def getGrad(self, system):
"""returns exact gradient"""
dim = self.domain.getDim()
if system:
g_ex = Data(0., (dim,dim), Solution(self.domain))
if dim == 2:
g_ex[0,0] = 2.
g_ex[0,1] = 3.
g_ex[1,0] = 3.
g_ex[1,1] = 2.
else:
g_ex[0,0] = 2.
g_ex[0,1] = 3.
g_ex[0,2] = 4.
g_ex[1,0] = 4.
g_ex[1,1] = 1.
g_ex[1,2] = -2.
g_ex[2,0] = 8.
g_ex[2,1] = 4.
g_ex[2,2] = 5.
else:
g_ex = Data(0., (dim,), Solution(self.domain))
if dim == 2:
g_ex[0] = 2.
g_ex[1] = 3.
else:
g_ex[0] = 2.
g_ex[1] = 3.
g_ex[2] = 4.
return g_ex
def createLevelSetFunction(self, *props):
"""
returns an instance of an object used to represent a level set function
initialized with zeros. Components can be overwritten by physical
properties `props`. If present entries must correspond to the
`mappings` arguments in the constructor. Use ``None`` for properties
for which no value is given.
"""
m=self.regularization.getPDE().createSolution()
if len(props) > 0:
for i in range(self.numMappings):
if props[i]:
mp, idx=self.mappings[i]
m2=mp.getInverse(props[i])
if idx:
if len(idx) == 1:
m[idx[0]]=m2
else:
for k in range(idx): m[idx[k]]=m2[k]
else:
if isinstance(m2, Data):
m=interpolate(m2, m.getFunctionSpace())
else:
m=Data(m2, m.getFunctionSpace())
return m
def createLevelSetFunction(self, *props):
"""
returns an instance of an object used to represent a level set function
initialized with zeros. Components can be overwritten by physical
properties `props`. If present entries must correspond to the
`mappings` arguments in the constructor. Use ``None`` for properties
for which no value is given.
"""
m=self.regularization.getPDE().createSolution()
if len(props) > 0:
for i in range(self.numMappings):
if props[i]:
mp, idx=self.mappings[i]
m2=mp.getInverse(props[i])
if idx:
if len(idx) == 1:
m[idx[0]]=m2
else:
for k in range(idx): m[idx[k]]=m2[k]
else:
if isinstance(m2, Data):
m=interpolate(m2, m.getFunctionSpace())
else:
m=Data(m2, m.getFunctionSpace())
return m
def _getGrad(self, system):
"""returns exact gradient"""
dim = self.domain.getDim()
x = Solution(self.domain).getX()
if system:
g_ex = Data(0., (dim, dim), Solution(self.domain))
if dim == 2:
g_ex[0, 0] = 2. + 8. * x[0] + 5. * x[1]
g_ex[0, 1] = 3. + 5. * x[0] + 12. * x[1]
g_ex[1, 0] = 4. + 2. * x[0] + 6. * x[1]
g_ex[1, 1] = 2. + 6. * x[0] + 8. * x[1]
else:
g_ex[0, 0] = 2. + 6. * x[1] + 8. * x[2] + 18. * x[0]
g_ex[0, 1] = 3. + 6. * x[0] + 7. * x[2] + 20. * x[1]
g_ex[0, 2] = 4. + 7. * x[1] + 8. * x[0] + 22. * x[2]
g_ex[1, 0] = 4. + 3. * x[1] - 8. * x[2] - 4. * x[0]
g_ex[1, 1] = 1. + 3. * x[0] + 2. * x[2] + 14. * x[1]
g_ex[1, 2] = -6. + 2. * x[1] - 8. * x[0] + 10. * x[2]
g_ex[2, 0] = 7. - 6. * x[1] + 2. * x[2] + 4. * x[0]
g_ex[2, 1] = 9. - 6. * x[0] + 8. * x[2] + 16. * x[1]
g_ex[2, 2] = 2. + 8. * x[1] + 2. * x[0] + 2. * x[2]
else:
g_ex = Data(0., (dim, ), Solution(self.domain))
if dim == 2:
g_ex[0] = 2. + 8. * x[0] + 5. * x[1]
g_ex[1] = 3. + 5. * x[0] + 12. * x[1]
else:
g_ex[0] = 2. + 6. * x[1] + 8. * x[2] + 18. * x[0]
g_ex[1] = 3. + 6. * x[0] + 7. * x[2] + 20. * x[1]
g_ex[2] = 4. + 7. * x[1] + 8. * x[0] + 22. * x[2]
return g_ex
def getGradient(self, m, grad_m):
"""
returns the gradient of the cost function J with respect to m.
:note: This implementation returns Y_k=dPsi/dm_k and X_kj=dPsi/dm_kj
"""
mu = self.__mu
mu_c = self.__mu_c
DIM = self.getDomain().getDim()
numLS = self.getNumLevelSets()
grad_m = grad(m, Function(m.getDomain()))
if self.__w0 is not None:
Y = m * self.__w0 * mu
else:
if numLS == 1:
Y = Scalar(0, grad_m.getFunctionSpace())
else:
Y = Data(0, (numLS, ), grad_m.getFunctionSpace())
if self.__w1 is not None:
if numLS == 1:
X = grad_m * self.__w1 * mu
else:
X = grad_m * self.__w1
for k in range(numLS):
X[k, :] *= mu[k]
else:
X = Data(0, grad_m.getShape(), grad_m.getFunctionSpace())
# cross gradient terms:
if numLS > 1:
for k in range(numLS):
grad_m_k = grad_m[k, :]
l2_grad_m_k = length(grad_m_k)**2
for l in range(k):
grad_m_l = grad_m[l, :]
l2_grad_m_l = length(grad_m_l)**2
grad_m_lk = inner(grad_m_l, grad_m_k)
f = mu_c[l, k] * self.__wc[l, k]
X[l, :] += f * (l2_grad_m_k * grad_m_l -
grad_m_lk * grad_m_k)
X[k, :] += f * (l2_grad_m_l * grad_m_k -
grad_m_lk * grad_m_l)
return ArithmeticTuple(Y, X)
def getProperties(self, m, return_list=False):
"""
returns a list of the physical properties from a given level set
function *m* using the mappings of the cost function.
:param m: level set function
:type m: `Data`
:param return_list: if ``True`` a list is returned.
:type return_list: ``bool``
:rtype: ``list`` of `Data`
"""
if not self.configured:
raise ValueError("This inversion function has not been configured yet")
#Since this involves solving a PDE (and therefore a domain, it must be kept local
#to each subworld
raise RuntimeError("This needs to run inside the subworld --- create a function for it")
props=[]
for i in range(self.numMappings):
mp, idx=self.mappings[i]
if idx:
if len(idx)==1:
p=mp.getValue(m[idx[0]])
else:
m2=Data(0.,(len(idx),),m.getFunctionSpace())
for k in range(len(idx)): m2[k]=m[idx[k]]
p=mp.getValue(m2)
else:
p=mp.getValue(m)
props.append(p)
def calculatePropertiesHelper(self, m, mappings):
"""
returns a list of the physical properties from a given level set
function *m* using the mappings of the cost function.
:param m: level set function
:type m: `Data`
:rtype: ``list`` of `Data`
"""
if not isinstance(self, Job):
raise RuntimeError("This function is designed to be run inside a Job.")
props=[]
for i in range(len(mappings)):
mp, idx=mappings[i]
if idx:
if len(idx)==1:
p=mp.getValue(m[idx[0]])
else:
m2=Data(0.,(len(idx),),m.getFunctionSpace())
for k in range(len(idx)): m2[k]=m[idx[k]]
p=mp.getValue(m2)
else:
p=mp.getValue(m)
props.append(p)
return props
def getProperties(self, m, return_list=False):
"""
returns a list of the physical properties from a given level set
function *m* using the mappings of the cost function.
:param m: level set function
:type m: `Data`
:param return_list: if ``True`` a list is returned.
:type return_list: ``bool``
:rtype: ``list`` of `Data`
"""
props=[]
for i in range(self.numMappings):
mp, idx=self.mappings[i]
if idx:
if len(idx)==1:
p=mp.getValue(m[idx[0]])
else:
m2=Data(0.,(len(idx),),m.getFunctionSpace())
for k in range(len(idx)): m2[k]=m[idx[k]]
p=mp.getValue(m2)
else:
p=mp.getValue(m)
props.append(p)
if self.numMappings > 1 or return_list:
return props
else:
return props[0]
def out(self):
x=self.domain.getX()
t=self.t
if isinstance(self.expression,str):
out=eval(self.expression)
else:
out=Data(0,(len(self.expression),),x.getFunctionSpace())
for i in range(len(self.expression)): out[i]=eval(self.expression[i])
return out
def getArguments(self, P):
"""
Returns precomputed values shared by `getDefect()` and `getGradient()`.
:param P: pressure
:type P: ``Scalar``
:return: displacement u
:rtype: ``Vector``
"""
DIM = self.__pde.getDim()
self.__pde.setValue(y=Data(), X=P * kronecker(DIM))
u = self.__pde.getSolution()
return u,
def __init__(self, **kwargs):
super(TemperatureAdvection, self).__init__(**kwargs)
self.declareParameter(domain=None, \
temperature=1., \
velocity=numpy.zeros([3]),
density=1., \
heat_capacity=1., \
thermal_permabilty=1., \
# reference_temperature=0., \
# radiation_coefficient=0., \
thermal_source=0., \
fixed_temperature=0.,
location_fixed_temperature=Data(),
safety_factor=0.1)
def getGradient(self, P, u):
"""
Returns the gradient of the defect with respect to susceptibility.
:param P: pressure
:type P: ``Scalar``
:param u: corresponding displacement
:type u: ``Vector``
:rtype: ``Scalar``
"""
d = inner(u, self.__w) - self.__d
self.__pde.setValue(y=d * self.__w, X=Data())
ustar = self.__pde.getSolution()
return div(ustar)
def combineData(array, shape):
"""
"""
# array could just be a single value
if not hasattr(array, '__len__') and shape == ():
return array
from esys.escript import Data
n = numpy.array(array) # for indexing
# find function space if any
dom = set()
fs = set()
for idx in numpy.ndindex(shape):
if isinstance(n[idx], Data):
fs.add(n[idx].getFunctionSpace())
dom.add(n[idx].getDomain())
if len(dom) > 1:
domain = dom.pop()
while len(dom) > 0:
if domain != dom.pop():
raise ValueError("Mixing of domains not supported")
if len(fs) > 0:
d = Data(0., shape,
fs.pop()) # maybe interpolate instead of using first?
else:
d = numpy.zeros(shape)
for idx in numpy.ndindex(shape):
#z=numpy.zeros(shape)
#z[idx]=1.
#d+=n[idx]*z # much slower!
if hasattr(n[idx], "ndim") and n[idx].ndim == 0:
d[idx] = float(n[idx])
else:
d[idx] = n[idx]
return d
def __init__(self, domain, omega, w, data, F, coordinates=None,
fixAtBottom=False, tol=1e-8, saveMemory=True, scaleF=True):
"""
initializes a new forward model with acoustic wave form inversion.
:param domain: domain of the model
:type domain: `Domain`
:param w: weighting factors
:type w: ``Scalar``
:param data: real and imaginary part of data
:type data: ``Data`` of shape (2,)
:param F: real and imaginary part of source given at Dirac points,
on surface or at volume.
:type F: ``Data`` of shape (2,)
:param coordinates: defines coordinate system to be used (not supported yet)
:type coordinates: `ReferenceSystem` or `SpatialCoordinateTransformation`
:param tol: tolerance of underlying PDE
:type tol: positive ``float``
:param saveMemory: if true stiffness matrix is deleted after solution
of PDE to minimize memory requests. This will
require more compute time as the matrix needs to be
reallocated.
:type saveMemory: ``bool``
:param scaleF: if true source F is scaled to minimize defect.
:type scaleF: ``bool``
:param fixAtBottom: if true pressure is fixed to zero at the bottom of
the domain
:type fixAtBottom: ``bool``
"""
super(AcousticWaveForm, self).__init__()
self.__trafo = makeTransformation(domain, coordinates)
if not self.getCoordinateTransformation().isCartesian():
raise ValueError("Non-Cartesian Coordinates are not supported yet.")
if not isinstance(data, Data):
raise ValueError("data must be an escript.Data object.")
if not data.getFunctionSpace() == FunctionOnBoundary(domain):
raise ValueError("data must be defined on boundary")
if not data.getShape() == (2,):
raise ValueError("data must have shape (2,) (real and imaginary part).")
if w is None:
w = 1.
if not isinstance(w, Data):
w = Data(w, FunctionOnBoundary(domain))
else:
if not w.getFunctionSpace() == FunctionOnBoundary(domain):
raise ValueError("Weights must be defined on boundary.")
if not w.getShape() == ():
raise ValueError("Weights must be scalar.")
self.__domain = domain
self.__omega = omega
self.__weight = w
self.__data = data
self.scaleF = scaleF
if scaleF:
A = integrate(self.__weight*length(self.__data)**2)
if A > 0:
self.__data*=1./sqrt(A)
self.__BX = boundingBox(domain)
self.edge_lengths = np.asarray(boundingBoxEdgeLengths(domain))
if not isinstance(F, Data):
F=interpolate(F, DiracDeltaFunctions(domain))
if not F.getShape() == (2,):
raise ValueError("Source must have shape (2,) (real and imaginary part).")
self.__F=Data()
self.__f=Data()
self.__f_dirac=Data()
if F.getFunctionSpace() == DiracDeltaFunctions(domain):
self.__f_dirac=F
elif F.getFunctionSpace() == FunctionOnBoundary(domain):
self.__f=F
else:
self.__F=F
self.__tol=tol
self.__fixAtBottom=fixAtBottom
self.__pde=None
if not saveMemory:
self.__pde=self.setUpPDE()
def _getGradient(self, m, *args):
"""
returns the gradient of the cost function at *m*.
If the pre-computed values are not supplied `getArguments()` is called.
:param m: current approximation of the level set function
:type m: `Data`
:param args: tuple of values of the parameters, pre-computed values
for the forward model and pre-computed values for the
regularization
:rtype: `ArithmeticTuple`
:note: returns (Y^,X) where Y^ is the gradient from regularization plus
gradients of fwd models. X is the gradient of the regularization
w.r.t. gradient of m.
"""
if not self.configured:
raise ValueError("This inversion function has not been configured yet")
raise RuntimeError("Call to getGradient -- temporary block to see where this is used")
if len(args)==0:
args = self.getArguments(m)
props=args[0]
args_f=args[1]
args_reg=args[2]
g_J = self.regularization.getGradient(m, *args_reg)
p_diffs=[]
# Find the derivative for each mapping
# If a mapping has a list of components (idx), then make a new Data object with only those
# components, pass it to the mapping and get the derivative.
for i in range(self.numMappings):
mm, idx=self.mappings[i]
if idx and self.numLevelSets > 1:
if len(idx)>1:
m2=Data(0,(len(idx),),m.getFunctionSpace())
for k in range(len(idx)): m2[k]=m[idx[k]]
dpdm = mm.getDerivative(m2)
else:
dpdm = mm.getDerivative(m[idx[0]])
else:
dpdm = mm.getDerivative(m)
p_diffs.append(dpdm)
Y=g_J[0] # Because g_J==(Y,X) Y_k=dKer/dm_k
for i in range(self.numModels):
mu=self.mu_model[i]
f, idx_f=self.forward_models[i]
args=tuple( [ props[k] for k in idx_f] + list( args_f[i] ) )
Ys = f.getGradient(*args) # this d Jf/d props
# in this case f depends on one parameter props only but this can
# still depend on several level set components
if Ys.getRank() == 0:
# run through all level sets k prop j is depending on:
idx_m=self.mappings[idx_f[0]][1]
# tmp[k] = dJ_f/d_prop * d prop/d m[idx_m[k]]
tmp=Ys * p_diffs[idx_f[0]] * mu
if idx_m:
if tmp.getRank()== 0:
for k in range(len(idx_m)):
Y[idx_m[k]]+=tmp # dJ_f /d m[idx_m[k]] = tmp
else:
for k in range(len(idx_m)):
Y[idx_m[k]]+=tmp[k] # dJ_f /d m[idx_m[k]] = tmp[k]
else:
Y+=tmp # dJ_f /d m[idx_m[k]] = tmp
else:
s=0
# run through all props j forward model f is depending on:
for j in range(len(idx_f)):
# run through all level sets k prop j is depending on:
idx_m=self.mappings[j][1]
if p_diffs[idx_f[j]].getRank() == 0 :
if idx_m: # this case is not needed (really?)
self.logger.error("something wrong A")
# tmp[k] = dJ_f/d_prop[j] * d prop[j]/d m[idx_m[k]]
tmp=Ys[s]*p_diffs[idx_f[j]] * mu
for k in range(len(idx_m)):
Y[idx_m[k]]+=tmp[k] # dJ_f /d m[idx_m[k]] = tmp[k]
else:
Y+=Ys[s]*p_diffs[idx_f[j]] * mu
s+=1
elif p_diffs[idx_f[j]].getRank() == 1 :
l=p_diffs[idx_f[j]].getShape()[0]
# tmp[k]=sum_j dJ_f/d_prop[j] * d prop[j]/d m[idx_m[k]]
tmp=inner(Ys[s:s+l], p_diffs[idx_f[j]]) * mu
if idx_m:
for k in range(len(idx_m)):
Y[idx_m[k]]+=tmp # dJ_f /d m[idx_m[k]] = tmp[k]
else:
Y+=tmp
s+=l
else: # rank 2 case
l=p_diffs[idx_f[j]].getShape()[0]
Yss=Ys[s:s+l]
if idx_m:
for k in range(len(idx_m)):
# dJ_f /d m[idx_m[k]] = tmp[k]
Y[idx_m[k]]+=inner(Yss, p_diffs[idx_f[j]][:,k])
else:
Y+=inner(Yss, p_diffs[idx_f[j]]) * mu
s+=l
return g_J
def calculateGradientWorker(self, **args):
"""
vnames1 gives the names to store the first component of the gradient in
vnames2 gives the names to store the second component of the gradient in
"""
vnames1=args['vnames1']
vnames2=args['vnames2']
props=self.importValue("props")
mods=self.importValue("fwdmodels")
reg=self.importValue("regularization")
mu_model=self.importValue("mu_model")
mappings=self.importValue("mappings")
m=self.importValue("current_point")
model_args=SplitInversionCostFunction.getModelArgs(self, mods)
g_J = reg.getGradientAtPoint()
p_diffs=[]
# Find the derivative for each mapping
# If a mapping has a list of components (idx), then make a new Data object with only those
# components, pass it to the mapping and get the derivative.
for i in range(len(mappings)):
mm, idx=mappings[i]
if idx and numLevelSets > 1:
if len(idx)>1:
m2=Data(0,(len(idx),),m.getFunctionSpace())
for k in range(len(idx)): m2[k]=m[idx[k]]
dpdm = mm.getDerivative(m2)
else:
dpdm = mm.getDerivative(m[idx[0]])
else:
dpdm = mm.getDerivative(m)
p_diffs.append(dpdm)
#Since we are going to be merging Y with other worlds, we need to make sure the the regularization
#component is only added once. However most of the ops below are in terms of += so we need to
#create a zero object to use as a starting point
if self.swid==0:
Y=g_J[0] # Because g_J==(Y,X) Y_k=dKer/dm_k
else:
Y=Data(0, g_J[0].getShape(), g_J[0].getFunctionSpace())
for i in range(len(mods)):
mu=mu_model[i]
f, idx_f=mods[i]
args=tuple( [ props[k] for k in idx_f] + list( model_args[i] ) )
Ys = f.getGradient(*args) # this d Jf/d props
# in this case f depends on one parameter props only but this can
# still depend on several level set components
if Ys.getRank() == 0:
# run through all level sets k prop j is depending on:
idx_m=mappings[idx_f[0]][1]
# tmp[k] = dJ_f/d_prop * d prop/d m[idx_m[k]]
tmp=Ys * p_diffs[idx_f[0]] * mu
if idx_m:
if tmp.getRank()== 0:
for k in range(len(idx_m)):
Y[idx_m[k]]+=tmp # dJ_f /d m[idx_m[k]] = tmp
else:
for k in range(len(idx_m)):
Y[idx_m[k]]+=tmp[k] # dJ_f /d m[idx_m[k]] = tmp[k]
else:
Y+=tmp # dJ_f /d m[idx_m[k]] = tmp
else:
s=0
# run through all props j forward model f is depending on:
for j in range(len(idx_f)):
# run through all level sets k prop j is depending on:
idx_m=mappings[j][1]
if p_diffs[idx_f[j]].getRank() == 0 :
if idx_m: # this case is not needed (really?)
raise RuntimeError("something wrong A")
# tmp[k] = dJ_f/d_prop[j] * d prop[j]/d m[idx_m[k]]
tmp=Ys[s]*p_diffs[idx_f[j]] * mu
for k in range(len(idx_m)):
Y[idx_m[k]]+=tmp[k] # dJ_f /d m[idx_m[k]] = tmp[k]
else:
Y+=Ys[s]*p_diffs[idx_f[j]] * mu
s+=1
elif p_diffs[idx_f[j]].getRank() == 1 :
l=p_diffs[idx_f[j]].getShape()[0]
# tmp[k]=sum_j dJ_f/d_prop[j] * d prop[j]/d m[idx_m[k]]
tmp=inner(Ys[s:s+l], p_diffs[idx_f[j]]) * mu
if idx_m:
for k in range(len(idx_m)):
Y[idx_m[k]]+=tmp # dJ_f /d m[idx_m[k]] = tmp[k]
else:
Y+=tmp
s+=l
else: # rank 2 case
l=p_diffs[idx_f[j]].getShape()[0]
Yss=Ys[s:s+l]
if idx_m:
for k in range(len(idx_m)):
# dJ_f /d m[idx_m[k]] = tmp[k]
Y[idx_m[k]]+=inner(Yss, p_diffs[idx_f[j]][:,k])
else:
Y+=inner(Yss, p_diffs[idx_f[j]]) * mu
s+=l
if isinstance(vnames1, str):
self.exportValue(vnames1, Y)
else:
for n in vnames1:
self.exportValue(n, Y)
if isinstance(vnames2, str): #The second component should be strictly local
self.exportValue(vnames2, g_J[1])
else:
for n in vnames2:
self.exportValue(n, g_J[1])
def __init__(self,
domain,
numLevelSets=1,
w0=None,
w1=None,
wc=None,
location_of_set_m=Data(),
useDiagonalHessianApproximation=False,
tol=1e-8,
coordinates=None,
scale=None,
scale_c=None):
"""
initialization.
:param domain: domain
:type domain: `Domain`
:param numLevelSets: number of level sets
:type numLevelSets: ``int``
:param w0: weighting factor for the m**2 term. If not set zero is assumed.
:type w0: ``Scalar`` if ``numLevelSets`` == 1 or `Data` object of shape
(``numLevelSets`` ,) if ``numLevelSets`` > 1
:param w1: weighting factor for the grad(m_i) terms. If not set zero is assumed
:type w1: ``Vector`` if ``numLevelSets`` == 1 or `Data` object of shape
(``numLevelSets`` , DIM) if ``numLevelSets`` > 1
:param wc: weighting factor for the cross gradient terms. If not set
zero is assumed. Used for the case if ``numLevelSets`` > 1
only. Only values ``wc[l,k]`` in the lower triangle (l<k)
are used.
:type wc: `Data` object of shape (``numLevelSets`` , ``numLevelSets``)
:param location_of_set_m: marks location of zero values of the level
set function ``m`` by a positive entry.
:type location_of_set_m: ``Scalar`` if ``numLevelSets`` == 1 or `Data`
object of shape (``numLevelSets`` ,) if ``numLevelSets`` > 1
:param useDiagonalHessianApproximation: if True cross gradient terms
between level set components are ignored when calculating
approximations of the inverse of the Hessian Operator.
This can speed-up the calculation of the inverse but may
lead to an increase of the number of iteration steps in the
inversion.
:type useDiagonalHessianApproximation: ``bool``
:param tol: tolerance when solving the PDE for the inverse of the
Hessian Operator
:type tol: positive ``float``
:param coordinates: defines coordinate system to be used
:type coordinates: ReferenceSystem` or `SpatialCoordinateTransformation`
:param scale: weighting factor for level set function variation terms.
If not set one is used.
:type scale: ``Scalar`` if ``numLevelSets`` == 1 or `Data` object of
shape (``numLevelSets`` ,) if ``numLevelSets`` > 1
:param scale_c: scale for the cross gradient terms. If not set
one is assumed. Used for the case if ``numLevelSets`` > 1
only. Only values ``scale_c[l,k]`` in the lower triangle
(l<k) are used.
:type scale_c: `Data` object of shape (``numLevelSets``,``numLevelSets``)
"""
if w0 is None and w1 is None:
raise ValueError("Values for w0 or for w1 must be given.")
if wc is None and numLevelSets > 1:
raise ValueError("Values for wc must be given.")
self.logger = logging.getLogger('inv.%s' % self.__class__.__name__)
self.__domain = domain
DIM = self.__domain.getDim()
self.__numLevelSets = numLevelSets
self.__trafo = makeTransformation(domain, coordinates)
self.__pde = LinearPDE(self.__domain,
numEquations=self.__numLevelSets,
numSolutions=self.__numLevelSets)
self.__pde.getSolverOptions().setTolerance(tol)
self.__pde.setSymmetryOn()
self.__pde.setValue(
A=self.__pde.createCoefficient('A'),
D=self.__pde.createCoefficient('D'),
)
try:
self.__pde.setValue(q=location_of_set_m)
except IllegalCoefficientValue:
raise ValueError(
"Unable to set location of fixed level set function.")
# =========== check the shape of the scales: ========================
if scale is None:
if numLevelSets == 1:
scale = 1.
else:
scale = np.ones((numLevelSets, ))
else:
scale = np.asarray(scale)
if numLevelSets == 1:
if scale.shape == ():
if not scale > 0:
raise ValueError("Value for scale must be positive.")
else:
raise ValueError("Unexpected shape %s for scale." %
scale.shape)
else:
if scale.shape is (numLevelSets, ):
if not min(scale) > 0:
raise ValueError(
"All values for scale must be positive.")
else:
raise ValueError("Unexpected shape %s for scale." %
scale.shape)
if scale_c is None or numLevelSets < 2:
scale_c = np.ones((numLevelSets, numLevelSets))
else:
scale_c = np.asarray(scale_c)
if scale_c.shape == (numLevelSets, numLevelSets):
if not all([[scale_c[l, k] > 0. for l in range(k)]
for k in range(1, numLevelSets)]):
raise ValueError(
"All values in the lower triangle of scale_c must be positive."
)
else:
raise ValueError("Unexpected shape %s for scale." %
scale_c.shape)
# ===== check the shape of the weights: =============================
if w0 is not None:
w0 = interpolate(w0,
self.__pde.getFunctionSpaceForCoefficient('D'))
s0 = w0.getShape()
if numLevelSets == 1:
if not s0 == ():
raise ValueError("Unexpected shape %s for weight w0." %
(s0, ))
else:
if not s0 == (numLevelSets, ):
raise ValueError("Unexpected shape %s for weight w0." %
(s0, ))
if not self.__trafo.isCartesian():
w0 *= self.__trafo.getVolumeFactor()
if not w1 is None:
w1 = interpolate(w1,
self.__pde.getFunctionSpaceForCoefficient('A'))
s1 = w1.getShape()
if numLevelSets == 1:
if not s1 == (DIM, ):
raise ValueError("Unexpected shape %s for weight w1." %
(s1, ))
else:
if not s1 == (numLevelSets, DIM):
raise ValueError("Unexpected shape %s for weight w1." %
(s1, ))
if not self.__trafo.isCartesian():
f = self.__trafo.getScalingFactors(
)**2 * self.__trafo.getVolumeFactor()
if numLevelSets == 1:
w1 *= f
else:
for i in range(numLevelSets):
w1[i, :] *= f
if numLevelSets == 1:
wc = None
else:
wc = interpolate(wc,
self.__pde.getFunctionSpaceForCoefficient('A'))
sc = wc.getShape()
if not sc == (numLevelSets, numLevelSets):
raise ValueError("Unexpected shape %s for weight wc." % (sc, ))
if not self.__trafo.isCartesian():
raise ValueError(
"Non-cartesian coordinates for cross-gradient term is not supported yet."
)
# ============= now we rescale weights: =============================
L2s = np.asarray(boundingBoxEdgeLengths(domain))**2
L4 = 1 / np.sum(1 / L2s)**2
if numLevelSets == 1:
A = 0
if w0 is not None:
A = integrate(w0)
if w1 is not None:
A += integrate(inner(w1, 1 / L2s))
if A > 0:
f = scale / A
if w0 is not None:
w0 *= f
if w1 is not None:
w1 *= f
else:
raise ValueError("Non-positive weighting factor detected.")
else: # numLevelSets > 1
for k in range(numLevelSets):
A = 0
if w0 is not None:
A = integrate(w0[k])
if w1 is not None:
A += integrate(inner(w1[k, :], 1 / L2s))
if A > 0:
f = scale[k] / A
if w0 is not None:
w0[k] *= f
if w1 is not None:
w1[k, :] *= f
else:
raise ValueError(
"Non-positive weighting factor for level set component %d detected."
% k)
# and now the cross-gradient:
if wc is not None:
for l in range(k):
A = integrate(wc[l, k]) / L4
if A > 0:
f = scale_c[l, k] / A
wc[l, k] *= f
# else:
# raise ValueError("Non-positive weighting factor for cross-gradient level set components %d and %d detected."%(l,k))
self.__w0 = w0
self.__w1 = w1
self.__wc = wc
self.__pde_is_set = False
if self.__numLevelSets > 1:
self.__useDiagonalHessianApproximation = useDiagonalHessianApproximation
else:
self.__useDiagonalHessianApproximation = True
self._update_Hessian = True
self.__num_tradeoff_factors = numLevelSets + (
(numLevelSets - 1) * numLevelSets) // 2
self.setTradeOffFactors()
self.__vol_d = vol(self.__domain)