File:Thiel-Sen estimator.svg

from pyx import canvas,path,color
from random import random,seed
seed(12345)

N = 103
noise = 10
slope = 1.0

def sample(x):
    y = x * slope
    if random() < (y/N)**3:
        y = random()*N      # outlier
    else:
        y += (random()-0.5)*noise # non-outlier, jitter
    return y

samples = [(i*1.0,sample(i)) for i in range(N)]

c = canvas.canvas()

for x,y in samples:
    c.fill(path.circle(x,y,0.5),[color.rgb.red])

def theilsen(samples):
    N = len(samples)
    def slope(i,j):
        xi,yi = samples[i]
        xj,yj = samples[j]
        return (yi-yj)/(xi-xj)
    
    def median(L):
        L.sort()
        if len(L) & 1:
            return L[len(L)//2]
        else:
            return (L[len(L)//2 - 1] + L[len(L)//2])/2.0
    
    m = median([slope(i,j) for i in range(N) for j in range(i)])
    
    def error(i):
        x,y = samples[i]
        return y - m*x
    
    b = median([error(i) for i in range(N)])
    
    return m,b

m,b = 1,0
c.stroke(path.line(0,b,N,N*m+b),[color.rgb.green])

m,b = theilsen(samples)
c.stroke(path.line(0,b,N,N*m+b),[color.rgb.black])

def slr(samples):
    N = len(samples)
    sumxy = sum([x*y for x,y in samples])
    sumx = sum([x for x,y in samples])
    sumy = sum([y for x,y in samples])
    sumxx = sum([x*x for x,y in samples])
    m = (sumxy - sumx*sumy/N)/(sumxx - sumx**2/N)
    b = sumy/N - m*sumx/N
    return m,b

m,b = slr(samples)
c.stroke(path.line(0,b,N,N*m+b),[color.rgb.blue])

c.writePDFfile("ThielSen")