NonlinearSolve.jl
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Published
20 hours ago •
SciML
SciML
Storing trace
I want to store the trace during solving. I would love to use the native NonlinearSolve methods for that, but it appears to me that no such thing is implemented. So I want to use the NLSolveJL interface. But from reading the documentation, I am still not able to see - how do i use it?
So far I have tried the following
#The functional version:
julia> solver = solve(probN, NewtonRaphson(), tol = 1e-9)
u: 8-element Vector{Float64}:
27.52327682597094
27.523962383296873
3.2064613688401113
13.258386042046885
0.8000852068277563
0.4578205135984268
27.929656903088112
124.54137097709595
#Failed attempts:
julia> solver = solve(probN, NLSolveJL(method=:newton,), tol = 1e-9)
ERROR: UndefVarError: NLSolveJL not defined
Stacktrace:
[1] top-level scope
@ REPL[9]:1
julia> solver = NLSolveJL(probN, tol = 1e-9, method=:newton)
ERROR: UndefVarError: NLSolveJL not defined
Stacktrace:
[1] top-level scope
@ REPL[11]:1
With NLSolveJL not being defined, I was wondering if it is simply not exported. But this seems not to be the case:
julia> NonlinearSolve.NLSolveJL
ERROR: UndefVarError: NLSolveJL not defined
Stacktrace:
[1] getproperty(x::Module, f::Symbol)
@ Base .\Base.jl:35
[2] top-level scope
@ REPL[12]:1
I think that a section with working examples in the docs of how to access non-native solvers would go a long ways.
In a fresh session:
julia> using NonlinearSolve
julia>
julia> v = 120 #kg
120
julia> k = 2.5 #m
2.5
julia> w = 4.0 #km/m
4.0
julia> α = 2e-7 #kg⁻¹
2.0e-7
julia>
julia> function F(x⃗, parameters)
L₀, L, p, x, θ, φ, a, H = tuple(x⃗...)
return [
a*(cosh(x/a)-1) - p,
2a * sinh(x/a) - L ,
2x + 2k*cos(θ) - parameters.d,
p+k*sin(θ) - parameters.n,
sinh(x/a) - tan(φ),
(1+v/(w*L₀)) * tan(φ) - tan(θ),
L₀ * (1 + α*H) - L,
w*L₀ / 2sin(φ) - H,
]
end
F (generic function with 1 method)
julia> params = (d=30, n=5)
(d = 30, n = 5)
julia> x₀ = [29, 27, 1, params.d/2, deg2rad(45), deg2rad(22.5), 40, 500]
8-element Vector{Float64}:
29.0
27.0
1.0
15.0
0.7853981633974483
0.39269908169872414
40.0
500.0
julia> probN = NonlinearProblem{false}(F, x₀, params)
NonlinearProblem with uType Vector{Float64}. In-place: false
u0: 8-element Vector{Float64}:
29.0
27.0
1.0
15.0
0.7853981633974483
0.39269908169872414
40.0
500.0
julia> solve(probN, NewtonRaphson(), tol = 1e-9)
u: 8-element Vector{Float64}:
27.52327682597094
27.523962383296873
3.2064613688401113
13.258386042046885
0.8000852068277563
0.4578205135984268
27.929656903088112
124.54137097709595
julia>
julia> using NLsolve
julia> solve(probN, NLSolveJL(method = :newton,), tol = 1e-9)
ERROR: UndefVarError: NLSolveJL not defined
Stacktrace:
[1] top-level scope
@ REPL[12]:1
julia> NLSolveJL(probN, method = :newton, tol = 1e-9)
ERROR: UndefVarError: NLSolveJL not defined
Stacktrace:
[1] top-level scope
@ REPL[13]:1
https://github.com/SciML/SciMLNLSolve.jl
It looks like that is documented? http://nonlinearsolve.sciml.ai/dev/solvers/NonlinearSystemSolvers/#SciMLNLSolve.jl
It was - I was not carefull enough in reading the documentation. The full working example is now
julia> using NonlinearSolve
julia>
julia> v = 120 #kg
120
julia> k = 2.5 #m
2.5
julia> w = 4.0 #km/m
4.0
julia> α = 2e-7 #kg⁻¹
2.0e-7
julia>
julia> function F(x⃗, parameters)
L₀, L, p, x, θ, φ, a, H = tuple(x⃗...)
return [
a*(cosh(x/a)-1) - p,
2a * sinh(x/a) - L ,
2x + 2k*cos(θ) - parameters.d,
p+k*sin(θ) - parameters.n,
sinh(x/a) - tan(φ),
(1+v/(w*L₀)) * tan(φ) - tan(θ),
L₀ * (1 + α*H) - L,
w*L₀ / 2sin(φ) - H,
]
end
F (generic function with 1 method)
julia> params = (d=30, n=5)
(d = 30, n = 5)
julia> x₀ = [29, 27, 1, params.d/2, deg2rad(45), deg2rad(22.5), 40, 500]
8-element Vector{Float64}:
29.0
27.0
1.0
15.0
0.7853981633974483
0.39269908169872414
40.0
500.0
julia> probN = NonlinearProblem{false}(F, x₀, params)
NonlinearProblem with uType Vector{Float64}. In-place: false
u0: 8-element Vector{Float64}:
29.0
27.0
1.0
15.0
0.7853981633974483
0.39269908169872414
40.0
500.0
julia> using SciMLNLSolve
julia> test = solve(probN, NLSolveJL(method = :newton, show_trace=true), tol = 1e-9)
Iter f(x) inf-norm Step 2-norm
------ -------------- --------------
0 3.484387e+02 NaN
1 3.846384e+00 1.430607e+05
2 2.695128e-02 1.122826e+01
3 2.280210e-04 5.025951e-02
4 1.677076e-08 3.750412e-06
u: 8-element Vector{Float64}:
27.52327682125824
27.523962378584063
3.2064613689525356
13.258386041929604
0.8000852067627725
0.4578205135111699
27.929656760847312
124.54137097770474
I think that for other careless readers like me, a simple example of how to use other solvers would be instructive.
using NonlinearSolve
v = 120 #kg
k = 2.5 #m
w = 4.0 #km/m
α = 2e-7 #kg⁻¹
function F(x⃗, parameters)
L₀, L, p, x, θ, φ, a, H = tuple(x⃗...)
return [
a * (cosh(x / a) - 1) - p,
2a * sinh(x / a) - L,
2x + 2k * cos(θ) - parameters.d,
p + k * sin(θ) - parameters.n,
sinh(x / a) - tan(φ),
(1 + v / (w * L₀)) * tan(φ) - tan(θ),
L₀ * (1 + α * H) - L,
w * L₀ / 2sin(φ) - H,
]
end
params = (d = 30, n = 5)
x₀ = [29, 27, 1, params.d / 2, deg2rad(45), deg2rad(22.5), 40, 500]
probN = NonlinearProblem{false}(F, x₀, params)
sol = solve(probN; abstol = 1e-9, show_trace = Val(true), trace_level = TraceAll(100),
store_trace = Val(true))
sol.trace will hold the trace of the solve process and it should display something like
Algorithm: GeneralKlement(linsolve = LUFactorization())
---- ------------- ----------- -------
Iter f(u) inf-norm Step 2-norm cond(J)
---- ------------- ----------- -------
0 3.48438696e+02 0.00000000e+00 1.00000000e+00
Final 4.58673147e+00
----------------------
Algorithm: GeneralBroyden()
---- ------------- ----------- -------
Iter f(u) inf-norm Step 2-norm cond(J)
---- ------------- ----------- -------
0 3.48438696e+02 0.00000000e+00 1.00000000e+00
100 2.21817021e+02 3.67955669e+01 8.24919384e+03
Final 5.63586054e+00
----------------------
Algorithm: NewtonRaphson(ad = AutoForwardDiff())
---- ------------- ----------- -------
Iter f(u) inf-norm Step 2-norm cond(J)
---- ------------- ----------- -------
0 3.48438696e+02 0.00000000e+00 Inf
Final 3.55271368e-15
----------------------
u: 8-element Vector{Float64}:
27.52327682597094
27.523962383296873
3.2064613688401113
13.258386042046885
0.8000852068277563
0.4578205135984268
27.929656903088112
124.54137097709595
