# Rosenbrock
def f(x, a=1, b=100):
y = (a - x[0])**2 + b * (x[1] - x[0]**2)**2
return y
x = sp.IndexedBase('x')
gradients = np.array([sp.diff(f(x), x[i]) for i in range(2)])
grads = sp.lambdify(x, gradients, 'numpy')
x_ = np.array([-2., 2.])
gd.GradientDescent(f, grads, x_, alpha=1E-1, verbose=True)
gd.ConjugateGradient(f, grads, x_)
gd.momentum(f, grads, x_, alpha=7E-4, verbose=True)
gd.nesterov(f, grads, x_, alpha=7E-4, verbose=True)
""" Huge-variate : e.g. Deep Learning """
gd.adagrad(f, grads, x_, alpha=3.05E-0, verbose=True)
""" RMSProp: Geoffrey Hinton """
def rmsprop(f,
grads,
x,
alpha,
decay=0.9,
epsilon=1E-7,
# Rosenbrock
def f(x, a=1, b=5):
y = (a - x[0])**2 + b * (x[1] - x[0]**2)**2
return y
x = sp.IndexedBase('x')
gradients = np.array([sp.diff(f(x), x[i]) for i in range(2)])
grads = sp.lambdify(x, gradients, 'numpy')
x_ = np.array([-2, 2])
alpha = 1E-2
gd.GradientDescent(f, grads, x_, alpha)
gd.ConjugateGradient(f, grads, x_)
############################################
""" 문제해결형 과제 (2) """
############################################
""" Branin Function """
def draw_branin(levels):
a = 1
b = 5.1 / (4 * np.pi**2)
c = 5 / np.pi
r = 6
s = 10
t = 1 / (8 * np.pi)
return y
x = sp.IndexedBase('x')
gradients = np.array([sp.diff(f(x), x[i]) for i in range(2)])
grads = sp.lambdify(x, gradients, 'numpy')
#### Branin fuction min value 4 ####
# Gradient Descent | ConjugateGradient
alpha = 1E-2 # learning rate
x_ = np.array([0., 15.])
gd.GradientDescent(f, grads, x_, alpha)
gd.ConjugateGradient(f, grads, x_, verbose=False)
x_ = np.array([5., 5.])
gd.GradientDescent(f, grads, x_, alpha)
gd.ConjugateGradient(f, grads, x_, verbose=False)
x_ = np.array([13., 5.])
gd.GradientDescent(f, grads, x_, alpha)
gd.ConjugateGradient(f, grads, x_, verbose=False)
x_ = np.array([20., 17.])
gd.GradientDescent(f, grads, x_, alpha)
gd.ConjugateGradient(f, grads, x_, verbose=False) # error
# Momentum