BoundsError when solving non linear system of equations

General Usage
1

Hi

I’ve been trying to solve a non linear system of equations, but I have 4 equations and two variables so I guess the system is overdetermined and maybe that is the issue, but Mathematica doesn’t seem to have any issues with it. I was wondering if there was a way for Julia to solve this as well. Here is the code that I’m working with:

using Calculus
using LinearAlgebra
using SymPy
const l=1
const A=l/(2*pi)
const alpha=0.
const Phi=pi/2


a(x)= (-A*sin(x/A))*[0 1-alpha 0 0]-A*cos(x/A)*[0 0 1-alpha 2*sqrt(alpha)*(1-alpha)] + A*(-sin(3*x/A)/3)*[0 alpha 0 0] -A*(cos(3*x/A)/3)*[0 0 alpha 0] + [x 0 0 0]

b(x)=(A *sin(x/A))*[0 1 0 0]- 
 A*cos(x/A)*[0 0 cos(Phi) sin(Phi)] + [x 0 0 0]

apnew=lambdify(diff(a))
bpnew=lambdify(diff(b))

function testf!(testF,xtest2)
    testF[1]=(apnew(xtest2[1])-bpnew(xtest2[2]))[1]
    testF[2]=(apnew(xtest2[1])-bpnew(xtest2[2]))[2]
    testF[3]=(apnew(xtest2[1])-bpnew(xtest2[2]))[3]
    testF[4]=(apnew(xtest2[1])-bpnew(xtest2[2]))[4]
end

using NLsolve
nlsolve(testf!,[1.0;1.0])

This is returning the error

BoundsError: attempt to access 2-element Vector{Float64} at index [3]

Any help would be appreciated. TIA!

2

Welcome! As it is, we can’t run your code (which package does nlsolve! come from?), so please provide a minimal (non-) working example, as described here:

It’ll also be easier to help if you use triple backticks (```) to quote your code, since that has syntax highlighting an preserves indentation.

3

Hello!
Thanks for the reply, I’ve edited my code.

4

Thank you, but it seems there’s still something missing - I get this error when defining apnew:

julia> apnew=lambdify(diff(a))
ERROR: ArgumentError: ref of NULL PyObject
Stacktrace:
 [1] _getproperty
   @ ~/.julia/packages/PyCall/BD546/src/PyCall.jl:299 [inlined]
 [2] __getproperty(o::PyCall.PyObject, s::Symbol)
   @ PyCall ~/.julia/packages/PyCall/BD546/src/PyCall.jl:306
 [3] getproperty
   @ ~/.julia/packages/PyCall/BD546/src/PyCall.jl:312 [inlined]
 [4] symbols(x::String; kwargs::Base.Pairs{Symbol, Union{}, Tuple{}, NamedTuple{(), Tuple{}}})
   @ SymPy ~/.julia/packages/SymPy/uawSQ/src/constructors.jl:16
 [5] symbols
   @ ~/.julia/packages/SymPy/uawSQ/src/constructors.jl:16 [inlined]
 [6] #symbols#16
   @ ~/.julia/packages/SymPy/uawSQ/src/constructors.jl:18 [inlined]
 [7] symbols
   @ ~/.julia/packages/SymPy/uawSQ/src/constructors.jl:18 [inlined]
 [8] diff(f::typeof(a), n::Int64) (repeats 2 times)
   @ SymPy ~/.julia/packages/SymPy/uawSQ/src/mathfuns.jl:63
 [9] top-level scope

Can you post the error you get in full? I suspect there’s some helpful information in there, like where the bounds error was thrown and what operation caused it exactly.

5

That’s weird. I’m not sure why you’re getting that error. Here is the BoundsError that I’m getting:

BoundsError: attempt to access 2-element Vector{Float64} at index [3]

Stacktrace:
  [1] setindex!(A::Vector{Float64}, x::Float64, i1::Int64)
    @ Base ./array.jl:839
  [2] testf!(testF::Vector{Float64}, xtest2::Vector{Float64})
    @ Main ./In[150]:4
  [3] (::NLSolversBase.var"#fj_finitediff!#21"{typeof(testf!), FiniteDiff.JacobianCache{Vector{Float64}, Vector{Float64}, Vector{Float64}, UnitRange{Int64}, Nothing, Val{:central}(), Float64}})(F::Vector{Float64}, J::Matrix{Float64}, x::Vector{Float64})
    @ NLSolversBase ~/.julia/packages/NLSolversBase/GRQ1x/src/objective_types/oncedifferentiable.jl:138
  [4] value_jacobian!!(obj::OnceDifferentiable{Vector{Float64}, Matrix{Float64}, Vector{Float64}}, F::Vector{Float64}, J::Matrix{Float64}, x::Vector{Float64})
    @ NLSolversBase ~/.julia/packages/NLSolversBase/GRQ1x/src/interface.jl:124
  [5] value_jacobian!!
    @ ~/.julia/packages/NLSolversBase/GRQ1x/src/interface.jl:122 [inlined]
  [6] trust_region_(df::OnceDifferentiable{Vector{Float64}, Matrix{Float64}, Vector{Float64}}, initial_x::Vector{Float64}, xtol::Float64, ftol::Float64, iterations::Int64, store_trace::Bool, show_trace::Bool, extended_trace::Bool, factor::Float64, autoscale::Bool, cache::NLsolve.NewtonTrustRegionCache{Vector{Float64}})
    @ NLsolve ~/.julia/packages/NLsolve/gJL1I/src/solvers/trust_region.jl:119
  [7] trust_region (repeats 2 times)
    @ ~/.julia/packages/NLsolve/gJL1I/src/solvers/trust_region.jl:235 [inlined]
  [8] nlsolve(df::OnceDifferentiable{Vector{Float64}, Matrix{Float64}, Vector{Float64}}, initial_x::Vector{Float64}; method::Symbol, xtol::Float64, ftol::Float64, iterations::Int64, store_trace::Bool, show_trace::Bool, extended_trace::Bool, linesearch::Static, linsolve::NLsolve.var"#27#29", factor::Float64, autoscale::Bool, m::Int64, beta::Int64, aa_start::Int64, droptol::Float64)
    @ NLsolve ~/.julia/packages/NLsolve/gJL1I/src/nlsolve/nlsolve.jl:26
  [9] nlsolve(f::Function, initial_x::Vector{Float64}; method::Symbol, autodiff::Symbol, inplace::Bool, kwargs::Base.Iterators.Pairs{Union{}, Union{}, Tuple{}, NamedTuple{(), Tuple{}}})
    @ NLsolve ~/.julia/packages/NLsolve/gJL1I/src/nlsolve/nlsolve.jl:52
 [10] nlsolve(f::Function, initial_x::Vector{Float64})
    @ NLsolve ~/.julia/packages/NLsolve/gJL1I/src/nlsolve/nlsolve.jl:46
 [11] top-level scope
    @ In[151]:1
 [12] eval
    @ ./boot.jl:360 [inlined]
 [13] include_string(mapexpr::typeof(REPL.softscope), mod::Module, code::String, filename::String)
    @ Base ./loading.jl:1116
6

Seems like you get that BoundsError in line 4 of testf!, which would correspond to this:

testF[3]=(apnew(xtest2[1])-bpnew(xtest2[2]))[3]

Since nlsolve uses this function and presumably passes the original array you created into this function, I’d suggest using a larger array as a starting point, like this:

nlsolve(testf!, [1.0, 1.0, 1.0, 1.0])
7

I tried doing that, but it didn’t seem to converge. I’m expecting two zeros: (0,0.5) and (0.5,0).

8

Sounds like you have a nonlinear least squares problem and not a nonlinear system of equations.

A fast trip to Google found this

https://github.com/JuliaNLSolvers/LsqFit.jl

which seems to do something sensible.