def DerCost(self, GD, Cont):
u1 = np.ones(self.Ntrans)
u2 = np.zeros(self.Ntrans)
# Matrix with derivative wrt 1st component of covariance matrix
Partial1_covMat = usefun.Make_der_CovMat(np.transpose(np.array(GD)),
np.transpose(np.array(GD)),
np.array([u1, u2]),
self.partialder2kernel)
# Matrix with derivative wrt 2nd component of covariance matrix
Partial2_covMat = usefun.Make_der_CovMat(np.transpose(np.array(GD)),
np.transpose(np.array(GD)),
np.array([u2, u1]),
self.partialder2kernel)
der_1 = sum([
np.dot(Partial1_covMat, Contu) * Contu
for Contu in np.transpose(np.array(Cont))
])
der_2 = sum([
np.dot(Partial2_covMat, Contu) * Contu
for Contu in np.transpose(np.array(Cont))
])
return self.GDspace.element(np.transpose(np.array([der_1, der_2])))
def __init__(self, DomainField, Ntrans, kernel, partialderdim1kernel,
partialder2kernel):
"""Initialize a new instance.
DomainField : space on wich vector fields will be defined
Ntrans : number of translations
Kernel : kernel
partialderdim1kernel : partial derivative with respect to one componenet of
the 1st component,
to be used as partialder2kernel(x, y, d) where d is in [|0, dim-1|]
partialder2kernel : partial derivative with respect to 2nd component,
to be used as partialder2kernel(x, y, u) with x and y points, and u
vectors for differentiation (same number of vectors as the number of
points for y)
"""
self.Ntrans = Ntrans
self.kernel = kernel
self.partialderdim1kernel = partialderdim1kernel
self.partialder2kernel = partialder2kernel
self.dim = DomainField.ndim
self.get_unstructured_op = usefun.get_from_structured_to_unstructured(
DomainField, kernel)
self.gradient_op = Gradient(DomainField)
GDspace = odl.ProductSpace(odl.space.rn(self.dim), self.Ntrans)
Contspace = odl.ProductSpace(odl.space.rn(self.dim), self.Ntrans)
self.dimCont = self.Ntrans * self.dim
super().__init__(GDspace, Contspace, DomainField)
def ComputeFieldEvaluate(self, o, h, points):
" points is a list of points "
points = np.array(points)
mat = usefun.make_covariance_mixte_matrix(
np.transpose(np.array(points)), np.transpose(np.array(o)),
self.kernel)
return np.dot(mat, np.array(h))
def ComputeFieldEvaluateDer(self, o, h, points, vectors):
points = np.array(points)
vectors = np.array(vectors)
mat = usefun.Make_der_CovMat(np.transpose(np.array(o)),
np.transpose(points),
np.transpose(vectors),
self.partialder2kernel)
return np.dot(mat, np.array(h))
def Cost(self, GD, Cont):
mat = usefun.make_covariance_matrix(np.transpose(np.array(GD)),
self.kernel)
energy = sum([
np.dot(np.dot(np.transpose(np.array(Cont))[u], mat),
np.transpose(np.array(Cont))[u]) for u in range(self.dim)
])
return float(energy)
def __init__(self, DomainField, GDspace, NbGD, kernel,
partialderdim1kernel, partialder2kernel, pointfunctionlist,
pointfunctiondifflist, vectorfunctionlist,
vectorfunctiondifflist):
"""Initialize a new instance.
DomainField : space on wich vector fields will be defined
dimGD = dimension of GDspace
Kernel : kernel
partialderdim1kernel : partial derivative with respect to one componenet of
the 1st component,
to be used as partialder2kernel(x, y, d) where d is in [|0, dim-1|]
partialder2kernel : partial derivative with respect to 2nd component,
to be used as partialder2kernel(x, y, u) with x and y points, and u
vectors for differentiation (same number of vectors as the number of
points for y)
get_columnvector_gd : function that takes a GD and return a vector
so that when we multiply it by a point/vectorfunctiondiff we
obtain its differential
get_spaceelement_gd : function, inverse of get_columnvector_gd
(takes a vector and return the corresponding GD)
pointfunctionlist : list of functions, each one associating a list of
points to a geometrical descriptor
pointfunctiondifflist : list of functions, each one associating a list of
matrix to a geometrical descriptor, the k-th matrix is the differential
of the k-th point with respect to the geometrical descriptor
vectorfunctionlist : list of functions, each one associating a list of
vectors to a geometrical descriptor
vectorfunctiondifflist : list of functions, each one associating a list of
matrix to a geometrical descriptor, the k-th matrix is the differential
of the k-th vector with respect to the geometrical descriptor
"""
self.kernel = kernel
self.partialderdim1kernel = partialderdim1kernel
self.partialder2kernel = partialder2kernel
self.dim = DomainField.ndim
self.NbGD = NbGD
self.dimGD = NbGD * self.dim
self.get_unstructured_op = usefun.get_from_structured_to_unstructured(
DomainField, kernel)
self.gradient_op = Gradient(DomainField)
self.ptfun = pointfunctionlist
self.vecfun = vectorfunctionlist
self.ptfundiff = pointfunctiondifflist
self.vecfundiff = vectorfunctiondifflist
self.dimCont = len(pointfunctionlist)
Contspace = odl.space.rn(self.dimCont)
super().__init__(GDspace, Contspace, DomainField)
def ComputeFieldEvaluateDer(self, o, h, points, vectors):
points = np.array(points)
vectors = np.array(vectors)
mat_list = [
usefun.Make_der_CovMat(np.transpose(funi(o)), np.transpose(points),
np.transpose(vectors),
self.partialder2kernel)
for funi in self.ptfun
]
return sum([
np.dot(mat_list[i], h[i] * np.array(self.vecfun[i](o)))
for i in range(self.dimCont)
])
def ComputeFieldEvaluate(self, o, h, points):
" points is a list of points "
points = np.array(points)
mat_list = [
usefun.make_covariance_mixte_matrix(np.transpose(points),
np.transpose(funi(o)),
self.kernel)
for funi in self.ptfun
]
return sum([
np.dot(mat_list[i], h[i] * np.array(self.vecfun[i](o)))
for i in range(self.dimCont)
])
def InvCo(self, GD):
mat = usefun.make_covariance_matrix(np.transpose(np.array(GD)),
self.kernel)
return np.kron(np.linalg.inv(mat), np.identity(self.dim))
def AdjointApply(self, GD, Mom):
return usefun.Dirac(np.array(GD), np.array(Mom), self.domain)
def CreateStructuredFromGDCont(self, o, h):
return usefun.create_structured(np.transpose(np.array(o)),
np.transpose(np.array(h)))
def CreateStructuredListFromGD(self, o):
return [
usefun.create_structured(np.transpose(self.ptfun[i](o)),
np.transpose(self.vecfun[i](o)))
for i in range(self.dimCont)
]