# [SciPy-User] simplex algorithm and curve fitting

servant mathieu servant.mathieu@gmail....
Tue Feb 21 06:22:58 CST 2012

```Thanks for all Joseph, I perfectly understand the problem. Please correct
me if I'm wrong, but if it finally appears that curve_fit is an excellent
optimization solver, provided that you put relevant initial values for
parameters...
Best,
Mat

2012/2/21 <josef.pktd@gmail.com>

> On Tue, Feb 21, 2012 at 6:30 AM, servant mathieu
> <servant.mathieu@gmail.com> wrote:
> > Ok, so as far as I understand, curve fitting is not possible in
> scipy.. Many
> > researchers use the fminsearch function in matlab based on simplex
> standard
> > routines.  Is it a global optimizer?
>
> fminsearch in matlab uses 'Nelder-Mead simplex direct search' which is
> the same algorithm as scipy.optimize.fmin
>
> My impression is that your function does not have a solution with
> np.abs(tanh(A*k*x)) not equal to one, I didn't find one that would
> come close to the solution when the tanh part is one.
>
> curve_fitting is possible in scipy and works very well in many cases,
> and it finds a solution based on the A/(k*x) part, but it cannot do
> something impossible, but I didn't try 10000 starting values.
>
> In general, if it is a quadratic problem, then leastsq works very
> well, better than fmin or other fmin_xxx for unconstrained problems.
>
> Josef
>
> > Mat
> >
> > 2012/2/21 <josef.pktd@gmail.com>
> >>
> >> On Tue, Feb 21, 2012 at 5:19 AM, servant mathieu
> >> <servant.mathieu@gmail.com> wrote:
> >> > Thanks a lot Joseph. I've got a last question which concerns initials
> >> > guess
> >> > for parameters. In fact, in many papers, i read " we fitted both
> >> > functions
> >> > using standard simplex optimization routines. This was repeated 10000
> >> > times
> >> > with randomized initial values to avoid local minima."  The problemis
> >> > the
> >> > following: which range of values should we use for this randomization?
> >>
> >> I wanted to mention this before, all fmin are local optimizers, anneal
> >> is the only global optimizer in scipy, but a bit tricky to use. There
> >> are other global optimizers written in python that might work better,
> >> but I never tried any of these packages.
> >>
> >> Choosing (random) starting values depends completely on the function
> >> and there is no function independent recipe, since the
> >> parameterization of a function is pretty arbitrary. So, you need an
> >> "educated" guess over the possible range given the specific function
> >> and problem.
> >>
> >> For specific classes of functions in not too high dimension it would
> >> be possible to find (and code) starting values, or ranges for a random
> >> search.
> >>
> >> I haven't tried out what your function looks like, but I would guess
> >> that there are at least some sign restrictions. I usually try to see
> >> if I can guess starting values, and ranges for randomization, based on
> >> min, max and mean of the observations.
> >>
> >> Josef
> >>
> >> >
> >> > Best,
> >> > Mat
> >> >
> >> >
> >> > 2012/2/21 <josef.pktd@gmail.com>
> >> >
> >> >> On Tue, Feb 21, 2012 at 4:38 AM, servant mathieu
> >> >> <servant.mathieu@gmail.com> wrote:
> >> >> > Dear Scipy users,
> >> >> >
> >> >> > I've got some troubles with the scipy.optimize.curve_fit function.
> >> >> > This
> >> >> > function is based on the Levenburg-Maquardt algorithm, which is
> >> >> > extremely
> >> >> > rapid but usually finds a local minimum, not a global one (and thus
> >> >> > often
> >> >> > returns anormal parameter values). In my research field, we usually
> >> >> > use
> >> >> > Nelder Mead's simplex routines to avoid this problem. However, I
> >> >> > don't
> >> >> > know
> >> >> > if it is possible to perform curve fitting in scipy using simplex;
> >> >> > the
> >> >> > fmin
> >> >> > function  doesn't seem to perform adjustments to data.
> >> >> >
> >> >> > Here is my code for fitting a three parameters hyperbolic cotangent
> >> >> > function
> >> >> > using curve_fit:
> >> >> >
> >> >> > from scipy.optimize import curve_fit
> >> >> >
> >> >> > import numpy as np
> >> >> >
> >> >> >
> >> >> >
> >> >> > def func (x, A,k, r ):
> >> >> >
> >> >> > return r + (A /(k*x)) * np.tanh (A*k*x)
> >> >> >
> >> >> >
> >> >> >
> >> >> > xdata = np.array ([0.15,0.25,0.35,0.45, 0.55, 0.75])
> >> >> >
> >> >> >
> >> >> >
> >> >> > datacomp = np.array ([344.3276300, 324.0051063, 314.2693475,
> >> >> > 309.9906375,309.9251162, 307.3955800])
> >> >> >
> >> >> > dataincomp = np.array ([363.3839888, 343.5735787, 334.6013375,
> >> >> > 327.7868238,
> >> >> > 329.4642550, 328.0667050])
> >> >> >
> >> >> >
> >> >> >
> >> >> > poptcomp, pcovcomp = curve_fit (func, xdata, datacomp, maxfev =
> >> >> > 10000)
> >> >> >
> >> >> > poptincomp, pcovincomp = curve_fit (func, xdata, dataincomp,
> maxfev =
> >> >> > 10000)
> >> >> >
> >> >> >
> >> >> >
> >> >> >
> >> >> >
> >> >> > How could I proceed to perform the fitting using simplex?
> >> >>
> >> >> You need to define your own loss function for the optimizers like
> >> >> fmin, or in future version minimize
> >> >>
> >> >>
> >> >>
> >> >>
> >> >> something like this
> >> >>
> >> >> def loss(params, args)
> >> >>     A, k, r = params
> >> >>     y, x = args
> >> >>     return ((y - func (x, A,k, r ))**2).sum()
> >> >>
> >> >> and use loss in the call to fmin
> >> >>
> >> >> Josef
> >> >>
> >> >
> >> >
> >> >
> >> >
> >> >
> >> >>
> >> >> >
> >> >> >
> >> >> >
> >> >> > Best,
> >> >> >
> >> >> > Mat
> >> >> >
> >> >> >
> >> >> > _______________________________________________
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> >> >> >
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> >> >
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