How to make my pylab.poly1d (fit) pass zero?

Question

My code below gives a polyphit of points on my chart, but I want this correspondence to always go through zero, how to do it?

import pylab as pl import numpy as np y=(abs((UX2-UY2)+(2*UXY))) a=np.mean(y) y=ya x=(abs((X2-Y2)+(2*XY))) b=np.mean(x) x=xb ax=pl.subplot(1,4,4) #plot XY fit=pl.polyfit(x,y,1) slope4, fit_fn=pl.poly1d(fit) print slope4 fit_fn=pl.poly1d(fit) x_min=-2 x_max=5 n=10000 x_fit = pl.linspace(x_min, x_max, n) y_fit = fit_fn(x_fit) q=z=[-2,5] scat=pl.plot(x,y, 'o', x_fit,y_fit, '-r', z, q, 'g' ) 

Answer 1

When you set an n-degree polynomial p(x) = a0 + a1*x + a2*x**2 + ... + an*x**n into a set of data points (x0, y0), (x1, y1), ..., (xm, y_m) , the np.lstsq call is made using the coefficient matrix, which looks like this:

 [1 x0 x0**2 ... x0**n] [1 x1 x1**2 ... x1**n] ... [1 xm xm**2 ... xm**n] 

If you remove the j column from this matrix, you effectively set this coefficient in the polynomial to 0. Thus, to get rid of the coefficient a0 , you can do the following:

 def fit_poly_through_origin(x, y, n=1): a = x[:, np.newaxis] ** np.arange(1, n+1) coeff = np.linalg.lstsq(a, y)[0] return np.concatenate(([0], coeff)) n = 1000 x = np.random.rand(n) y = 1 + 3*x - 4*x**2 + np.random.rand(n)*0.25 c0 = np.polynomial.polynomial.polyfit(x, y, 2) c1 = fit_poly_through_origin(x, y, 2) p0 = np.polynomial.Polynomial(c0) p1 = np.polynomial.Polynomial(c1) plt.plot(x, y, 'kx') xx = np.linspace(0, 1, 1000) plt.plot(xx, p0(xx), 'r-', ) plt.plot(xx, p1(xx), 'b-', ) 

Answer 2

As already mentioned, you cannot do this explicitly with polyfit (but you can write your own function).

However, if you want to use polyfit() , you can try this mathematical hack: add a point to zero, and then use the w (weight) flag in polyfit() to give it a high weight, while all other points get a little weight. This will force the polynomial to pass at zero or very close.