def getPotentialNumeric(self):
"""
Returns 3 list each made up of a number of list containing primary, secondary and total
potentials diferences. Each of the lists contain a list for each value of n.
"""
primCon=self.primaryConductivity
coords=self.domain.getX()
tol=1e-8
pde=LinearPDE(self.domain, numEquations=1)
pde.getSolverOptions().setTolerance(tol)
pde.setSymmetryOn()
primaryPde=LinearPDE(self.domain, numEquations=1)
primaryPde.getSolverOptions().setTolerance(tol)
primaryPde.setSymmetryOn()
DIM=self.domain.getDim()
x=self.domain.getX()
q=whereZero(x[DIM-1]-inf(x[DIM-1]))
for i in xrange(DIM-1):
xi=x[i]
q+=whereZero(xi-inf(xi))+whereZero(xi-sup(xi))
A = self.secondaryConductivity * kronecker(self.domain)
APrimary = self.primaryConductivity * kronecker(self.domain)
pde.setValue(A=A,q=q)
primaryPde.setValue(A=APrimary,q=q)
delPhiSecondaryList = []
delPhiPrimaryList = []
delPhiTotalList = []
for i in range(1,self.n+1): # 1 to n
maxR = self.numElectrodes - 1 - (2*i) #max amount of readings that will fit in the survey
delPhiSecondary = []
delPhiPrimary = []
delPhiTotal = []
for j in range(maxR):
y_dirac=Scalar(0,DiracDeltaFunctions(self.domain))
y_dirac.setTaggedValue(self.electrodeTags[j],self.current)
y_dirac.setTaggedValue(self.electrodeTags[j + ((2*i) + 1)],-self.current)
self.sources.append([self.electrodeTags[j], self.electrodeTags[j + ((2*i) + 1)]])
primaryPde.setValue(y_dirac=y_dirac)
numericPrimaryPot = primaryPde.getSolution()
X=(primCon-self.secondaryConductivity) * grad(numericPrimaryPot)
pde.setValue(X=X)
u=pde.getSolution()
loc=Locator(self.domain,[self.electrodes[j+i],self.electrodes[j+i+1]])
self.samples.append([self.electrodeTags[j+i],self.electrodeTags[j+i+1]])
valPrimary=loc.getValue(numericPrimaryPot)
valSecondary=loc.getValue(u)
delPhiPrimary.append(valPrimary[1]-valPrimary[0])
delPhiSecondary.append(valSecondary[1]-valSecondary[0])
delPhiTotal.append(delPhiPrimary[j]+delPhiSecondary[j])
delPhiPrimaryList.append(delPhiPrimary)
delPhiSecondaryList.append(delPhiSecondary)
delPhiTotalList.append(delPhiTotal)
self.delPhiPrimaryList=delPhiPrimaryList
self.delPhiSecondaryList=delPhiSecondaryList
self.delPhiTotalList = delPhiTotalList
return [delPhiPrimaryList, delPhiSecondaryList, delPhiTotalList]
def getGradient(self, sigma, phi, loc_phi):
"""
Returns the gradient of the defect with respect to density.
:param sigma: a suggestison for conductivity
:type sigma: ``Data`` of shape (1,)
:param phi: potential field
:type phi: ``Data`` of shape (1,)
"""
val = loc_phi
if not isinstance(val, list):
tmp = val
val = [tmp]
sampleTags = self.__sampleTags
jointSamples = {}
for i in range(0, 2 * len(sampleTags),
2): #2*len because sample tags is a list of tuples
half = i // 2
if sampleTags[half][1] != "-":
tmp = (val[i + 1] - val[i] - self.delphiIn[half]) * self.__w[i]
else:
tmp = (val[i] - self.delphiIn[i // 2]) * self.__w[i]
sample = sampleTags[half]
if sample[1] != "-":
if sample[0] in jointSamples.keys():
jointSamples[sample[0]].append((sample[1], -tmp))
else:
jointSamples[sampleTags[half][0]] = [(sample[1], -tmp)]
if sample[1] in jointSamples.keys():
jointSamples[sample[1]].append((sample[0], tmp))
else:
jointSamples[sample[1]] = [(sample[0], tmp)]
else:
if sample[0] in jointSamples.keys():
jointSamples[sample[0]].append((sample[1], tmp))
else:
jointSamples[sampleTags[half][0]] = [(sample[1], tmp)]
pde = self.setUpPDE()
dom = self.__domain
# conPrimary=self.__sigmaPrimary
# APrimary = conPrimary * kronecker(dom)
y_dirac = Scalar(0, DiracDeltaFunctions(dom))
for i in jointSamples:
total = 0
for j in jointSamples[i]:
total += j[1]
y_dirac.setTaggedValue(i, total)
pde.setValue(A=sigma * kronecker(dom), y_dirac=y_dirac)
u = pde.getSolution()
retVal = -inner(grad(u), grad(phi + self.__phiPrimary))
return retVal
def getGradient(self, sigma, phi, loc_phi):
"""
Returns the gradient of the defect with respect to density.
:param sigma: a suggestison for conductivity
:type sigma: ``Data`` of shape (1,)
:param phi: potential field
:type phi: ``Data`` of shape (1,)
"""
val=loc_phi
if not isinstance(val,list):
tmp=val
val=[tmp]
sampleTags=self.__sampleTags
jointSamples={}
for i in range(0,2*len(sampleTags),2): #2*len because sample tags is a list of tuples
half = i//2
if sampleTags[half][1]!="-":
tmp=(val[i+1]-val[i]-self.delphiIn[half])*self.__w[i]
else:
tmp=(val[i]-self.delphiIn[i//2]) *self.__w[i]
sample = sampleTags[half]
if sample[1]!="-":
if sample[0] in jointSamples.keys():
jointSamples[sample[0]].append((sample[1], -tmp))
else:
jointSamples[sampleTags[half][0]]=[(sample[1],-tmp)]
if sample[1] in jointSamples.keys():
jointSamples[sample[1]].append((sample[0], tmp))
else:
jointSamples[sample[1]]=[(sample[0], tmp)]
else:
if sample[0] in jointSamples.keys():
jointSamples[sample[0]].append((sample[1], tmp))
else:
jointSamples[sampleTags[half][0]]=[(sample[1],tmp)]
pde =self.setUpPDE()
dom=self.__domain
# conPrimary=self.__sigmaPrimary
# APrimary = conPrimary * kronecker(dom)
y_dirac = Scalar(0,DiracDeltaFunctions(dom))
for i in jointSamples:
total=0
for j in jointSamples[i]:
total+=j[1]
y_dirac.setTaggedValue(i,total)
pde.setValue(A=sigma*kronecker(dom), y_dirac=y_dirac)
u=pde.getSolution()
retVal=-inner(grad(u),grad(phi+self.__phiPrimary))
return retVal
def makeTagField(functionspace):
"""
this creates a data object making the tagged regions with the corresponding tag id
:param functionspace: function space to create tags for
:type functionspace: `esys.escript.FunctionSpace`
:return: `esys.escript.Scalar` with tags
"""
out = Scalar(-1, functionspace)
for t in functionspace.getListOfTags():
out.setTaggedValue(t, t)
out.expand()
return out
def true_properties(domain):
from esys.escript import Scalar, Function
sigma_true = Scalar(sigma_background, Function(domain))
sigma_true.setTaggedValue("InnerBox", sigma_background)
sigma_true.setTaggedValue("Anomaly1", sigma_background * 10)
sigma_true.setTaggedValue("Anomaly2", sigma_background * 10)
sigma_true.setTaggedValue("Anomaly3", sigma_background)
gamma_background = eta_background / (1 - eta_background)
gamma_true = Scalar(gamma_background, Function(domain))
gamma_true.setTaggedValue("InnerBox", gamma_background)
gamma_true.setTaggedValue("Anomaly1", gamma_background)
gamma_true.setTaggedValue("Anomaly2", gamma_background * 20)
gamma_true.setTaggedValue("Anomaly3", gamma_background * 20)
return sigma_true, gamma_true
def true_properties(domain):
from esys.escript import Scalar, Function
sigma_true = Scalar(sigma_background, Function(domain))
sigma_true.setTaggedValue("R1", 0.01)
sigma_true.setTaggedValue("R2", 0.1)
gamma_background = eta_background / (1 - eta_background)
gamma_true = Scalar(gamma_background, Function(domain))
gamma_true.setTaggedValue("R1", 0.02)
gamma_true.setTaggedValue("R2", 0.2)
return sigma_true, gamma_true
