ratfun.jl's Introduction

RatFun.jl

RatFun is a package for working with functions expressible as a Fun divided by another Fun. The numerator and denominator may be different types of Funs.

Example usage

Define two functions on an interval using ApproxFun:

using ApproxFun
using RatFun
p = Fun(x->exp(-10x^2))
q = Fun(x->-1+.5x*sin(100x^2)

You can define a RationalFun, representing p/q, as follows.

r = p // q

We use Plots.jl to plot it.

using Plots
plot(plot(p,title="p"),plot(q,title="q"),plot(r,title="r=p/q"),layout=grid(3,1))

You can also do the same for Funs with more exotic types, such as those with Dirac deltas, as follows.

p2 = .7*DiracDelta(-1.25) - .9*DiracDelta(.5) + p
q2 = .5*KroneckerDelta(-1.25) - .7*KroneckerDelta(.5) + q
r2 = p2 // q2
plot(plot(p2,title="p2"),plot(q2,title="q2"),plot(r2,title="r2=p2/q2"),layout=grid(3,1))

RationalFuns with Dirac deltas in the numerator are used in the SpectralMeasures package.

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ratfun.jl's Issues

installation problem??

Ovverride denominator/numerator

Add sum(::RatFun)

Moved issue from JuliaApproximation/SpectralMeasures.jl#13

roots() not working for RatFun

Can not use roots() on a rational function.

MWE:

using ApproxFun,RatFun
function mwe()
	t = Fun(identity,0..pi)
	f = (2-2*cos(t))^2
	g = 2-2*cos(t)
	r = f//g
	display(roots(f-3.5))
	display(roots(g-3.5))
	display(roots(r-3.5))
end

Output:

julia> mwe()
1-element Array{Float64,1}:
 1.5061656879014247
1-element Array{Float64,1}:
 2.41885840577638
ERROR: MethodError: no method matching -(::RationalFun{Fun{Chebyshev{Interval{:closed,:closed,Float64},Float64},Float64,Array{Float64,1}},Fun{Chebyshev{Interval{:closed,:closed,Float64},Float64},Float64,Array{Float64,1}}}, ::Float64)
Closest candidates are:
  -(::Float64, ::Float64) at float.jl:397
  -(::Complex{Bool}, ::Real) at complex.jl:298
  -(::Missing, ::Number) at missing.jl:93

julia> versioninfo()
Julia Version 1.0.3
Commit 099e826241 (2018-12-18 01:34 UTC)
Platform Info:
  OS: Linux (x86_64-pc-linux-gnu)
  CPU: Intel(R) Core(TM) i5-4200U CPU @ 1.60GHz
  WORD_SIZE: 64
  LIBM: libopenlibm
  LLVM: libLLVM-6.0.0 (ORCJIT, haswell)

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