def covfunc_se(amplitude, lengthscale, x1, x2=None, gradient=False):
# Make sure that hyperparameters are scalars, not an array objects
amplitude = utils.array_to_scalar(amplitude)
lengthscale = utils.array_to_scalar(lengthscale)
# Compute covariance matrix
if x2 is None:
x1 = gp_preprocess_inputs(x1)
#x = inputs[0]
# Compute variance vector
N = np.shape(x1)[0]
K = np.ones(N)
np.multiply(K, amplitude**2, out=K)
# Compute gradient w.r.t. lengthscale
if gradient:
# TODO: Use sparse matrices?
gradient_lengthscale = np.zeros(N)
else:
(x1,x2) = gp_preprocess_inputs(x1,x2)
x1 = x1 / (lengthscale)
x2 = x2 / (lengthscale)
# Compute distance matrix
K = squared_distance(x1, x2)
# Compute gradient partly
if gradient:
gradient_lengthscale = np.divide(K, lengthscale)
# Compute covariance matrix
gp_cov_se(K, overwrite=True)
np.multiply(K, amplitude**2, out=K)
# Compute gradient w.r.t. lengthscale
if gradient:
gradient_lengthscale *= K
# Gradient w.r.t. amplitude
if gradient:
gradient_amplitude = K * (2 / amplitude)
# Return values
if gradient:
print("se grad", gradient_amplitude, gradient_lengthscale)
return (K, (gradient_amplitude, gradient_lengthscale))
else:
return K
def covfunc_se(amplitude, lengthscale, x1, x2=None, gradient=False):
# Make sure that hyperparameters are scalars, not an array objects
amplitude = utils.array_to_scalar(amplitude)
lengthscale = utils.array_to_scalar(lengthscale)
# Compute covariance matrix
if x2 is None:
x1 = gp_preprocess_inputs(x1)
#x = inputs[0]
# Compute variance vector
N = np.shape(x1)[0]
K = np.ones(N)
np.multiply(K, amplitude**2, out=K)
# Compute gradient w.r.t. lengthscale
if gradient:
# TODO: Use sparse matrices?
gradient_lengthscale = np.zeros(N)
else:
(x1, x2) = gp_preprocess_inputs(x1, x2)
x1 = x1 / (lengthscale)
x2 = x2 / (lengthscale)
# Compute distance matrix
K = squared_distance(x1, x2)
# Compute gradient partly
if gradient:
gradient_lengthscale = np.divide(K, lengthscale)
# Compute covariance matrix
gp_cov_se(K, overwrite=True)
np.multiply(K, amplitude**2, out=K)
# Compute gradient w.r.t. lengthscale
if gradient:
gradient_lengthscale *= K
# Gradient w.r.t. amplitude
if gradient:
gradient_amplitude = K * (2 / amplitude)
# Return values
if gradient:
print("se grad", gradient_amplitude, gradient_lengthscale)
return (K, (gradient_amplitude, gradient_lengthscale))
else:
return K
def covfunc_delta(amplitude, x1, x2=None, gradient=False):
# Make sure that amplitude is a scalar, not an array object
amplitude = utils.array_to_scalar(amplitude)
## if gradient:
## gradient_amplitude = gradient[0]
## else:
## gradient_amplitude = []
## inputs = gp_preprocess_inputs(*inputs)
# Compute distance and covariance matrix
if x2 is None:
x1 = gp_preprocess_inputs(x1)
# Only variance vector asked
#x = inputs[0]
N = np.shape(x1)[0]
K = np.ones(N) * amplitude**2
else:
(x1,x2) = gp_preprocess_inputs(x1,x2)
# Full covariance matrix asked
#x1 = inputs[0]
#x2 = inputs[1]
# Number of inputs x1
N1 = np.shape(x1)[0]
# x1 == x2?
if x1 is x2:
delta = True
# Delta covariance
#
# FIXME: Broadcasting doesn't work with sparse matrices,
# so must use scalar multiplication
K = gp_cov_delta(N1) * amplitude**2
#K = gp_cov_delta(N1).multiply(amplitude**2)
else:
delta = False
# Number of inputs x2
N2 = np.shape(x2)[0]
# Zero covariance
if N1 > 0 and N2 > 0:
K = sp.csc_matrix((N1,N2))
else:
K = np.zeros((N1,N2))
# Gradient w.r.t. amplitude
if gradient:
# FIXME: Broadcasting doesn't work with sparse matrices,
# so must use scalar multiplication
gradient_amplitude = K*(2/amplitude)
print("noise grad", gradient_amplitude)
return (K, (gradient_amplitude,))
else:
return K
def covfunc_delta(amplitude, x1, x2=None, gradient=False):
# Make sure that amplitude is a scalar, not an array object
amplitude = utils.array_to_scalar(amplitude)
## if gradient:
## gradient_amplitude = gradient[0]
## else:
## gradient_amplitude = []
## inputs = gp_preprocess_inputs(*inputs)
# Compute distance and covariance matrix
if x2 is None:
x1 = gp_preprocess_inputs(x1)
# Only variance vector asked
#x = inputs[0]
N = np.shape(x1)[0]
K = np.ones(N) * amplitude**2
else:
(x1, x2) = gp_preprocess_inputs(x1, x2)
# Full covariance matrix asked
#x1 = inputs[0]
#x2 = inputs[1]
# Number of inputs x1
N1 = np.shape(x1)[0]
# x1 == x2?
if x1 is x2:
delta = True
# Delta covariance
#
# FIXME: Broadcasting doesn't work with sparse matrices,
# so must use scalar multiplication
K = gp_cov_delta(N1) * amplitude**2
#K = gp_cov_delta(N1).multiply(amplitude**2)
else:
delta = False
# Number of inputs x2
N2 = np.shape(x2)[0]
# Zero covariance
if N1 > 0 and N2 > 0:
K = sp.csc_matrix((N1, N2))
else:
K = np.zeros((N1, N2))
# Gradient w.r.t. amplitude
if gradient:
# FIXME: Broadcasting doesn't work with sparse matrices,
# so must use scalar multiplication
gradient_amplitude = K * (2 / amplitude)
print("noise grad", gradient_amplitude)
return (K, (gradient_amplitude, ))
else:
return K
def covfunc_pp2(amplitude, lengthscale, x1, x2=None, gradient=False):
# Make sure that hyperparameters are scalars, not an array objects
amplitude = utils.array_to_scalar(amplitude)
lengthscale = utils.array_to_scalar(lengthscale)
#amplitude = theta[0]
#lengthscale = theta[1]
## if gradient:
## gradient_amplitude = gradient[0]
## gradient_lengthscale = gradient[1]
## else:
## gradient_amplitude = []
## gradient_lengthscale = []
## inputs = gp_preprocess_inputs(*inputs)
# Compute covariance matrix
if x2 is None:
x1 = gp_preprocess_inputs(x1)
# Compute variance vector
K = np.ones(np.shape(x)[:-1])
K *= amplitude**2
# Compute gradient w.r.t. lengthscale
if gradient:
gradient_lengthscale = np.zeros(np.shape(x1)[:-1])
else:
(x1,x2) = gp_preprocess_inputs(x1,x2)
# Compute (sparse) distance matrix
if x1 is x2:
x1 = x1 / (lengthscale)
x2 = x1
D2 = distance.sparse_pdist(x1, 1.0, form="full", format="csc")
else:
x1 = x1 / (lengthscale)
x2 = x2 / (lengthscale)
D2 = distance.sparse_cdist(x1, x2, 1.0, format="csc")
r = np.sqrt(D2.data)
N1 = np.shape(x1)[0]
N2 = np.shape(x2)[0]
# Compute the covariances
if gradient:
(k, dk) = gp_cov_pp2(r, np.shape(x1)[-1], gradient=True)
else:
k = gp_cov_pp2(r, np.shape(x1)[-1])
k *= amplitude**2
# Compute gradient w.r.t. lengthscale
if gradient:
if N1 >= 1 and N2 >= 1:
dk *= r * (-amplitude**2 / lengthscale)
gradient_lengthscale = sp.csc_matrix((dk, D2.indices, D2.indptr),
shape=(N1,N2))
else:
gradient_lengthscale = np.empty((N1,N2))
# Form sparse covariance matrix
if N1 >= 1 and N2 >= 1:
## K = sp.csc_matrix((k, ij), shape=(N1,N2))
K = sp.csc_matrix((k, D2.indices, D2.indptr), shape=(N1,N2))
else:
K = np.empty((N1, N2))
#print(K.__class__)
# Gradient w.r.t. amplitude
if gradient:
gradient_amplitude = K * (2 / amplitude)
# Return values
if gradient:
print("pp2 grad", gradient_lengthscale)
return (K, (gradient_amplitude, gradient_lengthscale))
else:
return K
def covfunc_pp2(amplitude, lengthscale, x1, x2=None, gradient=False):
# Make sure that hyperparameters are scalars, not an array objects
amplitude = utils.array_to_scalar(amplitude)
lengthscale = utils.array_to_scalar(lengthscale)
#amplitude = theta[0]
#lengthscale = theta[1]
## if gradient:
## gradient_amplitude = gradient[0]
## gradient_lengthscale = gradient[1]
## else:
## gradient_amplitude = []
## gradient_lengthscale = []
## inputs = gp_preprocess_inputs(*inputs)
# Compute covariance matrix
if x2 is None:
x1 = gp_preprocess_inputs(x1)
# Compute variance vector
K = np.ones(np.shape(x)[:-1])
K *= amplitude**2
# Compute gradient w.r.t. lengthscale
if gradient:
gradient_lengthscale = np.zeros(np.shape(x1)[:-1])
else:
(x1, x2) = gp_preprocess_inputs(x1, x2)
# Compute (sparse) distance matrix
if x1 is x2:
x1 = x1 / (lengthscale)
x2 = x1
D2 = distance.sparse_pdist(x1, 1.0, form="full", format="csc")
else:
x1 = x1 / (lengthscale)
x2 = x2 / (lengthscale)
D2 = distance.sparse_cdist(x1, x2, 1.0, format="csc")
r = np.sqrt(D2.data)
N1 = np.shape(x1)[0]
N2 = np.shape(x2)[0]
# Compute the covariances
if gradient:
(k, dk) = gp_cov_pp2(r, np.shape(x1)[-1], gradient=True)
else:
k = gp_cov_pp2(r, np.shape(x1)[-1])
k *= amplitude**2
# Compute gradient w.r.t. lengthscale
if gradient:
if N1 >= 1 and N2 >= 1:
dk *= r * (-amplitude**2 / lengthscale)
gradient_lengthscale = sp.csc_matrix(
(dk, D2.indices, D2.indptr), shape=(N1, N2))
else:
gradient_lengthscale = np.empty((N1, N2))
# Form sparse covariance matrix
if N1 >= 1 and N2 >= 1:
## K = sp.csc_matrix((k, ij), shape=(N1,N2))
K = sp.csc_matrix((k, D2.indices, D2.indptr), shape=(N1, N2))
else:
K = np.empty((N1, N2))
#print(K.__class__)
# Gradient w.r.t. amplitude
if gradient:
gradient_amplitude = K * (2 / amplitude)
# Return values
if gradient:
print("pp2 grad", gradient_lengthscale)
return (K, (gradient_amplitude, gradient_lengthscale))
else:
return K