# BoundsError when solving non linear system of equations
**URL:** https://discourse.julialang.org/t/boundserror-when-solving-non-linear-system-of-equations/70180
**Category:** General Usage
**Created:** [October 21, 2021, 10:12pm UTC](https://discourse.julialang.org/t/boundserror-when-solving-non-linear-system-of-equations/70180 "2021-10-21T22:12:51Z")
**Posts on this page:** 8
**Page:** 1
### Author:  [@Namitha\_Suresh](https://discourse.julialang.org/u/Namitha_Suresh)
#### Post date: [October 21, 2021, 10:12pm UTC](https://discourse.julialang.org/t/boundserror-when-solving-non-linear-system-of-equations/70180/1 "2021-10-21T22:12:51Z")
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:
```julia
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!
---
### Author:  [@Sukera](https://discourse.julialang.org/u/Sukera)
#### Post date: [October 21, 2021, 10:23pm UTC](https://discourse.julialang.org/t/boundserror-when-solving-non-linear-system-of-equations/70180/2 "2021-10-21T22:23:56Z")
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:
> [@Please read: make it easier to help you](https://discourse.julialang.org/t/please-read-make-it-easier-to-help-you/14757):
>
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---
### Author:  [@Namitha\_Suresh](https://discourse.julialang.org/u/Namitha_Suresh)
#### Post date: [October 22, 2021, 2:27pm UTC](https://discourse.julialang.org/t/boundserror-when-solving-non-linear-system-of-equations/70180/3 "2021-10-22T14:27:20Z")
Hello!
Thanks for the reply, I’ve edited my code.
---
### Author:  [@Sukera](https://discourse.julialang.org/u/Sukera)
#### Post date: [October 22, 2021, 4:58pm UTC](https://discourse.julialang.org/t/boundserror-when-solving-non-linear-system-of-equations/70180/4 "2021-10-22T16:58:08Z")
Thank you, but it seems there’s still something missing - I get this error when defining `apnew`:
```julia
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.
---
### Author:  [@Namitha\_Suresh](https://discourse.julialang.org/u/Namitha_Suresh)
#### Post date: [October 23, 2021, 1:58pm UTC](https://discourse.julialang.org/t/boundserror-when-solving-non-linear-system-of-equations/70180/5 "2021-10-23T13:58:04Z")
That’s weird. I’m not sure why you’re getting that error. Here is the BoundsError that I’m getting:
```julia
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
```
---
### Author:  [@Sukera](https://discourse.julialang.org/u/Sukera)
#### Post date: [October 23, 2021, 5:24pm UTC](https://discourse.julialang.org/t/boundserror-when-solving-non-linear-system-of-equations/70180/6 "2021-10-23T17:24:06Z")
> [@Namitha\_Suresh](#):
>
> ```julia
> 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
>
> ```
Seems like you get that `BoundsError` in line 4 of `testf!`, which would correspond to this:
```julia
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:
```julia
nlsolve(testf!, [1.0, 1.0, 1.0, 1.0])
```
---
### Author:  [@Namitha\_Suresh](https://discourse.julialang.org/u/Namitha_Suresh)
#### Post date: [October 24, 2021, 10:17pm UTC](https://discourse.julialang.org/t/boundserror-when-solving-non-linear-system-of-equations/70180/7 "2021-10-24T22:17:48Z")
I tried doing that, but it didn’t seem to converge. I’m expecting two zeros: (0,0.5) and (0.5,0).
---
### Author:  [@ctkelley](https://discourse.julialang.org/u/ctkelley)
#### Post date: [October 24, 2021, 11:40pm UTC](https://discourse.julialang.org/t/boundserror-when-solving-non-linear-system-of-equations/70180/8 "2021-10-24T23:40:17Z")
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](https://github.com/JuliaNLSolvers/LsqFit.jl)
which seems to do something sensible.