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Initial work Mag inversion
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SEOGI KANG committed
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+29
-12
@@ -42,13 +42,13 @@ class BaseMagData(Data.BaseData):
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"""
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This function projects the fields onto the data space.
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Esepcially, here for we use total magnetic intensity (TMI) data,
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which is common in practice.
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Esepcially, here for we use total magnetic intensity (TMI) data,
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which is common in practice.
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First we project our B on to data location
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First we project our B on to data location
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.. math::
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\mathbf{B}_{rec} = \mathbf{P} \mathbf{B}
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then we take the dot product between B and b_0
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@@ -121,13 +121,30 @@ class BaseMagModel(Model.BaseModel):
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def __init__(self, mesh, **kwargs):
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Model.BaseModel.__init__(self, mesh)
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def transform(self, m, asMu=True):
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if asMu:
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return mu_0*(1 + m)
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return m
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def transform(self, m):
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def transformDeriv(self, m, asMu=True):
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if asMu:
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return mu_0*sp.identity(self.nP)
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return sp.identity(self.nP)
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return mu_0*(1 + m)
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def transformDeriv(self, m):
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return mu_0*sp.identity(self.nP)
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class BaseDepthModel(Model.BaseModel):
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"""BaseDepthMagModel"""
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def __init__(self, mesh, **kwargs):
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Model.BaseModel.__init__(self, mesh)
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self.mesh = mesh
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self.active_ind = kwargs['active_ind']
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def transform(self, m):
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weight = abs(self.mesh.gridCC[:,2])**1.0
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weight = weight/weight.max()
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weight[~self.active_ind] = 1.
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return m*weight
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def transformDeriv(self, m):
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weight = abs(self.mesh.gridCC[:,2])**1.0
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weight = weight/weight.max()
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weight[~self.active_ind] = 1.
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return Utils.sdiag(weight)
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+102
-65
@@ -1,4 +1,4 @@
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from SimPEG import Mesh, Problem, Utils, np, sp, Tests
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from SimPEG import *
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import BaseMag
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from scipy.constants import mu_0
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from MagAnalytics import spheremodel, CongruousMagBC
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@@ -51,7 +51,7 @@ class MagneticsDiffSecondary(Problem.BaseProblem):
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def getRHS(self, m):
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"""
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.. math ::
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\mathbf{rhs} = \Div(\MfMui)^{-1}\mathbf{M}^f_{\mu_0^{-1}}\mathbf{B}_0 - \Div\mathbf{B}_0+\diag(v)\mathbf{D} \mathbf{P}_{out}^T \mathbf{B}_{sBC}
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@@ -61,7 +61,9 @@ class MagneticsDiffSecondary(Problem.BaseProblem):
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Dface = self.mesh.faceDiv
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Mc = Utils.sdiag(self.mesh.vol)
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chi = self.model.transform(m, asMu=False)
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mu = self.model.transform(m)
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chi = mu/mu_0-1
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Bbc, Bbc_const = CongruousMagBC(self.mesh, self.data.B0, chi)
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self.Bbc = Bbc
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self.Bbc_const = Bbc_const
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@@ -105,11 +107,11 @@ class MagneticsDiffSecondary(Problem.BaseProblem):
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return {'B': B, 'u': u}
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@Utils.timeIt
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def Jvec(self, m, v, fields=None):
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def Jvec(self, m, v, u=None):
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"""
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Computing Jacobian multiplied by vector
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By setting our problem as
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By setting our problem as
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.. math ::
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@@ -124,51 +126,51 @@ class MagneticsDiffSecondary(Problem.BaseProblem):
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\\frac{\delta \mathbf{u}}{\delta \mathbf{m}} = - [\\nabla_u \mathbf{C}(\mathbf{u})]^{-1}\\nabla_m \mathbf{C}(\mathbf{m})
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With some linear algebra we can have
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With some linear algebra we can have
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.. math ::
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\\nabla_u \mathbf{C}(\mathbf{u}) = \mathbf{A}
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\\nabla_m \mathbf{C}(\mathbf{m}) =
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\\frac{\partial \mathbf{A}}{\partial \mathbf{m}}(\mathbf{m})\mathbf{u} - \\frac{\partial \mathbf{rhs}(\mathbf{m})}{\partial \mathbf{m}}
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\\nabla_m \mathbf{C}(\mathbf{m}) =
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\\frac{\partial \mathbf{A}}{\partial \mathbf{m}}(\mathbf{m})\mathbf{u} - \\frac{\partial \mathbf{rhs}(\mathbf{m})}{\partial \mathbf{m}}
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.. math ::
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.. math ::
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\\frac{\partial \mathbf{A}}{\partial \mathbf{m}}(\mathbf{m})\mathbf{u} =
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\\frac{\partial \mathbf{A}}{\partial \mathbf{m}}(\mathbf{m})\mathbf{u} =
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\\frac{\partial \mathbf{\mu}}{\partial \mathbf{m}} \left[\Div \diag (\Div^T \mathbf{u}) \dMfMuI \\right]
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\dMfMuI = \diag(\MfMui)^{-1}_{vec} \mathbf{Av}_{F2CC}^T\diag(\mathbf{v})\diag(\\frac{1}{\mu^2})
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\\frac{\partial \mathbf{rhs}(\mathbf{m})}{\partial \mathbf{m}} = \\frac{\partial \mathbf{\mu}}{\partial \mathbf{m}} \left[
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\\frac{\partial \mathbf{rhs}(\mathbf{m})}{\partial \mathbf{m}} = \\frac{\partial \mathbf{\mu}}{\partial \mathbf{m}} \left[
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\Div \diag(\M^f_{\mu_{0}^{-1}}\mathbf{B}_0) \dMfMuI \\right] - \diag(\mathbf{v})\mathbf{D} \mathbf{P}_{out}^T\\frac{\partial B_{sBC}}{\partial \mathbf{m}}
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In the end,
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In the end,
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.. math ::
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\\frac{\delta \mathbf{u}}{\delta \mathbf{m}} =
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- [ \mathbf{A} ]^{-1}\left[ \\frac{\partial \mathbf{A}}{\partial \mathbf{m}}(\mathbf{m})\mathbf{u}
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\\frac{\delta \mathbf{u}}{\delta \mathbf{m}} =
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- [ \mathbf{A} ]^{-1}\left[ \\frac{\partial \mathbf{A}}{\partial \mathbf{m}}(\mathbf{m})\mathbf{u}
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- \\frac{\partial \mathbf{rhs}(\mathbf{m})}{\partial \mathbf{m}} \\right]
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A little tricky point here is we are not interested in potential (u), but interested in magnetic flux (B).
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Thus, we need sensitivity for B. Now we take derivative of B w.r.t m and have
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A little tricky point here is we are not interested in potential (u), but interested in magnetic flux (B).
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Thus, we need sensitivity for B. Now we take derivative of B w.r.t m and have
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.. math ::
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\\frac{\delta \mathbf{B}} {\delta \mathbf{m}} = \\frac{\partial \mathbf{\mu} } {\partial \mathbf{m} }
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\left[
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\\frac{\delta \mathbf{B}} {\delta \mathbf{m}} = \\frac{\partial \mathbf{\mu} } {\partial \mathbf{m} }
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\left[
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\diag(\M^f_{\mu_{0}^{-1} } \mathbf{B}_0) \dMfMuI \\
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- \diag (\Div^T\mathbf{u})\dMfMuI
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\\right ]
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- (\MfMui)^{-1}\Div^T\\frac{\delta\mathbf{u}}{\delta \mathbf{m}}
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Finally we evaluate the above, but we should remember that
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- (\MfMui)^{-1}\Div^T\\frac{\delta\mathbf{u}}{\delta \mathbf{m}}
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.. note ::
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Finally we evaluate the above, but we should remember that
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We only want to evalute
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.. note ::
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We only want to evalute
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.. math ::
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@@ -178,13 +180,13 @@ class MagneticsDiffSecondary(Problem.BaseProblem):
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"""
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if fields is None:
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fields = self.fields(m)
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if u is None:
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u = self.fields(m)
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B, u = fields['B'], fields['u']
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mu = self.model.transform(m, asMu=True)
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dmudm = self.model.transformDeriv(m, asMu=True)
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dmdmu = Utils.sdiag(1/(dmudm.diagonal()))
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B, u = u['B'], u['u']
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mu = self.model.transform(m)
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dmudm = self.model.transformDeriv(m)
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dchidmu = Utils.sdiag(1/mu_0*np.ones(self.mesh.nC))
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vol = self.mesh.vol
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Div = self._Div
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@@ -204,42 +206,43 @@ class MagneticsDiffSecondary(Problem.BaseProblem):
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dCdm_A = Div * ( Utils.sdiag( Div.T * u )* dMfMuI *dmudm )
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dCdm_RHS1 = Div * (Utils.sdiag( self.MfMu0*B0 ) * dMfMuI)
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temp1 = (Dface*(self._Pout.T*self.Bbc_const*self.Bbc))
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dCdm_RHS2v = (Utils.sdiag(vol)*temp1)*np.inner(vol, v)
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dCdm_RHSv = dCdm_RHS1*(dmudm*v) + dCdm_RHS2v
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dCdm_RHS2v = (Utils.sdiag(vol)*temp1)*np.inner(vol, dchidmu*dmudm*v)
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dCdm_RHSv = dCdm_RHS1*(dmudm*v) + dCdm_RHS2v
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dCdm_v = dCdm_A*v - dCdm_RHSv
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m1 = sp.linalg.interface.aslinearoperator(Utils.sdiag(1/dCdu.diagonal()))
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sol, info = sp.linalg.bicgstab(dCdu, dCdm_v, tol=1e-8, maxiter=1000, M=m1)
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m1 = sp.linalg.interface.aslinearoperator(Utils.sdiag(1/dCdu.diagonal()))
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sol, info = sp.linalg.bicgstab(dCdu, dCdm_v, tol=1e-6, maxiter=1000, M=m1)
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if info > 0:
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raise Exception ("Iterative solver did not work well")
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print "Iterative solver did not work well (Jvec)"
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# raise Exception ("Iterative solver did not work well")
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# B = self.MfMuI*self.MfMu0*B0-B0-self.MfMuI*self._Div.T*u
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# dBdm = d\mudm*dBd\mu
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dudm = -sol
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dudm = -sol
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dBdmv = ( Utils.sdiag(self.MfMu0*B0)*(dMfMuI * (dmudm*v)) \
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- Utils.sdiag(Div.T*u)*(dMfMuI* (dmudm*v)) \
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- self.MfMuI*(Div.T* (dudm)) )
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- self.MfMuI*(Div.T* (dudm)) )
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return Utils.mkvc(P*dBdmv)
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@Utils.timeIt
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def Jtvec(self, m, v, fields=None):
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def Jtvec(self, m, v, u=None):
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"""
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Computing Jacobian^T multiplied by vector.
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.. math ::
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(\\frac{\delta \mathbf{P}\mathbf{B}} {\delta \mathbf{m}})^{T} = \left[ \mathbf{P}_{deriv}\\frac{\partial \mathbf{\mu} } {\partial \mathbf{m} }
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\left[
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(\\frac{\delta \mathbf{P}\mathbf{B}} {\delta \mathbf{m}})^{T} = \left[ \mathbf{P}_{deriv}\\frac{\partial \mathbf{\mu} } {\partial \mathbf{m} }
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\left[
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\diag(\M^f_{\mu_{0}^{-1} } \mathbf{B}_0) \dMfMuI \\
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- \diag (\Div^T\mathbf{u})\dMfMuI
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\\right ]\\right]^{T}
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\\right ]\\right]^{T}
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- \left[\mathbf{P}_{deriv}(\MfMui)^{-1}\Div^T\\frac{\delta\mathbf{u}}{\delta \mathbf{m}} \\right]^{T}
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where
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where
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.. math ::
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@@ -247,20 +250,20 @@ class MagneticsDiffSecondary(Problem.BaseProblem):
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.. note ::
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Here we only want to compute
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Here we only want to compute
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.. math ::
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\mathbf{J}^{T}\mathbf{v} = (\\frac{\delta \mathbf{P}\mathbf{B}} {\delta \mathbf{m}})^{T} \mathbf{v}
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"""
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if fields is None:
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fields = self.fields(m)
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if u is None:
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u = self.fields(m)
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B, u = fields['B'], fields['u']
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mu = self.model.transform(m, asMu=True)
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dmudm = self.model.transformDeriv(m, asMu=True)
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dmdmu = Utils.sdiag(1/(dmudm.diagonal()))
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B, u = u['B'], u['u']
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mu = self.model.transform(m)
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dmudm = self.model.transformDeriv(m)
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dchidmu = Utils.sdiag(1/mu_0*np.ones(self.mesh.nC))
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vol = self.mesh.vol
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Div = self._Div
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@@ -279,26 +282,33 @@ class MagneticsDiffSecondary(Problem.BaseProblem):
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dCdu = self.getA(m)
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s = Div * ( self.MfMuI.T * ( P.T*v ) )
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m1 = sp.linalg.interface.aslinearoperator(Utils.sdiag(1/(dCdu.T).diagonal()))
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sol, info = sp.linalg.bicgstab(dCdu.T, s, tol=1e-8, maxiter=1000, M=m1)
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m1 = sp.linalg.interface.aslinearoperator(Utils.sdiag(1/(dCdu.T).diagonal()))
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sol, info = sp.linalg.bicgstab(dCdu.T, s, tol=1e-6, maxiter=1000, M=m1)
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if info > 0:
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raise Exception ("Iterative solver did not work well")
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print "Iterative solver did not work well (Jtvec)"
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# raise Exception ("Iterative solver did not work well")
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# dCdm_A = Div * ( Utils.sdiag( Div.T * u )* dMfMuI *dmudm )
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dCdm_Atsol = ( dMfMuI.T*( Utils.sdiag( Div.T * u ) * (Div.T * dmudm)) ) * sol
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# dCdm_Atsol = ( dMfMuI.T*( Utils.sdiag( Div.T * u ) * (Div.T * dmudm)) ) * sol
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dCdm_Atsol = ( dmudm.T * dMfMuI.T*( Utils.sdiag( Div.T * u ) * Div.T ) ) * sol
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# dCdm_RHS1 = Div * (Utils.sdiag( self.MfMu0*B0 ) * dMfMuI)
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# dCdm_RHS1tsol = (dMfMuI.T*( Utils.sdiag( self.MfMu0*B0 ) ) * Div.T * dmudm) * sol
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dCdm_RHS1tsol = ( dmudm.T * dMfMuI.T*( Utils.sdiag( self.MfMu0*B0 ) ) * Div.T ) * sol
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# dCdm_RHS1 = Div * (Utils.sdiag( self.MfMu0*B0 ) * dMfMuI)
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dCdm_RHS1tsol = (dMfMuI.T*( Utils.sdiag( self.MfMu0*B0 ) ) * Div.T * dmudm) * sol
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# temp1 = (Dface*(self._Pout.T*self.Bbc_const*self.Bbc))
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# dCdm_RHS2v = (Utils.sdiag(vol)*temp1)*np.inner(vol, v)
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temp1sol = ( Dface.T*( Utils.sdiag(vol)*sol ) )
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temp2 = self.Bbc_const*(self._Pout.T*self.Bbc).T
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dCdm_RHS2tsol = vol*np.inner(temp2, temp1sol)
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# dCdm_RHS2v = (Utils.sdiag(vol)*temp1)*np.inner(vol, dchidmu*dmudm*v)
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dCdm_RHS2tsol = (dmudm.T*dchidmu.T*vol)*np.inner(temp2, temp1sol)
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# dCdm_RHSv = dCdm_RHS1*(dmudm*v) + dCdm_RHS2v
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dCdm_RHStsol = dCdm_RHS1tsol - dCdm_RHS2tsol
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# dCdm_RHSv = dCdm_RHS1*(dmudm*v) + dCdm_RHS2v
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# dCdm_RHSv = dCdm_RHS1*(dmudm*v) + dCdm_RHS2v
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# dCdm_v = dCdm_A*v - dCdm_RHSv
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Ctv = dCdm_Atsol - dCdm_RHStsol
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@@ -311,7 +321,35 @@ class MagneticsDiffSecondary(Problem.BaseProblem):
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Btemp = Utils.sdiag(Div.T*u)*(dMfMuI* (dmudm))
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Jtv = Atemp.T*(P.T*v) - Btemp.T*(P.T*v) - Ctv
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return Utils.mkvc(Jtv)
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return Utils.mkvc(Jtv)
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def MagneticsDiffSecondaryInv(mesh, model, data, **kwargs):
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"""
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Inversion module for MagneticsDiffSecondary
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"""
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from SimPEG import Optimization, Regularization, Parameters, ObjFunction, Inversion
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prob = MagneticsDiffSecondary(mesh, model)
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if prob.ispaired:
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prob.unpair()
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if data.ispaired:
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data.unpair()
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prob.pair(data)
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# Create an optimization program
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opt = Optimization.InexactGaussNewton(maxIter=5)
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opt.bfgsH0 = Solver(sp.identity(model.nP),flag='D')
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# Create a regularization program
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reg = Regularization.Tikhonov(model)
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# Create an objective function
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beta = Parameters.BetaSchedule(beta0=1e0)
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obj = ObjFunction.BaseObjFunction(data, reg, beta=beta)
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# Create an inversion object
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inv = Inversion.BaseInversion(obj, opt)
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return inv, reg
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@@ -337,7 +375,7 @@ if __name__ == '__main__':
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Btot = 51000
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data.setBackgroundField(Inc, Dec, Btot)
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xr = np.linspace(-300, 300, 41)
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yr = np.linspace(-300, 300, 41)
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X, Y = np.meshgrid(xr, yr)
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@@ -346,7 +384,6 @@ if __name__ == '__main__':
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data.rxLoc = rxLoc
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prob = MagneticsDiffSecondary(mesh, model)
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prob.pair(data)
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dpred = data.dpred(chi)
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@@ -30,11 +30,11 @@ class MagFwdProblemTests(unittest.TestCase):
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data = PF.BaseMag.BaseMagData()
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Inc = 90.
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Dec = 0.
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Inc = 45.
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Dec = 45.
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Btot = 51000
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b0 = PF.MagAnalytics.IDTtoxyz(Inc, Dec, Btot)
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b0 = PF.MagAnalytics.IDTtoxyz(Inc, Dec, Btot)
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data.setBackgroundField(Inc, Dec, Btot)
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xr = np.linspace(-300, 300, 41)
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yr = np.linspace(-300, 300, 41)
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@@ -42,21 +42,25 @@ class MagFwdProblemTests(unittest.TestCase):
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Z = np.ones((xr.size, yr.size))*150
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rxLoc = np.c_[Utils.mkvc(X), Utils.mkvc(Y), Utils.mkvc(Z)]
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data.rxLoc = rxLoc
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self.prob.pair(data)
|
||||
u = self.prob.fields(self.chi)
|
||||
B = u['B']
|
||||
|
||||
bxa,bya,bza = PF.MagAnalytics.MagSphereAnalFunA(rxLoc[:,0],rxLoc[:,1],rxLoc[:,2],100.,0.,0.,0.,0.01, b0,'secondary')
|
||||
|
||||
bxa,bya,bza = PF.MagAnalytics.MagSphereAnalFunA(rxLoc[:,0],rxLoc[:,1],rxLoc[:,2],100.,0.,0.,0.,0.01, b0,'secondary')
|
||||
|
||||
dpred = data.projectFieldsAsVector(B)
|
||||
err = np.linalg.norm(dpred-np.r_[bxa, bya, bza])/np.linalg.norm(np.r_[bxa, bya, bza])
|
||||
|
||||
plt.plot(dpred)
|
||||
plt.plot(np.r_[bxa, bya, bza])
|
||||
plt.show()
|
||||
|
||||
if err > 0.05:
|
||||
raise Exception('Anaytic test is failed T.T')
|
||||
else:
|
||||
print "Anaytic test is passed"
|
||||
pass
|
||||
|
||||
|
||||
if __name__ == '__main__':
|
||||
unittest.main()
|
||||
@@ -18,7 +18,7 @@ class MagSensProblemTests(unittest.TestCase):
|
||||
chibkg = 0.001
|
||||
chiblk = 0.01
|
||||
chi = np.ones(M.nC)*chibkg
|
||||
|
||||
|
||||
Inc = 90.
|
||||
Dec = 0.
|
||||
Btot = 51000
|
||||
@@ -58,7 +58,7 @@ class MagSensProblemTests(unittest.TestCase):
|
||||
|
||||
def test_mass(self):
|
||||
print '\n >>Derivative for MfMuI works.'
|
||||
mu = self.model.transform(self.chi, asMu=True)
|
||||
mu = self.model.transform(self.chi)
|
||||
def MfmuI(mu):
|
||||
|
||||
chi = mu/mu_0-1
|
||||
@@ -70,36 +70,36 @@ class MagSensProblemTests(unittest.TestCase):
|
||||
return MfMuI
|
||||
|
||||
def dMfmuI(mu, v):
|
||||
|
||||
|
||||
chi = mu/mu_0-1
|
||||
self.prob.makeMassMatrices(chi)
|
||||
vol = self.prob.mesh.vol
|
||||
aveF2CC = self.prob.mesh.aveF2CC
|
||||
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
|
||||
|
||||
d_mu = mu*0.8
|
||||
derChk = lambda m: [MfmuI(m), lambda mx: dMfmuI(self.chi, mx)]
|
||||
passed = Tests.checkDerivative(derChk, mu, num=4, dx = d_mu, plotIt=False)
|
||||
|
||||
|
||||
|
||||
|
||||
self.assertTrue(passed)
|
||||
|
||||
|
||||
|
||||
def test_dCdm_Av(self):
|
||||
print '\n >>Derivative for Cm_A.'
|
||||
Div = self.prob._Div
|
||||
Div = self.prob._Div
|
||||
vol = self.prob.mesh.vol
|
||||
aveF2CC = self.prob.mesh.aveF2CC
|
||||
|
||||
def Cm_A(chi):
|
||||
dmudm = self.model.transformDeriv(chi, asMu=True)
|
||||
dmudm = self.model.transformDeriv(chi)
|
||||
u = self.u
|
||||
# chi = mu/mu_0-1
|
||||
self.prob.makeMassMatrices(chi)
|
||||
mu = self.model.transform(self.chi, asMu=True)
|
||||
mu = self.model.transform(self.chi)
|
||||
A = self.prob.getA(self.chi)
|
||||
MfMuIvec = 1/self.prob.MfMui.diagonal()
|
||||
dMfMuI = Utils.sdiag(MfMuIvec**2)*aveF2CC.T*Utils.sdiag(vol*1./mu**2)
|
||||
@@ -109,11 +109,11 @@ class MagSensProblemTests(unittest.TestCase):
|
||||
return Cm_A
|
||||
|
||||
def dCdm_A(chi, v):
|
||||
|
||||
dmudm = self.model.transformDeriv(chi, asMu=True)
|
||||
|
||||
dmudm = self.model.transformDeriv(chi)
|
||||
u = self.u
|
||||
self.prob.makeMassMatrices(chi)
|
||||
mu = self.model.transform(self.chi, asMu=True)
|
||||
mu = self.model.transform(self.chi)
|
||||
A = self.prob.getA(self.chi)
|
||||
MfMuIvec = 1/self.prob.MfMui.diagonal()
|
||||
dMfMuI = Utils.sdiag(MfMuIvec**2)*aveF2CC.T*Utils.sdiag(vol*1./mu**2)
|
||||
@@ -133,7 +133,7 @@ class MagSensProblemTests(unittest.TestCase):
|
||||
print '\n >>Derivative for Cm_RHS.'
|
||||
u = self.u
|
||||
Div = self.prob._Div
|
||||
mu = self.model.transform(self.chi, asMu=True)
|
||||
mu = self.model.transform(self.chi)
|
||||
vol = self.prob.mesh.vol
|
||||
Mc = Utils.sdiag(vol)
|
||||
aveF2CC = self.prob.mesh.aveF2CC
|
||||
@@ -143,45 +143,45 @@ class MagSensProblemTests(unittest.TestCase):
|
||||
def Cm_RHS(chi):
|
||||
|
||||
self.prob.makeMassMatrices(chi)
|
||||
dmudm = self.model.transformDeriv(chi, asMu=True)
|
||||
dmudm = self.model.transformDeriv(chi)
|
||||
dchidmu = Utils.sdiag(1/(dmudm.diagonal()))
|
||||
Bbc, Bbc_const = PF.MagAnalytics.CongruousMagBC(self.prob.mesh, self.data.B0, chi)
|
||||
MfMuIvec = 1/self.prob.MfMui.diagonal()
|
||||
dMfMuI = Utils.sdiag(MfMuIvec**2)*aveF2CC.T*Utils.sdiag(vol*1./mu**2)
|
||||
RHS1 = Div*self.prob.MfMuI*self.prob.MfMu0*B0
|
||||
RHS2 = Mc*Dface*self.prob._Pout.T*Bbc
|
||||
RHS = RHS1 + RHS2 + Div*B0
|
||||
RHS1 = Div*self.prob.MfMuI*self.prob.MfMu0*B0
|
||||
RHS2 = Mc*Dface*self.prob._Pout.T*Bbc
|
||||
RHS = RHS1 + RHS2 + Div*B0
|
||||
|
||||
return RHS
|
||||
|
||||
|
||||
def dCdm_RHS(chi, v):
|
||||
|
||||
|
||||
|
||||
self.prob.makeMassMatrices(chi)
|
||||
dmudm = self.model.transformDeriv(chi, asMu=True)
|
||||
dmudm = self.model.transformDeriv(chi)
|
||||
dmdmu = Utils.sdiag(1/(dmudm.diagonal()))
|
||||
Bbc, Bbc_const = PF.MagAnalytics.CongruousMagBC(self.prob.mesh, self.data.B0, chi)
|
||||
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)
|
||||
temp1 = (Dface*(self.prob._Pout.T*Bbc_const*Bbc))
|
||||
dCdm_RHS2v = (Utils.sdiag(vol)*temp1)*np.inner(vol, v)
|
||||
dCdm_RHSv = dCdm_RHS1*(dmudm*v) + dCdm_RHS2v
|
||||
|
||||
|
||||
return dCdm_RHSv
|
||||
|
||||
d_chi = self.chi*0.8
|
||||
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)
|
||||
self.assertTrue(passed)
|
||||
self.assertTrue(passed)
|
||||
|
||||
|
||||
def test_dudm(self):
|
||||
print ">> Derivative test for dudm"
|
||||
u = self.u
|
||||
Div = self.prob._Div
|
||||
mu = self.model.transform(self.chi, asMu=True)
|
||||
mu = self.model.transform(self.chi)
|
||||
vol = self.prob.mesh.vol
|
||||
Mc = Utils.sdiag(vol)
|
||||
aveF2CC = self.prob.mesh.aveF2CC
|
||||
@@ -193,11 +193,11 @@ class MagSensProblemTests(unittest.TestCase):
|
||||
return u
|
||||
|
||||
def dudm(chi, v):
|
||||
|
||||
|
||||
chi = mu/mu_0-1
|
||||
self.prob.makeMassMatrices(chi)
|
||||
self.prob.makeMassMatrices(chi)
|
||||
u = self.u
|
||||
dmudm = self.model.transformDeriv(chi, asMu=True)
|
||||
dmudm = self.model.transformDeriv(chi)
|
||||
dmdmu = Utils.sdiag(1/(dmudm.diagonal()))
|
||||
Bbc, Bbc_const = PF.MagAnalytics.CongruousMagBC(self.prob.mesh, self.data.B0, chi)
|
||||
MfMuIvec = 1/self.prob.MfMui.diagonal()
|
||||
@@ -207,21 +207,21 @@ class MagSensProblemTests(unittest.TestCase):
|
||||
dCdm_RHS1 = Div * (Utils.sdiag( self.prob.MfMu0*B0 ) * dMfMuI)
|
||||
temp1 = (Dface*(self.prob._Pout.T*Bbc_const*Bbc))
|
||||
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
|
||||
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)
|
||||
|
||||
dudm = -sol
|
||||
dudm = -sol
|
||||
|
||||
return dudm
|
||||
|
||||
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_chi[d_sph_ind] = 0.1
|
||||
d_chi[d_sph_ind] = 0.1
|
||||
|
||||
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)
|
||||
self.assertTrue(passed)
|
||||
|
||||
@@ -230,7 +230,7 @@ class MagSensProblemTests(unittest.TestCase):
|
||||
print ">> Derivative test for dBdm"
|
||||
u = self.u
|
||||
Div = self.prob._Div
|
||||
mu = self.model.transform(self.chi, asMu=True)
|
||||
mu = self.model.transform(self.chi)
|
||||
vol = self.prob.mesh.vol
|
||||
Mc = Utils.sdiag(vol)
|
||||
aveF2CC = self.prob.mesh.aveF2CC
|
||||
@@ -242,11 +242,11 @@ class MagSensProblemTests(unittest.TestCase):
|
||||
return B
|
||||
|
||||
def dBdm(chi, v):
|
||||
|
||||
|
||||
chi = mu/mu_0-1
|
||||
self.prob.makeMassMatrices(chi)
|
||||
self.prob.makeMassMatrices(chi)
|
||||
u = self.u
|
||||
dmudm = self.model.transformDeriv(chi, asMu=True)
|
||||
dmudm = self.model.transformDeriv(chi)
|
||||
dmdmu = Utils.sdiag(1/(dmudm.diagonal()))
|
||||
Bbc, Bbc_const = PF.MagAnalytics.CongruousMagBC(self.prob.mesh, self.data.B0, chi)
|
||||
MfMuIvec = 1/self.prob.MfMui.diagonal()
|
||||
@@ -256,47 +256,47 @@ class MagSensProblemTests(unittest.TestCase):
|
||||
dCdm_RHS1 = Div * (Utils.sdiag( self.prob.MfMu0*B0 ) * dMfMuI)
|
||||
temp1 = (Dface*(self.prob._Pout.T*Bbc_const*Bbc))
|
||||
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
|
||||
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)
|
||||
|
||||
dudm = -sol
|
||||
dudm = -sol
|
||||
dBdmv = ( Utils.sdiag(self.prob.MfMu0*B0)*(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
|
||||
|
||||
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_chi[d_sph_ind] = 0.1
|
||||
d_chi[d_sph_ind] = 0.1
|
||||
|
||||
derChk = lambda m: [Bfun(m), lambda mx: dBdm(self.chi, mx)]
|
||||
# TODO: I am not sure why the order get worse as step decreases .. --;
|
||||
passed = Tests.checkDerivative(derChk, self.chi, num=3, dx = d_chi, plotIt=False)
|
||||
# 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)
|
||||
self.assertTrue(passed)
|
||||
|
||||
|
||||
|
||||
def test_Jvec(self):
|
||||
print ">> Derivative test for Jvec"
|
||||
mu = self.model.transform(self.chi, asMu=True)
|
||||
mu = self.model.transform(self.chi)
|
||||
|
||||
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_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.data.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)
|
||||
self.assertTrue(passed)
|
||||
|
||||
def test_Jtvec(self):
|
||||
print ">> Derivative test for Jtvec"
|
||||
mu = self.model.transform(self.chi, asMu=True)
|
||||
mu = self.model.transform(self.chi)
|
||||
dobs = self.data.dpred(self.chi)
|
||||
|
||||
def misfit (m, dobs):
|
||||
@@ -307,10 +307,10 @@ class MagSensProblemTests(unittest.TestCase):
|
||||
|
||||
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(derChk, self.chi, num=4, plotIt=False)
|
||||
self.assertTrue(passed)
|
||||
self.assertTrue(passed)
|
||||
|
||||
if __name__ == '__main__':
|
||||
unittest.main()
|
||||
@@ -0,0 +1,546 @@
|
||||
{
|
||||
"metadata": {
|
||||
"name": ""
|
||||
},
|
||||
"nbformat": 3,
|
||||
"nbformat_minor": 0,
|
||||
"worksheets": [
|
||||
{
|
||||
"cells": [
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"from SimPEG import *\n",
|
||||
"%pylab inline"
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"output_type": "stream",
|
||||
"stream": "stdout",
|
||||
"text": [
|
||||
"Warning: Python backend is being used for solver. Run setup.py from the command line.\n",
|
||||
"Warning: mumps solver not available.\n",
|
||||
"Warning: upgrade your scipy to 0.13.0"
|
||||
]
|
||||
},
|
||||
{
|
||||
"output_type": "stream",
|
||||
"stream": "stdout",
|
||||
"text": [
|
||||
"\n",
|
||||
"Populating the interactive namespace from numpy and matplotlib"
|
||||
]
|
||||
},
|
||||
{
|
||||
"output_type": "stream",
|
||||
"stream": "stdout",
|
||||
"text": [
|
||||
"\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 1
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"### $$ Kernel(x, k) = e^{-pkx}cos(2 \\pi q k x) $$"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"M = Mesh.TensorMesh([1000]) # Make a 1D mesh from 0-1 with 1000 cells\n",
|
||||
"\n",
|
||||
"nk = 20 #: The number of kernals\n",
|
||||
"p = q = 0.25 #: Some constants\n",
|
||||
"\n",
|
||||
"# Create a function for each row of the matrix\n",
|
||||
"g = lambda k, x: np.exp(-p*k*x)*np.cos(2*np.pi*q*k*x)\n",
|
||||
"\n",
|
||||
"# Concatenate each row, and reshape\n",
|
||||
"G = np.concatenate([g(i,M.vectorCCx) for i in range(nk)])\n",
|
||||
"G.shape = (nk, M.nC)\n",
|
||||
"\n",
|
||||
"figure(figsize=(12,4))\n",
|
||||
"plot(G.T)\n",
|
||||
"title('Rows of G')"
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"metadata": {},
|
||||
"output_type": "pyout",
|
||||
"prompt_number": 2,
|
||||
"text": [
|
||||
"<matplotlib.text.Text at 0x9bf1940>"
|
||||
]
|
||||
},
|
||||
{
|
||||
"metadata": {},
|
||||
"output_type": "display_data",
|
||||
"png": 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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0x9bdef60>"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 2
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"## $$ \\mathbf{d}_{pred} = \\mathbf{G}\\mathbf{m} $$"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"mtrue = np.zeros(M.nC) # Create a zeros vector, here nC means: number of cells\n",
|
||||
"mtrue[M.vectorCCx > 0.3] = 1.\n",
|
||||
"mtrue[M.vectorCCx > 0.45] = -0.5\n",
|
||||
"mtrue[M.vectorCCx > 0.6] = 0\n",
|
||||
"figure(figsize=(12,4))\n",
|
||||
"subplot(121)\n",
|
||||
"# Create a few models\n",
|
||||
"models = np.c_[mtrue, np.r_[mtrue[200:],mtrue[:200]]*0.5 - 0.2, \n",
|
||||
" M.vectorCCx - 0.5, -M.vectorCCx + 0.75, \n",
|
||||
" Utils.ModelBuilder.randomModel(1000,seed=751,its=20000)-0.3]\n",
|
||||
"plot(M.vectorCCx, models)\n",
|
||||
"title('A few synthetic model.')\n",
|
||||
"xlabel('x');ylabel('Amplitude')\n",
|
||||
"data = G.dot(models) #: this is matrix multiplication!!\n",
|
||||
"subplot(122)\n",
|
||||
"plot(data)\n",
|
||||
"title('The data created by each model.')\n",
|
||||
"xlim([0,19]);xlabel('Kernal Number, i');ylabel('g(i) * x')"
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"metadata": {},
|
||||
"output_type": "pyout",
|
||||
"prompt_number": 3,
|
||||
"text": [
|
||||
"<matplotlib.text.Text at 0x9fe2cc0>"
|
||||
]
|
||||
},
|
||||
{
|
||||
"metadata": {},
|
||||
"output_type": "display_data",
|
||||
"png": 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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0x9fb59b0>"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 3
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"class LinearProblem(Problem.BaseProblem):\n",
|
||||
" \n",
|
||||
" def __init__(self, mesh, model, G, **kwargs):\n",
|
||||
" Problem.BaseProblem.__init__(self, mesh, model, **kwargs)\n",
|
||||
" self.G = G\n",
|
||||
"\n",
|
||||
" def fields(self, m, u=None):\n",
|
||||
" return self.G.dot(m)\n",
|
||||
"\n",
|
||||
" def Jvec(self, m, v, u=None):\n",
|
||||
" return self.G.dot(v)\n",
|
||||
"\n",
|
||||
" def Jtvec(self, m, v, u=None):\n",
|
||||
" return self.G.T.dot(v)"
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"prompt_number": 4
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"# Create a model, by default this is a model on the mesh\n",
|
||||
"model = Model.BaseModel(M)\n",
|
||||
"# Create the problem\n",
|
||||
"prob = LinearProblem(M, model, G)\n",
|
||||
"# create a simpeg data object, using a synthetic model and 5% noise\n",
|
||||
"data = prob.createSyntheticData(models[:,0],std=0.05)\n",
|
||||
"# Create an optimization program\n",
|
||||
"opt = Optimization.InexactGaussNewton(maxIter=10)\n",
|
||||
"# Create a regularization program\n",
|
||||
"reg = Regularization.Tikhonov(model)\n",
|
||||
"# Create an objective function\n",
|
||||
"beta = Parameters.BetaSchedule??\n",
|
||||
"obj = ObjFunction.BaseObjFunction(data, reg, beta=beta)\n",
|
||||
"# Create an inversion object\n",
|
||||
"inv = Inversion.BaseInversion(obj, opt)\n",
|
||||
"# Start the inversion with a model of zeros, and run the inversion\n",
|
||||
"m0 = data.mtrue*0\n",
|
||||
"mopt = inv.run(m0)"
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"output_type": "stream",
|
||||
"stream": "stdout",
|
||||
"text": [
|
||||
"Warning: Parameter beta has switched to a new parent.\n",
|
||||
"Regularization has not set mref. SimPEG will set it to m0.\n",
|
||||
"============================ Inexact Gauss Newton ============================\n",
|
||||
" # beta phi_d phi_m f |proj(x-g)-x| LS Comment \n",
|
||||
"-----------------------------------------------------------------------------\n",
|
||||
" 0 1.00e+00 3.83e+03 0.00e+00 3.83e+03 1.94e+04 0 \n",
|
||||
" 1 1.00e+00 3.78e+03 8.61e-06 3.78e+03 7.51e+02 0 \n",
|
||||
" 2 1.00e+00 1.90e+02 2.66e+01 2.16e+02 1.24e+04 0 \n",
|
||||
" 3 5.00e-01 1.10e+02 2.46e+01 1.22e+02 1.23e+04 0 Skip BFGS \n",
|
||||
" 4 5.00e-01 6.72e+01 2.66e+01 8.05e+01 1.22e+04 0 \n",
|
||||
" 5 5.00e-01 4.98e+01 2.38e+01 6.17e+01 1.21e+04 0 \n",
|
||||
" 6 2.50e-01 3.05e+01 2.35e+01 3.64e+01 1.21e+04 0 "
|
||||
]
|
||||
},
|
||||
{
|
||||
"output_type": "stream",
|
||||
"stream": "stdout",
|
||||
"text": [
|
||||
"\n",
|
||||
" 7 2.50e-01 2.52e+01 2.57e+01 3.17e+01 1.19e+04 0 Skip BFGS \n",
|
||||
" 8 2.50e-01 2.46e+01 2.28e+01 3.03e+01 1.18e+04 0 \n",
|
||||
" 9 1.25e-01 2.42e+01 2.27e+01 2.71e+01 1.17e+04 0 \n",
|
||||
" 10 1.25e-01 2.29e+01 2.63e+01 2.62e+01 1.15e+04 0 "
|
||||
]
|
||||
},
|
||||
{
|
||||
"output_type": "stream",
|
||||
"stream": "stdout",
|
||||
"text": [
|
||||
"\n",
|
||||
"------------------------- STOP! -------------------------\n",
|
||||
"1 : |fc-fOld| = 8.7439e-01 <= tolF*(1+|f0|) = 3.8260e+02\n",
|
||||
"0 : |xc-x_last| = 2.1814e-01 <= tolX*(1+|x0|) = 1.0000e-01\n",
|
||||
"0 : |proj(x-g)-x| = 1.1490e+04 <= tolG = 1.0000e-01\n",
|
||||
"0 : |proj(x-g)-x| = 1.1490e+04 <= 1e3*eps = 1.0000e-02\n",
|
||||
"1 : maxIter = 10 <= iter = 10\n",
|
||||
"------------------------- DONE! -------------------------\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 25
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"beta = Parameters.BetaSchedule"
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": []
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"plot(M.vectorCCx, np.c_[data.mtrue, mopt])\n",
|
||||
"xlabel('x')\n",
|
||||
"legend(('true model','recovered model'))"
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"metadata": {},
|
||||
"output_type": "pyout",
|
||||
"prompt_number": 8,
|
||||
"text": [
|
||||
"<matplotlib.legend.Legend at 0xa5f54e0>"
|
||||
]
|
||||
},
|
||||
{
|
||||
"metadata": {},
|
||||
"output_type": "display_data",
|
||||
"png": 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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0xa28e400>"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 8
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"def MagInversion(mesh, model, data):\n",
|
||||
" \n",
|
||||
" \n",
|
||||
" # Create a model, by default this is a model on the mesh\n",
|
||||
" model = Model.BaseModel(M)\n",
|
||||
" # Create the problem\n",
|
||||
" prob = LinearProblem(M, model, G)\n",
|
||||
" # create a simpeg data object, using a synthetic model and 5% noise\n",
|
||||
"# data = prob.createSyntheticData(models[:,0],std=0.05)\n",
|
||||
" if prob.ispaired:\n",
|
||||
" prob.unpair()\n",
|
||||
" if data.ispaired:\n",
|
||||
" data.unpair()\n",
|
||||
" prob.pair(data)\n",
|
||||
" # Create an optimization program\n",
|
||||
" opt = Optimization.InexactGaussNewton(maxIter=10)\n",
|
||||
" # Create a regularization program\n",
|
||||
" reg = Regularization.Tikhonov(model)\n",
|
||||
" # Create an objective function\n",
|
||||
" beta = Parameters.BetaSchedule(beta0=1e0)\n",
|
||||
" obj = ObjFunction.BaseObjFunction(data, reg, beta=beta)\n",
|
||||
" # Create an inversion object\n",
|
||||
" inv = Inversion.BaseInversion(obj, opt)\n",
|
||||
" # Start the inversion with a model of zeros, and run the inversion\n",
|
||||
"# mopt = inv.run(m0)\n",
|
||||
" \n",
|
||||
" return inv"
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"prompt_number": 12
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"inv = MagInversion(M, model, data)\n",
|
||||
"m0 = data.mtrue*0"
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"prompt_number": 14
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
" out = inv.run(m0)"
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"output_type": "stream",
|
||||
"stream": "stdout",
|
||||
"text": [
|
||||
"============================ Inexact Gauss Newton ============================\n",
|
||||
" # beta phi_d phi_m f |proj(x-g)-x| LS Comment \n",
|
||||
"-----------------------------------------------------------------------------\n",
|
||||
" 0 1.00e+00 3.83e+03 0.00e+00 3.83e+03 2.00e+04 0 \n",
|
||||
" 1 1.00e+00 3.78e+03 8.67e-06 3.78e+03 7.64e+02 0 \n",
|
||||
" 2 1.00e+00 1.37e+02 2.71e+01 1.64e+02 8.09e+03 0 Skip BFGS \n",
|
||||
" 3 5.00e-01 1.30e+02 2.71e+01 1.43e+02 1.69e+02 0 \n",
|
||||
" 4 5.00e-01 4.12e+01 3.94e+01 6.09e+01 2.11e+02 0 Skip BFGS \n",
|
||||
" 5 5.00e-01 2.33e+01 2.06e+01 3.36e+01 6.27e+01 0 \n",
|
||||
" 6 2.50e-01 1.26e+01 2.20e+01 1.80e+01 3.70e+01 0 \n",
|
||||
" 7 2.50e-01 5.46e+00 2.09e+01 1.07e+01 6.26e+01 0 "
|
||||
]
|
||||
},
|
||||
{
|
||||
"output_type": "stream",
|
||||
"stream": "stdout",
|
||||
"text": [
|
||||
"\n",
|
||||
" 8 2.50e-01 4.19e+00 2.09e+01 9.41e+00 6.06e+01 0 Skip BFGS \n",
|
||||
" 9 1.25e-01 3.80e+00 2.08e+01 6.41e+00 2.69e+02 0 \n",
|
||||
" 10 1.25e-01 3.52e+00 2.12e+01 6.17e+00 6.18e+01 0 Skip BFGS \n",
|
||||
"------------------------- STOP! -------------------------\n",
|
||||
"1 : |fc-fOld| = 2.4171e-01 <= tolF*(1+|f0|) = 3.8275e+02\n",
|
||||
"0 : |xc-x_last| = 1.5878e-01 <= tolX*(1+|x0|) = 1.0000e-01\n",
|
||||
"0 : |proj(x-g)-x| = 6.1841e+01 <= tolG = 1.0000e-01\n",
|
||||
"0 : |proj(x-g)-x| = 6.1841e+01 <= 1e3*eps = 1.0000e-02\n",
|
||||
"1 : maxIter = 10 <= iter = 10\n",
|
||||
"------------------------- DONE! -------------------------\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 16
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"dpred1 = data.dpred(out)"
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"prompt_number": 18
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"plot(np.arange(20), np.c_[data.dpred(data.mtrue), dpred1])"
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"metadata": {},
|
||||
"output_type": "pyout",
|
||||
"prompt_number": 24,
|
||||
"text": [
|
||||
"[<matplotlib.lines.Line2D at 0xcd43828>,\n",
|
||||
" <matplotlib.lines.Line2D at 0xcd43a20>]"
|
||||
]
|
||||
},
|
||||
{
|
||||
"metadata": {},
|
||||
"output_type": "display_data",
|
||||
"png": 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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0xa8d3278>"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 24
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"print dpred1.shape"
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"output_type": "stream",
|
||||
"stream": "stdout",
|
||||
"text": [
|
||||
"(20L,)\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 19
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"class MyBetaSchedule(Parameters.BetaEstimate)"
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": []
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"def test(x, **kwargs):\n",
|
||||
" \n",
|
||||
" return x, kwargs['A'], kwargs['B']"
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"prompt_number": 38
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"a = np.ones(3)\n",
|
||||
"b = a\n",
|
||||
"options = {'A': a, 'B': b}\n",
|
||||
"\n",
|
||||
"test(a, **options)"
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"metadata": {},
|
||||
"output_type": "pyout",
|
||||
"prompt_number": 39,
|
||||
"text": [
|
||||
"(array([ 1., 1., 1.]), array([ 1., 1., 1.]), array([ 1., 1., 1.]))"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 39
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"class blah(object):\n",
|
||||
" A = None\n",
|
||||
" B = None\n",
|
||||
" def __init__(self,*args,**kwargs):\n",
|
||||
" Utils.setKwargs(self, **kwargs)"
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"prompt_number": 40
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"a = np.ones(3)\n",
|
||||
"b = a\n",
|
||||
"options = {'A': a, 'B': b}\n",
|
||||
"\n",
|
||||
"BLAH = blah(a,**options)"
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"prompt_number": 46
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"print options.get('notthere','default')"
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"output_type": "stream",
|
||||
"stream": "stdout",
|
||||
"text": [
|
||||
"default\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 55
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": []
|
||||
}
|
||||
],
|
||||
"metadata": {}
|
||||
}
|
||||
]
|
||||
}
|
||||
@@ -0,0 +1,598 @@
|
||||
{
|
||||
"metadata": {
|
||||
"name": ""
|
||||
},
|
||||
"nbformat": 3,
|
||||
"nbformat_minor": 0,
|
||||
"worksheets": [
|
||||
{
|
||||
"cells": [
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"from SimPEG import *\n",
|
||||
"from simpegPF import BaseMag\n",
|
||||
"from scipy.constants import mu_0\n",
|
||||
"from simpegPF.MagAnalytics import spheremodel, CongruousMagBC\n",
|
||||
"from simpegPF.Magnetics import MagneticsDiffSecondary, MagneticsDiffSecondaryInv\n",
|
||||
"%pylab inline"
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"output_type": "stream",
|
||||
"stream": "stdout",
|
||||
"text": [
|
||||
"Warning: Python backend is being used for solver. Run setup.py from the command line.\n",
|
||||
"Warning: mumps solver not available.\n",
|
||||
"Warning: upgrade your scipy to 0.13.0"
|
||||
]
|
||||
},
|
||||
{
|
||||
"output_type": "stream",
|
||||
"stream": "stdout",
|
||||
"text": [
|
||||
"\n",
|
||||
"Populating the interactive namespace from numpy and matplotlib"
|
||||
]
|
||||
},
|
||||
{
|
||||
"output_type": "stream",
|
||||
"stream": "stdout",
|
||||
"text": [
|
||||
"\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 1
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"# import matplotlib.pyplot as plt\n",
|
||||
"hxind = ((5,25,1.5),(21, 25),(5,25,1.5))\n",
|
||||
"hyind = ((5,25,1.5),(21, 25),(5,25,1.5))\n",
|
||||
"hzind = ((5,25,1.5),(20, 25),(5,25,1.5))\n",
|
||||
"hx, hy, hz = Utils.meshTensors(hxind, hyind, hzind)\n",
|
||||
"mesh = Mesh.TensorMesh([hx, hy, hz], [-hx.sum()/2,-hy.sum()/2,-hz.sum()/2])\n",
|
||||
"\n",
|
||||
"chibkg = 1e-7\n",
|
||||
"chiblk = 0.1\n",
|
||||
"chi = np.ones(mesh.nC)*chibkg\n",
|
||||
"sph_ind = spheremodel(mesh, 0., 0., -200., 80)\n",
|
||||
"chi[sph_ind] = chiblk\n",
|
||||
"# model = BaseMag.BaseMagModel(mesh)\n",
|
||||
"\n",
|
||||
"active_ind = ((mesh.gridCC[:,2]>-500)&(mesh.gridCC[:,2]<0)) & ((mesh.gridCC[:,0]>-800) & (mesh.gridCC[:,0]<800) & (mesh.gridCC[:,1]>-800) &(mesh.gridCC[:,1]<800))\n",
|
||||
"\n",
|
||||
"activemodel = Model.ActiveModel(mesh, active_ind, 1e-4)\n",
|
||||
"options = {'active_ind': active_ind}\n",
|
||||
"depthmodel = BaseMag.BaseDepthModel(mesh, **options)\n",
|
||||
"model = Model.ComboModel(mesh, [BaseMag.BaseMagModel, depthmodel, activemodel ])\n",
|
||||
"\n",
|
||||
"# mu = (1.+chi)*mu_0\n",
|
||||
"\n",
|
||||
"data = BaseMag.BaseMagData()\n",
|
||||
"Inc = 90.\n",
|
||||
"Dec = 0.\n",
|
||||
"Btot = 51000\n",
|
||||
"\n",
|
||||
"data.setBackgroundField(Inc, Dec, Btot)\n",
|
||||
"\n",
|
||||
"xr = np.linspace(-300, 300, 41)\n",
|
||||
"yr = np.linspace(-300, 300, 41)\n",
|
||||
"X, Y = np.meshgrid(xr, yr)\n",
|
||||
"Z = np.ones((xr.size, yr.size))*(0.)\n",
|
||||
"rxLoc = np.c_[Utils.mkvc(X), Utils.mkvc(Y), Utils.mkvc(Z)]\n",
|
||||
"data.rxLoc = rxLoc\n",
|
||||
"prob = MagneticsDiffSecondary(mesh, model)\n",
|
||||
"prob.pair(data)"
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"prompt_number": 2
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"weight = abs(mesh.gridCC[:,2])**1.0\n",
|
||||
"weight = weight/weight.max()\n",
|
||||
"weight[~active_ind] = 1.\n",
|
||||
"data.mtrue = (chi*1/weight)[active_ind]\n",
|
||||
"# data.mtrue = (chi)[active_ind]\n",
|
||||
"\n",
|
||||
"# data.mtrue = chi\n",
|
||||
"\n",
|
||||
"data.dtrue = data.dpred(data.mtrue)\n",
|
||||
"std = 0.1\n",
|
||||
"noise = std*np.linalg.norm(data.dtrue)/np.sqrt(data.dtrue.size)*np.random.randn(*data.dtrue.shape) #(*??)\n",
|
||||
"data.dobs = data.dtrue+noise\n",
|
||||
"data.std = std"
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"prompt_number": 3
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"fig, ax = plt.subplots(1,2, figsize = (8,5) )\n",
|
||||
"dat = ax[0].imshow(np.reshape(noise, (xr.size, yr.size), order='F'), extent=[min(xr), max(xr), min(yr), max(yr)])\n",
|
||||
"plt.colorbar(dat, ax = ax[0])\n",
|
||||
"dat2 = ax[1].imshow(np.reshape(data.dobs, (xr.size, yr.size), order='F'), extent=[min(xr), max(xr), min(yr), max(yr)])\n",
|
||||
"plt.colorbar(dat2, ax = ax[1])\n",
|
||||
"plt.show()"
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"metadata": {},
|
||||
"output_type": "display_data",
|
||||
"png": 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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0xa401400>"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 4
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"plt.plot(noise)\n",
|
||||
"plt.plot(data.dobs)"
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"metadata": {},
|
||||
"output_type": "pyout",
|
||||
"prompt_number": 5,
|
||||
"text": [
|
||||
"[<matplotlib.lines.Line2D at 0xa3ced68>]"
|
||||
]
|
||||
},
|
||||
{
|
||||
"metadata": {},
|
||||
"output_type": "display_data",
|
||||
"png": "iVBORw0KGgoAAAANSUhEUgAAAYAAAAD9CAYAAAC1DKAUAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0xa3cecc0>"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 5
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"inv, reg = MagneticsDiffSecondaryInv(mesh, model, data)"
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"prompt_number": 6
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"m0 = (np.ones(mesh.nC)*1e-4*1/weight)[active_ind]\n",
|
||||
"# m0 = (np.ones(mesh.nC)*1e-4)[active_ind]\n",
|
||||
"\n",
|
||||
"reg.mref = m0*0."
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"prompt_number": 7
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"dobj = inv.objFunc.dataObj(m0)\n",
|
||||
"print dobj\n",
|
||||
"print model.transform(m0)"
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"output_type": "stream",
|
||||
"stream": "stdout",
|
||||
"text": [
|
||||
"550874.334999\n",
|
||||
"[ 1.25676273e-06 1.25676273e-06 1.25676273e-06 ..., 1.25676273e-06\n",
|
||||
" 1.25676273e-06 1.25676273e-06]\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 8
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"data_ini = data.dpred(m0)\n",
|
||||
"colorbar(mesh.plotImage(model.transform(m0)))"
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"output_type": "stream",
|
||||
"stream": "stderr",
|
||||
"text": [
|
||||
"C:\\Users\\SEOGI\\AppData\\Local\\Enthought\\Canopy\\App\\appdata\\canopy-1.0.1.1189.win-x86_64\\lib\\site-packages\\matplotlib\\colorbar.py:808: RuntimeWarning: invalid value encountered in divide\n",
|
||||
" z = np.take(y, i0) + (xn-np.take(b,i0))*dy/db\n",
|
||||
"C:\\Users\\SEOGI\\AppData\\Local\\Enthought\\Canopy\\App\\appdata\\canopy-1.0.1.1189.win-x86_64\\lib\\site-packages\\matplotlib\\colorbar.py:561: RuntimeWarning: invalid value encountered in greater\n",
|
||||
" inrange = (ticks > -0.001) & (ticks < 1.001)\n",
|
||||
"C:\\Users\\SEOGI\\AppData\\Local\\Enthought\\Canopy\\App\\appdata\\canopy-1.0.1.1189.win-x86_64\\lib\\site-packages\\matplotlib\\colorbar.py:561: RuntimeWarning: invalid value encountered in less\n",
|
||||
" inrange = (ticks > -0.001) & (ticks < 1.001)\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"metadata": {},
|
||||
"output_type": "pyout",
|
||||
"prompt_number": 9,
|
||||
"text": [
|
||||
"<matplotlib.colorbar.Colorbar instance at 0x000000000E4D3408>"
|
||||
]
|
||||
},
|
||||
{
|
||||
"metadata": {},
|
||||
"output_type": "display_data",
|
||||
"png": 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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0xa394940>"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 9
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"print (model.transform(m0)/mu_0).max()\n",
|
||||
"print model.transform(m0)"
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"output_type": "stream",
|
||||
"stream": "stdout",
|
||||
"text": [
|
||||
"1.0001\n",
|
||||
"[ 1.25676273e-06 1.25676273e-06 1.25676273e-06 ..., 1.25676273e-06\n",
|
||||
" 1.25676273e-06 1.25676273e-06]\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 10
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"fig, ax = plt.subplots(1,2, figsize = (8,5) )\n",
|
||||
"dat = ax[0].imshow(np.reshape(data_ini, (xr.size, yr.size), order='F'), extent=[min(xr), max(xr), min(yr), max(yr)])\n",
|
||||
"plt.colorbar(dat, ax = ax[0])\n",
|
||||
"dat2 = ax[1].imshow(np.reshape(data.dobs, (xr.size, yr.size), order='F'), extent=[min(xr), max(xr), min(yr), max(yr)])\n",
|
||||
"plt.colorbar(dat2, ax = ax[1])\n",
|
||||
"plt.show()"
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"metadata": {},
|
||||
"output_type": "display_data",
|
||||
"png": 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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0xb4096d8>"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 11
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"beta = Parameters.BetaSchedule(coolingFactor = 10, coolingRate = 2, beta0 = 1e14)\n",
|
||||
"inv.objFunc.beta = beta\n",
|
||||
"inv.opt.maxIterLS = 40\n"
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"prompt_number": 12
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"inv.objFunc.data.Wd = 10."
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"prompt_number": 13
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"reg.alpha_s = 1e-4\n",
|
||||
"reg.alpha_x = 1.\n",
|
||||
"reg.alpha_y = 1.\n",
|
||||
"reg.alpha_z = 1."
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"prompt_number": 20
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"out = inv.run(m0)\n",
|
||||
"# reg = Regularization.Tikhonov(model)"
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"output_type": "stream",
|
||||
"stream": "stdout",
|
||||
"text": [
|
||||
"============================ Inexact Gauss Newton ============================\n",
|
||||
" # beta phi_d phi_m f |proj(x-g)-x| LS Comment \n",
|
||||
"-----------------------------------------------------------------------------\n",
|
||||
" 0 1.00e+14 1.67e+08 1.28e-07 1.80e+08 9.58e+08 0 Skip BFGS "
|
||||
]
|
||||
},
|
||||
{
|
||||
"output_type": "stream",
|
||||
"stream": "stdout",
|
||||
"text": [
|
||||
"\n",
|
||||
" 1 1.00e+14 1.36e+07 1.29e-07 2.64e+07 1.11e+08 0 Skip BFGS "
|
||||
]
|
||||
},
|
||||
{
|
||||
"output_type": "stream",
|
||||
"stream": "stdout",
|
||||
"text": [
|
||||
"\n",
|
||||
"Iterative solver did not work well (Jvec)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"output_type": "stream",
|
||||
"stream": "stdout",
|
||||
"text": [
|
||||
"\n",
|
||||
" 2 1.00e+13 1.36e+07 1.29e-07 1.49e+07 1.09e+08 5 Skip BFGS "
|
||||
]
|
||||
},
|
||||
{
|
||||
"output_type": "stream",
|
||||
"stream": "stdout",
|
||||
"text": [
|
||||
"\n",
|
||||
" 3 1.00e+13 1.29e+07 1.29e-07 1.42e+07 1.06e+08 5 Skip BFGS "
|
||||
]
|
||||
},
|
||||
{
|
||||
"output_type": "stream",
|
||||
"stream": "stdout",
|
||||
"text": [
|
||||
"\n",
|
||||
"Iterative solver did not work well (Jvec)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"output_type": "stream",
|
||||
"stream": "stdout",
|
||||
"text": [
|
||||
"\n",
|
||||
"Iterative solver did not work well (Jvec)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"output_type": "stream",
|
||||
"stream": "stdout",
|
||||
"text": [
|
||||
"\n",
|
||||
" 4 1.00e+12 7.14e+06 1.29e-07 7.27e+06 1.94e+08 3 "
|
||||
]
|
||||
},
|
||||
{
|
||||
"output_type": "stream",
|
||||
"stream": "stdout",
|
||||
"text": [
|
||||
"\n",
|
||||
"Iterative solver did not work well (Jvec)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"output_type": "stream",
|
||||
"stream": "stdout",
|
||||
"text": [
|
||||
"\n",
|
||||
" 5 1.00e+12 7.14e+06 1.29e-07 7.27e+06 1.94e+08 17 Skip BFGS "
|
||||
]
|
||||
},
|
||||
{
|
||||
"output_type": "stream",
|
||||
"stream": "stdout",
|
||||
"text": [
|
||||
"\n",
|
||||
"------------------------- STOP! -------------------------\n",
|
||||
"1 : |fc-fOld| = 7.5435e+01 <= tolF*(1+|f0|) = 1.7998e+07\n",
|
||||
"1 : |xc-x_last| = 6.9661e-07 <= tolX*(1+|x0|) = 1.1412e-01\n",
|
||||
"0 : |proj(x-g)-x| = 1.9436e+08 <= tolG = 1.0000e-01\n",
|
||||
"0 : |proj(x-g)-x| = 1.9436e+08 <= 1e3*eps = 1.0000e-02\n",
|
||||
"1 : maxIter = 5 <= iter = 5\n",
|
||||
"------------------------- DONE! -------------------------\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 21
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"indx = 15\n",
|
||||
"fig, axes = subplots(1,2, figsize = (12, 5))\n",
|
||||
"ps1 = mesh.plotSlice(chi, vType='CC', ind=indx, normal='X',ax = axes[0], grid=True, gridOpts={'color':'b','lw':0.3, 'alpha':0.5}); axes[0].set_title('$\\chi_{true}$', fontsize = 16);\n",
|
||||
"ps2 = mesh.plotSlice(model.transform(out\n",
|
||||
" )/mu_0-1, vType='CC', ind=indx, normal='X', ax = axes[1], grid=True, gridOpts={'color':'b','lw':0.3, 'alpha':0.5}); axes[1].set_title('$\\chi_{pred}$', fontsize = 16);\n",
|
||||
"colorbar(ps1[0], ax = axes[0])\n",
|
||||
"colorbar(ps2[0], ax = axes[1])\n",
|
||||
"print 'x=', mesh.vectorCCx[indx]"
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"output_type": "stream",
|
||||
"stream": "stdout",
|
||||
"text": [
|
||||
"x= 0.0\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"metadata": {},
|
||||
"output_type": "display_data",
|
||||
"png": 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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0xe4c6780>"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 22
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"fig, axes = subplots(1,2, figsize = (12, 5))\n",
|
||||
"mesh.plotImage(model.transform(out)/mu_0-1, ax = axes[0])\n",
|
||||
"mesh.plotImage(chi, ax = axes[1])"
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"metadata": {},
|
||||
"output_type": "pyout",
|
||||
"prompt_number": 23,
|
||||
"text": [
|
||||
"<matplotlib.collections.QuadMesh at 0xa40ce10>"
|
||||
]
|
||||
},
|
||||
{
|
||||
"metadata": {},
|
||||
"output_type": "display_data",
|
||||
"png": 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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0xb42da90>"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 23
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"dpredout = data.dpred(out)"
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"prompt_number": 24
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"fig, ax = plt.subplots(1,2, figsize = (8,5) )\n",
|
||||
"dat = ax[0].imshow(np.reshape(dpredout, (xr.size, yr.size), order='F'), extent=[min(xr), max(xr), min(yr), max(yr)])\n",
|
||||
"plt.colorbar(dat, ax = ax[0])\n",
|
||||
"dat2 = ax[1].imshow(np.reshape(data.dobs, (xr.size, yr.size), order='F'), extent=[min(xr), max(xr), min(yr), max(yr)])\n",
|
||||
"plt.colorbar(dat2, ax = ax[1])\n",
|
||||
"plt.show()"
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"metadata": {},
|
||||
"output_type": "display_data",
|
||||
"png": "iVBORw0KGgoAAAANSUhEUgAAAe8AAAElCAYAAADN+mofAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0xa3e4b00>"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 25
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"prompt_number": 19
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"prompt_number": 19
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"prompt_number": 19
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": []
|
||||
}
|
||||
],
|
||||
"metadata": {}
|
||||
}
|
||||
]
|
||||
}
|
||||
@@ -1,142 +0,0 @@
|
||||
|
||||
from SimPEG.Utils.matutils import kron3, speye, sdiag
|
||||
from SimPEG import *
|
||||
import numpy as np
|
||||
import scipy.sparse as sp
|
||||
def ddxFaceDivBC(n, bc):
|
||||
|
||||
ij = (np.array([0, n-1]),np.array([0, 1]))
|
||||
vals = np.zeros(2)
|
||||
|
||||
# Set the first side
|
||||
if(bc[0] == 'dirichlet'):
|
||||
vals[0] = 0
|
||||
elif(bc[0] == 'neumann'):
|
||||
vals[0] = -1
|
||||
# Set the second side
|
||||
if(bc[1] == 'dirichlet'):
|
||||
vals[1] = 0
|
||||
elif(bc[1] == 'neumann'):
|
||||
vals[1] = 1
|
||||
D = sp.csr_matrix((vals, ij), shape=(n,2))
|
||||
return D
|
||||
|
||||
|
||||
def faceDivBC(mesh, BC, ind):
|
||||
"""
|
||||
The facd divergence boundary condtion matrix
|
||||
|
||||
.. math::
|
||||
|
||||
|
||||
|
||||
"""
|
||||
# The number of cell centers in each direction
|
||||
n = mesh.nCv
|
||||
# Compute faceDivergence operator on faces
|
||||
if(mesh.dim == 1):
|
||||
D = ddxFaceDivBC(n[0], BC[0])
|
||||
elif(mesh.dim == 2):
|
||||
D1 = sp.kron(speye(n[1]), ddxFaceDivBC(n[0]), BC[0])
|
||||
D2 = sp.kron(ddxFaceDivBC(n[1], BC[1]), speye(n[0]))
|
||||
D = sp.hstack((D1, D2), format="csr")
|
||||
elif(mesh.dim == 3):
|
||||
D1 = kron3(speye(n[2]), speye(n[1]), ddxFaceDivBC(n[0], BC[0]))
|
||||
D2 = kron3(speye(n[2]), ddxFaceDivBC(n[1], BC[1]), speye(n[0]))
|
||||
D3 = kron3(ddxFaceDivBC(n[2], BC[2]), speye(n[1]), speye(n[0]))
|
||||
D = sp.hstack((D1, D2, D3), format="csr")
|
||||
# Compute areas of cell faces & volumes
|
||||
S = mesh.area[ind]
|
||||
V = mesh.vol
|
||||
mesh._faceDiv = sdiag(1/V)*D*sdiag(S)
|
||||
|
||||
return mesh._faceDiv
|
||||
|
||||
|
||||
def faceBCind(mesh):
|
||||
"""
|
||||
Find indices of boundary faces in each direction
|
||||
|
||||
"""
|
||||
if(mesh.dim==1):
|
||||
indxd = (mesh.gridFx[:,0]==min(mesh.gridFx[:,0]))
|
||||
indxu = (mesh.gridFx[:,0]==max(mesh.gridFx[:,0]))
|
||||
return indxd, indxu
|
||||
elif(mesh.dim==1):
|
||||
indxd = (mesh.gridFx[:,0]==min(mesh.gridFx[:,0]))
|
||||
indxu = (mesh.gridFx[:,0]==max(mesh.gridFx[:,0]))
|
||||
indyd = (mesh.gridFy[:,1]==min(mesh.gridFy[:,1]))
|
||||
indyu = (mesh.gridFy[:,1]==max(mesh.gridFy[:,1]))
|
||||
return indxd, indxu, indyd, indyu
|
||||
elif(mesh.dim==3):
|
||||
indxd = (mesh.gridFx[:,0]==min(mesh.gridFx[:,0]))
|
||||
indxu = (mesh.gridFx[:,0]==max(mesh.gridFx[:,0]))
|
||||
indyd = (mesh.gridFy[:,1]==min(mesh.gridFy[:,1]))
|
||||
indyu = (mesh.gridFy[:,1]==max(mesh.gridFy[:,1]))
|
||||
indzd = (mesh.gridFz[:,2]==min(mesh.gridFz[:,2]))
|
||||
indzu = (mesh.gridFz[:,2]==max(mesh.gridFz[:,2]))
|
||||
return indxd, indxu, indyd, indyu, indzd, indzu
|
||||
|
||||
|
||||
def spheremodel(mesh, x0, y0, z0, r):
|
||||
"""
|
||||
Generate model indicies for sphere
|
||||
- (x0, y0, z0 ): is the center location of sphere
|
||||
- r: is the radius of the sphere
|
||||
- it returns logical indicies of cell-center model
|
||||
"""
|
||||
ind = np.sqrt((mesh.gridCC[:,0]-x0)**2+(mesh.gridCC[:,1]-y0)**2+(mesh.gridCC[:,2]-z0)**2 ) < r
|
||||
return ind
|
||||
|
||||
|
||||
|
||||
def MagSphereAnalFun(x, y, z, R, x0, y0, z0, mu1, mu2, H0, flag):
|
||||
"""
|
||||
Analytic function for Magnetics problem. The set up here is
|
||||
magnetic sphere in whole-space.
|
||||
- (x0,y0,z0)
|
||||
- (x0, y0, z0 ): is the center location of sphere
|
||||
- r: is the radius of the sphere
|
||||
|
||||
.. math::
|
||||
|
||||
\mathbf{H}^p = H_0\hat{x}
|
||||
|
||||
|
||||
"""
|
||||
if (~np.size(x)==np.size(y)==np.size(z)):
|
||||
print "Specify same size of x, y, z"
|
||||
return
|
||||
dim = x.shape
|
||||
x = Utils.mkvc(x)
|
||||
y = Utils.mkvc(y)
|
||||
z = Utils.mkvc(z)
|
||||
|
||||
ind = np.sqrt((x-x0)**2+(y-y0)**2+(z-z0)**2 ) < R
|
||||
r = Utils.mkvc(np.sqrt((x-x0)**2+(y-y0)**2+(z-z0)**2 ))
|
||||
Bx = np.zeros(x.size)
|
||||
By = np.zeros(x.size)
|
||||
Bz = np.zeros(x.size)
|
||||
|
||||
# Inside of the sphere
|
||||
rf2 = 3*mu1/(mu2+2*mu1)
|
||||
if (flag == 'total'):
|
||||
Bx[ind] = mu2*H0*(rf2)
|
||||
elif (flag == 'secondary'):
|
||||
Bx[ind] = mu2*H0*(rf2)-mu1*H0
|
||||
|
||||
By[ind] = 0.
|
||||
Bz[ind] = 0.
|
||||
# Outside of the sphere
|
||||
rf1 = (mu2-mu1)/(mu2+2*mu1)
|
||||
if (flag == 'total'):
|
||||
Bx[~ind] = mu1*(H0+H0/r[~ind]**5*(R**3)*rf1*(2*x[~ind]**2-y[~ind]**2-z[~ind]**2))
|
||||
elif (flag == 'secondary'):
|
||||
Bx[~ind] = mu1*(H0/r[~ind]**5*(R**3)*rf1*(2*x[~ind]**2-y[~ind]**2-z[~ind]**2))
|
||||
|
||||
By[~ind] = mu1*(H0/r[~ind]**5*(R**3)*rf1*(3*x[~ind]*y[~ind]))
|
||||
Bz[~ind] = mu1*(H0/r[~ind]**5*(R**3)*rf1*(3*x[~ind]*z[~ind]))
|
||||
|
||||
return np.reshape(Bx, x.shape, order='F'), np.reshape(By, x.shape, order='F'), np.reshape(Bz, x.shape, order='F')
|
||||
|
||||
|
||||
Reference in new issue
Block a user