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polyhedral for many parameters does not work #601

@oameye

Description

@oameye

It seems that target_parameters!(::PolyhedralTracker, ::AbstractVector) was never implemented.

using HomotopyContinuation
@var u1, v1, ω, α, γ, λ, ω0

eqs = [
    -u1*ω^2 + u1*ω0^2 + (3/4)*u1^3*α + (3/4)*u1*v1^2*α + (-1/2)*u1*λ*ω0^2 + v1*γ*ω,
    -v1*ω^2 + v1*ω0^2 + (3/4)*v1^3*α - u1*γ*ω + (3/4)*u1^2*v1*α + (1/2)*v1*λ*ω0^2,
]

F = System(eqs, parameters = [ω, α, γ, λ, ω0], variables = [u1, v1])

input_array = [
    [0.9, 1.0, 0.01, 0.01, 1.1],
    [0.9105263157894737, 1.0, 0.01, 0.01, 1.1],
    [0.9210526315789473, 1.0, 0.01, 0.01, 1.1],
    [0.9315789473684211, 1.0, 0.01, 0.01, 1.1],
    [0.9421052631578948, 1.0, 0.01, 0.01, 1.1],
    [0.9526315789473684, 1.0, 0.01, 0.01, 1.1]]

HomotopyContinuation.solve(
    F;
    start_system=:polyhedral,
    target_parameters=input_array,
    threading=true
)
ERROR: MethodError: no method matching target_parameters!(::PolyhedralTracker{…}, ::Vector{…})

Closest candidates are:
  target_parameters!(::CoefficientHomotopy, ::AbstractVector)
   @ HomotopyContinuation c:\Users\User\Documents\GitHub\HomotopyContinuation.jl\src\homotopies\coefficient_homotopy.jl:82
  target_parameters!(::Solver, ::Any)
   @ HomotopyContinuation c:\Users\User\Documents\GitHub\HomotopyContinuation.jl\src\solve.jl:645
  target_parameters!(::ExtrinsicSubspaceHomotopy, ::Any)
   @ HomotopyContinuation c:\Users\User\Documents\GitHub\HomotopyContinuation.jl\src\homotopies\extrinsic_subspace_homotopy.jl:60
  ...

Stacktrace:
 [1] target_parameters!
   @ c:\Users\User\Documents\GitHub\HomotopyContinuation.jl\src\solve.jl:647 [inlined]
 [2] many_solve(solver::Solver{…}, starts::PolyhedralStartSolutionsIterator, many_target_parameters::Vector{…}, progress::ProgressMeter.Progress, transform_result::typeof(tuple), transform_parameters::typeof(identity), ::Val{…}; threading::Bool, catch_interrupt::Bool)
   @ HomotopyContinuation c:\Users\User\Documents\GitHub\HomotopyContinuation.jl\src\solve.jl:753
 [3] solve(S::Solver{…}, starts::PolyhedralStartSolutionsIterator, target_parameters::Vector{…}; show_progress::Bool, threading::Bool, catch_interrupt::Bool, transform_result::Nothing, transform_parameters::Function, flatten::Nothing)
   @ HomotopyContinuation c:\Users\User\Documents\GitHub\HomotopyContinuation.jl\src\solve.jl:698
 [4] solve(args::System; show_progress::Bool, threading::Bool, catch_interrupt::Bool, target_parameters::Vector{…}, stop_early_cb::Function, transform_result::Nothing, transform_parameters::typeof(identity), flatten::Nothing, target_subspaces::Nothing, kwargs::@Kwargs{})
   @ HomotopyContinuation c:\Users\User\Documents\GitHub\HomotopyContinuation.jl\src\solve.jl:475
 [5] top-level scope
   @ c:\Users\User\Documents\GitHub\HomotopyContinuation.jl\test\using HomotopyContinuation.jl:19
Some type information was truncated. Use `show(err)` to see complete types.

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