def Rwstar_matrix(X, ww, Smooth_lengths, npc):
ndim = len(Smooth_lengths)
npts = len(X[:, 0])
Rw_stars = matrix(zeros((npts, npc)))
for i in xrange(npc):
if npc == 1:
Y = ww
else:
Y = ww[i, :npts]
kernel = SE(params=Smooth_lengths, dimensions=ndim) + noise([0.15])
#kernel=SoftenedSquaredExponentialKernel(Smooth_lengths,1)
gpnow = GaussianProcess(X, Y, kernel)
Rw_stars[:, i] = np.array(gpnow._alpha)
return Rw_stars
def plot_gp(gp, fig_title, filename):
figure()
plot([x[0] for x in X], Y, 'ks')
mean, sigma, LL = gp.predict(support)
gp_plot_prediction(support, mean, sigma)
xlabel('x')
ylabel('f(x)')
title(fig_title)
savefig('%s.png' % filename)
savefig('%s.eps' % filename)
#
# Create a kernel with reasonable parameters and plot the GP predictions
#
kernel = SE([1.]) + noise(1.)
gp = GaussianProcess(X, Y, kernel)
plot_gp(
gp=gp,
fig_title='Initial parameters: kernel = SE([1]) + noise(1)',
filename='learning_first_guess'
)
#
# Learn the covariance function's parameters and replot
#
gp_learn_hyperparameters(gp)
plot_gp(
gp=gp,
fig_title='Learnt parameters: kernel = SE([%.2f]) + noise(%.2f)' % (
kernel.k1.params[0],
Y = [2.5, 2, -.5, 0.]
def plot_for_kernel(kernel, fig_title, filename):
figure()
plot([x[0] for x in X], Y, 'ks')
gp = GaussianProcess(X, Y, kernel)
mean, sigma, LL = gp.predict(support)
gp_plot_prediction(support, mean, sigma)
xlabel('x')
ylabel('f(x)')
title(fig_title)
savefig('%s.png' % filename)
savefig('%s.eps' % filename)
plot_for_kernel(
kernel=SE([1.]) + noise(.1),
fig_title='k = SE + noise(.1)',
filename='noise_mid'
)
plot_for_kernel(
kernel=SE([1.]) + noise(1.),
fig_title='k = SE + noise(1)',
filename='noise_high'
)
plot_for_kernel(
kernel=SE([1.]) + noise(.0001),
fig_title='k = SE + noise(.0001)',
filename='noise_low'
)