FrameFun.jl

Exploring practical possibilities of approximating functions with frames rather than with a basis
Author JuliaApproximation
Popularity
21 Stars
Updated Last
11 Months Ago
Started In
November 2014
Build Status Coverage
Build Status Coverage

FrameFun

Exploring practical possibilities of approximating functions with frames rather than with a basis. The package is heavily inspired by the Chebfun project and the Julia package ApproxFun.

using BasisFunctions, Plots, DomainSets, FrameFun
gr();

Frame Approximations in 1D

After choosing a suitable Basis and Domain, any function can be approximated in the resulting frame:

B = Fourier(61) → -1..1
D = -0.5..0.5
f = x->x
F = Fun(f,B,D)

P = plot(F,layout = 2)
plot!(F,f,subplot=2)

The bases support any AbstractFloat subtype, so high precision approximations are straightforward:

B = Fourier(61) → big(-1)..big(1)
F = Fun(f,B,D)

P = plot(F,layout=2)
plot!(F,f,subplot=2)

Frame Approximations in 2D

In higher dimensions, a basis can be any tensorproduct of (scaled) lower dimensional bases:

using StaticArrays
C = Disk(1.0)\Disk(0.3,SVector(0.2, 0.5))
B = (Fourier(31) → -1.3..1.3)^2
f = (x,y)->exp(x+y)
F = Fun(f,B,C)

P = heatmap(F,layout=2,aspect_ratio=1)
plot!(F,f,subplot=2,aspect_ratio=1)

Even fractal domains are not a problem:

B = (Fourier(31) → -1.0..0.35) ⊗ (Fourier(31) → -0.65..0.65)
f = (x,y)->cos(10*x*y)
F = Fun(f, B, mandelbrot())

P = heatmap(F,layout=2,aspect_ratio=1)
plot!(F,f,aspect_ratio=1,subplot=2)

Installation

From the Julia REPL, type ] to enter Pkg mode and run

pkg> add DomainSets, BasisFunctions, FrameFun