[SciPy-User] Re : Least-square fitting of a 3rd degree polynomial

[camille chambon]

Thanks for your answer.

But I would like to fit 'a' while 'b', 'c' and 'd' are fixed.Your method gives me another b, c and d. Is there any way to fit a polynomial fixing some coefficients?


Cheers,

Camille



________________________________
 De : Charles R Harris <charlesr.harris at gmail.com>
À : camille chambon <camillechambon at yahoo.fr>; SciPy Users List <scipy-user at scipy.org> 
Envoyé le : Mardi 1 mai 2012 19h45
Objet : Re: [SciPy-User] Least-square fitting of a 3rd degree polynomial
 




On Tue, May 1, 2012 at 11:31 AM, camille chambon <camillechambon at yahoo.fr> wrote:

Hello,
>
>I would like to fit 'a' such as y = a * x**3 + b * x**2 + 
c * x + d, 
>where x and y are measured data,
and b = 0.0, c = -0.00458844157413 and d = 5.8 are fixed. 
>
>According to http://www.scipy.org/Cookbook/FittingData#head-27373a786baa162a2e8a910ee0b8a48838082262, I try to use scipy.optimize.leastsq fit routine like that: 
>
>#### CODE ##### 
>
>from numpy import *
>from pylab import *
>from scipy import optimize
>
># My data points
>x = array([1078.0, 1117.0, 1212.1, 1368.7, 1686.8, 1880.0])
>y = array([5.8, 5.6, 5.4, 4.9, 2.4, 0.0])
>
>b, c, d =  0.0, -0.00458844157413, 5.8 # Fixed parameters
>
>fitfunc = lambda p, x: poly1d([p[0], b, c, d])(x) # Target function
>errfunc = lambda p, x, y: fitfunc(p, x) - y # Distance to the target function
>
>p0 = [-4.0E-09] # Initial guess for the parameters
>p1, success = optimize.leastsq(errfunc, p0[:], args=(x, y))
>
>time = linspace(x.min(), x.max(), 100)
>plot(x, y, "ro", time, fitfunc(p1, time), "r-") # Plot of the data and the fit
>
>title("a fitting")
>xlabel("time [day]")
>ylabel("number []")
>legend(('x position', 'x fit', 'y position', 'y fit'))
>
>show()
>
>################################
>
>But the fit does not work (as one can see on the attached image).
>
>Does someone
 have any idea of what I'm doing wrong?
>
>Thanks in advance for your help.
>
>Cheers,
>
>Camille
>
>

You can use numpy for this.

In [1]: from numpy.polynomial import Polynomial as P

In [2]: x = array([1078.0, 1117.0, 1212.1, 1368.7, 1686.8, 1880.0])

In [3]: y = array([5.8, 5.6, 5.4, 4.9, 2.4, 0.0])

In [4]: p = P.fit(x,y,3)

In [5]: plot(*p.linspace())
Out[5]: [<matplotlib.lines.Line2D at 0x2e51ad0>]

In [6]: plot(x, y, '.')
Out[6]: [<matplotlib.lines.Line2D at 0x2e62c90>]

In [7]: p.mapparms()
Out[7]: (-3.6882793017456361, 0.0024937655860349127)

Note two things, the coefficients go from degree zero upwards and you need to make the substitution x <- -3.6882793017456361 + 0024937655860349127*x if you want to use them in a publication.

Chuck 
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