CODEWITHSUNDEEP
pythonoptimizationnumpyscipyleast-squares
user1404919
user1404919

Reputation: 33

Least squares in a set of equations with optimize.leastsq() (Python)

I have two functions and a set of data. Both functions have the same x data and the same parameters. I want to obtain the parameters by least squares method that makes the best fit of my data.

The parameters are: ex,ey,ez.

The X data are: RA,DE (like 3000 points).

The Y data are: dRA,dDE.

I tried this but I obtained a wrong solution:

def residuals(p, dRA, dDE, RA, DEC):
    ex,ey,ez = p
    f1 = dRA-(ex*sin(DEC)*cos(RA)+ey*sin(DEC)*sin(RA)-ez*cos(DEC))
    f2 = dDE-(-ex*sin(RA)+ey*cos(RA))
    err = np.concatenate((f1,f2))
    return err

from scipy.optimize import leastsq
p0 = [0, 0., 0.]
plsq_coord = leastsq(residuals, p0, args=(dRA, dDE, RA, DE))
print plsq_coord[0]

Any kind of help would be very wellcome

Upvotes: 3

Views: 2032

Answers (1)

sega_sai
sega_sai

Reputation: 8528

As shown by this test code code

import numpy as np, numpy.random,scipy.optimize
def residuals(p, dRA, dDE, RA, DEC):
    ex,ey,ez = p
    f1 = dRA-(ex*np.sin(DEC)*np.cos(RA)+ey*np.sin(DEC)*np.sin(RA)-ez*np.cos(DEC))
    f2 = dDE-(-ex*np.sin(RA)+ey*np.cos(RA))
    err = np.concatenate((f1,f2))
    return err    
ex, ey, ez = 0.2, 0.3, 0.4
N = 100
err = 1e-3
ra, dec = np.random.uniform(0,1,N), np.random.uniform(0,.5,N)
dra = (ex*np.sin(dec)*np.cos(ra)+ey*np.sin(dec)*np.sin(ra)-ez*np.cos(dec))+np.random.normal(size=N)*err
ddec = (-ex*np.sin(ra)+ey*np.cos(ra))+np.random.normal(size=N)*err
print scipy.optimize.leastsq(residuals, p0, args=(dra, ddec, ra, dec))

your code should work fine, unless your function is written incorrectly (e.g. your ra,dec are in degrees, not radians) or you have some bad datapoints in the dataset which screw the chisq fit.

Upvotes: 1

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