methods

at :: interp mesh -> Double -> Double

Interpolate function at some point. Function should not fail outside of mesh however it may and most likely will give nonsensical results

unsafeTabulate :: Vector v Double => mesh -> v Double -> interp mesh

Use table of already evaluated function and mesh. Sizes of mesh and table must coincide but it's not checked. Do not use this function use tabulate instead.

interpolationMesh :: interp mesh -> mesh

Get mesh.

interpolationTable :: interp mesh -> Vector Double

Get table of function values

Instances

(Mesh mesh, ~ * (IndexVal mesh) Double) => Interpolation CubicSpline mesh

(Mesh mesh, ~ * (IndexVal mesh) Double) => Interpolation LinearInterp mesh

tabulate :: (Interpolation i m, Vector v Double) => m -> v Double -> i m

Use table of already evaluated function and mesh. Sizes of mesh and table must coincide.

tabulateFun :: Interpolation i m => m -> (Double -> Double) -> i m

Tabulate function.

Linear interpolation

data LinearInterp mesh

Data for linear interpolation

Instances

Typeable1 LinearInterp

(Mesh mesh, ~ * (IndexVal mesh) Double) => Interpolation LinearInterp mesh

Eq mesh => Eq (LinearInterp mesh)

Data mesh => Data (LinearInterp mesh)

Show mesh => Show (LinearInterp mesh)

(Mesh mesh, ~ * (IndexVal mesh) Double) => Indexable (LinearInterp mesh)

linearInterp :: LinearInterp mesh -> LinearInterp mesh

Function used to fix types

Cubic splines

data CubicSpline a

Natural cubic splines

Instances

Typeable1 CubicSpline

(Mesh mesh, ~ * (IndexVal mesh) Double) => Interpolation CubicSpline mesh

Eq a => Eq (CubicSpline a)

Data a => Data (CubicSpline a)

Show a => Show (CubicSpline a)

(Mesh mesh, ~ * (IndexVal mesh) Double) => Indexable (CubicSpline mesh)

cubicSpline :: CubicSpline a -> CubicSpline a

Function used to fix types

Reexport of mesh type

module Numeric.Tools.Mesh

Default methods

defaultInterpSize :: Interpolation i m => i m -> Int

Default implementation of size for interpolation algorithms.

defaultInterpIndex :: Interpolation i m => i m -> Int -> (Double, Double)

Default implementation of unsafeIndex for interpolation algorithms.