# Hello all. I've been trying to use \`LsqFit\` to fit a hyperbolic tangent function t

**URL:** <https://discourse.julialang.org/t/hello-all-ive-been-trying-to-use-lsqfit-to-fit-a-hyperbolic-tangent-function-t/55649>\
**Category:** General Usage\
**Tags:** fit\
**Created:** [February 19, 2021, 8:29pm UTC](https://discourse.julialang.org/t/hello-all-ive-been-trying-to-use-lsqfit-to-fit-a-hyperbolic-tangent-function-t/55649 "2021-02-19T20:29:41Z")\
**Posts on this page:** 3\
**Page:** 1

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**Post date:** [February 19, 2021, 8:29pm UTC](https://discourse.julialang.org/t/hello-all-ive-been-trying-to-use-lsqfit-to-fit-a-hyperbolic-tangent-function-t/55649/1 "2021-02-19T20:29:41Z")

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Hello all. I’ve been trying to use `LsqFit` to fit a hyperbolic tangent function to some data about terminal velocity in free fall. Using SciPy’s `curve_fit` function, it seems to work fine. However, in Julia, it’s nowhere near the correct fit.  
Here’s the function I’ve written to fit the curve -

```julia
function fit_terminal_velocity(data::CSV.File)
	# Create base model with random initial parameters
	p0 = rand(2)
	model(t, p) = p[1] .* tanh.(p[2]/p[1] .* t)
	
	# We are fitting v(t), so lets get those values
	# We also want to go from t = 0 to t = t_max
	t = data.t .- minimum(data.t)
	y = data.y
	
	v = diff(y) ./ diff(t)
	tv = t[1:end-1]
	
	
	fitted_model = lsqfit.curve_fit(model, v, tv, p0)
	
	return fitted_model, model
end

```

And it gives

```julia
p[1] = -1.04293e-10
p[2] = 0.00917912

```

Whereas Python gives `p = [-623.23056677, -319.5100746]` , which fit the model correctly. For reference, the code in python is

```julia
f = lambda t, g, vt : vt * np.tanh(g/vt * t)
popts, pcov = curve_fit(f, t[1:], v)

```

Where `curve_fit` is `scipy.optimize.curve_fit`.

I think it may be something to do with the fact that LsqFit requires `p0` but SciPy doesn’t? I would really appreciate if anybody can help me figure out why curve fitting isn’t working in Julia properly. Thank you so much!

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**Author:** ![cocoa1231](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/cocoa1231/32/22215_2.png) [@cocoa1231](https://discourse.julialang.org/u/cocoa1231)\
**Post date:** [February 19, 2021, 8:41pm UTC](https://discourse.julialang.org/t/hello-all-ive-been-trying-to-use-lsqfit-to-fit-a-hyperbolic-tangent-function-t/55649/2 "2021-02-19T20:41:20Z")

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Hello, I am the poster on slack. If anybody has a solution to this it would be greatly appreciated  
Here is the data I’m trying to fit - [https://transfer.sh/seiAb/0.0grams.csv](https://transfer.sh/seiAb/0.0grams.csv)

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**Author:** ![cocoa1231](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/cocoa1231/32/22215_2.png) [@cocoa1231](https://discourse.julialang.org/u/cocoa1231)\
**Post date:** [February 20, 2021, 7:33am UTC](https://discourse.julialang.org/t/hello-all-ive-been-trying-to-use-lsqfit-to-fit-a-hyperbolic-tangent-function-t/55649/3 "2021-02-20T07:33:17Z")

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Hello everybody!

I figured out the answer! Python’s `scipy.optimize.curve_fit` sets the array of initial parameters to ones if not supplied. `LsqFit` on the other hand does not try to determine the parameters automagically and thus needs them passed in. SciPy sets the initial parameters all to ones if not passed, so if I set the initial parameters to ones in Julia as well, I get the exact same fit. So the new code looks like -

```julia
function fit_terminal_velocity(data::CSV.File)
	# Create base model with random initial parameters
	p0 = ones(2)
	model(t, p) = p[1] .* tanh.(p[2]/p[1] .* t)
	
	# We are fitting v(t), so lets get those values
	# We also want to go from t = 0 to t = t_max
	t = data.t .- minimum(data.t)
	y = data.y
	
	v = diff(y) ./ diff(t)
	tv = t[1:end-1]
	
	
	fitted_model = lsqfit.curve_fit(model, v, tv, p0)
	
	return fitted_model, model
end

```

(changed `rand(2)` to `ones(2)`)  
Solved!