1 May 2012 19:45

Re: Least-square fitting of a 3rd degree polynomial

On Tue, May 1, 2012 at 11:31 AM, camille chambon 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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Gmane