# Exponential Curve Fit Equation
**URL:** https://discourse.julialang.org/t/exponential-curve-fit-equation/78608
**Category:** New to Julia
**Tags:** question
**Created:** [March 28, 2022, 12:14pm UTC](https://discourse.julialang.org/t/exponential-curve-fit-equation/78608 "2022-03-28T12:14:56Z")
**Posts on this page:** 7
**Page:** 1
### Author:  [@Mahmoud](https://discourse.julialang.org/u/Mahmoud)
#### Post date: [March 28, 2022, 12:14pm UTC](https://discourse.julialang.org/t/exponential-curve-fit-equation/78608/1 "2022-03-28T12:14:56Z")
I am trying to fit my data in figure 1
to be like figure 2 (exponential fit)
but my code does not do that
```julia
using LsqFit
#days = [1,2,3,4,5,6,7,8,9 ,...........]
#y = some code to update y value
@. model(days, p) = p[1] * days.^(-p[2])
fit = curve_fit(model, days, y, [0.5,0.5]) #
@show fit.param
plot(days, model(days, fit.param))
```
---
### Author:  [@feanor12](https://discourse.julialang.org/u/feanor12)
#### Post date: [March 28, 2022, 2:33pm UTC](https://discourse.julialang.org/t/exponential-curve-fit-equation/78608/2 "2022-03-28T14:33:34Z")
Fitting exponential data is a bit tricky.
If you want a quick fit try fitting the logarithm of the data. To get a correct uncertainty estimation, however, one has to use nonuniform weights.
This fit you can then use to get a better initial value.
Also your data does not look like to follow an exponential function. Maybe one could fit a sigmoid function or restrict the data range.
The function you use is also not an exponential.I would have expected something like this
```julia
@. model(days,p) = p[1] + exp(days*p[2])
```
For restricting the data range you can introduce a mask like this.
```julia
mask=y.<=50
curve_fit(model,days[mask],y[mask],[0.5,0.5])
```
In addition, I noticed that in your example there is a missing `]` for the initial value array.
One thing I wanted to do for some time was figuring out how to use GLM.jl for such applications. I think by selecting the correct link function this might work.
I hope my comments help somewhat.
---
### Author:  [@johnmyleswhite](https://discourse.julialang.org/u/johnmyleswhite)
#### Post date: [March 28, 2022, 2:55pm UTC](https://discourse.julialang.org/t/exponential-curve-fit-equation/78608/3 "2022-03-28T14:55:21Z")
This seems much easier to do by using blackbox optimization (via Optim) with the actual functional form you want that provides a closure over your data. It’s true that you can make this into a LsqFit problem, but the more general approach of blackbox optimization is easier once you’re used to it.
---
### Author:  [@feanor12](https://discourse.julialang.org/u/feanor12)
#### Post date: [March 28, 2022, 4:03pm UTC](https://discourse.julialang.org/t/exponential-curve-fit-equation/78608/4 "2022-03-28T16:03:43Z")
Here is a function that might work.
```julia
julia> using UnicodePlots
julia> scaled_sigmoid(x,low,high,a,b) = low+(high-low)*(1/(1+exp(a+b*x)))
scaled_sigmoid (generic function with 1 method)
julia> lineplot((x)->scaled_sigmoid(x,0,2,3,-1))
┌────────────────────────────────────────┐
2 │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠋⠉⠉⠉⠉⠉│ #9(x)
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
f(x) │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
0 │⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠤⠖⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
└────────────────────────────────────────┘
⠀-10⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀10⠀
```
At the high and low ends this can also be approximated by an exponential function. (See Fermi-Dirac statistics)
---
### Author:  [@Mahmoud](https://discourse.julialang.org/u/Mahmoud)
#### Post date: [March 28, 2022, 4:52pm UTC](https://discourse.julialang.org/t/exponential-curve-fit-equation/78608/5 "2022-03-28T16:52:30Z")
> [@feanor12](#):
>
> `lineplot((x)->scaled_sigmoid(x,0,2,3,-1))`
How to use it with vectors like
x=[1,2,3,4,5,6,7,…]
y=[2,3,3,4,6,7,8,…]
---
### Author:  [@feanor12](https://discourse.julialang.org/u/feanor12)
#### Post date: [March 28, 2022, 5:32pm UTC](https://discourse.julialang.org/t/exponential-curve-fit-equation/78608/6 "2022-03-28T17:32:51Z")
> [@feanor12](#):
>
> `scaled_sigmoid(x,low,high,a,b) = low+(high-low)*(1/(1+exp(a+b*x)))`
```julia
using LsqFit
using Plots
x=[1,2,3,4,5,6,7]
y=[2,3,3,4,6,7,8]
@. scaled_sigmoid(x,low,high,a,b) = low+(high-low)*(1/(1+exp(a+b*x)))
scaled_sigmoid(x,p) = scaled_sigmoid(x,p...)
p0 = [0,100,0.1,-1]
fit = curve_fit(scaled_sigmoid,x,y,p0)
scatter(x,y,label="data",xlabel="x",ylabel="y")
plot!((x)->scaled_sigmoid(x,p0),label="initial")
plot!((x)->scaled_sigmoid(x,coef(fit)),label="fit")
```
---
### Author:  [@andreypikunov](https://discourse.julialang.org/u/andreypikunov)
#### Post date: [March 28, 2022, 10:10pm UTC](https://discourse.julialang.org/t/exponential-curve-fit-equation/78608/7 "2022-03-28T22:10:26Z")
Easy, like this
```julia
using UnicodePlots
x = [1, 2, 3, 4, 5, 6, 7]
y = [2, 3, 3, 4, 6, 7, 8]
lineplot(x, y)
# result will be
┌────────────────────────────────────────┐
8 │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠁⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
│⠀⠀⠀⠀⠀⢀⡠⠤⠤⠤⠤⠤⠤⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
│⠀⠀⠀⡠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
2 │⣀⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
└────────────────────────────────────────┘
⠀1⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀7⠀
```
I recommend you check the docs, they are nice:
[https://github.com/JuliaPlots/UnicodePlots.jl](https://github.com/JuliaPlots/UnicodePlots.jl)
Or have a look at `methods(lineplot)`.
Good luck with Julia)