<jupyter_start><jupyter_text>Power function<jupyter_code>num_basis = 10

x = np.linspace(-1, 1, 100)
f_basis = []
for i in range(num_basis):
    f_basis.append(np.power(x, 1 + i))
f_basis = np.array(f_basis)

plot_kernel(f_basis, xd=-0.5)<jupyter_output><empty_output><jupyter_text>Gaussian<jupyter_code>num_basis = 11

f_basis = []
for i in range(num_basis):
    mu = (-1 + 2. / (num_basis - 1) * i)
    sigma = 0.2
    f_basis.append(np.exp(-np.square((x - mu) / sigma) / 2))
f_basis = np.array(f_basis)

plot_kernel(f_basis, xd=0.0)<jupyter_output><empty_output><jupyter_text>Sigmoid<jupyter_code>num_basis = 11

f_basis = []
for i in range(num_basis):
    mu = (-1 + 2. / (num_basis - 1) * i)
    sigma = 0.05
    f_basis.append(1. / (1 + np.exp(-(x - mu) / sigma)))
f_basis = np.array(f_basis)

plot_kernel(f_basis, xd=0.0)<jupyter_output><empty_output>
StarcoderdataJupyterStructuredCleanDedup