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seogi committed 2014-02-28 16:44:12 -08:00
1 parent 5816f75728
commit 18546d038b
6 files changed
+693 -215
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simpegPF/BaseMag.py
+47 -16
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@@ -11,10 +11,14 @@ class BaseMagData(Data.BaseData):
def __init__(self, **kwargs):
Data.BaseData.__init__(self, **kwargs)
#TODO: change to inc, dec, intensity
def setBackgroundField(self, x=1., y=0., z=0.):
# Primary field in x-direction (background)
self.B0 = np.r_[x,y,z]
def setBackgroundField(self, Inc, Dec, Btot):
Bx = Btot*np.cos(Inc/180.*np.pi)*np.sin(Dec/180.*np.pi)
By = Btot*np.cos(Inc/180.*np.pi)*np.cos(Dec/180.*np.pi)
Bz = -Btot*np.sin(Inc/180.*np.pi)
self.B0 = np.r_[Bx,By,Bz]
@property
def Qfx(self):
@@ -34,36 +38,63 @@ class BaseMagData(Data.BaseData):
self._Qfz = self.prob.mesh.getInterpolationMat(self.rxLoc,'Fz')
return self._Qfz
def projectFields(self, B):
def projectFields(self, u):
"""
This function projects the fields onto the data space.
Esepcially, here for we use total magnetic intensity (TMI) data,
which is common in practice.
First we project our B on to data location
.. math::
d_\\text{pred} = \mathbf{P} u(m)
\mathbf{B}_{rec} = \mathbf{P} \mathbf{B}
then we take the dot product between B and b_0
.. math ::
\\text{TMI} = \\vec{B}_s \cdot \hat{B}_0
"""
#TODO: There can be some different tyes of data like |B| or B
# bfx = self.Qfx*B
# bfy = self.Qfy*B
bfz = self.Qfz*B
return bfz
bfx = self.Qfx*u['B']
bfy = self.Qfy*u['B']
bfz = self.Qfz*u['B']
# return np.sqrt(bfx**2 + bfy**2 + bfz**2)
# Generate unit vector
B0 = self.prob.data.B0
Bot = np.sqrt(B0[0]**2+B0[1]**2+B0[2]**2)
box = B0[0]/Bot
boy = B0[1]/Bot
boz = B0[2]/Bot
# return bfx*box + bfx*boy + bfx*boz
return bfx*box + bfy*boy + bfz*boz
# return np.sqrt(bfx**2 + bfy**2 + bfz**2)
@Utils.count
def projectFieldsDeriv(self, B):
"""
This function projects the fields onto the data space.
.. math::
\\frac{\partial d_\\text{pred}}{\partial u} = \mathbf{P}
\\frac{\partial d_\\text{pred}}{\partial \mathbf{B}} = \mathbf{P}
Esepcially, this function is for TMI data type
"""
return self.Qfz
# Generate unit vector
B0 = self.prob.data.B0
Bot = np.sqrt(B0[0]**2+B0[1]**2+B0[2]**2)
box = B0[0]/Bot
boy = B0[1]/Bot
boz = B0[2]/Bot
return self.Qfx*box+self.Qfy*boy+self.Qfz*boz
def projectFieldsAsVector(self, B):
simpegPF/Magnetics.py
+195 -92
View File
@@ -41,6 +41,7 @@ class MagneticsDiffSecondary(Problem.BaseProblem):
self._MfMu0 = self.mesh.getFaceMass(1/mu_0)
# self._MfMu0 = self.mesh.getFaceInnerProduct(1/mu_0)
@Utils.requires('data')
def getB0(self):
b0 = self.data.B0
B0 = np.r_[b0[0]*np.ones(self.mesh.nFx),
@@ -49,17 +50,21 @@ class MagneticsDiffSecondary(Problem.BaseProblem):
return B0
def getRHS(self, m):
"""
.. math ::
\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}
"""
B0 = self.getB0()
Dface = self.mesh.faceDiv
Mc = Utils.sdiag(self.mesh.vol)
chi = self.model.transform(m, asMu=False)
Bbc, const = CongruousMagBC(self.mesh, self.data.B0, chi)
self.Bbc_const = const
Bbc, Bbc_const = CongruousMagBC(self.mesh, self.data.B0, chi)
self.Bbc = Bbc
#TODO: put congrous BC back in
# return self._Div*self.MfMuI*self.MfMu0*B0 - self._Div*B0 #+ Mc*Dface*self._Pout.T*Bbc
self.Bbc_const = Bbc_const
return self._Div*self.MfMuI*self.MfMu0*B0 - self._Div*B0 + Mc*Dface*self._Pout.T*Bbc
def getA(self, m):
@@ -68,41 +73,39 @@ class MagneticsDiffSecondary(Problem.BaseProblem):
The A matrix has the form:
.. math ::
\mathbf{A}\mathbf{u} = \mathbf{rhs}
\mathbf{A} = - \Div(\MfMui)^{-1}\Div^{T}
\mathbf{rhs} = - \Div(\MfMui)^{-1}\mathbf{M}^f_{\\frac{1}{\mu_0}}\mathbf{B}_0 + \Div\mathbf{B}_0-\diag(v)\mathbf{D} \mathbf{P}_{out}^T \mathbf{B}_{sBC}
.. math ::
\mathbf{A} = \Div(\MfMui)^{-1}\Div^{T}
"""
return self._Div*self.MfMuI*self._Div.T
def fields(self, m):
"""
Return magnetic potential (u) and flux (B)
u: defined on the cell center [nC x 1]
B: defined on the cell center [nF x 1]
After we compute u, then we update B.
.. math ::
\mathbf{B}_s = (\MfMui)^{-1}\mathbf{M}^f_{\mu_0^{-1}}\mathbf{B}_0-\mathbf{B}_0 -(\MfMui)^{-1}\Div^T \mathbf{u}
"""
self.makeMassMatrices(m)
A = self.getA(m)
rhs = self.getRHS(m)
m1 = sp.linalg.interface.aslinearoperator(Utils.sdiag(1/A.diagonal()))
u, info = sp.linalg.bicgstab(A, rhs, tol=1e-6, maxiter=1000, M=m1)
B0 = self.getB0()
B = self.MfMuI*self.MfMu0*B0-B0-self.MfMuI*self._Div.T*u
#TODO: Create a mag fields object class.
# F = self.getInitialFields()
# e.g. {'B': B, 'u': u}
return {'B': B, 'u': u}
# return self.forward(m, self.getRHS, self.calcFields, F=F)
@Utils.timeIt
def Jvec(self, m, v, u=None):
def Jvec(self, m, v, fields=None):
"""
Computing Jacobian multiplied by vector
@@ -122,7 +125,7 @@ class MagneticsDiffSecondary(Problem.BaseProblem):
\\frac{\delta \mathbf{u}}{\delta \mathbf{m}} = - [\\nabla_u \mathbf{C}(\mathbf{u})]^{-1}\\nabla_m \mathbf{C}(\mathbf{m})
With some linear algebra we can have
.. math ::
\\nabla_u \mathbf{C}(\mathbf{u}) = \mathbf{A}
@@ -138,66 +141,177 @@ class MagneticsDiffSecondary(Problem.BaseProblem):
\dMfMuI = \diag(\MfMui)^{-1}_{vec} \mathbf{Av}_{F2CC}^T\diag(\mathbf{v})\diag(\\frac{1}{\mu^2})
\\frac{\partial \mathbf{rhs}(\mathbf{m})}{\partial \mathbf{m}} = \\frac{\partial \mathbf{\mu}}{\partial \mathbf{m}} \left[
\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}}
\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}}
In the end,
.. math ::
\\frac{\delta \mathbf{u}}{\delta \mathbf{m}} =
- [ \mathbf{A} ]^{-1}\left[ \\frac{\partial \mathbf{A}}{\partial \mathbf{m}}(\mathbf{m})\mathbf{u}
- \\frac{\partial \mathbf{rhs}(\mathbf{m})}{\partial \mathbf{m}} \\right]
A little tricky point here is we are not interested in potential (u), but interested in magnetic flux (B).
Thus, we need sensitivity for B. Now we take derivative of B w.r.t m and have
.. math ::
\\frac{\delta \mathbf{B}} {\delta \mathbf{m}} = \\frac{\partial \mathbf{\mu} } {\partial \mathbf{m} }
\left[
\diag(\M^f_{\mu_{0}^{-1} } \mathbf{B}_0) \dMfMuI \\
- \diag (\Div^T\mathbf{u})\dMfMuI
\\right ]
- (\MfMui)^{-1}\Div^T\\frac{\delta\mathbf{u}}{\delta \mathbf{m}}
Finally we evaluate the above, but we should remember that
.. note ::
We only want to evalute
.. math ::
\mathbf{J}\mathbf{v} = \\frac{\delta \mathbf{P}\mathbf{B}} {\delta \mathbf{m}}\mathbf{v}
Since forming sensitivity matrix is very expensive in that this monster is "big" and "dense" matrix!!
"""
if u is None:
u = self.fields(m)
#TODO: B, u = u['B'], u['u']
B, u = u['B'], u['u']
if fields is None:
fields = self.fields(m)
B, u = fields['B'], fields['u']
mu = self.model.transform(m, asMu=True)
dmudm = self.model.transform(m, asMu=True)
P = self.data.projectFieldsDeriv(u)
A = self.getA(m)
dCdu = A
# (Av_m)^-1
# -(Av_m)^-2 * MfMu_dm * d/dm(1/mu(m))
# (Av_m)^-2 * MfMu_dm * diag(mu(m)^-2) * mT_dm
#TODO: only works for diagonal MfMui
# Some chain rule!
# harm_dm = Utils.sdiag(self.MfMui.diagonal()**(-2))
# MfMu_dm = self.mesh.getFaceMassDeriv()
# dmuI_dm = Utils.sdiag(mu**(-2))
# mT_dm = self.model.transformDeriv(m, asMu=True)
getFIPconst = 1./3
MfMuIvec = 1/self.MfMui.diagonal()*getFIPconst
dMfMuI = Utils.sdiag(MfMuIvec**2)*self.mesh.aveF2CC.T*Utils.sdiag(self.mesh.vol*1./mu**2)
dmudm = self.model.transformDeriv(m, asMu=True)
dmdmu = Utils.sdiag(1/(dmudm.diagonal()))
vol = self.mesh.vol
Div = self._Div
# lots-o-bracket for vector multiplication first!
# MfMu_dmXv = harm_dm * ( MfMu_dm * ( dmuI_dm * ( mT_dm * v ) ) )
#dCdm_A = D * ( Utils.sdiag( D.T * u ) * MfMu_dmXv )
dCdm_A = dmudm*Div * ( Utils.sdiag( Div.T * u * dMfMuI ) )
# rhs = D * MfMuI * MfMu0 * B0
Dface = self.mesh.faceDiv
P = self.data.projectFieldsDeriv(B) # Projection matrix
B0 = self.getB0()
#TODO: add congrous stuff
dCdm_RHS = dmudm* Div * Utils.sdiag( self.MfMu0*B0 ) * dMfMuI - Utils.sdiag(self.mesh.vol)*self.mesh.faceDiv*self.Pout.T*self.Bbc*self.Bbc_const
MfMuIvec = 1/self.MfMui.diagonal()
dMfMuI = Utils.sdiag(MfMuIvec**2)*self.mesh.aveF2CC.T*Utils.sdiag(vol*1./mu**2)
# A = self._Div*self.MfMuI*self._Div.T
# RHS = Div*MfMuI*MfMu0*B0 - Div*B0 + Mc*Dface*Pout.T*Bbc
# C(m,u) = A*m-rhs
# dudm = -(dCdu)^(-1)dCdm
# c(m,u) = A(m)u - rhs(m)
dCdm = dCdm_A - dCdm_RHS
dCdu = self.getA(m)
dCdm_A = Div * ( Utils.sdiag( Div.T * u )* dMfMuI *dmudm )
dCdm_RHS1 = Div * (Utils.sdiag( self.MfMu0*B0 ) * dMfMuI)
temp1 = (Dface*(self._Pout.T*self.Bbc_const*self.Bbc))
dCdm_RHS2v = (Utils.sdiag(vol)*temp1)*np.inner(vol, v)
dCdm_RHSv = dCdm_RHS1*(dmudm*v) + dCdm_RHS2v
dCdm_v = dCdm_A*v - dCdm_RHSv
solve = Solver(dCdu)
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)
#TODO: Multiply by the dP(u(m))/du
# We transformed u in our fields object.
# ( dBdu * + dBdm(u) )
Jv = - P * solve.solve(dCdm)
return Utils.mkvc(Jv)
if info > 0:
raise Exception ("Iterative solver did not work well")
# B = self.MfMuI*self.MfMu0*B0-B0-self.MfMuI*self._Div.T*u
# dBdm = d\mudm*dBd\mu
dudm = -sol
dBdmv = ( Utils.sdiag(self.MfMu0*B0)*(dMfMuI * (dmudm*v)) \
- Utils.sdiag(Div.T*u)*(dMfMuI* (dmudm*v)) \
- self.MfMuI*(Div.T* (dudm)) )
return Utils.mkvc(P*dBdmv)
@Utils.timeIt
def Jtvec(self, m, v, fields=None):
"""
Computing Jacobian^T multiplied by vector.
.. math ::
(\\frac{\delta \mathbf{P}\mathbf{B}} {\delta \mathbf{m}})^{T} = \left[ \mathbf{P}_{deriv}\\frac{\partial \mathbf{\mu} } {\partial \mathbf{m} }
\left[
\diag(\M^f_{\mu_{0}^{-1} } \mathbf{B}_0) \dMfMuI \\
- \diag (\Div^T\mathbf{u})\dMfMuI
\\right ]\\right]^{T}
- \left[\mathbf{P}_{deriv}(\MfMui)^{-1}\Div^T\\frac{\delta\mathbf{u}}{\delta \mathbf{m}} \\right]^{T}
where
.. math ::
\mathbf{P}_{derv} = \\frac{\partial \mathbf{P}}{\partial\mathbf{B}}
.. note ::
Here we only want to compute
.. math ::
\mathbf{J}^{T}\mathbf{v} = (\\frac{\delta \mathbf{P}\mathbf{B}} {\delta \mathbf{m}})^{T} \mathbf{v}
"""
if fields is None:
fields = self.fields(m)
B, u = fields['B'], fields['u']
mu = self.model.transform(m, asMu=True)
dmudm = self.model.transformDeriv(m, asMu=True)
dmdmu = Utils.sdiag(1/(dmudm.diagonal()))
vol = self.mesh.vol
Div = self._Div
Dface = self.mesh.faceDiv
P = self.data.projectFieldsDeriv(B) # Projection matrix
B0 = self.getB0()
MfMuIvec = 1/self.MfMui.diagonal()
dMfMuI = Utils.sdiag(MfMuIvec**2)*self.mesh.aveF2CC.T*Utils.sdiag(vol*1./mu**2)
# A = self._Div*self.MfMuI*self._Div.T
# RHS = Div*MfMuI*MfMu0*B0 - Div*B0 + Mc*Dface*Pout.T*Bbc
# C(m,u) = A*m-rhs
# dudm = -(dCdu)^(-1)dCdm
dCdu = self.getA(m)
s = Div * ( self.MfMuI.T * ( P.T*v ) )
m1 = sp.linalg.interface.aslinearoperator(Utils.sdiag(1/(dCdu.T).diagonal()))
sol, info = sp.linalg.bicgstab(dCdu.T, s, tol=1e-8, maxiter=1000, M=m1)
if info > 0:
raise Exception ("Iterative solver did not work well")
# dCdm_A = Div * ( Utils.sdiag( Div.T * u )* dMfMuI *dmudm )
dCdm_Atsol = ( dMfMuI.T*( Utils.sdiag( Div.T * u ) * (Div.T * dmudm)) ) * sol
# dCdm_RHS1 = Div * (Utils.sdiag( self.MfMu0*B0 ) * dMfMuI)
dCdm_RHS1tsol = (dMfMuI.T*( Utils.sdiag( self.MfMu0*B0 ) ) * Div.T * dmudm) * sol
# temp1 = (Dface*(self._Pout.T*self.Bbc_const*self.Bbc))
# dCdm_RHS2v = (Utils.sdiag(vol)*temp1)*np.inner(vol, v)
temp1sol = ( Dface.T*( Utils.sdiag(vol)*sol ) )
temp2 = self.Bbc_const*(self._Pout.T*self.Bbc).T
dCdm_RHS2tsol = vol*np.inner(temp2, temp1sol)
dCdm_RHStsol = dCdm_RHS1tsol - dCdm_RHS2tsol
# dCdm_RHSv = dCdm_RHS1*(dmudm*v) + dCdm_RHS2v
# dCdm_v = dCdm_A*v - dCdm_RHSv
Ctv = dCdm_Atsol - dCdm_RHStsol
# B = self.MfMuI*self.MfMu0*B0-B0-self.MfMuI*self._Div.T*u
# dBdm = d\mudm*dBd\mu
# dPBdm^T*v = Atemp^T*P^T*v - Btemp^T*P^T*v - Ctv
Atemp = Utils.sdiag(self.MfMu0*B0)*(dMfMuI * (dmudm))
Btemp = Utils.sdiag(Div.T*u)*(dMfMuI* (dmudm))
Jtv = Atemp.T*(P.T*v) - Btemp.T*(P.T*v) - Ctv
return Utils.mkvc(Jtv)
@@ -218,7 +332,12 @@ if __name__ == '__main__':
# mu = (1.+chi)*mu_0
data = BaseMag.BaseMagData()
data.setBackgroundField(x=1., y=1., z=0.)
Inc = 90.
Dec = 0.
Btot = 51000
data.setBackgroundField(Inc, Dec, Btot)
xr = np.linspace(-300, 300, 41)
yr = np.linspace(-300, 300, 41)
X, Y = np.meshgrid(xr, yr)
@@ -230,30 +349,14 @@ if __name__ == '__main__':
prob.pair(data)
B = prob.fields(chi)
# mesh.plotSlice(B, 'F', view='vec', showIt=True)
dpred = data.dpred(chi)
fig = plt.figure( figsize = (8,5) )
ax = plt.subplot(111)
dat = plt.imshow(np.reshape(dpred, (xr.size, yr.size), order='F'), extent=[min(xr), max(xr), min(yr), max(yr)])
plt.colorbar(dat, ax = ax)
plt.show()
dpred = data.dpred(chi, u=B)
# ##################
# # Test J
# ##################
# d_chi = 0.8*chi #np.random.rand(mesh.nCz)
# d_sph_ind = spheremodel(mesh, 0., 0., -100., 50)
# d_chi[d_sph_ind] = 0.02
# from SimPEG.Tests import checkDerivative
# derChk = lambda m: [prob.data.dpred(m), lambda mx: -prob.Jvec(chi, mx)]
# print '\n'
# passed = checkDerivative(derChk, chi, plotIt=False, dx=d_chi, num=2)
# # plt.pcolor(X, Y, dpred.reshape(X.shape, order='F'))
# # plt.show()
simpegPF/Tests/test_forward_PFproblem.py
+12 -5
View File
@@ -4,7 +4,7 @@ import matplotlib.pyplot as plt
import simpegPF as PF
class MagProblemTests(unittest.TestCase):
class MagFwdProblemTests(unittest.TestCase):
def setUp(self):
@@ -29,7 +29,13 @@ class MagProblemTests(unittest.TestCase):
def test_anal_forward(self):
data = PF.BaseMag.BaseMagData()
data.setBackgroundField(x=1., y=1., z=0.)
Inc = 90.
Dec = 0.
Btot = 51000
b0 = PF.MagAnalytics.IDTtoxyz(Inc, Dec, Btot)
data.setBackgroundField(Inc, Dec, Btot)
xr = np.linspace(-300, 300, 41)
yr = np.linspace(-300, 300, 41)
X, Y = np.meshgrid(xr, yr)
@@ -38,9 +44,10 @@ class MagProblemTests(unittest.TestCase):
data.rxLoc = rxLoc
self.prob.pair(data)
B = self.prob.fields(self.chi)
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,np.array([1.,1.,0.]),'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])
@@ -50,6 +57,6 @@ class MagProblemTests(unittest.TestCase):
else:
print "Anaytic test is passed"
pass
if __name__ == '__main__':
unittest.main()
simpegPF/Tests/test_sensitivity_PFproblem.py
+316
View File
@@ -0,0 +1,316 @@
import unittest
from SimPEG import *
from simpegPF import BaseMag
import matplotlib.pyplot as plt
import simpegPF as PF
from scipy.constants import mu_0
class MagSensProblemTests(unittest.TestCase):
def setUp(self):
hxind = ((5,25,1.3),(21, 25.),(5,25,1.3))
hyind = ((5,25,1.3),(21, 25.),(5,25,1.3))
hzind = ((5,25,1.3),(20, 25.),(5,25,1.3))
hx, hy, hz = Utils.meshTensors(hxind, hyind, hzind)
M = Mesh.TensorMesh([hx, hy, hz], [-hx.sum()/2,-hy.sum()/2,-hz.sum()/2])
chibkg = 0.001
chiblk = 0.01
chi = np.ones(M.nC)*chibkg
Inc = 90.
Dec = 0.
Btot = 51000
b0 = PF.MagAnalytics.IDTtoxyz(Inc, Dec, Btot)
sph_ind = PF.MagAnalytics.spheremodel(M, 0., 0., 0., 100)
chi[sph_ind] = chiblk
model = PF.BaseMag.BaseMagModel(M)
data = BaseMag.BaseMagData()
data.setBackgroundField(Inc, Dec, Btot)
xr = np.linspace(-300, 300, 41)
yr = np.linspace(-300, 300, 41)
X, Y = np.meshgrid(xr, yr)
Z = np.ones((xr.size, yr.size))*150
rxLoc = np.c_[Utils.mkvc(X), Utils.mkvc(Y), Utils.mkvc(Z)]
data.rxLoc = rxLoc
prob = PF.Magnetics.MagneticsDiffSecondary(M, model)
prob.pair(data)
dpre = data.dpred(chi)
fields = prob.fields(chi)
self.u = fields['u']
self.B = fields['B']
self.data = data
self.model = model
self.prob = prob
self.M = M
self.chi = chi
def test_mass(self):
print '\n >>Derivative for MfMuI works.'
mu = self.model.transform(self.chi, asMu=True)
def MfmuI(mu):
chi = mu/mu_0-1
self.prob.makeMassMatrices(chi)
vol = self.prob.mesh.vol
aveF2CC = self.prob.mesh.aveF2CC
MfMuI = self.prob.MfMuI.diagonal()
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)
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
vol = self.prob.mesh.vol
aveF2CC = self.prob.mesh.aveF2CC
def Cm_A(chi):
dmudm = self.model.transformDeriv(chi, asMu=True)
u = self.u
# chi = mu/mu_0-1
self.prob.makeMassMatrices(chi)
mu = self.model.transform(self.chi, asMu=True)
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)
Cm_A = A*u
return Cm_A
def dCdm_A(chi, v):
dmudm = self.model.transformDeriv(chi, asMu=True)
u = self.u
self.prob.makeMassMatrices(chi)
mu = self.model.transform(self.chi, asMu=True)
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)
Cm_A = A*u
dCdm_A = Div * ( Utils.sdiag( Div.T * u )* dMfMuI *dmudm )
return dCdm_A*v
d_chi = self.chi*0.8
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)
self.assertTrue(passed)
def test_dCdmu_RHS(self):
print '\n >>Derivative for Cm_RHS.'
u = self.u
Div = self.prob._Div
mu = self.model.transform(self.chi, asMu=True)
vol = self.prob.mesh.vol
Mc = Utils.sdiag(vol)
aveF2CC = self.prob.mesh.aveF2CC
B0 = self.prob.getB0()
Dface = self.prob.mesh.faceDiv
def Cm_RHS(chi):
self.prob.makeMassMatrices(chi)
dmudm = self.model.transformDeriv(chi, asMu=True)
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
return RHS
def dCdm_RHS(chi, v):
self.prob.makeMassMatrices(chi)
dmudm = self.model.transformDeriv(chi, asMu=True)
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)
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)
def test_dudm(self):
print ">> Derivative test for dudm"
u = self.u
Div = self.prob._Div
mu = self.model.transform(self.chi, asMu=True)
vol = self.prob.mesh.vol
Mc = Utils.sdiag(vol)
aveF2CC = self.prob.mesh.aveF2CC
B0 = self.prob.getB0()
Dface = self.prob.mesh.faceDiv
def ufun(chi):
u = self.prob.fields(chi)['u']
return u
def dudm(chi, v):
chi = mu/mu_0-1
self.prob.makeMassMatrices(chi)
u = self.u
dmudm = self.model.transformDeriv(chi, asMu=True)
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)
dCdu = self.prob.getA(chi)
dCdm_A = Div * ( Utils.sdiag( Div.T * u )* dMfMuI *dmudm )
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_v = dCdm_A*v - dCdm_RHSv
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
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
derChk = lambda m: [ufun(m), lambda mx: dudm(self.chi, mx)]
# 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_dBdm(self):
print ">> Derivative test for dBdm"
u = self.u
Div = self.prob._Div
mu = self.model.transform(self.chi, asMu=True)
vol = self.prob.mesh.vol
Mc = Utils.sdiag(vol)
aveF2CC = self.prob.mesh.aveF2CC
B0 = self.prob.getB0()
Dface = self.prob.mesh.faceDiv
def Bfun(chi):
B = self.prob.fields(chi)['B']
return B
def dBdm(chi, v):
chi = mu/mu_0-1
self.prob.makeMassMatrices(chi)
u = self.u
dmudm = self.model.transformDeriv(chi, asMu=True)
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)
dCdu = self.prob.getA(chi)
dCdm_A = Div * ( Utils.sdiag( Div.T * u )* dMfMuI *dmudm )
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_v = dCdm_A*v - dCdm_RHSv
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
dBdmv = ( Utils.sdiag(self.prob.MfMu0*B0)*(dMfMuI * (dmudm*v)) \
- Utils.sdiag(Div.T*u)*(dMfMuI* (dmudm*v)) \
- 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
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)
self.assertTrue(passed)
def test_Jvec(self):
print ">> Derivative test for Jvec"
mu = self.model.transform(self.chi, asMu=True)
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
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 .. --;
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)
dobs = self.data.dpred(self.chi)
def misfit (m, dobs):
dpre = self.data.dpred(m)
misfit = 0.5*np.linalg.norm(dpre-dobs)**2
residual = dpre-dobs
dmisfit = self.prob.Jtvec(self.chi, residual)
return misfit, dmisfit
# 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)
if __name__ == '__main__':
unittest.main()
simpegPF/notebooks/Jacobian.ipynb
+101 -99
View File
@@ -28,31 +28,30 @@
]
}
],
"prompt_number": 3
"prompt_number": 15
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"hxind = ((5,25,1.3),(21, 25.),(5,25,1.3))\n",
"hyind = ((5,25,1.3),(21, 25.),(5,25,1.3))\n",
"hzind = ((5,25,1.3),(20, 25.),(5,25,1.3))\n",
"hx, hy, hz = Utils.meshTensors(hxind, hyind, hzind)\n",
"M3 = Mesh.TensorMesh([hx, hy, hz], [-sum(hx)/2,-sum(hy)/2,-sum(hz)/2])"
],
"input": [],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 4
"prompt_number": 16
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import matplotlib.pyplot as plt\n",
"hxind = ((5,25,1.3),(41, 12.5),(5,25,1.3))\n",
"hyind = ((5,25,1.3),(41, 12.5),(5,25,1.3))\n",
"hzind = ((5,25,1.3),(40, 12.5),(5,25,1.3))\n",
"# hxind = ((5,25,1.3),(41, 12.5),(5,25,1.3))\n",
"# hyind = ((5,25,1.3),(41, 12.5),(5,25,1.3))\n",
"# hzind = ((5,25,1.3),(40, 12.5),(5,25,1.3))\n",
"\n",
"hxind = ((5,25,1.3),(21, 25.),(5,25,1.3))\n",
"hyind = ((5,25,1.3),(21, 25.),(5,25,1.3))\n",
"hzind = ((5,25,1.3),(20, 25.),(5,25,1.3))\n",
"\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",
@@ -80,50 +79,22 @@
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 5
"prompt_number": 50
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"phi, B = prob.fields(chi)\n",
"fields = prob.fields(chi)\n",
"u = fields['u']\n",
"B = fields['B']\n",
"# mesh.plotSlice(B, 'F', view='vec', showIt=True)\n",
"dpred = data.dpred(chi, u=B)"
"dpred = data.dpred(chi, fields)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 4
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"test = {'B': B, 'u': phi}"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 5
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"print test['B']"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"[ 0.001 0.00032989 0.00039923 ..., 0. 0. 0. ]\n"
]
}
],
"prompt_number": 7
"prompt_number": 51
},
{
"cell_type": "markdown",
@@ -147,11 +118,11 @@
"output_type": "stream",
"stream": "stdout",
"text": [
"6.99232804893\n"
"9.55511263546\n"
]
}
],
"prompt_number": 6
"prompt_number": 52
},
{
"cell_type": "code",
@@ -165,21 +136,21 @@
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 7,
"prompt_number": 53,
"text": [
"[<matplotlib.lines.Line2D at 0x301f910>]"
"[<matplotlib.lines.Line2D at 0x3363350>]"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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"png": 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truncated
"text": [
"<matplotlib.figure.Figure at 0x2d7f0d0>"
"<matplotlib.figure.Figure at 0x1fa10d0>"
]
}
],
"prompt_number": 7
"prompt_number": 53
},
{
"cell_type": "code",
@@ -201,7 +172,7 @@
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 8
"prompt_number": 54
},
{
"cell_type": "code",
@@ -221,7 +192,7 @@
"==================== checkDerivative ====================\n",
"iter\th\t\t|J0-Jt|\t\t|J0+h*dJ'*dx-Jt|\tOrder\n",
"---------------------------------------------------------\n",
"0\t1.00e-01\t7.240e-08\t\t1.904e-22\t\tnan"
"0\t1.00e-01\t4.299e-09\t\t1.152e-23\t\tnan"
]
},
{
@@ -229,7 +200,7 @@
"stream": "stdout",
"text": [
"\n",
"1\t1.00e-02\t7.240e-09\t\t1.009e-22\t\t0.276"
"1\t1.00e-02\t4.299e-10\t\t7.723e-24\t\t0.174"
]
},
{
@@ -237,7 +208,7 @@
"stream": "stdout",
"text": [
"\n",
"2\t1.00e-03\t7.240e-10\t\t2.166e-22\t\t-0.332"
"2\t1.00e-03\t4.299e-11\t\t1.170e-23\t\t-0.180"
]
},
{
@@ -245,7 +216,7 @@
"stream": "stdout",
"text": [
"\n",
"3\t1.00e-04\t7.240e-11\t\t9.316e-23\t\t0.366"
"3\t1.00e-04\t4.299e-12\t\t8.749e-24\t\t0.126"
]
},
{
@@ -253,7 +224,7 @@
"stream": "stdout",
"text": [
"\n",
"4\t1.00e-05\t7.240e-12\t\t2.209e-22\t\t-0.375"
"4\t1.00e-05\t4.299e-13\t\t1.107e-23\t\t-0.102"
]
},
{
@@ -262,35 +233,72 @@
"text": [
"\n",
"========================= PASS! =========================\n",
"You are awesome.\n",
"Once upon a time, a happy little test passed.\n",
"\n"
]
},
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 9,
"prompt_number": 55,
"text": [
"True"
]
}
],
"prompt_number": 9
"prompt_number": 55
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def derBbc(chi):\n",
" Bbc, const = CongruousMagBC(mesh, np.array([1., 0., 0.]), chi)\n",
" bc = Utils.sdiag(prob.mesh.vol)*prob.mesh.faceDiv*prob._Pout.T*Bbc \n",
" dBbc = lambda x: Utils.sdiag(prob.mesh.vol)*prob.mesh.faceDiv*prob._Pout.T*const*Bbc*(np.inner(prob.mesh.vol, x))\n",
" Bbc, const = CongruousMagBC(mesh, np.array([1., 1., 0.]), chi)\n",
" bc = Utils.sdiag(prob.mesh.vol)*prob.mesh.faceDiv*prob._Pout.T*Bbc \n",
" print const, np.linalg.norm(Bbc)\n",
" dBbc = lambda x: (Utils.sdiag(prob.mesh.vol)*(prob.mesh.faceDiv*prob._Pout.T*const*Bbc))*(np.inner(prob.mesh.vol, x)) \n",
" return bc, dBbc"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 8
"prompt_number": 56
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"a, b = derBbc(chi)\n",
"print np.linalg.norm(a), np.linalg.norm(b(chi))\n",
"print np.linalg.norm(chi)\n",
"print np.array([1., 1., 0.])\n",
"print mesh"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"7.65830184557e-07 0.0659506783728\n",
"55.718105908 55.6914561973\n",
"1.6089045963\n",
"[ 1. 1. 0.]\n",
" ---- 3-D TensorMesh ---- \n",
" x0: -488.58\n",
" y0: -488.58\n",
" z0: -476.08\n",
" nCx: 31\n",
" nCy: 31\n",
" nCz: 30\n",
" hx: 71.40, 54.93, 42.25, 32.50, 23*25.00, 32.50, 42.25, 54.93, 71.40\n",
" hy: 71.40, 54.93, 42.25, 32.50, 23*25.00, 32.50, 42.25, 54.93, 71.40\n",
" hz: 71.40, 54.93, 42.25, 32.50, 22*25.00, 32.50, 42.25, 54.93, 71.40\n"
]
}
],
"prompt_number": 57
},
{
"cell_type": "code",
@@ -310,85 +318,79 @@
"==================== checkDerivative ====================\n",
"iter\th\t\t|J0-Jt|\t\t|J0+h*dJ'*dx-Jt|\tOrder\n",
"---------------------------------------------------------\n",
"0\t1.00e-01\t2.212e+00\t\t8.604e-05\t\tnan"
"7.65830184557e-07"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"1\t1.00e-02\t2.212e-01\t\t8.604e-07\t\t2.000"
" 0.0659506783728\n",
"7.0907489096e-07"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"2\t1.00e-03\t2.212e-02\t\t8.574e-09\t\t2.001"
" 0.0712240073538\n",
"0\t1.00e-01\t4.455e+00\t\t1.705e-04\t\tnan\n",
"7.59749260143e-07"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"3\t1.00e-04\t2.212e-03\t\t9.857e-11\t\t1.939"
" 0.0664780294308\n",
"1\t1.00e-02\t4.455e-01\t\t1.705e-06\t\t2.000\n",
"7.65217717349e-07"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"4\t1.00e-05\t2.212e-04\t\t1.424e-11\t\t0.840"
" 0.0660034136602\n",
"2\t1.00e-03\t4.455e-02\t\t1.706e-08\t\t2.000\n",
"7.65768893742e-07"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
" 0.0659559519034\n",
"3\t1.00e-04\t4.455e-03\t\t1.749e-10\t\t1.989\n",
"7.65824055034e-07"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
" 0.0659512057259\n",
"4\t1.00e-05\t4.455e-04\t\t2.506e-12\t\t1.844\n",
"========================= PASS! =========================\n",
"Awesome, Seogi, just awesome.\n",
"The test be workin!\n",
"\n"
]
},
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 9,
"prompt_number": 58,
"text": [
"True"
]
}
],
"prompt_number": 9
"prompt_number": 58
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"##################\n",
"# Test J\n",
"##################\n",
"\n",
"d_chi = 0.8*chi #np.random.rand(mesh.nCz)\n",
"d_sph_ind = spheremodel(mesh, 0., 0., -100., 50)\n",
"d_chi[d_sph_ind] = 0.02\n",
"\n",
"from SimPEG.Tests import checkDerivative\n",
"\n",
"derChk = lambda m: [prob.data.dpred(m), lambda mx: -prob.Jvec(chi, mx)]\n",
"print '\\n'\n",
"passed = checkDerivative(derChk, chi, plotIt=False, dx=d_chi, num=2)\n",
"\n",
"\n",
"# plt.pcolor(X, Y, dpred.reshape(X.shape, order='F'))\n",
"\n",
"# plt.show()"
],
"input": [],
"language": "python",
"metadata": {},
"outputs": []