def rbf_sympy(input_dim, ARD=False, variance=1., lengthscale=1.):
"""
Radial Basis Function covariance.
"""
X = [sp.var('x%i' % i) for i in range(input_dim)]
Z = [sp.var('z%i' % i) for i in range(input_dim)]
rbf_variance = sp.var('rbf_variance', positive=True)
if ARD:
rbf_lengthscales = [
sp.var('rbf_lengthscale_%i' % i, positive=True)
for i in range(input_dim)
]
dist_string = ' + '.join([
'(x%i-z%i)**2/rbf_lengthscale_%i**2' % (i, i, i)
for i in range(input_dim)
])
dist = parse_expr(dist_string)
f = rbf_variance * sp.exp(-dist / 2.)
else:
rbf_lengthscale = sp.var('rbf_lengthscale', positive=True)
dist_string = ' + '.join(
['(x%i-z%i)**2' % (i, i) for i in range(input_dim)])
dist = parse_expr(dist_string)
f = rbf_variance * sp.exp(-dist / (2 * rbf_lengthscale**2))
return kern(input_dim, [spkern(input_dim, f)])
def rbf_sympy(input_dim, ARD=False, variance=1., lengthscale=1.):
"""
Radial Basis Function covariance.
"""
X = [sp.var('x%i' % i) for i in range(input_dim)]
Z = [sp.var('z%i' % i) for i in range(input_dim)]
rbf_variance = sp.var('rbf_variance',positive=True)
if ARD:
rbf_lengthscales = [sp.var('rbf_lengthscale_%i' % i, positive=True) for i in range(input_dim)]
dist_string = ' + '.join(['(x%i-z%i)**2/rbf_lengthscale_%i**2' % (i, i, i) for i in range(input_dim)])
dist = parse_expr(dist_string)
f = rbf_variance*sp.exp(-dist/2.)
else:
rbf_lengthscale = sp.var('rbf_lengthscale',positive=True)
dist_string = ' + '.join(['(x%i-z%i)**2' % (i, i) for i in range(input_dim)])
dist = parse_expr(dist_string)
f = rbf_variance*sp.exp(-dist/(2*rbf_lengthscale**2))
return kern(input_dim, [spkern(input_dim, f)])
def sympykern(input_dim, k):
"""
A kernel from a symbolic sympy representation
"""
return kern(input_dim, [spkern(input_dim, k)])
def sympykern(input_dim, k):
"""
A kernel from a symbolic sympy representation
"""
return kern(input_dim, [spkern(input_dim, k)])