def f(x):
return x * np.sin(x)
X = 10 * np.random.rand(50)
# Observations
y = f(X).ravel()
yerr = np.ones_like(y)
x = np.atleast_2d(np.linspace(-5, 15, 1001)).T
gp = GaussianProcess([0.1, 1.0])
gp.optimize(X, y, yerr=yerr)
mu, var = gp.predict(x)
print(gp.evaluate())
std = np.sqrt(var.diagonal())
vals = np.random.multivariate_normal(mu, var, 100)
pl.plot(x, mu, "k")
pl.plot(x, vals.T, "k", alpha=0.1)
pl.plot(x, mu + std, ":r")
pl.plot(x, mu - std, ":r")
pl.errorbar(X, y, yerr=yerr, fmt=".r")
pl.savefig("debug.png")
def f(x):
return np.exp(-0.5 * (x[:, 0]**2 + x[:, 1]**2 / 0.1))
x = np.random.randn(200).reshape([100, 2])
y = f(x)
yerr = 0.01 * np.ones_like(y)
gp = GaussianProcess([0.1, 1.0, 1.0])
gp.optimize(x, y, yerr=yerr)
print(gp.pars)
# Grid.
X, Y = np.meshgrid(np.linspace(-3, 3, 40), np.linspace(-3, 3, 40))
mu, var = gp.predict(np.vstack([X.ravel(), Y.ravel()]).T)
ymin, ymax = y.min(), y.max()
colors = (y - ymin) / ymax
pl.figure(figsize=[4, 4])
samples = np.random.multivariate_normal(mu, var, 100)
for i in range(samples.shape[0]):
pl.clf()
pl.imshow((samples[i].reshape([40, 40]) - ymin) / ymax,
extent=[-3, 3, -3, 3])
pl.scatter(x[:, 0], x[:, 1], c=colors)
pl.xlim([-3, 3])
pl.ylim([-3, 3])
pl.gca().set_xticklabels([])
pl.gca().set_yticklabels([])
def f(x):
return x * np.sin(x)
X = 10 * np.random.rand(50)
# Observations
y = f(X).ravel()
yerr = np.ones_like(y)
x = np.atleast_2d(np.linspace(-5, 15, 1001)).T
gp = GaussianProcess([0.1, 1.0])
gp.optimize(X, y, yerr=yerr)
mu, var = gp.predict(x)
print(gp.evaluate())
std = np.sqrt(var.diagonal())
vals = np.random.multivariate_normal(mu, var, 100)
pl.plot(x, mu, "k")
pl.plot(x, vals.T, "k", alpha=0.1)
pl.plot(x, mu + std, ":r")
pl.plot(x, mu - std, ":r")
pl.errorbar(X, y, yerr=yerr, fmt=".r")
pl.savefig("debug.png")
def f(x):
return np.exp(-0.5 * (x[:, 0] ** 2 + x[:, 1] ** 2 / 0.1))
x = np.random.randn(200).reshape([100, 2])
y = f(x)
yerr = 0.01 * np.ones_like(y)
gp = GaussianProcess([0.1, 1.0, 1.0])
gp.optimize(x, y, yerr=yerr)
print(gp.pars)
# Grid.
X, Y = np.meshgrid(np.linspace(-3, 3, 40), np.linspace(-3, 3, 40))
mu, var = gp.predict(np.vstack([X.ravel(), Y.ravel()]).T)
ymin, ymax = y.min(), y.max()
colors = (y - ymin) / ymax
pl.figure(figsize=[4, 4])
samples = np.random.multivariate_normal(mu, var, 100)
for i in range(samples.shape[0]):
pl.clf()
pl.imshow((samples[i].reshape([40, 40]) - ymin) / ymax,
extent=[-3, 3, -3, 3])
pl.scatter(x[:, 0], x[:, 1], c=colors)
pl.xlim([-3, 3])
pl.ylim([-3, 3])
pl.gca().set_xticklabels([])
pl.gca().set_yticklabels([])
