Morten Hjorth-Jensen
74 lines
2.4 KiB
Python
74 lines
2.4 KiB
Python
from math import sqrt
|
|
from numpy import asarray
|
|
from numpy import arange
|
|
from numpy.random import rand
|
|
from numpy.random import seed
|
|
from numpy import meshgrid
|
|
from matplotlib import pyplot
|
|
from mpl_toolkits.mplot3d import Axes3D
|
|
|
|
# objective function
|
|
def objective(x, y):
|
|
return x**2.0 + y**2.0
|
|
|
|
# derivative of objective function
|
|
def derivative(x, y):
|
|
return asarray([x * 2.0, y * 2.0])
|
|
|
|
# gradient descent algorithm with adagrad
|
|
def adagrad(objective, derivative, bounds, n_iter, step_size):
|
|
# track all solutions
|
|
solutions = list()
|
|
# generate an initial point
|
|
solution = bounds[:, 0] + rand(len(bounds)) * (bounds[:, 1] - bounds[:, 0])
|
|
# list of the sum square gradients for each variable
|
|
sq_grad_sums = [0.0 for _ in range(bounds.shape[0])]
|
|
# run the gradient descent
|
|
for it in range(n_iter):
|
|
# calculate gradient
|
|
gradient = derivative(solution[0], solution[1])
|
|
# update the sum of the squared partial derivatives
|
|
for i in range(gradient.shape[0]):
|
|
sq_grad_sums[i] += gradient[i]**2.0
|
|
# build solution
|
|
new_solution = list()
|
|
for i in range(solution.shape[0]):
|
|
# calculate the learning rate for this variable
|
|
alpha = step_size / (1e-8 + sqrt(sq_grad_sums[i]))
|
|
# calculate the new position in this variable
|
|
value = solution[i] - alpha * gradient[i]
|
|
new_solution.append(value)
|
|
# store the new solution
|
|
solution = asarray(new_solution)
|
|
solutions.append(solution)
|
|
# evaluate candidate point
|
|
solution_eval = objective(solution[0], solution[1])
|
|
# report progress
|
|
print('>%d f(%s) = %.5f' % (it, solution, solution_eval))
|
|
return solutions
|
|
|
|
# seed the pseudo random number generator
|
|
seed(1)
|
|
# define range for input
|
|
bounds = asarray([[-1.0, 1.0], [-1.0, 1.0]])
|
|
# define the total iterations
|
|
n_iter = 50
|
|
# define the step size
|
|
step_size = 0.1
|
|
# perform the gradient descent search
|
|
solutions = adagrad(objective, derivative, bounds, n_iter, step_size)
|
|
# sample input range uniformly at 0.1 increments
|
|
xaxis = arange(bounds[0,0], bounds[0,1], 0.1)
|
|
yaxis = arange(bounds[1,0], bounds[1,1], 0.1)
|
|
# create a mesh from the axis
|
|
x, y = meshgrid(xaxis, yaxis)
|
|
# compute targets
|
|
results = objective(x, y)
|
|
# create a filled contour plot with 50 levels and jet color scheme
|
|
pyplot.contourf(x, y, results, levels=50, cmap='jet')
|
|
# plot the sample as black circles
|
|
solutions = asarray(solutions)
|
|
pyplot.plot(solutions[:, 0], solutions[:, 1], '.-', color='w')
|
|
# show the plot
|
|
pyplot.show()
|