def MeSigmaIDeriv(self, u, v, adjoint=False):
"""
Derivative of :code:`MeSigmaI` with respect to the model
"""
if self.sigmaMap is None:
return Utils.Zero()
if len(self.sigma.shape) > 1:
if self.sigma.shape[1] > self.mesh.dim:
raise NotImplementedError(
"Full anisotropy is not implemented for MeSigmaIDeriv.")
dMeSigmaI_dI = -self.MeSigmaI**2
if self.storeInnerProduct:
if adjoint:
return self.MeSigmaDerivMat.T * (Utils.sdiag(u) *
(dMeSigmaI_dI.T * v))
else:
return dMeSigmaI_dI * Utils.sdiag(u) * (self.MeSigmaDerivMat *
v)
else:
dMe_dsig = self.mesh.getEdgeInnerProductDeriv(self.sigma)(u)
if adjoint:
return self.sigmaDeriv.T * (dMe_dsig.T * (dMeSigmaI_dI.T * v))
else:
return dMeSigmaI_dI * (dMe_dsig * (self.sigmaDeriv * v))
def edgeCurl(self):
"""The edgeCurl property."""
if self.nCy > 1:
raise NotImplementedError('Edge curl not yet implemented for '
'nCy > 1')
if getattr(self, '_edgeCurl', None) is None:
# 1D Difference matricies
dr = sp.spdiags((np.ones((self.nCx + 1, 1)) * [-1, 1]).T, [-1, 0],
self.nCx,
self.nCx,
format="csr")
dz = sp.spdiags((np.ones((self.nCz + 1, 1)) * [-1, 1]).T, [0, 1],
self.nCz,
self.nCz + 1,
format="csr")
# 2D Difference matricies
Dr = sp.kron(sp.identity(self.nNz), dr)
Dz = -sp.kron(dz, sp.identity(self.nCx))
A = self.area
E = self.edge
# Edge curl operator
self._edgeCurl = (Utils.sdiag(1 / A) * sp.vstack(
(Dz, Dr)) * Utils.sdiag(E))
return self._edgeCurl
def solve_2D_J(rho1, rho2, h, A, B):
ex, ez, V = solve_2D_E(rho1, rho2, h, A, B)
sigma = 1. / rho2 * np.ones(mesh.nC)
sigma[mesh.gridCC[:, 1] >= -h] = 1. / rho1 # since the model is 2D
return Utils.sdiag(sigma) * ex, Utils.sdiag(sigma) * ez, V
def MccRhoiDeriv(self, u, v, adjoint=False):
"""
Derivative of :code:`MccRhoi` with respect to the model.
"""
if self.rhoMap is None:
return Utils.Zero()
if len(self.rho.shape) > 1:
if self.rho.shape[1] > self.mesh.dim:
raise NotImplementedError(
"Full anisotropy is not implemented for MccRhoiDeriv.")
if self.storeInnerProduct:
if adjoint:
return self.MccRhoiDerivMat.T * (Utils.sdiag(u) * v)
else:
return Utils.sdiag(u) * (self.MccRhoiDerivMat * v)
else:
vol = self.mesh.vol
rho = self.rho
if adjoint:
return self.rhoDeriv.T * (Utils.sdiag(u * vol *
(-1. / rho**2)) * v)
else:
return (Utils.sdiag(u * vol *
(-1. / rho**2))) * (self.rhoDeriv * v)
def MeSigmaDeriv(self, u, v, adjoint=False):
"""
Derivative of MeSigma with respect to the model times a vector (u)
"""
if self.storeInnerProduct:
if adjoint:
return self.MeSigmaDerivMat.T * (Utils.sdiag(u)*v)
else:
return Utils.sdiag(u)*(self.MeSigmaDerivMat * v)
else:
if self.storeJ:
dsigma_dlogsigma = Utils.sdiag(self.sigma)*self.actMap.P
else:
dsigma_dlogsigma = Utils.sdiag(self.sigma)
if adjoint:
return (
dsigma_dlogsigma.T * (
self.mesh.getEdgeInnerProductDeriv(self.sigma)(u).T * v
)
)
else:
return (
self.mesh.getEdgeInnerProductDeriv(self.sigma)(u) *
(dsigma_dlogsigma * v)
)
def getResidual(self, m, hn, h, dt, bc, return_g=True):
"""
Where h is the proposed value for the next time iterate (h_{n+1})
"""
DIV = self.mesh.faceDiv
GRAD = self.mesh.cellGrad
BC = self.mesh.cellGradBC
AV = self.mesh.aveF2CC.T
Dz = self.Dz
T = self.modelMap.theta(h, m)
dT = self.modelMap.thetaDerivU(h, m)
Tn = self.modelMap.theta(hn, m)
K = self.modelMap.k(h, m)
dK = self.modelMap.kDerivU(h, m)
aveK = 1. / (AV * (1. / K))
RHS = DIV * Utils.sdiag(aveK) * (GRAD * h + BC * bc) + Dz * aveK
if self.method == 'mixed':
r = (T - Tn) / dt - RHS
elif self.method == 'head':
r = dT * (h - hn) / dt - RHS
if not return_g:
return r
J = dT / dt - DIV * Utils.sdiag(aveK) * GRAD
if self.doNewton:
DDharmAve = Utils.sdiag(aveK**2) * AV * Utils.sdiag(K**(-2)) * dK
J = J - DIV * Utils.sdiag(GRAD * h +
BC * bc) * DDharmAve - Dz * DDharmAve
return r, J
def test_updateMultipliers(self):
nP = 10
m = np.random.rand(nP)
W1 = Utils.sdiag(np.random.rand(nP))
W2 = Utils.sdiag(np.random.rand(nP))
phi1 = ObjectiveFunction.L2ObjectiveFunction(W=W1)
phi2 = ObjectiveFunction.L2ObjectiveFunction(W=W2)
phi = phi1 + phi2
self.assertTrue(phi(m) == phi1(m) + phi2(m))
phi.multipliers[0] = Utils.Zero()
self.assertTrue(phi(m) == phi2(m))
phi.multipliers[0] = 1.
phi.multipliers[1] = Utils.Zero()
self.assertTrue(len(phi.objfcts) == 2)
self.assertTrue(len(phi.multipliers) == 2)
self.assertTrue(len(phi) == 2)
self.assertTrue(phi(m) == phi1(m))
def MfRhoIDeriv(self, u, v, adjoint=False):
"""
Derivative of :code:`MfRhoI` with respect to the model.
"""
dMfRhoI_dI = -self.MfRhoI**2
if self.storeInnerProduct:
if adjoint:
return (
self.MfRhoDerivMat.T * (
Utils.sdiag(u) * (dMfRhoI_dI.T * v)
)
)
else:
return dMfRhoI_dI * (Utils.sdiag(u) * (self.MfRhoDerivMat*v))
else:
if self.storeJ:
drho_dlogrho = Utils.sdiag(self.rho)*self.actMap.P
else:
drho_dlogrho = Utils.sdiag(self.rho)
dMf_drho = self.mesh.getFaceInnerProductDeriv(self.rho)(u)
if adjoint:
return drho_dlogrho.T * (dMf_drho.T * (dMfRhoI_dI.T*v))
else:
return dMfRhoI_dI * (dMf_drho * (drho_dlogrho*v))
def test_updateMultipliers(self):
nP = 10
m = np.random.rand(nP)
W1 = Utils.sdiag(np.random.rand(nP))
W2 = Utils.sdiag(np.random.rand(nP))
phi1 = ObjectiveFunction.L2ObjectiveFunction(W=W1)
phi2 = ObjectiveFunction.L2ObjectiveFunction(W=W2)
phi = phi1 + phi2
self.assertTrue(phi(m) == phi1(m) + phi2(m))
phi.multipliers[0] = Utils.Zero()
self.assertTrue(phi(m) == phi2(m))
phi.multipliers[0] = 1.
phi.multipliers[1] = Utils.Zero()
self.assertTrue(len(phi.objfcts) == 2)
self.assertTrue(len(phi.multipliers) == 2)
self.assertTrue(len(phi) == 2)
self.assertTrue(phi(m) == phi1(m))
def evalDeriv(self, f, freq, P0, df_dm_v=None, v=None, adjoint=False):
if adjoint:
if self.component == "real":
PTvr = (P0.T*v).astype(complex)
dZr_dfT_v = Utils.sdiag((1./(f**2)))*PTvr
return dZr_dfT_v
elif self.component == "imag":
PTvi = P0.T*v*-1j
dZi_dfT_v = Utils.sdiag((1./(f**2)))*PTvi
return dZi_dfT_v
elif self.component == "both":
PTvr = (P0.T*np.r_[v[0]]).astype(complex)
PTvi = P0.T*np.r_[v[1]]*-1j
dZr_dfT_v = Utils.sdiag((1./(f**2)))*PTvr
dZi_dfT_v = Utils.sdiag((1./(f**2)))*PTvi
return dZr_dfT_v + dZi_dfT_v
else:
raise NotImplementedError('must be real, imag or both')
else:
dZd_dm_v = P0 * (Utils.sdiag(1./(f**2)) * df_dm_v)
if self.component == "real":
return dZd_dm_v.real
elif self.component == "imag":
return dZd_dm_v.imag
elif self.component == "both":
return np.r_[dZd_dm_v.real, dZd_dm_v.imag]
else:
raise NotImplementedError('must be real, imag or both')
def evalDeriv(self, f, freq, P0, df_dm_v=None, v=None, adjoint=False):
if adjoint:
if self.component == "real":
PTvr = (P0.T * v).astype(complex)
dZr_dfT_v = Utils.sdiag((1. / (f**2))) * PTvr
return dZr_dfT_v
elif self.component == "imag":
PTvi = P0.T * v * -1j
dZi_dfT_v = Utils.sdiag((1. / (f**2))) * PTvi
return dZi_dfT_v
elif self.component == "both":
PTvr = (P0.T * np.r_[v[0]]).astype(complex)
PTvi = P0.T * np.r_[v[1]] * -1j
dZr_dfT_v = Utils.sdiag((1. / (f**2))) * PTvr
dZi_dfT_v = Utils.sdiag((1. / (f**2))) * PTvi
return dZr_dfT_v + dZi_dfT_v
else:
raise NotImplementedError('must be real, imag or both')
else:
dZd_dm_v = P0 * (Utils.sdiag(1. / (f**2)) * df_dm_v)
if self.component == "real":
return dZd_dm_v.real
elif self.component == "imag":
return dZd_dm_v.imag
elif self.component == "both":
return np.r_[dZd_dm_v.real, dZd_dm_v.imag]
else:
raise NotImplementedError('must be real, imag or both')
def _fastInnerProduct(self, projType, prop=None, invProp=False, invMat=False):
"""
Fast version of getFaceInnerProduct.
This does not handle the case of a full tensor prop.
:param numpy.array prop: material property (tensor properties are possible) at each cell center (nC, (1, 3, or 6))
:param str projType: 'E' or 'F'
:param bool returnP: returns the projection matrices
:param bool invProp: inverts the material property
:param bool invMat: inverts the matrix
:rtype: scipy.sparse.csr_matrix
:return: M, the inner product matrix (nF, nF)
"""
assert projType in ['F', 'E'], ("projType must be 'F' for faces or 'E'"
" for edges")
if prop is None:
prop = np.ones(self.nC)
if invProp:
prop = 1./prop
if Utils.isScalar(prop):
prop = prop*np.ones(self.nC)
# number of elements we are averaging (equals dim for regular
# meshes, but for cyl, where we use symmetry, it is 1 for edge
# variables and 2 for face variables)
if self._meshType == 'CYL':
n_elements = np.sum(getattr(self, 'vn'+projType).nonzero())
else:
n_elements = self.dim
# Isotropic? or anisotropic?
if prop.size == self.nC:
Av = getattr(self, 'ave'+projType+'2CC')
Vprop = self.vol * Utils.mkvc(prop)
M = n_elements * Utils.sdiag(Av.T * Vprop)
elif prop.size == self.nC*self.dim:
Av = getattr(self, 'ave'+projType+'2CCV')
# if cyl, then only certain components are relevant due to symmetry
# for faces, x, z matters, for edges, y (which is theta) matters
if self._meshType == 'CYL':
if projType == 'E':
prop = prop[:, 1] # this is the action of a projection mat
elif projType == 'F':
prop = prop[:, [0, 2]]
V = sp.kron(sp.identity(n_elements), Utils.sdiag(self.vol))
M = Utils.sdiag(Av.T * V * Utils.mkvc(prop))
else:
return None
if invMat:
return Utils.sdInv(M)
else:
return M
def MnSigmaDeriv(self, u):
"""
Derivative of MnSigma with respect to the model
"""
sigma = self.curModel.sigma
sigmaderiv = self.curModel.sigmaDeriv
vol = self.mesh.vol
return Utils.sdiag(u)*self.mesh.aveN2CC.T*Utils.sdiag(vol) * self.curModel.sigmaDeriv
def _fastInnerProduct(self, projType, prop=None, invProp=False, invMat=False):
"""
Fast version of getFaceInnerProduct.
This does not handle the case of a full tensor prop.
:param numpy.array prop: material property (tensor properties are possible) at each cell center (nC, (1, 3, or 6))
:param str projType: 'E' or 'F'
:param bool returnP: returns the projection matrices
:param bool invProp: inverts the material property
:param bool invMat: inverts the matrix
:rtype: scipy.sparse.csr_matrix
:return: M, the inner product matrix (nF, nF)
"""
assert projType in ["F", "E"], "projType must be 'F' for faces or 'E'" " for edges"
if prop is None:
prop = np.ones(self.nC)
if invProp:
prop = 1.0 / prop
if Utils.isScalar(prop):
prop = prop * np.ones(self.nC)
# number of elements we are averaging (equals dim for regular
# meshes, but for cyl, where we use symmetry, it is 1 for edge
# variables and 2 for face variables)
if self._meshType == "CYL":
n_elements = np.sum(getattr(self, "vn" + projType).nonzero())
else:
n_elements = self.dim
# Isotropic? or anisotropic?
if prop.size == self.nC:
Av = getattr(self, "ave" + projType + "2CC")
Vprop = self.vol * Utils.mkvc(prop)
M = n_elements * Utils.sdiag(Av.T * Vprop)
elif prop.size == self.nC * self.dim:
Av = getattr(self, "ave" + projType + "2CCV")
# if cyl, then only certain components are relevant due to symmetry
# for faces, x, z matters, for edges, y (which is theta) matters
if self._meshType == "CYL":
if projType == "E":
prop = prop[:, 1] # this is the action of a projection mat
elif projType == "F":
prop = prop[:, [0, 2]]
V = sp.kron(sp.identity(n_elements), Utils.sdiag(self.vol))
M = Utils.sdiag(Av.T * V * Utils.mkvc(prop))
else:
return None
if invMat:
return Utils.sdInv(M)
else:
return M
def diagsJacobian(self, m, hn, hn1, dt, bc):
"""Diagonals and rhs of the jacobian system
The matrix that we are computing has the form::
.- -. .- -. .- -.
| Adiag | | h1 | | b1 |
| Asub Adiag | | h2 | | b2 |
| Asub Adiag | | h3 | = | b3 |
| ... ... | | .. | | .. |
| Asub Adiag | | hn | | bn |
'- -' '- -' '- -'
"""
if m is not None:
self.model = m
DIV = self.mesh.faceDiv
GRAD = self.mesh.cellGrad
BC = self.mesh.cellGradBC
AV = self.mesh.aveF2CC.T
Dz = self.Dz
dT = self.water_retention.derivU(hn)
dT1 = self.water_retention.derivU(hn1)
dTm = self.water_retention.derivM(hn)
dTm1 = self.water_retention.derivM(hn1)
K1 = self.hydraulic_conductivity(hn1)
dK1 = self.hydraulic_conductivity.derivU(hn1)
dKm1 = self.hydraulic_conductivity.derivM(hn1)
# Compute part of the derivative of:
#
# DIV*diag(GRAD*hn1+BC*bc)*(AV*(1.0/K))^-1
DdiagGh1 = DIV*Utils.sdiag(GRAD*hn1+BC*bc)
diagAVk2_AVdiagK2 = (
Utils.sdiag((AV*(1./K1))**(-2)) *
AV*Utils.sdiag(K1**(-2))
)
Asub = (-1.0/dt)*dT
Adiag = (
(1.0/dt)*dT1 -
DdiagGh1*diagAVk2_AVdiagK2*dK1 -
DIV*Utils.sdiag(1./(AV*(1./K1)))*GRAD -
Dz*diagAVk2_AVdiagK2*dK1
)
B = (
DdiagGh1*diagAVk2_AVdiagK2*dKm1 +
Dz*diagAVk2_AVdiagK2*dKm1 +
(1.0/dt)*(dTm - dTm1)
)
return Asub, Adiag, B
def MnSigmaDeriv(self, u):
"""
Derivative of MnSigma with respect to the model
"""
sigma = self.curModel.sigma
sigmaderiv = self.curModel.sigmaDeriv
vol = self.mesh.vol
return (Utils.sdiag(u) * self.mesh.aveN2CC.T * Utils.sdiag(vol) *
self.curModel.sigmaDeriv)
def BiotSavartFun(self, rxlocs, component='z'):
"""
Compute systematrix G using Biot-Savart Law
G = np.vstack((G1,G2,G3..,Gnpts)
.. math::
"""
if rxlocs.ndim == 1:
npts = 1
else:
npts = rxlocs.shape[0]
e = np.ones((self.mesh.nC, 1))
o = np.zeros((self.mesh.nC, 1))
const = mu_0/4/np.pi
if self.mesh._meshType == "CYL":
G = np.zeros((npts, self.mesh.nC))
else:
G = np.zeros((npts, self.mesh.nC*3))
# TODO: this works fine, but potential improvement by analyticially
# evaluating integration.
for i in range(npts):
if npts == 1:
r_rx = np.repeat(
Utils.mkvc(rxlocs).reshape([1, -1]), self.mesh.nC, axis = 0
)
else:
r_rx = np.repeat(
rxlocs[i, :].reshape([1, -1]), self.mesh.nC, axis = 0
)
r_CC = self.mesh.gridCC
r = r_rx-r_CC
r_abs = np.sqrt((r**2).sum(axis=1))
rxind = r_abs == 0.
# r_abs[rxind] = self.mesh.vol.min()**(1./3.)*0.5
r_abs[rxind] = 1e20
Sx = const*Utils.sdiag(self.mesh.vol*r[:, 0]/r_abs**3)
Sy = const*Utils.sdiag(self.mesh.vol*r[:, 1]/r_abs**3)
Sz = const*Utils.sdiag(self.mesh.vol*r[:, 2]/r_abs**3)
if self.mesh._meshType == "CYL":
if component == 'x':
G_temp = np.hstack((e.T*Sz))
elif component == 'z':
G_temp = np.hstack((-e.T*Sx))
else:
if component == 'x':
G_temp = np.hstack((o.T, e.T*Sz, -e.T*Sy))
elif component == 'y':
G_temp = np.hstack((-e.T*Sz, o.T, e.T*Sx))
elif component == 'z':
G_temp = np.hstack((e.T*Sy, -e.T*Sx, o.T))
G[i, :] = G_temp
return G
def MnSigma(self):
"""
Node inner product matrix for \\(\\sigma\\). Used in the E-B formulation
"""
# TODO: only works isotropic sigma
sigma = self.curModel.sigma
vol = self.mesh.vol
MnSigma = Utils.sdiag(self.mesh.aveN2CC.T*(Utils.sdiag(vol)*sigma))
return MnSigma
def getADeriv(self, ky, u, v, adjoint= False):
D = self.Div
G = self.Grad
vol = self.mesh.vol
MfRhoIDeriv = self.MfRhoIDeriv
rho = self.curModel.rho
if adjoint:
return(MfRhoIDeriv( G * u ).T) * ( D.T * v) + ky**2*Utils.sdiag(u.flatten()*vol*(-1./rho**2))*v
return D * ((MfRhoIDeriv( G * u )) * v) + ky**2*Utils.sdiag(u.flatten()*vol*(-1./rho**2))*v
def getError(self):
# Test function
def phi_fun(x):
return np.cos(np.pi * x)
def j_fun(x):
return np.pi * np.sin(np.pi * x)
def phi_deriv(x):
return -j_fun(x)
def q_fun(x):
return (np.pi**2) * np.cos(np.pi * x)
xc_ana = phi_fun(self.M.gridCC)
q_ana = q_fun(self.M.gridCC)
j_ana = j_fun(self.M.gridFx)
# Get boundary locations
vecN = self.M.vectorNx
vecC = self.M.vectorCCx
# Setup Mixed B.C (alpha, beta, gamma)
alpha_xm, alpha_xp = 1., 1.
beta_xm, beta_xp = 1., 1.
alpha = np.r_[alpha_xm, alpha_xp]
beta = np.r_[beta_xm, beta_xp]
vecN = self.M.vectorNx
vecC = self.M.vectorCCx
phi_bc = phi_fun(vecN[[0, -1]])
phi_deriv_bc = phi_deriv(vecN[[0, -1]])
gamma = alpha * phi_bc + beta * phi_deriv_bc
x_BC, y_BC = getxBCyBC_CC(self.M, alpha, beta, gamma)
sigma = np.ones(self.M.nC)
Mfrho = self.M.getFaceInnerProduct(1. / sigma)
MfrhoI = self.M.getFaceInnerProduct(1. / sigma, invMat=True)
V = Utils.sdiag(self.M.vol)
Div = V * self.M.faceDiv
P_BC, B = self.M.getBCProjWF_simple()
q = q_fun(self.M.gridCC)
M = B * self.M.aveCC2F
G = Div.T - P_BC * Utils.sdiag(y_BC) * M
# Mrhoj = D.T V phi + P_BC*Utils.sdiag(y_BC)*M phi - P_BC*x_BC
rhs = V * q + Div * MfrhoI * P_BC * x_BC
A = Div * MfrhoI * G
if self.myTest == 'xc':
# TODO: fix the null space
Ainv = Solver(A)
xc = Ainv * rhs
err = np.linalg.norm((xc - xc_ana), np.inf)
else:
NotImplementedError
return err
def MccRhoiDerivMat(self):
"""
Derivative of MccRho with respect to the model
"""
if getattr(self, '_MccRhoiDerivMat', None) is None:
rho = self.rho
vol = self.mesh.vol
drho_dlogrho = Utils.sdiag(rho) * self.etaDeriv
self._MccRhoiDerivMat = (Utils.sdiag(vol * (-1. / rho**2)) *
drho_dlogrho)
return self._MccRhoiDerivMat
def MnSigmaDerivMat(self):
"""
Derivative of MnSigma with respect to the model
"""
if getattr(self, '_MnSigmaDerivMat', None) is None:
sigma = self.sigma
vol = self.mesh.vol
dsigma_dlogsigma = Utils.sdiag(sigma) * self.etaDeriv
self._MnSigmaDerivMat = (self.mesh.aveN2CC.T * Utils.sdiag(vol) *
dsigma_dlogsigma)
return self._MnSigmaDerivMat
def MnSigma(self):
"""
Node inner product matrix for \\(\\sigma\\). Used in the E-B
formulation
"""
# TODO: only works isotropic sigma
sigma = self.curModel.sigma
vol = self.mesh.vol
MnSigma = Utils.sdiag(self.mesh.aveN2CC.T * (Utils.sdiag(vol) * sigma))
return MnSigma
def faceDivz(self):
"""
Construct divergence operator in the z component
(face-stg to cell-centres).
"""
if getattr(self, "_faceDivz", None) is None:
D3 = Utils.kron3(Utils.ddx(self.nCz), Utils.speye(self.nCy), Utils.speye(self.nCx))
S = self.r(self.area, "F", "Fz", "V")
V = self.vol
self._faceDivz = Utils.sdiag(1 / V) * D3 * Utils.sdiag(S)
return self._faceDivz
def casing_currents(j, mesh, model_parameters):
"""
Compute the current (A) within the casing
:param numpy.ndarray j: current density
:param discretize.BaseMesh mesh: the discretize mesh which the casing is on
:param casingSimulations.model.BaseCasingParametersMixin: a model with
casing
:return: :code:`(ix_casing, iz_casing)`
"""
casing_a = model_parameters.casing_a
casing_b = model_parameters.casing_b
casing_z = model_parameters.casing_z
IxCasing = {}
IzCasing = {}
casing_faces_x = ((mesh.gridFx[:, 0] >= casing_a) &
(mesh.gridFx[:, 0] <= casing_b) &
(mesh.gridFx[:, 2] <= casing_z[1]) &
(mesh.gridFx[:, 2] >= casing_z[0]))
casing_faces_y = np.zeros(mesh.nFy, dtype=bool)
casing_faces_z = ((mesh.gridFz[:, 0] >= casing_a) &
(mesh.gridFz[:, 0] <= casing_b) &
(mesh.gridFz[:, 2] <= casing_z[1]) &
(mesh.gridFz[:, 2] >= casing_z[0]))
jA = Utils.sdiag(mesh.area) * j
jACasing = Utils.sdiag(
np.hstack([casing_faces_x, casing_faces_y, casing_faces_z])) * jA
jxCasing = jACasing[:mesh.nFx, :].reshape(mesh.vnFx[0],
mesh.vnFx[1],
mesh.vnFx[2],
order='F')
jzCasing = jACasing[mesh.nFx + mesh.nFy:, :].reshape(mesh.vnFz[0],
mesh.vnFz[1],
mesh.vnFz[2],
order='F')
ixCasing = jxCasing.sum(0).sum(0)
izCasing = jzCasing.sum(0).sum(0)
ix_inds = (mesh.vectorCCz > casing_z[0]) & (mesh.vectorCCz < casing_z[1])
z_ix = mesh.vectorCCz[ix_inds]
iz_inds = (mesh.vectorNz > casing_z[0]) & (mesh.vectorNz < casing_z[1])
z_iz = mesh.vectorNz[iz_inds]
return {"x": (z_ix, ixCasing[ix_inds]), "z": (z_iz, izCasing[iz_inds])}
def MfRhoIDeriv(self, u):
"""
Derivative of :code:`MfRhoI` with respect to the model.
"""
dMfRhoI_dI = -self.MfRhoI**2
dMf_drho = self.mesh.getFaceInnerProductDeriv(self.rho)(u)
if self.storeJ:
drho_dlogrho = Utils.sdiag(self.rho)*self.actMap.P
else:
drho_dlogrho = Utils.sdiag(self.rho)
return dMfRhoI_dI * (dMf_drho * drho_dlogrho)
def MeSigmaDeriv(self, u):
"""
Derivative of MeSigma with respect to the model
"""
if self.storeJ:
dsigma_dlogsigma = Utils.sdiag(self.sigma)*self.actMap.P
else:
dsigma_dlogsigma = Utils.sdiag(self.sigma)
return (
self.mesh.getEdgeInnerProductDeriv(self.sigma)(u)
* dsigma_dlogsigma
)
def MfRhoDerivMat(self):
"""
Derivative of MfRho with respect to the model
"""
if getattr(self, '_MfRhoDerivMat', None) is None:
if self.storeJ:
drho_dlogrho = Utils.sdiag(self.rho) * self.actMap.P
else:
drho_dlogrho = Utils.sdiag(self.rho)
self._MfRhoDerivMat = self.mesh.getFaceInnerProductDeriv(
np.ones(self.mesh.nC))(np.ones(self.mesh.nF)) * drho_dlogrho
return self._MfRhoDerivMat
def faceDivz(self):
"""
Construct divergence operator in the z component
(face-stg to cell-centres).
"""
if getattr(self, '_faceDivz', None) is None:
D3 = Utils.kron3(Utils.ddx(self.nCz), Utils.speye(self.nCy),
Utils.speye(self.nCx))
S = self.r(self.area, 'F', 'Fz', 'V')
V = self.vol
self._faceDivz = Utils.sdiag(1/V)*D3*Utils.sdiag(S)
return self._faceDivz
def MccRhoiDerivMat(self):
"""
Derivative of MccRho with respect to the model
"""
if getattr(self, '_MccRhoiDerivMat', None) is None:
rho = self.rho
vol = self.mesh.vol
drho_dlogrho = Utils.sdiag(rho)*self.etaDeriv
self._MccRhoiDerivMat = (
Utils.sdiag(vol*(-1./rho**2))*drho_dlogrho
)
return self._MccRhoiDerivMat
def MnSigmaDerivMat(self):
"""
Derivative of MnSigma with respect to the model
"""
if getattr(self, '_MnSigmaDerivMat', None) is None:
sigma = self.sigma
vol = self.mesh.vol
dsigma_dlogsigma = Utils.sdiag(sigma)*self.etaDeriv
self._MnSigmaDerivMat = (
self.mesh.aveN2CC.T * Utils.sdiag(vol) * dsigma_dlogsigma
)
return self._MnSigmaDerivMat
def MnSigma(self):
"""
Node inner product matrix for \\(\\sigma\\). Used in the E-B
formulation
"""
# TODO: only works isotropic sigma
if getattr(self, '_MnSigma', None) is None:
sigma = self.sigma
vol = self.mesh.vol
self._MnSigma = Utils.sdiag(self.mesh.aveN2CC.T *
(Utils.sdiag(vol) * sigma))
return self._MnSigma
def MeSigmaDerivMat(self):
"""
Derivative of MeSigma with respect to the model
"""
if getattr(self, '_MeSigmaDerivMat', None) is None:
if self.storeJ:
dsigma_dlogsigma = Utils.sdiag(self.sigma) * self.actMap.P
else:
dsigma_dlogsigma = Utils.sdiag(self.sigma)
self._MeSigmaDerivMat = self.mesh.getEdgeInnerProductDeriv(
np.ones(self.mesh.nC))(np.ones(
self.mesh.nE)) * dsigma_dlogsigma
return self._MeSigmaDerivMat
def MeSigmaDerivMat(self):
"""
Derivative of MeSigma with respect to the model
"""
if getattr(self, '_MeSigmaDerivMat', None) is None:
if self.storeJ:
dsigma_dlogsigma = Utils.sdiag(self.sigma)*self.actMap.P
else:
dsigma_dlogsigma = Utils.sdiag(self.sigma)
self._MeSigmaDerivMat = self.mesh.getEdgeInnerProductDeriv(
np.ones(self.mesh.nC)
)(np.ones(self.mesh.nE)) * dsigma_dlogsigma
return self._MeSigmaDerivMat
def getADeriv(self, ky, u, v, adjoint=False):
D = self.Div
G = self.Grad
vol = self.mesh.vol
MfRhoIDeriv = self.MfRhoIDeriv
rho = self.curModel.rho
if adjoint:
return ((MfRhoIDeriv(G * u).T) * (D.T * v) +
ky**2 * Utils.sdiag(u.flatten() * vol *
(-1. / rho**2)) * v)
return (D * ((MfRhoIDeriv(G * u)) * v) +
ky**2 * Utils.sdiag(u.flatten() * vol * (-1. / rho**2)) * v)
def MfRhoDerivMat(self):
"""
Derivative of MfRho with respect to the model
"""
if getattr(self, '_MfRhoDerivMat', None) is None:
if self.storeJ:
drho_dlogrho = Utils.sdiag(self.rho)*self.actMap.P
else:
drho_dlogrho = Utils.sdiag(self.rho)
self._MfRhoDerivMat = self.mesh.getFaceInnerProductDeriv(
np.ones(self.mesh.nC)
)(np.ones(self.mesh.nF)) * drho_dlogrho
return self._MfRhoDerivMat
def getError(self):
# Test function
def phi_fun(x): return np.cos(np.pi*x)
def j_fun(x): return np.pi*np.sin(np.pi*x)
def phi_deriv(x): return -j_fun(x)
def q_fun(x): return (np.pi**2)*np.cos(np.pi*x)
xc_ana = phi_fun(self.M.gridCC)
q_ana = q_fun(self.M.gridCC)
j_ana = j_fun(self.M.gridFx)
# Get boundary locations
vecN = self.M.vectorNx
vecC = self.M.vectorCCx
# Setup Mixed B.C (alpha, beta, gamma)
alpha_xm, alpha_xp = 1., 1.
beta_xm, beta_xp = 1., 1.
alpha = np.r_[alpha_xm, alpha_xp]
beta = np.r_[beta_xm, beta_xp]
vecN = self.M.vectorNx
vecC = self.M.vectorCCx
phi_bc = phi_fun(vecN[[0, -1]])
phi_deriv_bc = phi_deriv(vecN[[0, -1]])
gamma = alpha*phi_bc + beta*phi_deriv_bc
x_BC, y_BC = getxBCyBC_CC(self.M, alpha, beta, gamma)
sigma = np.ones(self.M.nC)
Mfrho = self.M.getFaceInnerProduct(1./sigma)
MfrhoI = self.M.getFaceInnerProduct(1./sigma, invMat=True)
V = Utils.sdiag(self.M.vol)
Div = V*self.M.faceDiv
P_BC, B = self.M.getBCProjWF_simple()
q = q_fun(self.M.gridCC)
M = B*self.M.aveCC2F
G = Div.T - P_BC*Utils.sdiag(y_BC)*M
# Mrhoj = D.T V phi + P_BC*Utils.sdiag(y_BC)*M phi - P_BC*x_BC
rhs = V*q + Div*MfrhoI*P_BC*x_BC
A = Div*MfrhoI*G
if self.myTest == 'xc':
# TODO: fix the null space
Ainv = Solver(A)
xc = Ainv*rhs
err = np.linalg.norm((xc-xc_ana), np.inf)
else:
NotImplementedError
return err
def faceDivy(self):
"""
Construct divergence operator in the y component
(face-stg to cell-centres).
"""
raise NotImplementedError("Wrapping the Utils.ddx is not yet " "implemented.")
if getattr(self, "_faceDivy", None) is None:
# TODO: this needs to wrap to join up faces which are
# connected in the cylinder
D2 = Utils.kron3(Utils.speye(self.nCz), Utils.ddx(self.nCy), Utils.speye(self.nCx))
S = self.r(self.area, "F", "Fy", "V")
V = self.vol
self._faceDivy = Utils.sdiag(1 / V) * D2 * Utils.sdiag(S)
return self._faceDivy
def test_sum_fail(self):
nP1 = 10
nP2 = 30
phi1 = ObjectiveFunction.L2ObjectiveFunction(
W=Utils.sdiag(np.random.rand(nP1)))
phi2 = ObjectiveFunction.L2ObjectiveFunction(
W=Utils.sdiag(np.random.rand(nP2)))
with self.assertRaises(Exception):
phi = phi1 + phi2
with self.assertRaises(Exception):
phi = phi1 + 100 * phi2
def BiotSavartFun(mesh, r_pts, component="z"):
"""
Compute systematrix G using Biot-Savart Law
G = np.vstack((G1,G2,G3..,Gnpts)
.. math::
"""
if r_pts.ndim == 1:
npts = 1
else:
npts = r_pts.shape[0]
e = np.ones((mesh.nC, 1))
o = np.zeros((mesh.nC, 1))
const = mu_0 / 4 / np.pi
G = np.zeros((npts, mesh.nC * 3))
for i in range(npts):
if npts == 1:
r_rx = np.repeat(Utils.mkvc(r_pts).reshape([1, -1]),
mesh.nC,
axis=0)
else:
r_rx = np.repeat(r_pts[i, :].reshape([1, -1]), mesh.nC, axis=0)
r_CC = mesh.gridCC
r = r_rx - r_CC
r_abs = np.sqrt((r**2).sum(axis=1))
rxind = r_abs == 0.0
# r_abs[rxind] = mesh.vol.min()**(1./3.)*0.5
r_abs[rxind] = 1e20
Sx = const * Utils.sdiag(mesh.vol * r[:, 0] / r_abs**3)
Sy = const * Utils.sdiag(mesh.vol * r[:, 1] / r_abs**3)
Sz = const * Utils.sdiag(mesh.vol * r[:, 2] / r_abs**3)
# G_temp = sp.vstack((sp.hstack(( o.T, e.T*Sz, -e.T*Sy)), \
# sp.hstack((-e.T*Sz, o.T, e.T*Sx)), \
# sp.hstack((-e.T*Sy, e.T*Sx, o.T ))))
if component == "x":
G_temp = np.hstack((o.T, e.T * Sz, -e.T * Sy))
elif component == "y":
G_temp = np.hstack((-e.T * Sz, o.T, e.T * Sx))
elif component == "z":
G_temp = np.hstack((e.T * Sy, -e.T * Sx, o.T))
G[i, :] = G_temp
return G
def CasingCurrents(cp, fields, mesh, survey):
IxCasing = {}
IzCasing = {}
# casing_ind = sigma_m.copy()
# casing_ind[[0, 1, 3]] = 0. # zero outside casing
# casing_ind[2] = 1. # 1 inside casing
# actMap_Zeros = Maps.InjectActiveCells(mesh, indActive, 0.)
# indCasing = actMap_Zeros * casingMap * casing_ind
# casing_faces = mesh.aveF2CC.T * indCasing
# casing_faces[casing_faces < 0.25] = 0
casing_faces_x = ((mesh.gridFx[:, 0] >= cp.casing_a) &
(mesh.gridFx[:, 0] <= cp.casing_b) &
(mesh.gridFx[:, 2] <= cp.casing_z[1]) &
(mesh.gridFx[:, 2] >= cp.casing_z[0]))
casing_faces_z = ((mesh.gridFz[:, 0] >= cp.casing_a) &
(mesh.gridFz[:, 0] <= cp.casing_b) &
(mesh.gridFz[:, 2] <= cp.casing_z[1]) &
(mesh.gridFz[:, 2] >= cp.casing_z[0]))
for mur in cp.muModels:
j = fields[mur][:, 'j']
jA = Utils.sdiag(mesh.area) * j
jACasing = Utils.sdiag(np.hstack([casing_faces_x, casing_faces_z
])) * jA
ixCasing = []
izCasing = []
for ind in range(len(survey.srcList)):
jxCasing = jACasing[:mesh.nFx, ind].reshape(mesh.vnFx[0],
mesh.vnFx[2],
order='F')
jzCasing = jACasing[mesh.nFx:, ind].reshape(mesh.vnFz[0],
mesh.vnFz[2],
order='F')
ixCasing.append(jxCasing.sum(0))
izCasing.append(jzCasing.sum(0))
IxCasing[mur] = ixCasing
IzCasing[mur] = izCasing
return IxCasing, IzCasing
def CasingMagDipole2Deriv_z_z(z):
obsloc = np.vstack([xobs, yobs, z]).T
f = Casing._getCasingHertzMagDipoleDeriv_z(srcloc, obsloc, freq, sigma, a, b, mu)
g = Utils.sdiag(Casing._getCasingHertzMagDipole2Deriv_z_z(srcloc, obsloc, freq, sigma, a, b, mu))
return f, g
def CasingMagDipoleDeriv_r(x):
obsloc = np.vstack([x, yobs, zobs]).T
f = Casing._getCasingHertzMagDipole(srcloc, obsloc, freq, sigma, a, b, mu)
g = Utils.sdiag(Casing._getCasingHertzMagDipoleDeriv_r(srcloc, obsloc, freq, sigma, a, b, mu))
return f, g
def getInterpolationMatCartMesh(self, Mrect, locType="CC", locTypeTo=None):
"""
Takes a cartesian mesh and returns a projection to translate onto
the cartesian grid.
"""
assert self.isSymmetric, (
"Currently we have not taken into account " "other projections for more complicated " "CylMeshes"
)
if locTypeTo is None:
locTypeTo = locType
if locType == "F":
# do this three times for each component
X = self.getInterpolationMatCartMesh(Mrect, locType="Fx", locTypeTo=locTypeTo + "x")
Y = self.getInterpolationMatCartMesh(Mrect, locType="Fy", locTypeTo=locTypeTo + "y")
Z = self.getInterpolationMatCartMesh(Mrect, locType="Fz", locTypeTo=locTypeTo + "z")
return sp.vstack((X, Y, Z))
if locType == "E":
X = self.getInterpolationMatCartMesh(Mrect, locType="Ex", locTypeTo=locTypeTo + "x")
Y = self.getInterpolationMatCartMesh(Mrect, locType="Ey", locTypeTo=locTypeTo + "y")
Z = Utils.spzeros(getattr(Mrect, "n" + locTypeTo + "z"), self.nE)
return sp.vstack((X, Y, Z))
grid = getattr(Mrect, "grid" + locTypeTo)
# This is unit circle stuff, 0 to 2*pi, starting at x-axis, rotating
# counter clockwise in an x-y slice
theta = -np.arctan2(grid[:, 0] - self.cartesianOrigin[0], grid[:, 1] - self.cartesianOrigin[1]) + np.pi / 2
theta[theta < 0] += np.pi * 2.0
r = ((grid[:, 0] - self.cartesianOrigin[0]) ** 2 + (grid[:, 1] - self.cartesianOrigin[1]) ** 2) ** 0.5
if locType in ["CC", "N", "Fz", "Ez"]:
G, proj = np.c_[r, theta, grid[:, 2]], np.ones(r.size)
else:
dotMe = {
"Fx": Mrect.normals[: Mrect.nFx, :],
"Fy": Mrect.normals[Mrect.nFx : (Mrect.nFx + Mrect.nFy), :],
"Fz": Mrect.normals[-Mrect.nFz :, :],
"Ex": Mrect.tangents[: Mrect.nEx, :],
"Ey": Mrect.tangents[Mrect.nEx : (Mrect.nEx + Mrect.nEy), :],
"Ez": Mrect.tangents[-Mrect.nEz :, :],
}[locTypeTo]
if "F" in locType:
normals = np.c_[np.cos(theta), np.sin(theta), np.zeros(theta.size)]
proj = (normals * dotMe).sum(axis=1)
if "E" in locType:
tangents = np.c_[-np.sin(theta), np.cos(theta), np.zeros(theta.size)]
proj = (tangents * dotMe).sum(axis=1)
G = np.c_[r, theta, grid[:, 2]]
interpType = locType
if interpType == "Fy":
interpType = "Fx"
elif interpType == "Ex":
interpType = "Ey"
Pc2r = self.getInterpolationMat(G, interpType)
Proj = Utils.sdiag(proj)
return Proj * Pc2r
def fields(self, m):
"""
Return magnetic potential (u) and flux (B)
u: defined on the cell nodes [nC x 1]
gField: defined on the cell faces [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}
"""
from scipy.constants import G as NewtG
self.makeMassMatrices(m)
A = self.getA(m)
RHS = self.getRHS(m)
if self.solver is None:
m1 = sp.linalg.interface.aslinearoperator(Utils.sdiag(1/A.diagonal()))
u, info = sp.linalg.bicgstab(A, RHS, tol=1e-6, maxiter=1000, M=m1)
else:
print("Solving with Paradiso")
Ainv = self.solver(A)
u = Ainv*RHS
gField = 4.*np.pi*NewtG*1e+8*self._Div*u
return {'G': gField, 'u': u}
def transformDerivU(self, u, m):
self.setModel(m)
alpha = self.alpha
I = self.I
n = self.n
Ks = self.Ks
m = 1.0 - 1.0 / n
g = I * alpha * n * np.exp(Ks) * abs(alpha * u) ** (n - 1.0) * np.sign(alpha * u) * (1.0 / n - 1.0) * (
(abs(alpha * u) ** n + 1) ** (1.0 / n - 1)
) ** (I - 1) * (
(1 - 1.0 / ((abs(alpha * u) ** n + 1) ** (1.0 / n - 1)) ** (1.0 / (1.0 / n - 1))) ** (1 - 1.0 / n) - 1
) ** 2 * (
abs(alpha * u) ** n + 1
) ** (
1.0 / n - 2
) - (
2
* alpha
* n
* np.exp(Ks)
* abs(alpha * u) ** (n - 1)
* np.sign(alpha * u)
* (1.0 / n - 1)
* ((abs(alpha * u) ** n + 1) ** (1.0 / n - 1)) ** I
* ((1 - 1.0 / ((abs(alpha * u) ** n + 1) ** (1.0 / n - 1)) ** (1.0 / (1.0 / n - 1))) ** (1 - 1.0 / n) - 1)
* (abs(alpha * u) ** n + 1) ** (1.0 / n - 2)
) / (
((abs(alpha * u) ** n + 1) ** (1.0 / n - 1)) ** (1.0 / (1.0 / n - 1) + 1)
* (1 - 1.0 / ((abs(alpha * u) ** n + 1) ** (1.0 / n - 1)) ** (1.0 / (1.0 / n - 1))) ** (1.0 / n)
)
g[u >= 0] = 0
g = Utils.sdiag(g)
return g
def Wd(self):
"""getWd(survey)
The data weighting matrix.
The default is based on the norm of the data plus a noise floor.
:rtype: scipy.sparse.csr_matrix
:return: Wd
"""
if getattr(self, '_Wd', None) is None:
survey = self.survey
if getattr(survey,'std', None) is None:
print('SimPEG.DataMisfit.l2_DataMisfit assigning default std of 5%')
survey.std = 0.05
if getattr(survey, 'eps', None) is None:
print('SimPEG.DataMisfit.l2_DataMisfit assigning default eps of 1e-5 * ||dobs||')
survey.eps = np.linalg.norm(Utils.mkvc(survey.dobs),2)*1e-5
self._Wd = Utils.sdiag(1/(abs(survey.dobs)*survey.std+survey.eps))
return self._Wd
def makeMassMatrices(self, m):
mu = self.muMap*m
self._MfMui = self.mesh.getFaceInnerProduct(1./mu)/self.mesh.dim
# self._MfMui = self.mesh.getFaceInnerProduct(1./mu)
# TODO: this will break if tensor mu
self._MfMuI = Utils.sdiag(1./self._MfMui.diagonal())
self._MfMu0 = self.mesh.getFaceInnerProduct(1./mu_0)/self.mesh.dim
def Jvec(self, m, v, f=None):
J_sigma = self.getJ_sigma(m)
J_height = self.getJ_height(m)
# This is deprecated at the moment
# if self.parallel and self.parallel_jvec_jtvec:
# # Extra division of sigma is because:
# # J_sigma = dF/dlog(sigma)
# # And here sigmaMap also includes ExpMap
# v_sigma = Utils.sdiag(1./self.sigma) * self.sigmaMap.deriv(m, v)
# V_sigma = v_sigma.reshape((self.n_sounding, self.n_layer))
# pool = Pool(self.n_cpu)
# Jv = np.hstack(
# pool.map(
# dot,
# [(J_sigma[i], V_sigma[i, :]) for i in range(self.n_sounding)]
# )
# )
# if self.hMap is not None:
# v_height = self.hMap.deriv(m, v)
# V_height = v_height.reshape((self.n_sounding, self.n_layer))
# Jv += np.hstack(
# pool.map(
# dot,
# [(J_height[i], V_height[i, :]) for i in range(self.n_sounding)]
# )
# )
# pool.close()
# pool.join()
# else:
Jv = J_sigma*(Utils.sdiag(1./self.sigma)*(self.sigmaDeriv * v))
if self.hMap is not None:
Jv += J_height*(self.hDeriv * v)
return Jv
def Jtvec(self, m, v, f=None):
J_sigma = self.getJ_sigma(m)
J_height = self.getJ_height(m)
# This is deprecated at the moment
# if self.parallel and self.parallel_jvec_jtvec:
# pool = Pool(self.n_cpu)
# Jtv = np.hstack(
# pool.map(
# dot,
# [(J_sigma[i].T, v[self.data_index[i]]) for i in range(self.n_sounding)]
# )
# )
# if self.hMap is not None:
# Jtv_height = np.hstack(
# pool.map(
# dot,
# [(J_sigma[i].T, v[self.data_index[i]]) for i in range(self.n_sounding)]
# )
# )
# # This assumes certain order for model, m = (sigma, height)
# Jtv = np.hstack((Jtv, Jtv_height))
# pool.close()
# pool.join()
# return Jtv
# else:
# Extra division of sigma is because:
# J_sigma = dF/dlog(sigma)
# And here sigmaMap also includes ExpMap
Jtv = self.sigmaDeriv.T * (Utils.sdiag(1./self.sigma) * (J_sigma.T*v))
if self.hMap is not None:
Jtv += self.hDeriv.T*(J_height.T*v)
return Jtv
def MccSigma(self):
"""
Diagonal matrix for \\(\\sigma\\).
"""
if getattr(self, '_MccSigma', None) is None:
self._MccSigma = Utils.sdiag(self.sigma)
return self._MccSigma
def MccEpsilon(self):
"""
Diagonal matrix for \\(\\epsilon\\).
"""
if getattr(self, '_MccEpsilon', None) is None:
self._MccEpsilon = Utils.sdiag(self.epsilon)
return self._MccEpsilon
def fields(self, m):
"""
Return gravity potential (u) and field (g)
u: defined on the cell nodes [nC x 1]
gField: defined on the cell faces [nF x 1]
"""
from scipy.constants import G as NewtG
self.makeMassMatrices(m)
A = self.getA(m)
RHS = self.getRHS(m)
if self.solver is None:
m1 = sp.linalg.interface.aslinearoperator(
Utils.sdiag(1 / A.diagonal())
)
u, info = sp.linalg.bicgstab(A, RHS, tol=1e-6, maxiter=1000, M=m1)
else:
print("Solving with Paradiso")
Ainv = self.solver(A)
u = Ainv * RHS
gField = 4. * np.pi * NewtG * 1e+8 * self._Div * u
return {'G': gField, 'u': u}
def test_early_exits(self):
nP = 10
m = np.random.rand(nP)
v = np.random.rand(nP)
W1 = Utils.sdiag(np.random.rand(nP))
phi1 = ObjectiveFunction.L2ObjectiveFunction(W=W1)
phi2 = Error_if_Hit_ObjFct()
objfct = phi1 + 0 * phi2
self.assertTrue(len(objfct) == 2)
self.assertTrue(np.all(objfct.multipliers == np.r_[1, 0]))
self.assertTrue(objfct(m) == phi1(m))
self.assertTrue(np.all(objfct.deriv(m) == phi1.deriv(m)))
self.assertTrue(np.all(objfct.deriv2(m, v) == phi1.deriv2(m, v)))
objfct.multipliers[1] = Utils.Zero()
self.assertTrue(len(objfct) == 2)
self.assertTrue(np.all(objfct.multipliers == np.r_[1, 0]))
self.assertTrue(objfct(m) == phi1(m))
self.assertTrue(np.all(objfct.deriv(m) == phi1.deriv(m)))
self.assertTrue(np.all(objfct.deriv2(m, v) == phi1.deriv2(m, v)))
def test_basic(self):
expMap = Maps.ExpMap(Mesh.TensorMesh((3,)))
assert expMap.nP == 3
for Example in [SimpleExample, ShortcutExample]:
PM = Example(sigmaMap=expMap)
assert PM.sigmaMap is not None
assert PM.sigmaMap is expMap
# There is currently no model, so sigma, which is mapped, fails
self.assertRaises(AttributeError, getattr, PM, 'sigma')
PM.model = np.r_[1., 2., 3.]
assert np.all(PM.sigma == np.exp(np.r_[1., 2., 3.]))
# PM = pickle.loads(pickle.dumps(PM))
# PM = Maps.ExpMap.deserialize(PM.serialize())
assert np.all(
PM.sigmaDeriv.todense() ==
Utils.sdiag(np.exp(np.r_[1., 2., 3.])).todense()
)
# If we set sigma, we should delete the mapping
PM.sigma = np.r_[1., 2., 3.]
assert np.all(PM.sigma == np.r_[1., 2., 3.])
# PM = pickle.loads(pickle.dumps(PM))
assert PM.sigmaMap is None
assert PM.sigmaDeriv == 0
del PM.model
# sigma is not changed
assert np.all(PM.sigma == np.r_[1., 2., 3.])
def V(self):
"""
:code:`V`
"""
if getattr(self, "_V", None) is None:
self._V = Utils.sdiag(self.mesh.vol)
return self._V
def test_early_exits(self):
nP = 10
m = np.random.rand(nP)
v = np.random.rand(nP)
W1 = Utils.sdiag(np.random.rand(nP))
phi1 = ObjectiveFunction.L2ObjectiveFunction(W=W1)
phi2 = Error_if_Hit_ObjFct()
objfct = phi1 + 0*phi2
self.assertTrue(len(objfct) == 2)
self.assertTrue(np.all(objfct.multipliers == np.r_[1, 0]))
self.assertTrue(objfct(m) == phi1(m))
self.assertTrue(np.all(objfct.deriv(m) == phi1.deriv(m)))
self.assertTrue(np.all(objfct.deriv2(m, v) == phi1.deriv2(m, v)))
objfct.multipliers[1] = Utils.Zero()
self.assertTrue(len(objfct) == 2)
self.assertTrue(np.all(objfct.multipliers == np.r_[1, 0]))
self.assertTrue(objfct(m) == phi1(m))
self.assertTrue(np.all(objfct.deriv(m) == phi1.deriv(m)))
self.assertTrue(np.all(objfct.deriv2(m, v) == phi1.deriv2(m, v)))
