def rescaleWeights(self, scale=1., sigma_scale=1.):
"""
rescales the weights such that
:math: integrate( ( w omega**2 * sigma_scale * data * ((1/L_j)**2)**-1) +1 )/(data*omega**2 * ((1/L_j)**2)**-1) * sigma_scale )=scale
:param scale: scale of data weighting factors
:type scale: positive ``float``
:param sigma_scale: scale of 1/vp**2 velocity.
:type sigma_scale: ``Scalar``
"""
raise Warning("rescaleWeights is not tested yet.")
if not scale > 0:
raise ValueError("Value for scale must be positive.")
if not sigma_scale * omega**2 * d > 0:
raise ValueError(
"Rescaling of weights failed due to zero denominator.")
# copy back original weights before rescaling
#self.__weight=[1.*ow for ow in self.__origweight]
L2 = 1 / escript.length(1 / self.edge_length)**2
d = Lsup(escript.length(data))
A = escript.integrate(self.__weight *
(sigma_scale * omega**2 * d + 1) /
(sigma_scale * omega**2 * d))
if A > 0:
self.__weight *= 1. / A
if self.scaleF:
self.__data *= escript.sqrt(A)
else:
raise ValueError("Rescaling of weights failed.")
def getGradientAtPoint(self):
"""
returns the gradient of the cost function J with respect to m.
:note: This implementation returns Y_k=dPsi/dm_k and X_kj=dPsi/dm_kj
"""
# Using cached values
m = self.__pre_input
grad_m = self.__pre_args
mu = self.__mu
mu_c = self.__mu_c
DIM = self.getDomain().getDim()
numLS = self.getNumLevelSets()
grad_m = escript.grad(m, escript.Function(m.getDomain()))
if self.__w0 is not None:
Y = m * self.__w0 * mu
else:
if numLS == 1:
Y = escript.Scalar(0, grad_m.getFunctionSpace())
else:
Y = escript.Data(0, (numLS, ), grad_m.getFunctionSpace())
if self.__w1 is not None:
if numLS == 1:
X = grad_m * self.__w1 * mu
else:
X = grad_m * self.__w1
for k in range(numLS):
X[k, :] *= mu[k]
else:
X = escript.Data(0, grad_m.getShape(), grad_m.getFunctionSpace())
# cross gradient terms:
if numLS > 1:
for k in range(numLS):
grad_m_k = grad_m[k, :]
l2_grad_m_k = escript.length(grad_m_k)**2
for l in range(k):
grad_m_l = grad_m[l, :]
l2_grad_m_l = escript.length(grad_m_l)**2
grad_m_lk = inner(grad_m_l, grad_m_k)
f = mu_c[l, k] * self.__wc[l, k]
X[l, :] += f * (l2_grad_m_k * grad_m_l -
grad_m_lk * grad_m_k)
X[k, :] += f * (l2_grad_m_l * grad_m_k -
grad_m_lk * grad_m_l)
return pdetools.ArithmeticTuple(Y, X)
def getGradientAtPoint(self):
"""
returns the gradient of the cost function J with respect to m.
:note: This implementation returns Y_k=dPsi/dm_k and X_kj=dPsi/dm_kj
"""
# Using cached values
m = self.__pre_input
grad_m = self.__pre_args
mu = self.__mu
mu_c = self.__mu_c
DIM = self.getDomain().getDim()
numLS = self.getNumLevelSets()
grad_m = grad(m, Function(m.getDomain()))
if self.__w0 is not None:
Y = m * self.__w0 * mu
else:
if numLS == 1:
Y = Scalar(0, grad_m.getFunctionSpace())
else:
Y = Data(0, (numLS,), grad_m.getFunctionSpace())
if self.__w1 is not None:
if numLS == 1:
X = grad_m * self.__w1 * mu
else:
X = grad_m * self.__w1
for k in range(numLS):
X[k, :] *= mu[k]
else:
X = Data(0, grad_m.getShape(), grad_m.getFunctionSpace())
# cross gradient terms:
if numLS > 1:
for k in range(numLS):
grad_m_k = grad_m[k, :]
l2_grad_m_k = length(grad_m_k) ** 2
for l in range(k):
grad_m_l = grad_m[l, :]
l2_grad_m_l = length(grad_m_l) ** 2
grad_m_lk = inner(grad_m_l, grad_m_k)
f = mu_c[l, k] * self.__wc[l, k]
X[l, :] += f * (l2_grad_m_k * grad_m_l - grad_m_lk * grad_m_k)
X[k, :] += f * (l2_grad_m_l * grad_m_k - grad_m_lk * grad_m_l)
return ArithmeticTuple(Y, X)
def getWeightingFactor(self, x, wx0, x0, eta):
"""
returns the weighting factor
"""
try:
origin, spacing, NE = x.getDomain().getGridParameters()
cell = [int((x0[i] - origin[i]) / spacing[i]) for i in range(2)]
midpoint = [
origin[i] + cell[i] * spacing[i] + spacing[i] / 2.
for i in range(2)
]
return wx0 * escript.whereNegative(
escript.length(x - midpoint) - eta)
except:
return wx0 * escript.whereNegative(escript.length(x - x0) - eta)
def getValue(self, m, grad_m):
"""
returns the value of the cost function J with respect to m.
This equation is specified in the inversion cookbook.
:rtype: ``float``
"""
if m != self.__pre_input:
raise RuntimeError("Attempt to change point using getValue")
# substituting cached values
m = self.__pre_input
grad_m = self.__pre_args
mu = self.__mu
mu_c = self.__mu_c
DIM = self.getDomain().getDim()
numLS = self.getNumLevelSets()
A = 0
if self.__w0 is not None:
r = inner(escript.integrate(m**2 * self.__w0), mu)
self.logger.debug("J_R[m^2] = %e" % r)
A += r
if self.__w1 is not None:
if numLS == 1:
r = escript.integrate(inner(grad_m**2, self.__w1)) * mu
self.logger.debug("J_R[grad(m)] = %e" % r)
A += r
else:
for k in range(numLS):
r = mu[k] * escript.integrate(
inner(grad_m[k, :]**2, self.__w1[k, :]))
self.logger.debug("J_R[grad(m)][%d] = %e" % (k, r))
A += r
if numLS > 1:
for k in range(numLS):
gk = grad_m[k, :]
len_gk = escript.length(gk)
for l in range(k):
gl = grad_m[l, :]
r = mu_c[l, k] * escript.integrate(self.__wc[l, k] * (
(len_gk * escript.length(gl))**2 - inner(gk, gl)**2))
self.logger.debug("J_R[cross][%d,%d] = %e" % (l, k, r))
A += r
return A / 2
def getValue(self, m, grad_m):
"""
returns the value of the cost function J with respect to m.
This equation is specified in the inversion cookbook.
:rtype: ``float``
"""
if m != self.__pre_input:
raise RuntimeError("Attempt to change point using getValue")
# substituting cached values
m = self.__pre_input
grad_m = self.__pre_args
mu = self.__mu
mu_c = self.__mu_c
DIM = self.getDomain().getDim()
numLS = self.getNumLevelSets()
A = 0
if self.__w0 is not None:
r = inner(integrate(m ** 2 * self.__w0), mu)
self.logger.debug("J_R[m^2] = %e" % r)
A += r
if self.__w1 is not None:
if numLS == 1:
r = integrate(inner(grad_m ** 2, self.__w1)) * mu
self.logger.debug("J_R[grad(m)] = %e" % r)
A += r
else:
for k in range(numLS):
r = mu[k] * integrate(inner(grad_m[k, :] ** 2, self.__w1[k, :]))
self.logger.debug("J_R[grad(m)][%d] = %e" % (k, r))
A += r
if numLS > 1:
for k in range(numLS):
gk = grad_m[k, :]
len_gk = length(gk)
for l in range(k):
gl = grad_m[l, :]
r = mu_c[l, k] * integrate(self.__wc[l, k] * ((len_gk * length(gl)) ** 2 - inner(gk, gl) ** 2))
self.logger.debug("J_R[cross][%d,%d] = %e" % (l, k, r))
A += r
return A / 2
def getSafeTimeStepSize(self, dt):
"""
returns new step size
"""
h = self.domain.getSize()
return self.safety_factor * inf(
h**2 / (h * abs(self.heat_capacity * self.density) *
length(self.velocity) + self.thermal_permabilty))
def getNorm(self, m):
"""
returns the norm of ``m``.
:param m: level set function
:type m: `Data`
:rtype: ``float``
"""
return sqrt(integrate(length(m) ** 2) / self.__vol_d)
def getNorm(self, m):
"""
returns the norm of ``m``.
:param m: level set function
:type m: `Data`
:rtype: ``float``
"""
return sqrt(integrate(length(m)**2) / self.__vol_d)
def __setOutput(self):
x = self.domain.getX()
self.__location_of_constraint = es.Scalar(0, x.getFunctionSpace())
if self.domain.getDim() == 3:
vertex = [es.inf(x[0]), es.inf(x[1]), es.inf(x[2])]
else:
vertex = [es.inf(x[0]), es.inf(x[1])]
self.__location_of_constraint = es.whereZero(es.length(x - vertex),
self.tol)
if not self.value is None:
self.__value_of_constraint = self.__location_of_constraint * self.value
def getValue(self, m, grad_m):
"""
returns the value of the cost function J with respect to m.
This equation is specified in the inversion cookbook.
:rtype: ``float``
"""
mu = self.__mu
mu_c = self.__mu_c
DIM = self.getDomain().getDim()
numLS = self.getNumLevelSets()
A = 0
if self.__w0 is not None:
r = inner(integrate(m**2 * self.__w0), mu)
self.logger.debug("J_R[m^2] = %e" % r)
A += r
if self.__w1 is not None:
if numLS == 1:
r = integrate(inner(grad_m**2, self.__w1)) * mu
self.logger.debug("J_R[grad(m)] = %e" % r)
A += r
else:
for k in range(numLS):
r = mu[k] * integrate(
inner(grad_m[k, :]**2, self.__w1[k, :]))
self.logger.debug("J_R[grad(m)][%d] = %e" % (k, r))
A += r
if numLS > 1:
for k in range(numLS):
gk = grad_m[k, :]
len_gk = length(gk)
for l in range(k):
gl = grad_m[l, :]
r = mu_c[l, k] * integrate(self.__wc[l, k] * (
(len_gk * length(gl))**2 - inner(gk, gl)**2))
self.logger.debug("J_R[cross][%d,%d] = %e" % (l, k, r))
A += r
return A / 2
def out(self):
"""
Generate the Gaussian profile
Link against this method to get the output of this model.
"""
x = self.domain.getX()
dim = self.domain.getDim()
l = length(x - self.x_c[:dim])
m = whereNegative(l - self.r)
return (m + (1. - m) * exp(-log(2.) * (l / self.width)**2)) * self.A
def out(self):
"""
Generate the Gaussian profile
Link against this method to get the output of this model.
"""
x = self.domain.getX()
dim = self.domain.getDim()
l = length(x-self.x_c[:dim])
m = whereNegative(l-self.r)
return (m+(1.-m)*exp(-log(2.)*(l/self.width)**2))*self.A
def getSourceScaling(self, u):
"""
returns the scaling factor s required to rescale source F to minimize defect ``|s * u- data|^2``
:param u: value of pressure solution (real and imaginary part)
:type u: ``escript.Data`` of shape (2,)
:rtype: `complex`
"""
uTu = escript.integrate(self.__weight * escript.length(u)**2)
uTar = escript.integrate(self.__weight * ( u[0]*self.__data[0]+u[1]*self.__data[1]) )
uTai = escript.integrate(self.__weight * ( u[0]*self.__data[1]-u[1]*self.__data[0]) )
if uTu > 0:
return complex(uTar/uTu, uTai/uTu)
else:
return complex(1.,0)
def __setOutput(self):
x = self.domain.getX()
self.__location_of_constraint = es.Vector(0, x.getFunctionSpace())
if self.domain.getDim() == 3:
vertex = [es.inf(x[0]), es.inf(x[1]), es.inf(x[2])]
msk = numpy.zeros((3, ))
if self.comp_mask[0]: msk[0] = 1
if self.comp_mask[1]: msk[1] = 1
if self.comp_mask[2]: msk[2] = 1
else:
vertex = [es.inf(x[0]), es.inf(x[1])]
msk = numpy.zeros((2, ))
if self.comp_mask[0]: msk[0] = 1
if self.comp_mask[1]: msk[1] = 1
self.__location_of_constraint = es.whereZero(
es.length(x - vertex), self.tol) * numpy.ones(shape)
if not self.value is None:
self.__value_of_constraint = self.__location_of_constraint * self.value
def getArguments(self, sigma):
"""
Returns precomputed values shared by `getDefect()` and `getGradient()`.
:param sigma: a suggestion for complex 1/V**2
:type sigma: ``escript.Data`` of shape (2,)
:return: solution, uTar, uTai, uTu
:rtype: ``escript.Data`` of shape (2,), 3 x `float`
"""
pde=self.setUpPDE()
D=pde.getCoefficient('D')
D[0,0]=-self.__omega**2 * sigma[0]
D[0,1]= self.__omega**2 * sigma[1]
D[1,0]=-self.__omega**2 * sigma[1]
D[1,1]=-self.__omega**2 * sigma[0]
pde.setValue(D=D, Y=self.__F, y=self.__f, y_dirac=self.__f_dirac)
u=pde.getSolution()
uTar=escript.integrate(self.__weight * ( u[0]*self.__data[0]+u[1]*self.__data[1]) )
uTai=escript.integrate(self.__weight * ( u[0]*self.__data[1]-u[1]*self.__data[0]) )
uTu = escript.integrate( self.__weight * escript.length(u)**2 )
return u, uTar, uTai, uTu
def __setOutput(self):
if self.__location_of_constraint is None:
x = self.domain.getX()
val = self.value
if isinstance(val, int) or isinstance(val, float):
shape = ()
elif isinstance(val, list) or isinstance(val, tuple):
shape = (len(val), )
elif isinstance(val, numpy.ndarray):
shape = val.shape
elif val is None:
shape = ()
else:
shape = val.getShape()
if self.domain.getDim() == 3:
vertex = [es.inf(x[0]), es.inf(x[1]), es.inf(x[2])]
else:
vertex = [es.inf(x[0]), es.inf(x[1])]
self.__location_of_constraint = es.whereZero(
es.length(x - vertex), self.tol) * numpy.ones(shape)
if not self.value is None:
self.__value_of_constraint = self.__location_of_constraint * self.value
def getDefect(self, sigma, u, uTar, uTai, uTu):
"""
Returns the defect value.
:param sigma: a suggestion for complex 1/V**2
:type sigma: ``escript.Data`` of shape (2,)
:param u: a u vector
:type u: ``escript.Data`` of shape (2,)
:param uTar: equals `integrate( w * (data[0]*u[0]+data[1]*u[1]))`
:type uTar: `float`
:param uTai: equals `integrate( w * (data[1]*u[0]-data[0]*u[1]))`
:type uTa: `float`
:param uTu: equals `integrate( w * (u,u))`
:type uTu: `float`
:rtype: ``float``
"""
# assuming integrate(w * length(data)**2) =1
if self.scaleF and abs(uTu) >0:
A = 1.-(uTar**2 + uTai**2)/uTu
else:
A = escript.integrate(self.__weight*escript.length(self.__data)**2)- 2 * uTar + uTu
return A/2
def getSafeTimeStepSize(self,dt):
"""
returns new step size
"""
h=self.domain.getSize()
return self.safety_factor*inf(h**2/(h*abs(self.heat_capacity*self.density)*length(self.velocity)+self.thermal_permabilty))
def getInverseHessianApproximationAtPoint(self, r, solve=True):
"""
"""
# substituting cached values
m = self.__pre_input
grad_m = self.__pre_args
if self._new_mu or self._update_Hessian:
self._new_mu = False
self._update_Hessian = False
mu = self.__mu
mu_c = self.__mu_c
DIM = self.getDomain().getDim()
numLS = self.getNumLevelSets()
if self.__w0 is not None:
if numLS == 1:
D = self.__w0 * mu
else:
D = self.getPDE().getCoefficient("D")
D.setToZero()
for k in range(numLS):
D[k, k] = self.__w0[k] * mu[k]
self.getPDE().setValue(D=D)
A = self.getPDE().getCoefficient("A")
A.setToZero()
if self.__w1 is not None:
if numLS == 1:
for i in range(DIM):
A[i, i] = self.__w1[i] * mu
else:
for k in range(numLS):
for i in range(DIM):
A[k, i, k, i] = self.__w1[k, i] * mu[k]
if numLS > 1:
# this could be make faster by creating caches for grad_m_k, l2_grad_m_k and o_kk
for k in range(numLS):
grad_m_k = grad_m[k, :]
l2_grad_m_k = escript.length(grad_m_k)**2
o_kk = escript.outer(grad_m_k, grad_m_k)
for l in range(k):
grad_m_l = grad_m[l, :]
l2_grad_m_l = escript.length(grad_m_l)**2
i_lk = escript.inner(grad_m_l, grad_m_k)
o_lk = escript.outer(grad_m_l, grad_m_k)
o_kl = escript.outer(grad_m_k, grad_m_l)
o_ll = escript.outer(grad_m_l, grad_m_l)
f = mu_c[l, k] * self.__wc[l, k]
Z = f * (2 * o_lk - o_kl -
i_lk * escript.kronecker(DIM))
A[l, :,
l, :] += f * (l2_grad_m_k * escript.kronecker(DIM) -
o_kk)
A[l, :, k, :] += Z
A[k, :, l, :] += escript.transpose(Z)
A[k, :,
k, :] += f * (l2_grad_m_l * escript.kronecker(DIM) -
o_ll)
self.getPDE().setValue(A=A)
#self.getPDE().resetRightHandSideCoefficients()
#self.getPDE().setValue(X=r[1])
#print "X only: ",self.getPDE().getSolution()
#self.getPDE().resetRightHandSideCoefficients()
#self.getPDE().setValue(Y=r[0])
#print "Y only: ",self.getPDE().getSolution()
self.getPDE().resetRightHandSideCoefficients()
self.getPDE().setValue(X=r[1], Y=r[0])
if not solve:
return self.getPDE()
return self.getPDE().getSolution()
def setup(self,
domainbuilder,
k0=None,
dk=None,
z0=None,
beta=None,
w0=None,
w1=None,
k_at_depth=None):
"""
Sets up the inversion from a `DomainBuilder`.
If magnetic data are given as scalar it is assumed that values are
collected in direction of the background magnetic field.
:param domainbuilder: Domain builder object with gravity source(s)
:type domainbuilder: `DomainBuilder`
:param k0: reference susceptibility, see `SusceptibilityMapping`. If not specified, zero is used.
:type k0: ``float`` or ``Scalar``
:param dk: susceptibility scale, see `SusceptibilityMapping`. If not specified, 1. is used.
:type dk: ``float`` or ``Scalar``
:param z0: reference depth for depth weighting, see `SusceptibilityMapping`. If not specified, zero is used.
:type z0: ``float`` or ``Scalar``
:param beta: exponent for depth weighting, see `SusceptibilityMapping`. If not specified, zero is used.
:type beta: ``float`` or ``Scalar``
:param w0: weighting factor for level set term regularization. If not set zero is assumed.
:type w0: ``Scalar`` or ``float``
:param w1: weighting factor for the gradient term in the regularization. If not set zero is assumed
:type w1: ``Vector`` or list of ``float``
:param k_at_depth: value for susceptibility at depth, see `DomainBuilder`.
:type k_at_depth: ``float`` or ``None``
"""
self.logger.info('Retrieving domain...')
dom = domainbuilder.getDomain()
DIM = dom.getDim()
trafo = makeTransformation(dom, domainbuilder.getReferenceSystem())
#========================
self.logger.info('Creating mapping ...')
k_mask = domainbuilder.getSetSusceptibilityMask()
if k_at_depth:
k2 = k_mask * k_at_depth + (1 - k_mask) * k0
elif k0:
k2 = (1 - k_mask) * k0
else:
k2 = 0
k_mapping = SusceptibilityMapping(dom, k0=k2, dk=dk, z0=z0, beta=beta)
scale_mapping = k_mapping.getTypicalDerivative()
#========================
self.logger.info("Setting up regularization...")
if w1 is None:
w1 = [1.] * DIM
regularization = Regularization(dom,
numLevelSets=1,
w0=w0,
w1=w1,
location_of_set_m=k_mask,
coordinates=trafo)
#====================================================================
self.logger.info("Retrieving magnetic field surveys...")
d_b = es.normalize(domainbuilder.getBackgroundMagneticFluxDensity())
surveys = domainbuilder.getMagneticSurveys()
B = []
w = []
for B_i, sigma_i in surveys:
w_i = es.safeDiv(1., sigma_i)
if self.magnetic_intensity_data:
if not B_i.getRank() == 0:
B_i = es.length(B_i)
if not w_i.getRank() == 0:
w_i = length(w_i)
else:
if B_i.getRank() == 0:
B_i = B_i * d_b
if w_i.getRank() == 0:
w_i = w_i * d_b
B.append(B_i)
w.append(w_i)
self.logger.debug("Added magnetic survey:")
self.logger.debug("B = %s" % B_i)
self.logger.debug("sigma = %s" % sigma_i)
self.logger.debug("w = %s" % w_i)
#====================================================================
self.logger.info("Setting up model...")
if self.self_demagnetization:
forward_model = SelfDemagnetizationModel(
dom,
w,
B,
domainbuilder.getBackgroundMagneticFluxDensity(),
fixPotentialAtBottom=self._fixMagneticPotentialAtBottom,
coordinates=trafo)
else:
if self.magnetic_intensity_data:
forward_model = MagneticIntensityModel(
dom,
w,
B,
domainbuilder.getBackgroundMagneticFluxDensity(),
fixPotentialAtBottom=self._fixMagneticPotentialAtBottom,
coordinates=trafo)
else:
forward_model = MagneticModel(
dom,
w,
B,
domainbuilder.getBackgroundMagneticFluxDensity(),
fixPotentialAtBottom=self._fixMagneticPotentialAtBottom,
coordinates=trafo)
forward_model.rescaleWeights(k_scale=scale_mapping)
#====================================================================
self.logger.info("Setting cost function...")
self.setCostFunction(
InversionCostFunction(regularization, k_mapping, forward_model))
def setup(self,
domainbuilder,
rho0=None,
drho=None,
rho_z0=None,
rho_beta=None,
k0=None,
dk=None,
k_z0=None,
k_beta=None,
w0=None,
w1=None,
w_gc=None,
rho_at_depth=None,
k_at_depth=None):
"""
Sets up the inversion from an instance ``domainbuilder`` of a
`DomainBuilder`. Gravity and magnetic data attached to the
``domainbuilder`` are considered in the inversion.
If magnetic data are given as scalar it is assumed that values are
collected in direction of the background magnetic field.
:param domainbuilder: Domain builder object with gravity source(s)
:type domainbuilder: `DomainBuilder`
:param rho0: reference density, see `DensityMapping`. If not specified,
zero is used.
:type rho0: ``float`` or `Scalar`
:param drho: density scale, see `DensityMapping`. If not specified,
2750 kg/m^3 is used.
:type drho: ``float`` or `Scalar`
:param rho_z0: reference depth for depth weighting for density, see
`DensityMapping`. If not specified, zero is used.
:type rho_z0: ``float`` or `Scalar`
:param rho_beta: exponent for density depth weighting, see
`DensityMapping`. If not specified, zero is used.
:type rho_beta: ``float`` or `Scalar`
:param k0: reference susceptibility, see `SusceptibilityMapping`.
If not specified, zero is used.
:type k0: ``float`` or `Scalar`
:param dk: susceptibility scale, see `SusceptibilityMapping`. If not
specified, 1. is used.
:type dk: ``float`` or `Scalar`
:param k_z0: reference depth for susceptibility depth weighting, see
`SusceptibilityMapping`. If not specified, zero is used.
:type k_z0: ``float`` or `Scalar`
:param k_beta: exponent for susceptibility depth weighting, see
`SusceptibilityMapping`. If not specified, zero is used.
:type k_beta: ``float`` or `Scalar`
:param w0: weighting factor for level set term in the regularization.
If not set zero is assumed.
:type w0: ``Scalar`` or ``float``
:param w1: weighting factor for the gradient term in the regularization
see `Regularization`. If not set zero is assumed.
:type w1: `es.Data` or ``ndarray`` of shape (DIM,)
:param w_gc: weighting factor for the cross gradient term in the
regularization, see `Regularization`. If not set one is
assumed.
:type w_gc: `Scalar` or `float`
:param k_at_depth: value for susceptibility at depth, see `DomainBuilder`.
:type k_at_depth: ``float`` or ``None``
:param rho_at_depth: value for density at depth, see `DomainBuilder`.
:type rho_at_depth: ``float`` or ``None``
"""
self.logger.info('Retrieving domain...')
dom = domainbuilder.getDomain()
DIM = dom.getDim()
trafo = makeTransformation(dom, domainbuilder.getReferenceSystem())
rock_mask = wherePositive(domainbuilder.getSetDensityMask() +
domainbuilder.getSetSusceptibilityMask())
#========================
self.logger.info('Creating mappings ...')
if rho_at_depth:
rho2 = rock_mask * rho_at_depth + (1 - rock_mask) * rho0
elif rho0:
rho2 = (1 - rock_mask) * rho0
else:
rho2 = 0
if k_at_depth:
k2 = rock_mask * k_at_depth + (1 - rock_mask) * k0
elif k0:
k2 = (1 - rock_mask) * k0
else:
k2 = 0
rho_mapping = DensityMapping(dom,
rho0=rho2,
drho=drho,
z0=rho_z0,
beta=rho_beta)
rho_scale_mapping = rho_mapping.getTypicalDerivative()
self.logger.debug("rho_scale_mapping = %s" % rho_scale_mapping)
k_mapping = SusceptibilityMapping(dom,
k0=k2,
dk=dk,
z0=k_z0,
beta=k_beta)
k_scale_mapping = k_mapping.getTypicalDerivative()
self.logger.debug("k_scale_mapping = %s" % k_scale_mapping)
#========================
self.logger.info("Setting up regularization...")
if w1 is None:
w1 = [1.] * DIM
regularization = Regularization(dom,
numLevelSets=1,
w0=w0,
w1=w1,
location_of_set_m=rock_mask,
coordinates=trafo)
#====================================================================
self.logger.info("Retrieving gravity surveys...")
surveys = domainbuilder.getGravitySurveys()
g = []
w = []
for g_i, sigma_i in surveys:
w_i = es.safeDiv(1., sigma_i)
if g_i.getRank() == 0:
g_i = g_i * es.kronecker(DIM)[DIM - 1]
if w_i.getRank() == 0:
w_i = w_i * es.kronecker(DIM)[DIM - 1]
g.append(g_i)
w.append(w_i)
self.logger.debug("Added gravity survey:")
self.logger.debug("g = %s" % g_i)
self.logger.debug("sigma = %s" % sigma_i)
self.logger.debug("w = %s" % w_i)
self.logger.info("Setting up gravity model...")
gravity_model = GravityModel(
dom,
w,
g,
fixPotentialAtBottom=self._fixGravityPotentialAtBottom,
coordinates=trafo)
gravity_model.rescaleWeights(rho_scale=rho_scale_mapping)
#====================================================================
self.logger.info("Retrieving magnetic field surveys...")
d_b = es.normalize(domainbuilder.getBackgroundMagneticFluxDensity())
surveys = domainbuilder.getMagneticSurveys()
B = []
w = []
for B_i, sigma_i in surveys:
w_i = es.safeDiv(1., sigma_i)
if self.magnetic_intensity_data:
if not B_i.getRank() == 0:
B_i = es.length(B_i)
if not w_i.getRank() == 0:
w_i = length(w_i)
else:
if B_i.getRank() == 0:
B_i = B_i * d_b
if w_i.getRank() == 0:
w_i = w_i * d_b
B.append(B_i)
w.append(w_i)
self.logger.debug("Added magnetic survey:")
self.logger.debug("B = %s" % B_i)
self.logger.debug("sigma = %s" % sigma_i)
self.logger.debug("w = %s" % w_i)
self.logger.info("Setting up magnetic model...")
if self.self_demagnetization:
magnetic_model = SelfDemagnetizationModel(
dom,
w,
B,
domainbuilder.getBackgroundMagneticFluxDensity(),
fixPotentialAtBottom=self._fixMagneticPotentialAtBottom,
coordinates=trafo)
else:
if self.magnetic_intensity_data:
magnetic_model = MagneticIntensityModel(
dom,
w,
B,
domainbuilder.getBackgroundMagneticFluxDensity(),
fixPotentialAtBottom=self._fixMagneticPotentialAtBottom,
coordinates=trafo)
else:
magnetic_model = MagneticModel(
dom,
w,
B,
domainbuilder.getBackgroundMagneticFluxDensity(),
fixPotentialAtBottom=self._fixMagneticPotentialAtBottom,
coordinates=trafo)
magnetic_model.rescaleWeights(k_scale=k_scale_mapping)
#====================================================================
self.logger.info("Setting cost function...")
self.setCostFunction(
InversionCostFunction(regularization, (rho_mapping, k_mapping),
((gravity_model, 0), (magnetic_model, 1))))
def getInverseHessianApproximationAtPoint(self, r, solve=True):
"""
"""
# substituting cached values
m = self.__pre_input
grad_m = self.__pre_args
if self._new_mu or self._update_Hessian:
self._new_mu = False
self._update_Hessian = False
mu = self.__mu
mu_c = self.__mu_c
DIM = self.getDomain().getDim()
numLS = self.getNumLevelSets()
if self.__w0 is not None:
if numLS == 1:
D = self.__w0 * mu
else:
D = self.getPDE().getCoefficient("D")
D.setToZero()
for k in range(numLS):
D[k, k] = self.__w0[k] * mu[k]
self.getPDE().setValue(D=D)
A = self.getPDE().getCoefficient("A")
A.setToZero()
if self.__w1 is not None:
if numLS == 1:
for i in range(DIM):
A[i, i] = self.__w1[i] * mu
else:
for k in range(numLS):
for i in range(DIM):
A[k, i, k, i] = self.__w1[k, i] * mu[k]
if numLS > 1:
# this could be make faster by creating caches for grad_m_k, l2_grad_m_k and o_kk
for k in range(numLS):
grad_m_k = grad_m[k, :]
l2_grad_m_k = length(grad_m_k) ** 2
o_kk = outer(grad_m_k, grad_m_k)
for l in range(k):
grad_m_l = grad_m[l, :]
l2_grad_m_l = length(grad_m_l) ** 2
i_lk = inner(grad_m_l, grad_m_k)
o_lk = outer(grad_m_l, grad_m_k)
o_kl = outer(grad_m_k, grad_m_l)
o_ll = outer(grad_m_l, grad_m_l)
f = mu_c[l, k] * self.__wc[l, k]
Z = f * (2 * o_lk - o_kl - i_lk * kronecker(DIM))
A[l, :, l, :] += f * (l2_grad_m_k * kronecker(DIM) - o_kk)
A[l, :, k, :] += Z
A[k, :, l, :] += transpose(Z)
A[k, :, k, :] += f * (l2_grad_m_l * kronecker(DIM) - o_ll)
self.getPDE().setValue(A=A)
# self.getPDE().resetRightHandSideCoefficients()
# self.getPDE().setValue(X=r[1])
# print "X only: ",self.getPDE().getSolution()
# self.getPDE().resetRightHandSideCoefficients()
# self.getPDE().setValue(Y=r[0])
# print "Y only: ",self.getPDE().getSolution()
self.getPDE().resetRightHandSideCoefficients()
self.getPDE().setValue(X=r[1], Y=r[0])
if not solve:
return self.getPDE()
return self.getPDE().getSolution()
def __init__(self,
domain,
omega,
w,
data,
F,
coordinates=None,
fixAtBottom=False,
tol=1e-10,
saveMemory=True,
scaleF=True):
"""
initializes a new forward model with acoustic wave form inversion.
:param domain: domain of the model
:type domain: `Domain`
:param w: weighting factors
:type w: ``Scalar``
:param data: real and imaginary part of data
:type data: ``escript.Data`` of shape (2,)
:param F: real and imaginary part of source given at Dirac points,
on surface or at volume.
:type F: ``escript.Data`` of shape (2,)
:param coordinates: defines coordinate system to be used (not supported yet)
:type coordinates: `ReferenceSystem` or `SpatialCoordinateTransformation`
:param tol: tolerance of underlying PDE
:type tol: positive ``float``
:param saveMemory: if true stiffness matrix is deleted after solution
of PDE to minimize memory requests. This will
require more compute time as the matrix needs to be
reallocated.
:type saveMemory: ``bool``
:param scaleF: if true source F is scaled to minimize defect.
:type scaleF: ``bool``
:param fixAtBottom: if true pressure is fixed to zero at the bottom of
the domain
:type fixAtBottom: ``bool``
"""
super(AcousticWaveForm, self).__init__()
self.__trafo = edc.makeTransformation(domain, coordinates)
if not self.getCoordinateTransformation().isCartesian():
raise ValueError(
"Non-Cartesian Coordinates are not supported yet.")
if not isinstance(data, escript.Data):
raise ValueError("data must be an escript.Data object.")
if not data.getFunctionSpace() == escript.FunctionOnBoundary(domain):
raise ValueError("data must be defined on boundary")
if not data.getShape() == (2, ):
raise ValueError(
"data must have shape (2,) (real and imaginary part).")
if w is None:
w = 1.
if not isinstance(w, escript.Data):
w = escript.Data(w, escript.FunctionOnBoundary(domain))
else:
if not w.getFunctionSpace() == escript.FunctionOnBoundary(domain):
raise ValueError("Weights must be defined on boundary.")
if not w.getShape() == ():
raise ValueError("Weights must be scalar.")
self.__domain = domain
self.__omega = omega
self.__weight = w
self.__data = data
self.scaleF = scaleF
if scaleF:
A = escript.integrate(self.__weight *
escript.length(self.__data)**2)
if A > 0:
self.__data *= 1. / escript.sqrt(A)
self.__BX = escript.boundingBox(domain)
self.edge_lengths = np.asarray(escript.boundingBoxEdgeLengths(domain))
if not isinstance(F, escript.Data):
F = escript.interpolate(F, escript.DiracDeltaFunctions(domain))
if not F.getShape() == (2, ):
raise ValueError(
"Source must have shape (2,) (real and imaginary part).")
self.__F = escript.Data()
self.__f = escript.Data()
self.__f_dirac = escript.Data()
if F.getFunctionSpace() == escript.DiracDeltaFunctions(domain):
self.__f_dirac = F
elif F.getFunctionSpace() == escript.FunctionOnBoundary(domain):
self.__f = F
else:
self.__F = F
self.__tol = tol
self.__fixAtBottom = fixAtBottom
self.__pde = None
if not saveMemory:
self.__pde = self.setUpPDE()