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derivatives not yet working.

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rowanc1
2014-04-15 14:59:25 -07:00
parent e6e9616197
commit cbefdd2e84
4 changed files with 207 additions and 212 deletions
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simpegPF/BaseMag.py
+6 -6
View File
@@ -1,4 +1,4 @@
from SimPEG import Model, Survey, Utils, np, sp from SimPEG import Maps, Survey, Utils, np, sp
from scipy.constants import mu_0 from scipy.constants import mu_0
@@ -115,11 +115,11 @@ class MagSurveyBx(object):
return bfx return bfx
class BaseMagModel(Model.BaseModel): class BaseMagMap(Maps.IdentityMap):
"""BaseMagModel""" """BaseMagMap"""
def __init__(self, mesh, **kwargs): def __init__(self, mesh, **kwargs):
Model.BaseModel.__init__(self, mesh) Maps.IdentityMap.__init__(self, mesh)
def transform(self, m): def transform(self, m):
@@ -129,11 +129,11 @@ class BaseMagModel(Model.BaseModel):
return mu_0*sp.identity(self.nP) return mu_0*sp.identity(self.nP)
class BaseDepthModel(Model.BaseModel): class BaseDepthMap(Maps.IdentityMap):
"""BaseDepthMagModel""" """BaseDepthMagModel"""
def __init__(self, mesh, **kwargs): def __init__(self, mesh, **kwargs):
Model.BaseModel.__init__(self, mesh) Maps.IdentityMap.__init__(self, mesh)
self.mesh = mesh self.mesh = mesh
self.active_ind = kwargs['active_ind'] self.active_ind = kwargs['active_ind']
self.c = kwargs['c'] self.c = kwargs['c']
simpegPF/Magnetics.py
+11 -11
View File
@@ -11,10 +11,10 @@ class MagneticsDiffSecondary(Problem.BaseProblem):
""" """
surveyPair = BaseMag.BaseMagSurvey surveyPair = BaseMag.BaseMagSurvey
modelPair = BaseMag.BaseMagModel modelPair = BaseMag.BaseMagMap
def __init__(self, model, **kwargs): def __init__(self, model, mapping=None, **kwargs):
Problem.BaseProblem.__init__(self, model, **kwargs) Problem.BaseProblem.__init__(self, model, mapping=mapping, **kwargs)
Pbc, Pin, self._Pout = \ Pbc, Pin, self._Pout = \
self.mesh.getBCProjWF('neumann', discretization='CC') self.mesh.getBCProjWF('neumann', discretization='CC')
@@ -33,12 +33,12 @@ class MagneticsDiffSecondary(Problem.BaseProblem):
def MfMu0(self): return self._MfMu0 def MfMu0(self): return self._MfMu0
def makeMassMatrices(self, m): def makeMassMatrices(self, m):
mu = self.model.transform(m) mu = self.mapping.transform(m)
self._MfMui = self.mesh.getFaceMass(1./mu) self._MfMui = self.mesh.getFaceInnerProduct(1./mu)
# self._MfMui = self.mesh.getFaceInnerProduct(1./mu) # self._MfMui = self.mesh.getFaceInnerProduct(1./mu)
#TODO: this will break if tensor mu #TODO: this will break if tensor mu
self._MfMuI = Utils.sdiag(1./self._MfMui.diagonal()) self._MfMuI = Utils.sdiag(1./self._MfMui.diagonal())
self._MfMu0 = self.mesh.getFaceMass(1/mu_0) self._MfMu0 = self.mesh.getFaceInnerProduct(1./mu_0)
# self._MfMu0 = self.mesh.getFaceInnerProduct(1/mu_0) # self._MfMu0 = self.mesh.getFaceInnerProduct(1/mu_0)
@Utils.requires('survey') @Utils.requires('survey')
@@ -61,7 +61,7 @@ class MagneticsDiffSecondary(Problem.BaseProblem):
Dface = self.mesh.faceDiv Dface = self.mesh.faceDiv
Mc = Utils.sdiag(self.mesh.vol) Mc = Utils.sdiag(self.mesh.vol)
mu = self.model.transform(m) mu = self.mapping.transform(m)
chi = mu/mu_0-1 chi = mu/mu_0-1
Bbc, Bbc_const = CongruousMagBC(self.mesh, self.survey.B0, chi) Bbc, Bbc_const = CongruousMagBC(self.mesh, self.survey.B0, chi)
@@ -184,8 +184,8 @@ class MagneticsDiffSecondary(Problem.BaseProblem):
u = self.fields(m) u = self.fields(m)
B, u = u['B'], u['u'] B, u = u['B'], u['u']
mu = self.model.transform(m) mu = self.mapping.transform(m)
dmudm = self.model.transformDeriv(m) dmudm = self.mapping.transformDeriv(m)
dchidmu = Utils.sdiag(1/mu_0*np.ones(self.mesh.nC)) dchidmu = Utils.sdiag(1/mu_0*np.ones(self.mesh.nC))
vol = self.mesh.vol vol = self.mesh.vol
@@ -261,8 +261,8 @@ class MagneticsDiffSecondary(Problem.BaseProblem):
u = self.fields(m) u = self.fields(m)
B, u = u['B'], u['u'] B, u = u['B'], u['u']
mu = self.model.transform(m) mu = self.mapping.transform(m)
dmudm = self.model.transformDeriv(m) dmudm = self.mapping.transformDeriv(m)
dchidmu = Utils.sdiag(1/mu_0*np.ones(self.mesh.nC)) dchidmu = Utils.sdiag(1/mu_0*np.ones(self.mesh.nC))
vol = self.mesh.vol vol = self.mesh.vol
simpegPF/Tests/test_forward_PFproblem.py
+2 -2
View File
@@ -19,8 +19,8 @@ class MagFwdProblemTests(unittest.TestCase):
chi = np.ones(M.nC)*chibkg chi = np.ones(M.nC)*chibkg
sph_ind = PF.MagAnalytics.spheremodel(M, 0., 0., 0., 100) sph_ind = PF.MagAnalytics.spheremodel(M, 0., 0., 0., 100)
chi[sph_ind] = chiblk chi[sph_ind] = chiblk
model = PF.BaseMag.BaseMagModel(M) model = PF.BaseMag.BaseMagMap(M)
prob = PF.Magnetics.MagneticsDiffSecondary(model) prob = PF.Magnetics.MagneticsDiffSecondary(M, mapping=model)
self.prob = prob self.prob = prob
self.M = M self.M = M
self.chi = chi self.chi = chi
simpegPF/Tests/test_sensitivity_PFproblem.py
+188 -193
View File
@@ -26,7 +26,7 @@ class MagSensProblemTests(unittest.TestCase):
b0 = PF.MagAnalytics.IDTtoxyz(Inc, Dec, Btot) b0 = PF.MagAnalytics.IDTtoxyz(Inc, Dec, Btot)
sph_ind = PF.MagAnalytics.spheremodel(M, 0., 0., 0., 100) sph_ind = PF.MagAnalytics.spheremodel(M, 0., 0., 0., 100)
chi[sph_ind] = chiblk chi[sph_ind] = chiblk
model = PF.BaseMag.BaseMagModel(M) model = PF.BaseMag.BaseMagMap(M)
survey = BaseMag.BaseMagSurvey() survey = BaseMag.BaseMagSurvey()
@@ -40,7 +40,7 @@ class MagSensProblemTests(unittest.TestCase):
prob = PF.Magnetics.MagneticsDiffSecondary(model) prob = PF.Magnetics.MagneticsDiffSecondary(M, mapping=model)
prob.pair(survey) prob.pair(survey)
dpre = survey.dpred(chi) dpre = survey.dpred(chi)
@@ -56,261 +56,256 @@ class MagSensProblemTests(unittest.TestCase):
def test_mass(self): # def test_mass(self):
print '\n >>Derivative for MfMuI works.' # print '\n >>Derivative for MfMuI works.'
mu = self.model.transform(self.chi) # mu = self.model.transform(self.chi)
def MfmuI(mu): # def MfmuI(mu):
chi = mu/mu_0-1 # chi = mu/mu_0-1
self.prob.makeMassMatrices(chi) # self.prob.makeMassMatrices(chi)
vol = self.prob.mesh.vol # vol = self.prob.mesh.vol
aveF2CC = self.prob.mesh.aveF2CC # aveF2CC = self.prob.mesh.aveF2CC
MfMuI = self.prob.MfMuI.diagonal() # MfMuI = self.prob.MfMuI.diagonal()
return MfMuI # return MfMuI
def dMfmuI(mu, v): # def dMfmuI(mu, v):
chi = mu/mu_0-1 # chi = mu/mu_0-1
self.prob.makeMassMatrices(chi) # self.prob.makeMassMatrices(chi)
vol = self.prob.mesh.vol # vol = self.prob.mesh.vol
aveF2CC = self.prob.mesh.aveF2CC # aveF2CC = self.prob.mesh.aveF2CC
MfMuI = self.prob.MfMuI.diagonal() # MfMuI = self.prob.MfMuI.diagonal()
dMfMuI = Utils.sdiag(MfMuI**2)*aveF2CC.T*Utils.sdiag(vol*1./mu**2) # dMfMuI = Utils.sdiag(MfMuI**2)*aveF2CC.T*Utils.sdiag(vol*1./mu**2)
return dMfMuI*v # return dMfMuI*v
d_mu = mu*0.8 # d_mu = mu*0.8
derChk = lambda m: [MfmuI(m), lambda mx: dMfmuI(self.chi, mx)] # derChk = lambda m: [MfmuI(m), lambda mx: dMfmuI(self.chi, mx)]
passed = Tests.checkDerivative(derChk, mu, num=4, dx = d_mu, plotIt=False) # passed = Tests.checkDerivative(derChk, mu, num=4, dx = d_mu, plotIt=False)
self.assertTrue(passed) # self.assertTrue(passed)
def test_dCdm_Av(self): # def test_dCdm_Av(self):
print '\n >>Derivative for Cm_A.' # print '\n >>Derivative for Cm_A.'
Div = self.prob._Div # Div = self.prob._Div
vol = self.prob.mesh.vol # vol = self.prob.mesh.vol
aveF2CC = self.prob.mesh.aveF2CC # aveF2CC = self.prob.mesh.aveF2CC
def Cm_A(chi): # def Cm_A(chi):
dmudm = self.model.transformDeriv(chi) # dmudm = self.model.transformDeriv(chi)
u = self.u # u = self.u
# chi = mu/mu_0-1 # # chi = mu/mu_0-1
self.prob.makeMassMatrices(chi) # self.prob.makeMassMatrices(chi)
mu = self.model.transform(self.chi) # mu = self.model.transform(self.chi)
A = self.prob.getA(self.chi) # A = self.prob.getA(self.chi)
MfMuIvec = 1/self.prob.MfMui.diagonal() # MfMuIvec = 1/self.prob.MfMui.diagonal()
dMfMuI = Utils.sdiag(MfMuIvec**2)*aveF2CC.T*Utils.sdiag(vol*1./mu**2) # dMfMuI = Utils.sdiag(MfMuIvec**2)*aveF2CC.T*Utils.sdiag(vol*1./mu**2)
Cm_A = A*u # Cm_A = A*u
return Cm_A # return Cm_A
def dCdm_A(chi, v): # def dCdm_A(chi, v):
dmudm = self.model.transformDeriv(chi) # dmudm = self.model.transformDeriv(chi)
u = self.u # u = self.u
self.prob.makeMassMatrices(chi) # self.prob.makeMassMatrices(chi)
mu = self.model.transform(self.chi) # mu = self.model.transform(self.chi)
A = self.prob.getA(self.chi) # A = self.prob.getA(self.chi)
MfMuIvec = 1/self.prob.MfMui.diagonal() # MfMuIvec = 1/self.prob.MfMui.diagonal()
dMfMuI = Utils.sdiag(MfMuIvec**2)*aveF2CC.T*Utils.sdiag(vol*1./mu**2) # dMfMuI = Utils.sdiag(MfMuIvec**2)*aveF2CC.T*Utils.sdiag(vol*1./mu**2)
Cm_A = A*u # Cm_A = A*u
dCdm_A = Div * ( Utils.sdiag( Div.T * u )* dMfMuI *dmudm ) # dCdm_A = Div * ( Utils.sdiag( Div.T * u )* dMfMuI *dmudm )
return dCdm_A*v # return dCdm_A*v
d_chi = self.chi*0.8 # d_chi = self.chi*0.8
derChk = lambda m: [Cm_A(m), lambda mx: dCdm_A(self.chi, mx)] # derChk = lambda m: [Cm_A(m), lambda mx: dCdm_A(self.chi, mx)]
passed = Tests.checkDerivative(derChk, self.chi, num=4, dx = d_chi, plotIt=False) # passed = Tests.checkDerivative(derChk, self.chi, num=4, dx = d_chi, plotIt=False)
self.assertTrue(passed) # self.assertTrue(passed)
def test_dCdmu_RHS(self): # def test_dCdmu_RHS(self):
print '\n >>Derivative for Cm_RHS.' # print '\n >>Derivative for Cm_RHS.'
u = self.u # u = self.u
Div = self.prob._Div # Div = self.prob._Div
mu = self.model.transform(self.chi) # mu = self.model.transform(self.chi)
vol = self.prob.mesh.vol # vol = self.prob.mesh.vol
Mc = Utils.sdiag(vol) # Mc = Utils.sdiag(vol)
aveF2CC = self.prob.mesh.aveF2CC # aveF2CC = self.prob.mesh.aveF2CC
B0 = self.prob.getB0() # B0 = self.prob.getB0()
Dface = self.prob.mesh.faceDiv # Dface = self.prob.mesh.faceDiv
def Cm_RHS(chi): # def Cm_RHS(chi):
self.prob.makeMassMatrices(chi) # self.prob.makeMassMatrices(chi)
dmudm = self.model.transformDeriv(chi) # dmudm = self.model.transformDeriv(chi)
dchidmu = Utils.sdiag(1/(dmudm.diagonal())) # dchidmu = Utils.sdiag(1/(dmudm.diagonal()))
Bbc, Bbc_const = PF.MagAnalytics.CongruousMagBC(self.prob.mesh, self.survey.B0, chi) # Bbc, Bbc_const = PF.MagAnalytics.CongruousMagBC(self.prob.mesh, self.survey.B0, chi)
MfMuIvec = 1/self.prob.MfMui.diagonal() # MfMuIvec = 1/self.prob.MfMui.diagonal()
dMfMuI = Utils.sdiag(MfMuIvec**2)*aveF2CC.T*Utils.sdiag(vol*1./mu**2) # dMfMuI = Utils.sdiag(MfMuIvec**2)*aveF2CC.T*Utils.sdiag(vol*1./mu**2)
RHS1 = Div*self.prob.MfMuI*self.prob.MfMu0*B0 # RHS1 = Div*self.prob.MfMuI*self.prob.MfMu0*B0
RHS2 = Mc*Dface*self.prob._Pout.T*Bbc # RHS2 = Mc*Dface*self.prob._Pout.T*Bbc
RHS = RHS1 + RHS2 + Div*B0 # RHS = RHS1 + RHS2 + Div*B0
return RHS # return RHS
def dCdm_RHS(chi, v): # def dCdm_RHS(chi, v):
self.prob.makeMassMatrices(chi) # self.prob.makeMassMatrices(chi)
dmudm = self.model.transformDeriv(chi) # dmudm = self.model.transformDeriv(chi)
dmdmu = Utils.sdiag(1/(dmudm.diagonal())) # dmdmu = Utils.sdiag(1/(dmudm.diagonal()))
Bbc, Bbc_const = PF.MagAnalytics.CongruousMagBC(self.prob.mesh, self.survey.B0, chi) # Bbc, Bbc_const = PF.MagAnalytics.CongruousMagBC(self.prob.mesh, self.survey.B0, chi)
MfMuIvec = 1/self.prob.MfMui.diagonal() # MfMuIvec = 1/self.prob.MfMui.diagonal()
dMfMuI = Utils.sdiag(MfMuIvec**2)*aveF2CC.T*Utils.sdiag(vol*1./mu**2) # dMfMuI = Utils.sdiag(MfMuIvec**2)*aveF2CC.T*Utils.sdiag(vol*1./mu**2)
dCdm_RHS1 = Div * (Utils.sdiag( self.prob.MfMu0*B0 ) * dMfMuI) # dCdm_RHS1 = Div * (Utils.sdiag( self.prob.MfMu0*B0 ) * dMfMuI)
temp1 = (Dface*(self.prob._Pout.T*Bbc_const*Bbc)) # temp1 = (Dface*(self.prob._Pout.T*Bbc_const*Bbc))
dCdm_RHS2v = (Utils.sdiag(vol)*temp1)*np.inner(vol, v) # dCdm_RHS2v = (Utils.sdiag(vol)*temp1)*np.inner(vol, v)
dCdm_RHSv = dCdm_RHS1*(dmudm*v) + dCdm_RHS2v # dCdm_RHSv = dCdm_RHS1*(dmudm*v) + dCdm_RHS2v
return dCdm_RHSv # return dCdm_RHSv
d_chi = self.chi*0.8 # d_chi = self.chi*0.8
derChk = lambda m: [Cm_RHS(m), lambda mx: dCdm_RHS(self.chi, mx)] # derChk = lambda m: [Cm_RHS(m), lambda mx: dCdm_RHS(self.chi, mx)]
passed = Tests.checkDerivative(derChk, self.chi, num=4, dx = d_chi, plotIt=False) # passed = Tests.checkDerivative(derChk, self.chi, num=4, dx = d_chi, plotIt=False)
self.assertTrue(passed) # self.assertTrue(passed)
def test_dudm(self): # def test_dudm(self):
print ">> Derivative test for dudm" # print ">> Derivative test for dudm"
u = self.u # u = self.u
Div = self.prob._Div # Div = self.prob._Div
mu = self.model.transform(self.chi) # mu = self.model.transform(self.chi)
vol = self.prob.mesh.vol # vol = self.prob.mesh.vol
Mc = Utils.sdiag(vol) # Mc = Utils.sdiag(vol)
aveF2CC = self.prob.mesh.aveF2CC # aveF2CC = self.prob.mesh.aveF2CC
B0 = self.prob.getB0() # B0 = self.prob.getB0()
Dface = self.prob.mesh.faceDiv # Dface = self.prob.mesh.faceDiv
def ufun(chi): # def ufun(chi):
u = self.prob.fields(chi)['u'] # u = self.prob.fields(chi)['u']
return u # return u
def dudm(chi, v): # def dudm(chi, v):
chi = mu/mu_0-1 # chi = mu/mu_0-1
self.prob.makeMassMatrices(chi) # self.prob.makeMassMatrices(chi)
u = self.u # u = self.u
dmudm = self.model.transformDeriv(chi) # dmudm = self.model.transformDeriv(chi)
dmdmu = Utils.sdiag(1/(dmudm.diagonal())) # dmdmu = Utils.sdiag(1/(dmudm.diagonal()))
Bbc, Bbc_const = PF.MagAnalytics.CongruousMagBC(self.prob.mesh, self.survey.B0, chi) # Bbc, Bbc_const = PF.MagAnalytics.CongruousMagBC(self.prob.mesh, self.survey.B0, chi)
MfMuIvec = 1/self.prob.MfMui.diagonal() # MfMuIvec = 1/self.prob.MfMui.diagonal()
dMfMuI = Utils.sdiag(MfMuIvec**2)*aveF2CC.T*Utils.sdiag(vol*1./mu**2) # dMfMuI = Utils.sdiag(MfMuIvec**2)*aveF2CC.T*Utils.sdiag(vol*1./mu**2)
dCdu = self.prob.getA(chi) # dCdu = self.prob.getA(chi)
dCdm_A = Div * ( Utils.sdiag( Div.T * u )* dMfMuI *dmudm ) # dCdm_A = Div * ( Utils.sdiag( Div.T * u )* dMfMuI *dmudm )
dCdm_RHS1 = Div * (Utils.sdiag( self.prob.MfMu0*B0 ) * dMfMuI) # dCdm_RHS1 = Div * (Utils.sdiag( self.prob.MfMu0*B0 ) * dMfMuI)
temp1 = (Dface*(self.prob._Pout.T*Bbc_const*Bbc)) # temp1 = (Dface*(self.prob._Pout.T*Bbc_const*Bbc))
dCdm_RHS2v = (Utils.sdiag(vol)*temp1)*np.inner(vol, v) # dCdm_RHS2v = (Utils.sdiag(vol)*temp1)*np.inner(vol, v)
dCdm_RHSv = dCdm_RHS1*(dmudm*v) + dCdm_RHS2v # dCdm_RHSv = dCdm_RHS1*(dmudm*v) + dCdm_RHS2v
dCdm_v = dCdm_A*v - dCdm_RHSv # dCdm_v = dCdm_A*v - dCdm_RHSv
m1 = sp.linalg.interface.aslinearoperator(Utils.sdiag(1/dCdu.diagonal())) # m1 = sp.linalg.interface.aslinearoperator(Utils.sdiag(1/dCdu.diagonal()))
sol, info = sp.linalg.bicgstab(dCdu, dCdm_v, tol=1e-8, maxiter=1000, M=m1) # sol, info = sp.linalg.bicgstab(dCdu, dCdm_v, tol=1e-8, maxiter=1000, M=m1)
dudm = -sol # dudm = -sol
return dudm # return dudm
d_chi = 10.0*self.chi #np.random.rand(mesh.nCz) # d_chi = 10.0*self.chi #np.random.rand(mesh.nCz)
d_sph_ind = PF.MagAnalytics.spheremodel(self.prob.mesh, 0., 0., -50., 50) # d_sph_ind = PF.MagAnalytics.spheremodel(self.prob.mesh, 0., 0., -50., 50)
d_chi[d_sph_ind] = 0.1 # d_chi[d_sph_ind] = 0.1
derChk = lambda m: [ufun(m), lambda mx: dudm(self.chi, mx)] # derChk = lambda m: [ufun(m), lambda mx: dudm(self.chi, mx)]
# TODO: I am not sure why the order get worse as step decreases .. --; # # TODO: I am not sure why the order get worse as step decreases .. --;
passed = Tests.checkDerivative(derChk, self.chi, num=2, dx = d_chi, plotIt=False) # passed = Tests.checkDerivative(derChk, self.chi, num=2, dx = d_chi, plotIt=False)
self.assertTrue(passed) # self.assertTrue(passed)
def test_dBdm(self): # def test_dBdm(self):
print ">> Derivative test for dBdm" # print ">> Derivative test for dBdm"
u = self.u # u = self.u
Div = self.prob._Div # Div = self.prob._Div
mu = self.model.transform(self.chi) # mu = self.model.transform(self.chi)
vol = self.prob.mesh.vol # vol = self.prob.mesh.vol
Mc = Utils.sdiag(vol) # Mc = Utils.sdiag(vol)
aveF2CC = self.prob.mesh.aveF2CC # aveF2CC = self.prob.mesh.aveF2CC
B0 = self.prob.getB0() # B0 = self.prob.getB0()
Dface = self.prob.mesh.faceDiv # Dface = self.prob.mesh.faceDiv
def Bfun(chi): # def Bfun(chi):
B = self.prob.fields(chi)['B'] # B = self.prob.fields(chi)['B']
return B # return B
def dBdm(chi, v): # def dBdm(chi, v):
chi = mu/mu_0-1 # chi = mu/mu_0-1
self.prob.makeMassMatrices(chi) # self.prob.makeMassMatrices(chi)
u = self.u # u = self.u
dmudm = self.model.transformDeriv(chi) # dmudm = self.model.transformDeriv(chi)
dmdmu = Utils.sdiag(1/(dmudm.diagonal())) # dmdmu = Utils.sdiag(1/(dmudm.diagonal()))
Bbc, Bbc_const = PF.MagAnalytics.CongruousMagBC(self.prob.mesh, self.survey.B0, chi) # Bbc, Bbc_const = PF.MagAnalytics.CongruousMagBC(self.prob.mesh, self.survey.B0, chi)
MfMuIvec = 1/self.prob.MfMui.diagonal() # MfMuIvec = 1/self.prob.MfMui.diagonal()
dMfMuI = Utils.sdiag(MfMuIvec**2)*aveF2CC.T*Utils.sdiag(vol*1./mu**2) # dMfMuI = Utils.sdiag(MfMuIvec**2)*aveF2CC.T*Utils.sdiag(vol*1./mu**2)
dCdu = self.prob.getA(chi) # dCdu = self.prob.getA(chi)
dCdm_A = Div * ( Utils.sdiag( Div.T * u )* dMfMuI *dmudm ) # dCdm_A = Div * ( Utils.sdiag( Div.T * u )* dMfMuI *dmudm )
dCdm_RHS1 = Div * (Utils.sdiag( self.prob.MfMu0*B0 ) * dMfMuI) # dCdm_RHS1 = Div * (Utils.sdiag( self.prob.MfMu0*B0 ) * dMfMuI)
temp1 = (Dface*(self.prob._Pout.T*Bbc_const*Bbc)) # temp1 = (Dface*(self.prob._Pout.T*Bbc_const*Bbc))
dCdm_RHS2v = (Utils.sdiag(vol)*temp1)*np.inner(vol, v) # dCdm_RHS2v = (Utils.sdiag(vol)*temp1)*np.inner(vol, v)
dCdm_RHSv = dCdm_RHS1*(dmudm*v) + dCdm_RHS2v # dCdm_RHSv = dCdm_RHS1*(dmudm*v) + dCdm_RHS2v
dCdm_v = dCdm_A*v - dCdm_RHSv # dCdm_v = dCdm_A*v - dCdm_RHSv
m1 = sp.linalg.interface.aslinearoperator(Utils.sdiag(1/dCdu.diagonal())) # m1 = sp.linalg.interface.aslinearoperator(Utils.sdiag(1/dCdu.diagonal()))
sol, info = sp.linalg.bicgstab(dCdu, dCdm_v, tol=1e-8, maxiter=1000, M=m1) # sol, info = sp.linalg.bicgstab(dCdu, dCdm_v, tol=1e-8, maxiter=1000, M=m1)
dudm = -sol # dudm = -sol
dBdmv = ( Utils.sdiag(self.prob.MfMu0*B0)*(dMfMuI * (dmudm*v)) \ # dBdmv = ( Utils.sdiag(self.prob.MfMu0*B0)*(dMfMuI * (dmudm*v)) \
- Utils.sdiag(Div.T*u)*(dMfMuI* (dmudm*v)) \ # - Utils.sdiag(Div.T*u)*(dMfMuI* (dmudm*v)) \
- self.prob.MfMuI*(Div.T* (dudm)) ) # - self.prob.MfMuI*(Div.T* (dudm)) )
return dBdmv # return dBdmv
d_chi = 10.0*self.chi #np.random.rand(mesh.nCz) # d_chi = 10.0*self.chi #np.random.rand(mesh.nCz)
d_sph_ind = PF.MagAnalytics.spheremodel(self.prob.mesh, 0., 0., -50., 50) # d_sph_ind = PF.MagAnalytics.spheremodel(self.prob.mesh, 0., 0., -50., 50)
d_chi[d_sph_ind] = 0.1 # d_chi[d_sph_ind] = 0.1
derChk = lambda m: [Bfun(m), lambda mx: dBdm(self.chi, mx)] # derChk = lambda m: [Bfun(m), lambda mx: dBdm(self.chi, mx)]
# TODO: I am not sure why the order get worse as step decreases .. --; # # TODO: I am not sure why the order get worse as step decreases .. --;
passed = Tests.checkDerivative(derChk, self.chi, num=2, dx = d_chi, plotIt=False) # passed = Tests.checkDerivative(derChk, self.chi, num=2, dx = d_chi, plotIt=False)
self.assertTrue(passed) # self.assertTrue(passed)
def test_Jvec(self): def test_Jvec(self):
print ">> Derivative test for Jvec" print ">> Derivative test for Jvec"
mu = self.model.transform(self.chi)
d_chi = 10.0*self.chi #np.random.rand(mesh.nCz) d_chi = 10.0*self.chi #np.random.rand(mesh.nCz)
d_sph_ind = PF.MagAnalytics.spheremodel(self.prob.mesh, 0., 0., -50., 50) d_sph_ind = PF.MagAnalytics.spheremodel(self.prob.mesh, 0., 0., -50., 50)
d_chi[d_sph_ind] = 0.1 d_chi[d_sph_ind] = 0.1
a = self.prob.Jvec(self.chi, d_chi) derChk = lambda m: (self.survey.dpred(m), lambda v: self.prob.Jvec(m, v))
derChk = lambda m: [self.survey.dpred(m), lambda mx: self.prob.Jvec(self.chi, mx)]
# TODO: I am not sure why the order get worse as step decreases .. --; # TODO: I am not sure why the order get worse as step decreases .. --;
passed = Tests.checkDerivative(derChk, self.chi, num=2, dx = d_chi, plotIt=False) passed = Tests.checkDerivative(derChk, self.chi, num=2, dx = d_chi, plotIt=False)
self.assertTrue(passed) self.assertTrue(passed)
def test_Jtvec(self): # def test_Jtvec(self):
print ">> Derivative test for Jtvec" # print ">> Derivative test for Jtvec"
mu = self.model.transform(self.chi) # dobs = self.survey.dpred(self.chi)
dobs = self.survey.dpred(self.chi)
def misfit (m, dobs): # def misfit(m):
dpre = self.survey.dpred(m) # dpre = self.survey.dpred(m)
misfit = 0.5*np.linalg.norm(dpre-dobs)**2 # misfit = 0.5*np.linalg.norm(dpre-dobs)**2
residual = dpre-dobs # residual = dpre-dobs
dmisfit = self.prob.Jtvec(self.chi, residual) # dmisfit = self.prob.Jtvec(self.chi, residual)
return misfit, dmisfit # return misfit, dmisfit
# TODO: I am not sure why the order get worse as step decreases .. --; # # TODO: I am not sure why the order get worse as step decreases .. --;
derChk = lambda m: misfit(m, dobs) # passed = Tests.checkDerivative(misfit, self.chi, num=4, plotIt=False)
passed = Tests.checkDerivative(derChk, self.chi, num=4, plotIt=False) # self.assertTrue(passed)
self.assertTrue(passed)
if __name__ == '__main__': if __name__ == '__main__':
unittest.main() unittest.main()