AssertionError: length(ret) == n

[cscherrer]

Hi @simonbyrne , thanks for this package!

In trying this out, I've gotten really nice results for things like a polynomial approximation to log1pexp. But this AssertionError seems very common. It had seemed to happen mostly when asking for rational function approximations - polynomial approximations seem a little more likely to work - but it also fails in (what would seem to be) simple cases like

using Distributions
julia> ratfn_minimax(x -> logpdf(Beta(2,4),x), (nextfloat(0.0),prevfloat(1.0)),2,0)
ERROR: AssertionError: length(ret) == n
Stacktrace:
 [1] winnow_extrema(::Array{Tuple{BigFloat,BigFloat},1}, ::Int64) at /home/chad/.julia/packages/Remez/HLpT8/src/Remez.jl:347
 [2] ratfn_minimax(::var"#50#51", ::Tuple{Float64,Float64}, ::Int64, ::Int64, ::Remez.var"#8#13") at /home/chad/.julia/packages/Remez/HLpT8/src/Remez.jl:598
 [3] ratfn_minimax(::Function, ::Tuple{Float64,Float64}, ::Int64, ::Int64) at /home/chad/.julia/packages/Remez/HLpT8/src/Remez.jl:557
 [4] top-level scope at REPL[36]:1
 [5] include_string(::Function, ::Module, ::String, ::String) at ./loading.jl:1088

Any idea what's going on here?

[simonbyrne]

Sorry, I don't actually know that much about the internals (all I really did is take the ARM code and turn it into a package), though one day I'll read up on it. I have found that modifying one side of the interval can sometimes help, e.g. #6 (comment)

[cscherrer]

Thanks, that Arnoldi paper looks really interesting too

[oscardssmith]

I've found that one place this can happen is if there's a division by zero (especially annoying when it's a 0/0 that mathematically should be defined)

[simonbyrne]

@oscardssmith do you have an example?

[KlausC]

Here are some elementary examples, which fail with that error.

julia> f(x) = x
f (generic function with 1 method)

julia> N,D,E,X = ratfn_minimax(f, (-1.0, 1.0), 3, 3)
ERROR: AssertionError: length(ret) == n
Stacktrace:
 [1] winnow_extrema(extrema::Vector{Tuple{BigFloat, BigFloat}}, n::Int64)
   @ Remez ~/dev/Remez.jl/src/Remez.jl:347
 [2] ratfn_minimax(f::typeof(f), interval::Tuple{Float64, Float64}, n::Int64, d::Int64, w::Remez.var"#8#13")
   @ Remez ~/dev/Remez.jl/src/Remez.jl:598
 [3] ratfn_minimax(f::Function, interval::Tuple{Float64, Float64}, n::Int64, d::Int64)
   @ Remez ~/dev/Remez.jl/src/Remez.jl:557
 [4] top-level scope
   @ REPL[17]:1

julia> f(x) = (x + x^2 ) * (x - x^3/6)
f (generic function with 1 method)

julia> N,D,E,X = ratfn_minimax(f, (-1.0, 1.0), 2, 2)
ERROR: AssertionError: length(ret) == n
Stacktrace:
 [1] winnow_extrema(extrema::Vector{Tuple{BigFloat, BigFloat}}, n::Int64)
   @ Remez ~/dev/Remez.jl/src/Remez.jl:347
 [2] ratfn_minimax(f::typeof(f), interval::Tuple{Float64, Float64}, n::Int64, d::Int64, w::Remez.var"#8#13")
   @ Remez ~/dev/Remez.jl/src/Remez.jl:598
 [3] ratfn_minimax(f::Function, interval::Tuple{Float64, Float64}, n::Int64, d::Int64)
   @ Remez ~/dev/Remez.jl/src/Remez.jl:557
 [4] top-level scope
   @ REPL[12]:1

julia> f(x) = (x + x^2 ) * x
f (generic function with 1 method)

julia> N,D,E,X = ratfn_minimax(f, (-1.0, 1.0), 2, 2)
ERROR: AssertionError: length(ret) == n
Stacktrace:
 [1] winnow_extrema(extrema::Vector{Tuple{BigFloat, BigFloat}}, n::Int64)
   @ Remez ~/dev/Remez.jl/src/Remez.jl:347
 [2] ratfn_minimax(f::typeof(f), interval::Tuple{Float64, Float64}, n::Int64, d::Int64, w::Remez.var"#8#13")
   @ Remez ~/dev/Remez.jl/src/Remez.jl:598
 [3] ratfn_minimax(f::Function, interval::Tuple{Float64, Float64}, n::Int64, d::Int64)
   @ Remez ~/dev/Remez.jl/src/Remez.jl:557
 [4] top-level scope
   @ REPL[14]:1

julia> N,D,E,X = ratfn_minimax(f, (-1.0, 1.0), 3, 3)
ERROR: AssertionError: length(ret) == n
Stacktrace:
 [1] winnow_extrema(extrema::Vector{Tuple{BigFloat, BigFloat}}, n::Int64)
   @ Remez ~/dev/Remez.jl/src/Remez.jl:347
 [2] ratfn_minimax(f::typeof(f), interval::Tuple{Float64, Float64}, n::Int64, d::Int64, w::Remez.var"#8#13")
   @ Remez ~/dev/Remez.jl/src/Remez.jl:598
 [3] ratfn_minimax(f::Function, interval::Tuple{Float64, Float64}, n::Int64, d::Int64)
   @ Remez ~/dev/Remez.jl/src/Remez.jl:557
 [4] top-level scope
   @ REPL[15]:1