# LsqFit.jl error on ODE data fitting

**URL:** <https://discourse.julialang.org/t/lsqfit-jl-error-on-ode-data-fitting/21587>\
**Category:** Optimization (Mathematical)\
**Tags:** question, diffeq, fit\
**Created:** [March 7, 2019, 5:25pm UTC](https://discourse.julialang.org/t/lsqfit-jl-error-on-ode-data-fitting/21587 "2019-03-07T17:25:35Z")\
**Posts on this page:** 3\
**Page:** 1

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**Author:** ![Andre\_Mello](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/andre_mello/32/7333_2.png) [@Andre\_Mello](https://discourse.julialang.org/u/Andre_Mello)\
**Post date:** [March 7, 2019, 5:25pm UTC](https://discourse.julialang.org/t/lsqfit-jl-error-on-ode-data-fitting/21587/1 "2019-03-07T17:25:36Z")

</div>

Hi all, my first post here so bare with me please.  
I’m also new to the Julia language and enjoying it very much so far.

Now to the point.  
I’ve been trying LsqFit and wanted to implement a simple curve fitting model using a single shooting method. My goal is to estimate the rate constants of a chemical kinetics model. My code is the following:

```julia
using Optim
using LsqFit
using DifferentialEquations

function floudas_one(dz_dt, z, phi, t)
    r_1 = phi[1]*z[1]
    r_2 = phi[2]*z[2]

    dz_dt[1] = -r_1
    dz_dt[2] = r_1 - r_2
end

ode_fun = floudas_one

data = Float64[1.0 0.57353 0.328937 0.188654 0.108198 0.0620545 0.0355906 0.0204132 0.011708 0.00671499; 
        0.0 0.401566 0.589647 0.659731 0.666112 0.639512 0.597179 0.54867 0.499168 0.451377]
t = Float64[0.0, 0.111111, 0.222222, 0.333333, 0.444444, 0.555556, 0.666667, 0.777778, 0.888889, 1.0]

function lsq_ss_estimator(time_array, phi)
    tspan = (t[1], t[end])
    ini_cond = data[:,1]
    oprob = ODEProblem(ode_fun, ini_cond, tspan, phi)
    osol = solve(oprob, Tsit5(), saveat=t)
    estimated = reduce(hcat, osol.u)
    return estimated
end

p0 = [5., 5.]
fit = curve_fit(lsq_ss_estimator, t, data, p0)

```

However, I get the following error:

```julia
MethodError: no method matching mul!(::Array{Float64,1}, ::LinearAlgebra.Transpose{Float64,Array{Float64,2}}, ::Array{Float64,2})
Closest candidates are:
  mul!(::AbstractArray, !Matched::Number, ::AbstractArray) at /buildworker/worker/package_linux64/build/usr/share/julia/stdlib/v1.1/LinearAlgebra/src/generic.jl:26
  
(...)

` in top-level scope at [base/none](#)

in curve_fit at [LsqFit/TBrzN/src/curve_fit.jl:87](#)

in #curve_fit#5 at [LsqFit/TBrzN/src/curve_fit.jl:89](#)

in lmfit at [LsqFit/TBrzN/src/curve_fit.jl:41](#)

in #lmfit#3 at [LsqFit/TBrzN/src/curve_fit.jl:44](#)

in lmfit at [LsqFit/TBrzN/src/curve_fit.jl:48](#)

in #lmfit#4 at [LsqFit/TBrzN/src/curve_fit.jl:48](#)

in levenberg_marquardt at [LsqFit/TBrzN/src/levenberg_marquardt.jl:36](#)

in #levenberg_marquardt#1 at [LsqFit/TBrzN/src/levenberg_marquardt.jl:107](#)
`

```

Since I’m new to Julia and LsqFit, I’m not so sure what I’m missing here.  
Any help would be appreciated.

PS: I’m aware of the DiffEqParamEstim package and it does an awesome job, I just wanted to try a few things by myself and ran into this issue.

---

<div class="post-metadata">

**Author:** ![mzaffalon](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/mzaffalon/32/214168_2.png) [@mzaffalon](https://discourse.julialang.org/u/mzaffalon)\
**Post date:** [March 8, 2019, 7:50am UTC](https://discourse.julialang.org/t/lsqfit-jl-error-on-ode-data-fitting/21587/2 "2019-03-08T07:50:48Z")

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The function you pass to `curve_fit` must return a vector, but `lsq_ss_estimator` returns a 2 by 10 matrix.

You could

1. replace `return estimated` by `return vec(estimated)` in lsq\_ss\_estimator and
2. call `fit = curve_fit(lsq_ss_estimator, t, vec(data), p0)` instead of your original call to `curve_fit`.

I don’t understand if there is a fundamental reason `curve_fit` cannot fit a data set with arbitrary dimensions, not just a vector.

---

<div class="post-metadata">

**Author:** ![Andre\_Mello](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/andre_mello/32/7333_2.png) [@Andre\_Mello](https://discourse.julialang.org/u/Andre_Mello)\
**Post date:** [March 8, 2019, 7:06pm UTC](https://discourse.julialang.org/t/lsqfit-jl-error-on-ode-data-fitting/21587/3 "2019-03-08T19:06:03Z")

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Oh, I see. That did the trick!  
Slowly but surely I’m finding my way in Julia.  
Thanks @mzaffalon!