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

[camille chambon]

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
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