Better warning/error message for monodromy_solve when start solution is wrong/bad

[TorkelE]

I try to find steady states using monodromy (from a case where I know one solution, but there are two additional ones):

using HomotopyContinuation
@var X Y k1 k2 k3 k4 
polys = [
    -k1*Y + 0.5*k2*X^2
    -X*k4 + 2*k1*Y - 0.5*k2*X^2 - Y*X*k3
]
sys = HomotopyContinuation.System(polys; parameters = [k1 ,k2, k3, k4])

p_vals = [8.0, 2.0, 1.0, 1.5]
ss_init = [4.5, 6.0]
mres = monodromy_solve(sys, ss_init, p_vals)

Here I get a:

┌ Warning: None of the provided solutions is a valid start solution.
└ @ HomotopyContinuation ~/.julia/packages/HomotopyContinuation/HdN5z/src/monodromy.jl:806

In this case I flipped it, and it should have been ss_init = [6.0, 4.5]. I presume that the problem is that the start solution does not solve the system (with the correct one, everything works flawlessly). However, it might be useful to have a note that this is the reason (if Homotopy Continuation knows this to bet he case).

[PBrdng]

I presume that the problem is that the start solution does not solve the system

Exactly, thats the reason. Doesn't the warning message

Warning: None of the provided solutions is a valid start solution.

say this explicitly? What do you suggest otherwise?

[TorkelE]

Basically, it would be an improvement (a mild improvement, this is not a biggie) to explicitly say that it is due to the solutions not actually being solutions to the system. I.e. I was uncertain if they were not valid because they had the wrong format or some other issue.

[PBrdng]

What about

Warning: None of the provided solutions is a valid start solution (F(x) ≠ 0).

[TorkelE]

Yes, that'd be perfect

[saschatimme]

It's also a non-valid start solution if the Jacobian doesn't have full column rank

[PBrdng]

True.

"None of the provided solutions is a valid start solution (F(x) ≠ 0 or det JF(x) = 0)"?

[PBrdng]

See #622