from scipy optimize import minimize_scalar def 350 f0 110 return sum f

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from scipy.optimize import minimize_scalar
def f(x, a = 350, b = 2, f0 = 110):
return sum([a*(x[i]**2 - x[i+1])**2 + b*(x[i] - 1)**2 for i in range(0, len(x)-1)]) + f0
def next_step(x, step, index):
x[index] += step
return x
def next_value(h):
return f(next_step(x, step, index))
def search(f, x0, e):
x = x0
while True:
for i in range(len(x)):
x_old = x
x = next_step(x, minimize_scalar(next_value).x, i)
if sum(x - x_old) * 1.0/len(x) < e:
break
return x
def pattern_search(f, x0, e, l):
while True:
x1, x2, x3, x4 = x0, exploring_search(f, x0), x1 + l*(x2-x1), exploring_search(f, x3)
if np.linalg.norm((x2 - x4))/len(x0) < e:
break
else:
x0 = x2
return x2, f(x2)
def gradient(x, a = 350, b = 2):
return np.array([2*a*x[0], a + b*x[1]*2 - 2*b])
def gradient_descent(x, nm, eps, max_step):
def reverce(a):
return f(x - a*gradient(x))
result = minimize_scalar(reverce(a), bounds = (-max_step, max_step), method = nm)
new_x = x - result.x*gradient(x)
if f(x) - f(new_x) < eps:
return (f(x), x)
return gradient_descent(new_x, nm)