# Non-diagonal noise

**URL:** <https://discourse.julialang.org/t/non-diagonal-noise/44004>\
**Category:** Modelling & Simulations\
**Tags:** first-steps\
**Created:** [July 30, 2020, 7:32pm UTC](https://discourse.julialang.org/t/non-diagonal-noise/44004 "2020-07-30T19:32:30Z")\
**Posts on this page:** 3\
**Page:** 1

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**Author:** ![mzhai2](https://avatars.discourse-cdn.com/v4/letter/m/c0e974/32.png) [@mzhai2](https://discourse.julialang.org/u/mzhai2)\
**Post date:** [July 30, 2020, 7:32pm UTC](https://discourse.julialang.org/t/non-diagonal-noise/44004/1 "2020-07-30T19:32:30Z")

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How am I supposed to use non-diagonal noise when du is a matrix? When I run the example below I get:

```julia
BoundsError: attempt to access 2-element Array{Float64,1} at index [1, 2]

```

```julia
using DifferentialEquations, LinearAlgebra
f(du,u,p,t) = (du.=1.01*u)
function g(du,u,p,t)
  du[1,1] = u[1]
  du[1,2] = u[1]
  du[2,1] = u[2]
  du[2,2] = u[2]
end

Γ = zeros(4,4)
Γ[diagind(Γ)] .= 1
Γ[1,2] = .99
Γ[2,1] = .99
noise = CorrelatedWienerProcess!(Γ,0.,zeros(4),zeros(4))
prob = SDEProblem(f,g,ones(2),(0.,1.),[],noise=noise)
sol = solve(prob,EM(),dt=1/1000)

```

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**Author:** ![contradict](https://avatars.discourse-cdn.com/v4/letter/c/ac91a4/32.png) [@contradict](https://discourse.julialang.org/u/contradict)\
**Post date:** [July 30, 2020, 10:56pm UTC](https://discourse.julialang.org/t/non-diagonal-noise/44004/2 "2020-07-30T22:56:59Z")

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The error here is because your `u₀` is initialized as `ones(2)`, a one-dimensional array and you index it with two indices in `g`.

I tried creating `u₀` as `ones(2,2)`, that causes an error as well. Perhaps you could try unrolling `u` to be length 4 instead of `2x2`.

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<div class="post-metadata">

**Author:** ![ChrisRackauckas](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/chrisrackauckas/32/77_2.png) [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)\
**Post date:** [August 1, 2020, 5:13pm UTC](https://discourse.julialang.org/t/non-diagonal-noise/44004/3 "2020-08-01T17:13:11Z")

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@contradict thanks for answering a lot lately, it’s been very helpful.