zpk conjugate pairup fails on 0.0 and -0.0

[albheim]

I ran in to this just now, seems like this should fix it.

Problem is that

julia> isequal(0.0, -0.0)
false

julia> ==(0.0, -0.0)
true

julia> H = tf([0.65, 0, 0.45], [1, 0, 0], 0.2)
TransferFunction{Discrete{Float64}, ControlSystems.SisoRational{Float64}}
0.65z^2 + 0.45
--------------
    1.0z^2

Sample Time: 0.2 (seconds)
Discrete-time transfer function model

julia> bodeplot(H)
ERROR: ArgumentError: zpk model should be real-valued, but zeros do not come in conjugate pairs.
Stacktrace:
  [1] ControlSystems.SisoZpk{Float64, ComplexF64}(z::Vector{ComplexF64}, p::Vector{ComplexF64}, k::Float64)
    @ ControlSystems ~/.julia/packages/ControlSystems/lbxGy/src/types/SisoTfTypes/SisoZpk.jl:16
  [2] ControlSystems.SisoZpk{Float64, ComplexF64}(z::Vector{ComplexF64}, p::Vector{Float64}, k::Float64)
    @ ControlSystems ~/.julia/packages/ControlSystems/lbxGy/src/types/SisoTfTypes/SisoZpk.jl:23
  [3] convert(#unused#::Type{ControlSystems.SisoZpk{Float64, ComplexF64}}, f::ControlSystems.SisoRational{Float64})
    @ ControlSystems ~/.julia/packages/ControlSystems/lbxGy/src/types/SisoTfTypes/conversion.jl:8
  [4] convert
    @ ~/.julia/packages/ControlSystems/lbxGy/src/types/SisoTfTypes/conversion.jl:14 [inlined]
  [5] _broadcast_getindex_evalf
    @ ./broadcast.jl:670 [inlined]
  [6] _broadcast_getindex
    @ ./broadcast.jl:653 [inlined]
  [7] getindex
    @ ./broadcast.jl:597 [inlined]
  [8] copy
    @ ./broadcast.jl:899 [inlined]
  [9] materialize
    @ ./broadcast.jl:860 [inlined]
 [10] convert(#unused#::Type{TransferFunction{Discrete{Float64}, ControlSystems.SisoZpk}}, G::TransferFunction{Discrete{Float64}, ControlSystems.SisoRational{Float64}})
    @ ControlSystems ~/.julia/packages/ControlSystems/lbxGy/src/types/conversion.jl:60
 [11] zpkdata
    @ ~/.julia/packages/ControlSystems/lbxGy/src/analysis.jl:132 [inlined]
 [12] _bounds_and_features(sys::TransferFunction{Discrete{Float64}, ControlSystems.SisoRational{Float64}}, plot::Val{:bode})
    @ ControlSystems ~/.julia/packages/ControlSystems/lbxGy/src/freqresp.jl:321
 [13] #157
    @ ~/.julia/packages/ControlSystems/lbxGy/src/freqresp.jl:307 [inlined]
 [14] iterate
    @ ./generator.jl:47 [inlined]
 [15] _collect(c::Vector{TransferFunction{Discrete{Float64}, ControlSystems.SisoRational{Float64}}}, itr::Base.Generator{Vector{TransferFunction{Discrete{Float64}, ControlSystems.SisoRational{Float64}}}, ControlSystems.var"#157#158"{Val{:bode}}}, #unused#::Base.EltypeUnknown, isz::Base.HasShape{1})
    @ Base ./array.jl:744
 [16] collect_similar(cont::Vector{TransferFunction{Discrete{Float64}, ControlSystems.SisoRational{Float64}}}, itr::Base.Generator{Vector{TransferFunction{Discrete{Float64}, ControlSystems.SisoRational{Float64}}}, ControlSystems.var"#157#158"{Val{:bode}}})
    @ Base ./array.jl:653
 [17] map(f::Function, A::Vector{TransferFunction{Discrete{Float64}, ControlSystems.SisoRational{Float64}}})
    @ Base ./abstractarray.jl:2849
 [18] _default_freq_vector(systems::Vector{TransferFunction{Discrete{Float64}, ControlSystems.SisoRational{Float64}}}, plot::Val{:bode})
    @ ControlSystems ~/.julia/packages/ControlSystems/lbxGy/src/freqresp.jl:307
 [19] _processfreqplot(plottype::Val{:bode}, systems::Vector{TransferFunction{Discrete{Float64}, ControlSystems.SisoRational{Float64}}})
    @ ControlSystems ~/.julia/packages/ControlSystems/lbxGy/src/plotting.jl:181
 [20] _processfreqplot(::Val{:bode}, ::TransferFunction{Discrete{Float64}, ControlSystems.SisoRational{Float64}})
    @ ControlSystems ~/.julia/packages/ControlSystems/lbxGy/src/plotting.jl:173
 [21] macro expansion
    @ ~/.julia/packages/ControlSystems/lbxGy/src/plotting.jl:204 [inlined]
 [22] apply_recipe(plotattributes::AbstractDict{Symbol, Any}, p::ControlSystems.Bodeplot)
    @ ControlSystems ~/.julia/packages/RecipesBase/qpxEX/src/RecipesBase.jl:289
 [23] _process_userrecipes!(plt::Any, plotattributes::Any, args::Any)
    @ RecipesPipeline ~/.julia/packages/RecipesPipeline/oVorB/src/user_recipe.jl:36
 [24] recipe_pipeline!(plt::Any, plotattributes::Any, args::Any)
    @ RecipesPipeline ~/.julia/packages/RecipesPipeline/oVorB/src/RecipesPipeline.jl:70
 [25] _plot!(plt::Plots.Plot, plotattributes::Any, args::Any)
    @ Plots ~/.julia/packages/Plots/LI4FE/src/plot.jl:208
 [26] plot(args::Any; kw::Base.Pairs{Symbol, V, Tuple{Vararg{Symbol, N}}, NamedTuple{names, T}} where {V, N, names, T<:Tuple{Vararg{Any, N}}})
    @ Plots ~/.julia/packages/Plots/LI4FE/src/plot.jl:91
 [27] plot
    @ ~/.julia/packages/Plots/LI4FE/src/plot.jl:85 [inlined]
 [28] bodeplot(::TransferFunction{Discrete{Float64}, ControlSystems.SisoRational{Float64}}, ::Vararg{Any}; kw::Base.Pairs{Symbol, Union{}, Tuple{}, NamedTuple{(), Tuple{}}})
    @ ControlSystems ~/.julia/packages/RecipesBase/qpxEX/src/RecipesBase.jl:364
 [29] bodeplot(::TransferFunction{Discrete{Float64}, ControlSystems.SisoRational{Float64}}, ::Vararg{Any})
    @ ControlSystems ~/.julia/packages/RecipesBase/qpxEX/src/RecipesBase.jl:364
 [30] top-level scope
    @ REPL[41]:1

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Plots were compared to references. 7/11 images have changed, see differences below.
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Difference	Reference Image	New Image
❌ 0.048
✔️ 0.001
✔️ 0.001
✔️ 0.0
❌ 0.043
❌ 0.046
✔️ 0.01

[codecov]

Codecov Report

Merging #674 (f49b6f0) into master (a8a53ac) will not change coverage.
The diff coverage is 100.00%.

@@           Coverage Diff           @@
##           master     #674   +/-   ##
=======================================
  Coverage   87.33%   87.33%           
=======================================
  Files          34       34           
  Lines        3522     3522           
=======================================
  Hits         3076     3076           
  Misses        446      446           

Impacted Files	Coverage Δ
src/types/SisoTfTypes/SisoZpk.jl	69.06% <100.00%> (ø)

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[JuliaControlBot]

This is an automated message.
Plots were compared to references. 7/11 images have changed, see differences below.
After pulling this PR, please update the reference images by creating a PR to ControlExamplePlots.jl here.

Difference	Reference Image	New Image
❌ 0.048
✔️ 0.001
✔️ 0.001
✔️ 0.0
❌ 0.043
❌ 0.046
✔️ 0.01

[baggepinnen]

Hmm, that's a bit unfortunate, isequal was used to work with symbolic coefficients. I wonder if there's a solution that works in both cases.

[albheim]

Ahh, that is annoying. Why does symbolics need isequal rather than ==?

[baggepinnen]

a==b with symbols produces a symbolic expression rather than a Bool. isequal always results in a Bool.

[albheim]

Hmm, not sure I like that. It seems like it would make it problematic to handle both symbolics and numerics with the same code as soon as you want to compare any of the numbers then?

The docs for == say

The result is of type Bool, except when one of the operands is missing, in
  which case missing is returned (three-valued logic
  (https://en.wikipedia.org/wiki/Three-valued_logic)). 

which even though possible to not get bool, it should then return missing. Isn't it frowned upon to add other meaning to operators defined in Base?