def make_matern(nu):
'''returns an instance of a Matern RBF with order *nu*'''
tol = 1e-10
r, eps = get_r(), get_eps() # get symbolic variables
coeff = 2**(1 - nu) / gamma(nu) * (np.sqrt(2 * nu) * r / eps)**nu
expr = coeff * besselk(nu, np.sqrt(2 * nu) * r / eps)
# Handle a removable singularity at r=0 by setting it to 1.
expr = Piecewise((1.0, r < tol), (expr, True))
return RBF(expr)
This script demonstrates how to create a periodic Gaussian process using the *gpiso* function. ''' import numpy as np import matplotlib.pyplot as plt from sympy import sin, exp, pi from rbf.basis import get_r, get_eps, RBF from rbf.gproc import gpiso np.random.seed(1) period = 5.0 cls = 0.5 # characteristic length scale var = 1.0 # variance r = get_r() # get symbolic variables eps = get_eps() # create a symbolic expression of the periodic covariance function expr = exp(-sin(r * pi / period)**2 / eps**2) # define a periodic RBF using the symbolic expression basis = RBF(expr) # define a Gaussian process using the periodic RBF gp = gpiso(basis, eps=cls, var=var) t = np.linspace(-10, 10, 1000)[:, None] sample = gp.sample(t) # draw a sample mu, sigma = gp(t) # evaluate mean and std. dev. # plot the results fig, ax = plt.subplots(figsize=(6, 4)) ax.grid(True) ax.plot(t[:, 0], mu, 'b-', label='mean') ax.fill_between(t[:, 0],
from rbf.gauss import gpiso
from scipy.signal import periodogram
def make_matern(nu):
'''returns an instance of a Matern RBF with order *nu*'''
tol = 1e-10
r, eps = get_r(), get_eps() # get symbolic variables
coeff = 2**(1 - nu) / gamma(nu) * (np.sqrt(2 * nu) * r / eps)**nu
expr = coeff * besselk(nu, np.sqrt(2 * nu) * r / eps)
# Handle a removable singularity at r=0 by setting it to 1.
expr = Piecewise((1.0, r < tol), (expr, True))
return RBF(expr)
r, eps = get_r(), get_eps()
se = RBF(exp(-r**2 / (2 * eps**2)))
ou = RBF(exp(-r / eps))
x = np.linspace(0.0, 3.0, 500)[:, None]
center = np.array([[0.0]])
fig, ax = plt.subplots()
for nu in [0.6, 2.0, 30.0]:
mat = make_matern(nu)
ax.plot(x, mat(x, center), label='$\\nu = $%s' % str(nu))
ax.plot(x, se(x, center), label='se')
ax.plot(x, ou(x, center), label='ou')
ax.set_xlim((0.0, 3.0))
'''
In this script we define and plot an RBF which is based on the sinc
function
'''
import numpy as np
import sympy
import matplotlib.pyplot as plt
from rbf.basis import RBF, get_r, get_eps
r, eps = get_r(), get_eps() # get symbolic variables
expr = sympy.sin(eps * r) / (eps * r) # symbolic expression for the RBF
sinc_rbf = RBF(expr) # instantiate the RBF
x = np.linspace(-5, 5, 500)
points = np.reshape(np.meshgrid(x, x), (2, 500 * 500)).T # interp points
centers = np.array([[0.0, -3.0], [3.0, 2.0], [-2.0, 1.0]]) # RBF centers
eps = np.array([5.0, 5.0, 5.0]) # shape parameters
values = sinc_rbf(points, centers, eps=eps) # Evaluate the RBFs
# plot the sum of each RBF
fig, ax = plt.subplots()
p = ax.tripcolor(points[:, 0],
points[:, 1],
np.sum(values, axis=1),
shading='gouraud',
cmap='viridis')
plt.colorbar(p, ax=ax)
ax.set_xlim((-5, 5))
ax.set_ylim((-5, 5))
plt.tight_layout()
plt.savefig('../figures/basis.b.png')
plt.show()