def test_input_consistency_checking():
with pytest.raises(ValueError):
GpRegressor(x=zeros(3), y=zeros(2))
with pytest.raises(ValueError):
GpRegressor(x=zeros([4, 3]), y=zeros(3))
with pytest.raises(ValueError):
GpRegressor(x=zeros([3, 1]), y=zeros([3, 2]))
def test_spatial_derivatives():
seed(4)
N = 10
S = 1.1
x = linspace(0, 10, N)
y = 0.3 * x + 0.02 * x**3 + 5.0 + normal(size=N) * S
err = zeros(N) + S
gp = GpRegressor(x, y, y_err=err)
sample_x = linspace(0, 10, 120)
delta = 1e-4
grad_mu, grad_var = gp.spatial_derivatives(sample_x)
mu_pos, sig_pos = gp(sample_x + delta)
mu_neg, sig_neg = gp(sample_x - delta)
fd_grad_mu = (mu_pos - mu_neg) / (2 * delta)
fd_grad_var = (sig_pos**2 - sig_neg**2) / (2 * delta)
mu_max_frac_error = (grad_mu / fd_grad_mu - 1.0).max()
var_max_frac_error = (grad_var / fd_grad_var - 1.0).max()
assert mu_max_frac_error < 1e-6
assert var_max_frac_error < 1e-6
def test_optimizers():
seed(1)
N = 20
S = 0.1
x = linspace(0, 10, N)
y = sin(x) + 3.0 + normal(size=N) * S
errors = zeros(N) + S
gpr = GpRegressor(x, y, y_err=errors, optimizer="bfgs")
gpr = GpRegressor(x, y, y_err=errors, optimizer="bfgs", n_processes=2)
gpr = GpRegressor(x, y, y_err=errors, optimizer="diffev")
def test_gradient():
seed(4)
N = 10
S = 1.1
x = linspace(0, 10, N)
y = 0.3 * x + 0.02 * x**3 + 5.0 + normal(size=N) * S
err = zeros(N) + S
gp = GpRegressor(x, y, y_err=err)
sample_x = linspace(0, 10, 120)
delta = 1e-4
grad, grad_sigma = gp.gradient(sample_x)
mu_pos, sig_pos = gp(sample_x + delta)
mu_neg, sig_neg = gp(sample_x - delta)
fd_grad = (mu_pos - mu_neg) / (2 * delta)
grad_max_frac_error = (grad / fd_grad - 1.0).max()
assert grad_max_frac_error < 1e-6
def test_marginal_likelihood_gradient():
seed(1)
N = 20
S = 0.1
x = linspace(0, 10, N)
y = sin(x) + 3.0 + normal(size=N) * S
errors = zeros(N) + S
gpr = GpRegressor(x, y, y_err=errors)
M = 2.5
A = 0.1
L = 0.6
delta = 1e-5
lml, grad_lml = gpr.marginal_likelihood_gradient(array([M, A, L]))
M_pos = gpr.marginal_likelihood(array([M * (1 + delta), A, L]))
M_neg = gpr.marginal_likelihood(array([M * (1 - delta), A, L]))
A_pos = gpr.marginal_likelihood(array([M, A * (1 + delta), L]))
A_neg = gpr.marginal_likelihood(array([M, A * (1 - delta), L]))
L_pos = gpr.marginal_likelihood(array([M, A, L * (1 + delta)]))
L_neg = gpr.marginal_likelihood(array([M, A, L * (1 - delta)]))
fd_grad_M = (M_pos - M_neg) / (2 * M * delta)
fd_grad_A = (A_pos - A_neg) / (2 * A * delta)
fd_grad_L = (L_pos - L_neg) / (2 * L * delta)
grad_M, grad_A, grad_L = grad_lml
M_fractional_error = abs(fd_grad_M / grad_M - 1.0).max()
A_fractional_error = abs(fd_grad_A / grad_A - 1.0).max()
L_fractional_error = abs(fd_grad_L / grad_L - 1.0).max()
assert M_fractional_error < 1e-6
assert A_fractional_error < 1e-6
assert L_fractional_error < 1e-6
x.extend(list(linspace(4, 9, Nx // 2)))
x = array(x)
# generate points q at which to evaluate the
# GP regression estimate
Nq = 200
q = linspace(-4, 10, Nq) # cover whole range, including the gap
sig = 0.1 # assumed normal error on the data points
y_c = (1. / (1 + exp(-q))) + 0.1 * sin(2 * q) # underlying function
y = (1. / (1 + exp(-x))) + 0.1 * sin(2 * x) + sig * normal(
size=len(x)) # sampled y data
errs = zeros(len(y)) + sig # y data errors
# initialise the class with the data and errors
GP = GpRegressor(x, y, y_err=errs)
# call the instance to get estimates for the points in q
mu_q, sig_q = GP(q)
# now plot the regression estimate and the data together
c1 = 'red'
c2 = 'blue'
c3 = 'green'
fig = plt.figure(figsize=(5, 4))
ax = fig.add_subplot(111)
ax.plot(q, mu_q, lw=2, color=c2, label='posterior mean')
ax.fill_between(q,
mu_q - sig_q,
mu_q - sig_q * 2,
color=c2,
ax.plot(q, y_c, lw=2, color='black', label='test function')
ax.plot(x, y, 'o', color='red', label='sampled data')
ax.errorbar(x, y, yerr=errs, fmt='none', ecolor='red')
ax.set_ylim([-0.5, 1.5])
ax.set_xlim([-4, 10])
ax.set_title('Generate simulated data from a test function', fontsize=12)
ax.set_ylabel('function value', fontsize=12)
ax.set_xlabel('spatial coordinate', fontsize=12)
ax.grid()
ax.legend(loc=2, fontsize=12)
plt.tight_layout()
plt.savefig('sampled_data.png')
plt.close()
# initialise the class with the data and errors
GP = GpRegressor(x, y, y_err=errs)
# call the instance to get estimates for the points in q
mu_q, sig_q = GP(q)
# now plot the regression estimate and the data together
c1 = 'red'
c2 = 'blue'
c3 = 'green'
fig = plt.figure(figsize=(9, 6))
ax = fig.add_subplot(111)
ax.plot(q, mu_q, lw=2, color=c2, label='posterior mean')
ax.fill_between(q,
mu_q - sig_q,
mu_q - sig_q * 2,
color=c2,