# [SciPy-User] Nonlinear fit to multiple data sets with a shared parameter, and three variable parameters.

josef.pktd@gmai... josef.pktd@gmai...
Wed Apr 3 12:44:16 CDT 2013

```On Wed, Apr 3, 2013 at 12:09 PM, Troels Emtekær Linnet
<tlinnet@gmail.com> wrote:
> Dear Scipy users.
>
> I am having trouble to implement what is probably known as:
> Nonlinear fit to multiple data sets with shared parameters
>
> I haven't been able to find a solution for this in scipy, and I would be
> happy to hear if someone could guide med how to fix this.
>
> I have a set of measured NMR peaks.
> Each peak has two eksperiment x values, x1, x2, which I can fit to a
> measured Y value.
> I have used lmfit, which extends scipy leastsq with some boundary options.
>
> For each peak, i can fit the following function:
>
> --------------------------------------
> def R1r_exch(pars,inp,data=None,eps=None):
>     tiltAngle,omega1=inp
>     R1 = pars['R1'].value
>     R2 = pars['R2'].value
>     kEX = pars['kEX'].value
>     phi = pars['phi'].value
>     model =
> R1*cos(tiltAngle*pi/180)**2+(R2+phi*kEX/((2*pi*omega1/tan(tiltAngle*pi/180))**2+(2*pi*omega1)**2+kEX**2))*sin(tiltAngle*pi/180)**2
>     if data is None:
>         return model
>     if eps is None:
>         return (model - data)
>     return (model-data)/eps
>
> calling with
>
> datX = [tilt,om1]
> par = lmfit.Parameters()
> par.add('R1', value=1.0, vary=True)
> par.add('R2', value=40.0, vary=True)
> par.add('kEX', value=10000.0, vary=False, min=0.0)
> par.add('phi', value=100000.0, vary=True, min=0.0)
> lmf = lmfit.minimize(R1r_exch, par, args=(datX, R1rex,
> R1rex_err),method='leastsq')
>
> print lmf.success, lmf.nfev
> print par['R1'].value, par['R2'].value, par['kEX'].value, par['phi'].value
> fig = figure('R1r %s'%NI)
> ax = fig.add_subplot(111)
> calcR1r = R1r_exch(par,datX)
> tilt_s, om1_s = zip(*sorted(zip(datX[0], datX[1])))
> datXs = [array(tilt_s), array(om1_s)]
> calcR1rs = f_R1r_exch_lmfit(par,datXs)
> -----------------------------------------------------------
>
> That goes fine for each single peak.
>
> But now I wan't to do global fitting.
> http://www.originlab.com/index.aspx?go=Products/Origin/DataAnalysis/CurveFitting/GlobalFitting
> http://www.wavemetrics.com/products/igorpro/dataanalysis/curvefitting/globalfitting.htm
>
> I would like to fit the nonlinear model to several peak data sets
> simultaneously.
> The parameters "R1,R2 and phi" should be allowed to vary for each NMR peak,
> while kEX should be global and shared for all NMR peaks.
>
>
> Is there anybody who would be able to help finding a solution or guide med
> to a package?

The general solution for this kind of problems in statistics is to stack the
fitting problems into one big problem.

Stack all observations, concatenate the sub-problem specific
parameters and the common parameters, and then write a model/error
function that calculates all sub-problems and returns the stacked
fitting error.

Josef

>
>
> Best
> Troels Emtekær Linnet
>
>
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> SciPy-User mailing list
> SciPy-User@scipy.org
> http://mail.scipy.org/mailman/listinfo/scipy-user
>
```

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