# Leastsq sudden problem

**URL:** <https://scilab.discourse.group/t/leastsq-sudden-problem/966>\
**Category:** Optimization\
**Created:** [June 10, 2025, 1:36am UTC](https://scilab.discourse.group/t/leastsq-sudden-problem/966 "2025-06-10T01:36:15Z")\
**Posts on this page:** 3\
**Page:** 1

<div class="post-metadata">

**Author:** ![heinznabielek](https://avatars.discourse-cdn.com/v4/letter/h/e47c2d/32.png) [@heinznabielek](https://scilab.discourse.group/u/heinznabielek)\
**Post date:** [June 10, 2025, 1:36am UTC](https://scilab.discourse.group/t/leastsq-sudden-problem/966/1 "2025-06-10T01:36:15Z")

</div>

Dear colleagues,

for years, I have successfully used “leastsq” and, suddenly, it gives wrong results. What had happened?

Heinz

```auto
// ------------------------------------------------------------------
// EMG fit (p = [mu, 1/lambda, sigma])
// • Model fitted as Frequency = f(Height)
// ------------------------------------------------------------------
clear; clc; close;

// 1. Load data ----------------------------------------------------
data = csvRead("histogramm_height_RK.csv", ";");
h = data(2:$, 1); // Height (m)
f = data(2:$, 2); // Frequency (counts)

// 2. Normalisation --------------------------------------------------
yy=f/sum(f)/2;

// 3. EMG function --------------------------------------------------
function yhat=pred(p, x)
a = 1 / p(2); // lambda
s = p(3); // sigma
xx = x - p(1); // x - mu
yhat = (a/2) .* exp((a/2) .* ((a*s^2) - 2*xx)) ...
.* erfc((a*s^2 - xx) ./ (s*sqrt(2)));
endfunction

// 4. Initial guess μ, τ=1/λ, σ and nonlinear least-squares fitting
p0=[5.73; 10.76; 75.1]
[fopt,p,gopt] = leastsq( #(p)->(pred(p,h)-yy) , p0);

// 5. Final result --- IS WRONG !
disp(p)

```

[histogramm\_height\_RK.csv](https://scilab.discourse.group/uploads/short-url/9Nj2kJJ146b1xJNe70aiy3DgZKW.csv) (1.6 KB)

---

<div class="post-metadata">

**Author:** ![mottelet](https://yyz2.discourse-cdn.com/free1/user_avatar/scilab.discourse.group/mottelet/32/13_2.png) [@mottelet](https://scilab.discourse.group/u/mottelet)\
**Post date:** [June 10, 2025, 6:53am UTC](https://scilab.discourse.group/t/leastsq-sudden-problem/966/2 "2025-06-10T06:53:30Z")

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Why do you say that results are wrong ? When increasing the verbosity:

```auto
[fopt,p,gopt] = leastsq(iprint=2, #(p)->(pred(p,h)-yy) , p0);
***** enters -qn code- (without bound cstr)
dimension= 3, epsq= 0.2220446049250313E-15, verbosity level: iprint= 2
max number of iterations allowed: iter= 100
max number of calls to costf allowed: nap= 100
------------------------------------------------
 iter num 1, nb calls= 1, f= 0.5649E-03
 iter num 2, nb calls= 6, f= 0.2239E-03
 iter num 3, nb calls= 7, f= 0.1741E-03
 iter num 4, nb calls= 9, f= 0.1630E-03
 iter num 5, nb calls= 10, f= 0.1452E-03
 iter num 6, nb calls= 11, f= 0.1170E-03
 iter num 7, nb calls= 12, f= 0.6976E-04
 iter num 8, nb calls= 13, f= 0.2580E-04
 iter num 9, nb calls= 15, f= 0.1072E-04
 iter num 10, nb calls= 17, f= 0.1065E-04
 iter num 11, nb calls= 18, f= 0.1063E-04
 iter num 12, nb calls= 19, f= 0.1063E-04
 iter num 13, nb calls= 20, f= 0.1063E-04
 iter num 14, nb calls= 21, f= 0.1063E-04
 iter num 15, nb calls= 22, f= 0.1063E-04
 iter num 16, nb calls= 33, f= 0.1063E-04
 iter num 16, nb calls= 44, f= 0.1063E-04
***** leaves -qn code-, gradient norm= 0.3476441030722958E-13
optim: End of optimization.

```

you can see that the optimum is reached. Plotting the fit vs the data confirms this:  
`plot(h,yy,h,pred(p,h)) legend("data","fit")`

 ![Screenshot 2025-06-10 at 08.53.18](https://global.discourse-cdn.com/free1/uploads/utc/original/1X/9b5febb680876ef1016301273a335c994c63fb91.jpeg)

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<div class="post-metadata">

**Author:** ![heinznabielek](https://avatars.discourse-cdn.com/v4/letter/h/e47c2d/32.png) [@heinznabielek](https://scilab.discourse.group/u/heinznabielek)\
**Post date:** [June 10, 2025, 8:13am UTC](https://scilab.discourse.group/t/leastsq-sudden-problem/966/3 "2025-06-10T08:13:29Z")

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SO SORRY: everything is perfect now (diagram below).  
Verbosity level is interesting!  
Thanks for quick response.  
Heinz

(Attachment Red kite flight altitude probabilities.pdf is missing)