import numpy as np
from utils import trace_grad_descent, animate_grad_descent
def x_squared(x):
return (1 - x)**2 + 2
def dx_squared(x):
return 2 * x - 2
X = np.linspace(start=-2, stop=4, num=50, endpoint=True)
Y = x_squared(X)
dY = dx_squared(X)
x0 = -2
alpha = 0.005
gd_X, gd_Y = trace_grad_descent(f=x_squared,
df=dx_squared,
x0=x0,
alpha=alpha,
n_iter=100)
ani = animate_grad_descent(X,
Y,
gd_X=gd_X,
gd_Y=gd_Y,
title='alpha = {}'.format(alpha))
def dz(x):
dx0 = 6 * x[0]
dx1 = 2 * x[1]
return np.array([dx0, dx1])
x = np.linspace(start=-10, stop=10, num=100, endpoint=True)
y = np.linspace(start=-10, stop=10, num=100, endpoint=True)
X, Y = np.meshgrid(x, y)
Z = z([X, Y])
alpha = 0.1
gd_X, gd_Z = trace_grad_descent(z,
dz,
x0=np.array([-9., -9.]),
alpha=alpha,
n_iter=100)
gd_X = np.array(gd_X)
gd_Z = np.array(gd_Z).reshape(-1, 1)
animate_grad_descent_2d(X,
Y,
Z,
min_point=(0, 0),
gd_X=gd_X,
title='$3x^2 + y^2$, alpha={}'.format(alpha))