# System of equation, domain error: initial value setting problem?

**URL:** <https://discourse.julialang.org/t/system-of-equation-domain-error-initial-value-setting-problem/15057>\
**Category:** Numerics\
**Created:** [September 17, 2018, 10:00am UTC](https://discourse.julialang.org/t/system-of-equation-domain-error-initial-value-setting-problem/15057 "2018-09-17T10:00:11Z")\
**Posts on this page:** 4\
**Page:** 1

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**Author:** ![axelle](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/axelle/32/4488_2.png) [@axelle](https://discourse.julialang.org/u/axelle)\
**Post date:** [September 17, 2018, 10:00am UTC](https://discourse.julialang.org/t/system-of-equation-domain-error-initial-value-setting-problem/15057/1 "2018-09-17T10:00:12Z")

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Good afternoon,

I have been blocked for a very long time on this so any help would really help me as I am completely stuck there. I am new to Julia so please pardon my errors.

I have a system of equations (very simplified below) and keep getting “domain error”. It works for certain initial values, or for some equations. I noticed that whenever the value of equations evaluated at the initial values are below zero, it seems to generate a domain error.

For instance, when i change equation F[1] of the sytem from `F[1]= x[2] * D` , it works i.e. I do not get domain error (- the algorithm does not converge but as this is a simplified version of my true system, I am not concerned about that for now).

But when I change it to `F[1]= x[2] * D + 2` , I get a domain error (so this is even before looking into convergence for a solution).

Would anyone know why? Understanding what is going on here would help me solve this error and the future ones. Many thanks for your help!

```julia
using QuantEcon
using NLsolve
using ForwardDiff

Re=5.0
Rl=2.0
E=4.0
D=0.1

function foc2(θlow::AbstractFloat,
                D::AbstractFloat) 
    
v(c) = 4 * c
c21(θ) = 1/ (1 - θ)   
val2(θ) = θ * D * v(c21(θ))
val22 = quadgk(val2, 0, θlow)[1]

return val22 
    
end 

 function f!(F ,x) 
            F[1]= x[2] * D
            F[2]= foc2(x[9], D)
            F[3]= D - x[3] - x[1] 
            F[4]= E - x[4] - D 
            F[5]= x[2] * D - x[5] * ((Re-Rl)/Rl) 
            F[6]= x[4] - x[6] - x[5]
            F[7]= x[8] - x[5] / x[1]  
            F[8]= x[9] - x[3]/ (D * x[2]) 
            F[9]= x[2] * D * x[7] + x[2] * D * (1 - x[7]) * (x[8]/Re) - x[3] - x[1] * x[8] 
       
end 
        
        
    initial_x = [D; D; 0.0; E/2.0; 0.01; E/2.0; 0.3; 0.1; 0.1] 
    initial_F = similar(initial_x)
        
    df = OnceDifferentiable(f!, initial_x, initial_F)
       
    results1_bk = mcpsolve(df, [0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01 , 0.0], 
                        [D, D, D, E, E, D, 0.9, 0.99, 0.9], initial_x )
 

```

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<div class="post-metadata">

**Author:** ![RogerP](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/rogerp/32/17496_2.png) [@RogerP](https://discourse.julialang.org/u/RogerP)\
**Post date:** [September 17, 2018, 10:28am UTC](https://discourse.julialang.org/t/system-of-equation-domain-error-initial-value-setting-problem/15057/2 "2018-09-17T10:28:45Z")

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Worked for me in v0.6.4 when I put `F[1]= x[2] * D + 2.0`. No “domain error”.

Please confirm you have checked for divide by zero etc and anything else you’ve tried. I always specify the type of arguments in functions as it sometimes helps. I also habitually write 0.0 for a float and 0 for an integer. If nothing else it makes code less ambiguous. I know Julia does the conversions so it’s largely unnecessary.

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<div class="post-metadata">

**Author:** ![axelle](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/axelle/32/4488_2.png) [@axelle](https://discourse.julialang.org/u/axelle)\
**Post date:** [September 17, 2018, 12:15pm UTC](https://discourse.julialang.org/t/system-of-equation-domain-error-initial-value-setting-problem/15057/3 "2018-09-17T12:15:10Z")

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Thanks a lot for your help! I tried `F[1]= x[2] * D - 2.0` (os changing to `.0` as you suggested and i still get a domain error. I am using Julia 0.6.3 . I am trying tu update to v0.6.4 to see if this is an error in my version of Julia maybe (but it would be surprising, right?)

Yes i had to correct for domain error coming indeed from dividing by 0. I also had another issue: some integrals were not defined for values of unknow near zero that I (probably artificially) solved by imposing the unknowns to be above 0.01 instead of zero.

Thanks again.

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<div class="post-metadata">

**Author:** ![platawiec](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/platawiec/32/31914_2.png) [@platawiec](https://discourse.julialang.org/u/platawiec)\
**Post date:** [September 17, 2018, 12:31pm UTC](https://discourse.julialang.org/t/system-of-equation-domain-error-initial-value-setting-problem/15057/4 "2018-09-17T12:31:04Z")

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I’m also able to reproduce in 0.7 for `F[1]= x[2] * D - 2` (previously you wrote `F[1]= x[2] * D + 2`, which did not produce the error). I had to add `using QuadGK` to get it to work on 0.7

I think the reason it’s not working is that this line:

```julia
c21(θ) = 1/ (1 - θ) 

```

produces `NaN` when `θ = 1`, which occurs if `θlow > 1`, which seems to happen for this particular system of equations. This integral does diverge, so it is perhaps not too surprising you’re seeing this behavior.