SharedLine search.sagewsOpen in CoCalc
Author: Neil Olver
Views : 28
Description: Line search algorithms
def dichotomous_search(f, a1, b1, eps, Delta): a = a1 b = b1 while b - a > eps: l = (a+b)/2 - Delta r = (a+b)/2 + Delta if f(l) <= f(r): b = r else: a = l return (a+b)/2
def golden_section(f, a1, b1, ell): alpha = 0.61803398874989 a = a1 b = b1 l = a + (1 - alpha)*(b - a) r = a + alpha*(b - a) fl = f(l) fr = f(r) while b - a > ell: if fl > fr: a = l l = r r = a + alpha*(b - a) fl = fr fr = f(r) else: b = r r = l l = a + (1 - alpha)*(b - a) fr = fl fl = f(l) return (a+b)/2
def newtons_method(f, start, eps): fp = f.derivative() fpp = fp.derivative() x = start finished = false while not finished: newx = x - fp(x) / fpp(x) if (abs(newx - x) < eps) or (abs(fp(x)) < eps): finished = true x = newx return x
g(x) = x^4 - 3*x^3 + 2*x^2
plot(g, -1,2)
dichotomous_search(g, 1, 2, 1e-4, 1e-5)
Error in lines 1-1 Traceback (most recent call last): File "/cocalc/lib/python2.7/site-packages/smc_sagews/sage_server.py", line 1188, in execute flags=compile_flags), namespace, locals) File "", line 1, in <module> NameError: name 'dichotomous_search' is not defined
newtons_method(g, 1.3, 1e-6)
1.64038820320221
newtons_method(g, 0.8, 1e-6)
0.609611796797793
golden_section(g, 1, 2, 1e-4)
1.64040730584972