aproksimacijos konvergavimo pavyzdys

def relaksacijos_metodas(function,interval,init,precision,bound=None,N=5000,lower=None,upper=None):
    a,b=interval[0],interval[1]
    def f(x): return function(x)+x
    def g(x,w): return (1-w)*x+w*f(x)
    dx=float(b-a)/N
    gx=[(a+i*dx,f(a+i*dx)) for i in range(N)]
    fx=[(a+i*dx,a+i*dx) for i in range(N)]
    if bound==None:
        diff=[(gx[i-1][1]-gx[i][1]) for i in range(1,N)]
        m,M=min(diff)/dx,max(diff)/dx
    else: m,M=bound[0],bound[1]
    w=2/(2+m+M)
    print 'pasirinkom: m =',m,', M =',M,', w =',w
    print '-'*100
    x=g(init,w)
    array=[(init,x),(x,x)]
    t=time()
    while abs(array[-2][1]-array[-2][0])>precision:
        x=g(array[-1][1],w)
        array+=[(array[-1][1],x)]
        if time()-t>0.3:
            print "nekonverguoja (per ilgas iteracijos procesas?), bet x reiksmes kinta intervale (", min(array)[0],max(array)[0],')'
            break
        if not(a<x<b):
            print "nekonverguoja, gautas x =",x,"neprikl. intervalui",interval
            break
        array+=[(x,x)]
    #print 'artejimas:', [n[0] for n in array[::2]]
    print 'galiausiai,',x
    graph([[("blue",5)]+fx,[("purple",5)]+gx,[("yellow",1)]+array],rounding=3,lower=lower, upper=upper)

relaksacijos_metodas(lambda x: 2*cos(x)-x,(0,3.84),0.1,0.001,N=5000)