def __init__(self,
domain,
v_p,
wavelet,
source_tag,
dt=None,
p0=None,
p0_t=None,
absorption_zone=300 * U.m,
absorption_cut=1e-2,
lumping=True):
"""
initialize the sonic wave solver
:param domain: domain of the problem
:type domain: `Domain`
:param v_p: p-velocity field
:type v_p: `escript.Scalar`
:param wavelet: wavelet to describe the time evolution of source term
:type wavelet: `Wavelet`
:param source_tag: tag of the source location
:type source_tag: 'str' or 'int'
:param dt: time step size. If not present a suitable time step size is calculated.
:param p0: initial solution. If not present zero is used.
:param p0_t: initial solution change rate. If not present zero is used.
:param absorption_zone: thickness of absorption zone
:param absorption_cut: boundary value of absorption decay factor
:param lumping: if True mass matrix lumping is being used. This is accelerates the computing but introduces some diffusion.
"""
f = createAbsorptionLayerFunction(
escript.Function(domain).getX(), absorption_zone, absorption_cut)
v_p = v_p * f
if p0 == None:
p0 = escript.Scalar(0., escript.Solution(domain))
else:
p0 = escript.interpolate(p0, escript.Solution(domain))
if p0_t == None:
p0_t = escript.Scalar(0., escript.Solution(domain))
else:
p0_t = escript.interpolate(p0_t, escript.Solution(domain))
if dt == None:
dt = min(escript.inf((1. / 5.) * domain.getSize() / v_p),
wavelet.getTimeScale())
super(SonicWave, self).__init__(dt, u0=p0, v0=p0_t, t0=0.)
self.__wavelet = wavelet
self.__mypde = lpde.LinearSinglePDE(domain)
if lumping:
self.__mypde.getSolverOptions().setSolverMethod(
lpde.SolverOptions.HRZ_LUMPING)
self.__mypde.setSymmetryOn()
self.__mypde.setValue(D=1. / v_p**2)
self.__source_tag = source_tag
self.__r = escript.Scalar(
0., escript.DiracDeltaFunctions(self.__mypde.getDomain()))
def createLevelSetFunction(self, *props):
"""
returns an instance of an object used to represent a level set function
initialized with zeros. Components can be overwritten by physical
properties `props`. If present entries must correspond to the
`mappings` arguments in the constructor. Use ``None`` for properties
for which no value is given.
"""
m=self.regularization.getPDE().createSolution()
if len(props) > 0:
for i in range(self.numMappings):
if props[i]:
mp, idx=self.mappings[i]
m2=mp.getInverse(props[i])
if idx:
if len(idx) == 1:
m[idx[0]]=m2
else:
for k in range(idx): m[idx[k]]=m2[k]
else:
if isinstance(m2, Data):
m=interpolate(m2, m.getFunctionSpace())
else:
m=Data(m2, m.getFunctionSpace())
return m
def createLevelSetFunction(self, *props):
"""
returns an instance of an object used to represent a level set function
initialized with zeros. Components can be overwritten by physical
properties `props`. If present entries must correspond to the
`mappings` arguments in the constructor. Use ``None`` for properties
for which no value is given.
"""
m=self.regularization.getPDE().createSolution()
if len(props) > 0:
for i in range(self.numMappings):
if props[i]:
mp, idx=self.mappings[i]
m2=mp.getInverse(props[i])
if idx:
if len(idx) == 1:
m[idx[0]]=m2
else:
for k in range(idx): m[idx[k]]=m2[k]
else:
if isinstance(m2, Data):
m=interpolate(m2, m.getFunctionSpace())
else:
m=Data(m2, m.getFunctionSpace())
return m
def getDefect(self, rho, Hx, g_Hx):
"""
Returns the defect value.
:param rho: a suggestion for resistivity
:type rho: ``Data`` of shape ()
:param Hx: magnetic field
:type Hx: ``Data`` of shape (2,)
:param g_Hx: gradient of magnetic field
:type g_Hx: ``Data`` of shape (2,2)
:rtype: ``float``
"""
x = g_Hx.getFunctionSpace().getX()
Hx = escript.interpolate(Hx, x.getFunctionSpace())
u0 = Hx[0]
u1 = Hx[1]
u01 = g_Hx[0, 1]
u11 = g_Hx[1, 1]
scale = rho / (u0**2 + u1**2)
Z = self._Z
A = escript.integrate(
self._weight * (Z[0]**2 + Z[1]**2 + scale *
(-2 * Z[0] * (u0 * u01 + u1 * u11) + 2 * Z[1] *
(u1 * u01 - u0 * u11) + rho * (u01**2 + u11**2))))
return A / 2
def getDefect(self, sigma, Ex, dExdz):
"""
Returns the defect value.
:param sigma: a suggestion for conductivity
:type sigma: ``Data`` of shape ()
:param Ex: electric field
:type Ex: ``Data`` of shape (2,)
:param dExdz: vertical derivative of electric field
:type dExdz: ``Data`` of shape (2,)
:rtype: ``float``
"""
x = dExdz.getFunctionSpace().getX()
Ex = escript.interpolate(Ex, x.getFunctionSpace())
u0 = Ex[0]
u1 = Ex[1]
u01 = dExdz[0]
u11 = dExdz[1]
scale = self._weight / (u01**2 + u11**2)
Z = self._Z
A = escript.integrate(
scale * ((Z[0]**2 + Z[1]**2) * (u01**2 + u11**2) + 2 * Z[1] *
(u0 * u11 - u01 * u1) - 2 * Z[0] *
(u0 * u01 + u11 * u1) + u0**2 + u1**2))
return A / 2
def getGradient(self, sigma, Ex, dExdz):
"""
Returns the gradient of the defect with respect to density.
:param sigma: a suggestion for conductivity
:type sigma: ``Data`` of shape ()
:param Ex: electric field
:type Ex: ``Data`` of shape (2,)
:param dExdz: vertical derivative of electric field
:type dExdz: ``Data`` of shape (2,)
"""
pde = self.setUpPDE()
DIM = self.getDomain().getDim()
x = dExdz.getFunctionSpace().getX()
Ex = escript.interpolate(Ex, x.getFunctionSpace())
u0 = Ex[0]
u1 = Ex[1]
u01 = dExdz[0]
u11 = dExdz[1]
D = pde.getCoefficient('D')
Y = pde.getCoefficient('Y')
X = pde.getCoefficient('X')
A = pde.getCoefficient('A')
A[0, :, 0, :] = escript.kronecker(DIM)
A[1, :, 1, :] = escript.kronecker(DIM)
f = self._omega_mu * sigma
D[0, 1] = f
D[1, 0] = -f
Z = self._Z
scale = 1. / (u01**2 + u11**2)
scale2 = scale**2
scale *= self._weight
scale2 *= self._weight
Y[0] = scale * (u0 - u01 * Z[0] + u11 * Z[1])
Y[1] = scale * (u1 - u01 * Z[1] - u11 * Z[0])
X[0,1] = scale2 * (2*u01*u11*(Z[0]*u1-Z[1]*u0) \
+ (Z[0]*u0+Z[1]*u1)*(u01**2-u11**2)
- u01*(u0**2 + u1**2))
X[1,1] = scale2 * (2*u01*u11*(Z[1]*u1+Z[0]*u0) \
+ (Z[1]*u0-Z[0]*u1)*(u01**2-u11**2)
- u11*(u0**2 + u1**2))
pde.setValue(A=A, D=D, X=X, Y=Y)
Zstar = pde.getSolution()
return (-self._omega_mu) * (Zstar[1] * u0 - Zstar[0] * u1)
def getGradient(self, sigma, u, uTar, uTai, uTu):
"""
Returns the gradient of the defect with respect to density.
: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`
"""
pde = self.setUpPDE()
if self.scaleF and abs(uTu) > 0:
Z = ((uTar**2 + uTai**2) / uTu**2) * escript.interpolate(
u, self.__data.getFunctionSpace())
Z[0] += (-uTar / uTu) * self.__data[0] + (-uTai /
uTu) * self.__data[1]
Z[1] += (-uTar /
uTu) * self.__data[1] + uTai / uTu * self.__data[0]
else:
Z = u - self.__data
if Z.getFunctionSpace() == escript.DiracDeltaFunctions(
self.getDomain()):
pde.setValue(y_dirac=self.__weight * Z)
else:
pde.setValue(y=self.__weight * Z)
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)
ZTo2 = pde.getSolution() * self.__omega**2
return escript.inner(
ZTo2, u) * [1, 0] + (ZTo2[1] * u[0] - ZTo2[0] * u[1]) * [0, 1]
def __init__(self,
domain,
numLevelSets=1,
w0=None,
w1=None,
wc=None,
location_of_set_m=escript.Data(),
useDiagonalHessianApproximation=False,
tol=1e-8,
coordinates=None,
scale=None,
scale_c=None):
"""
initialization.
:param domain: domain
:type domain: `Domain`
:param numLevelSets: number of level sets
:type numLevelSets: ``int``
:param w0: weighting factor for the m**2 term. If not set zero is assumed.
:type w0: ``Scalar`` if ``numLevelSets`` == 1 or `Data` object of shape
(``numLevelSets`` ,) if ``numLevelSets`` > 1
:param w1: weighting factor for the grad(m_i) terms. If not set zero is assumed
:type w1: ``Vector`` if ``numLevelSets`` == 1 or `Data` object of shape
(``numLevelSets`` , DIM) if ``numLevelSets`` > 1
:param wc: weighting factor for the cross gradient terms. If not set
zero is assumed. Used for the case if ``numLevelSets`` > 1
only. Only values ``wc[l,k]`` in the lower triangle (l<k)
are used.
:type wc: `Data` object of shape (``numLevelSets`` , ``numLevelSets``)
:param location_of_set_m: marks location of zero values of the level
set function ``m`` by a positive entry.
:type location_of_set_m: ``Scalar`` if ``numLevelSets`` == 1 or `Data`
object of shape (``numLevelSets`` ,) if ``numLevelSets`` > 1
:param useDiagonalHessianApproximation: if True cross gradient terms
between level set components are ignored when calculating
approximations of the inverse of the Hessian Operator.
This can speed-up the calculation of the inverse but may
lead to an increase of the number of iteration steps in the
inversion.
:type useDiagonalHessianApproximation: ``bool``
:param tol: tolerance when solving the PDE for the inverse of the
Hessian Operator
:type tol: positive ``float``
:param coordinates: defines coordinate system to be used
:type coordinates: ReferenceSystem` or `SpatialCoordinateTransformation`
:param scale: weighting factor for level set function variation terms.
If not set one is used.
:type scale: ``Scalar`` if ``numLevelSets`` == 1 or `Data` object of
shape (``numLevelSets`` ,) if ``numLevelSets`` > 1
:param scale_c: scale for the cross gradient terms. If not set
one is assumed. Used for the case if ``numLevelSets`` > 1
only. Only values ``scale_c[l,k]`` in the lower triangle
(l<k) are used.
:type scale_c: `Data` object of shape (``numLevelSets``,``numLevelSets``)
"""
if w0 is None and w1 is None:
raise ValueError("Values for w0 or for w1 must be given.")
if wc is None and numLevelSets > 1:
raise ValueError("Values for wc must be given.")
self.__pre_input = None
self.__pre_args = None
self.logger = logging.getLogger('inv.%s' % self.__class__.__name__)
self.__domain = domain
DIM = self.__domain.getDim()
self.__numLevelSets = numLevelSets
self.__trafo = makeTransformation(domain, coordinates)
self.__pde = linearPDEs.LinearPDE(self.__domain,
numEquations=self.__numLevelSets,
numSolutions=self.__numLevelSets)
self.__pde.getSolverOptions().setTolerance(tol)
self.__pde.setSymmetryOn()
self.__pde.setValue(
A=self.__pde.createCoefficient('A'),
D=self.__pde.createCoefficient('D'),
)
try:
self.__pde.setValue(q=location_of_set_m)
except linearPDEs.IllegalCoefficientValue:
raise ValueError(
"Unable to set location of fixed level set function.")
# =========== check the shape of the scales: ========================
if scale is None:
if numLevelSets == 1:
scale = 1.
else:
scale = np.ones((numLevelSets, ))
else:
scale = np.asarray(scale)
if numLevelSets == 1:
if scale.shape == ():
if not scale > 0:
raise ValueError("Value for scale must be positive.")
else:
raise ValueError("Unexpected shape %s for scale." %
scale.shape)
else:
if scale.shape is (numLevelSets, ):
if not min(scale) > 0:
raise ValueError(
"All values for scale must be positive.")
else:
raise ValueError("Unexpected shape %s for scale." %
scale.shape)
if scale_c is None or numLevelSets < 2:
scale_c = np.ones((numLevelSets, numLevelSets))
else:
scale_c = np.asarray(scale_c)
if scale_c.shape == (numLevelSets, numLevelSets):
if not all([[scale_c[l, k] > 0. for l in range(k)]
for k in range(1, numLevelSets)]):
raise ValueError(
"All values in the lower triangle of scale_c must be positive."
)
else:
raise ValueError("Unexpected shape %s for scale." %
scale_c.shape)
# ===== check the shape of the weights: =============================
if w0 is not None:
w0 = escript.interpolate(
w0, self.__pde.getFunctionSpaceForCoefficient('D'))
s0 = w0.getShape()
if numLevelSets == 1:
if not s0 == ():
raise ValueError("Unexpected shape %s for weight w0." %
(s0, ))
else:
if not s0 == (numLevelSets, ):
raise ValueError("Unexpected shape %s for weight w0." %
(s0, ))
if not self.__trafo.isCartesian():
w0 *= self.__trafo.getVolumeFactor()
if not w1 is None:
w1 = escript.interpolate(
w1, self.__pde.getFunctionSpaceForCoefficient('A'))
s1 = w1.getShape()
if numLevelSets == 1:
if not s1 == (DIM, ):
raise ValueError("Unexpected shape %s for weight w1." %
(s1, ))
else:
if not s1 == (numLevelSets, DIM):
raise ValueError("Unexpected shape %s for weight w1." %
(s1, ))
if not self.__trafo.isCartesian():
f = self.__trafo.getScalingFactors(
)**2 * self.__trafo.getVolumeFactor()
if numLevelSets == 1:
w1 *= f
else:
for i in range(numLevelSets):
w1[i, :] *= f
if numLevelSets == 1:
wc = None
else:
wc = escript.interpolate(
wc, self.__pde.getFunctionSpaceForCoefficient('A'))
sc = wc.getShape()
if not sc == (numLevelSets, numLevelSets):
raise ValueError("Unexpected shape %s for weight wc." % (sc, ))
if not self.__trafo.isCartesian():
raise ValueError(
"Non-cartesian coordinates for cross-gradient term is not supported yet."
)
# ============= now we rescale weights: =============================
L2s = np.asarray(escript.boundingBoxEdgeLengths(domain))**2
L4 = 1 / np.sum(1 / L2s)**2
if numLevelSets == 1:
A = 0
if w0 is not None:
A = escript.integrate(w0)
if w1 is not None:
A += escript.integrate(inner(w1, 1 / L2s))
if A > 0:
f = scale / A
if w0 is not None:
w0 *= f
if w1 is not None:
w1 *= f
else:
raise ValueError("Non-positive weighting factor detected.")
else: # numLevelSets > 1
for k in range(numLevelSets):
A = 0
if w0 is not None:
A = escript.integrate(w0[k])
if w1 is not None:
A += escript.integrate(inner(w1[k, :], 1 / L2s))
if A > 0:
f = scale[k] / A
if w0 is not None:
w0[k] *= f
if w1 is not None:
w1[k, :] *= f
else:
raise ValueError(
"Non-positive weighting factor for level set component %d detected."
% k)
# and now the cross-gradient:
if wc is not None:
for l in range(k):
A = escript.integrate(wc[l, k]) / L4
if A > 0:
f = scale_c[l, k] / A
wc[l, k] *= f
# else:
# raise ValueError("Non-positive weighting factor for cross-gradient level set components %d and %d detected."%(l,k))
self.__w0 = w0
self.__w1 = w1
self.__wc = wc
self.__pde_is_set = False
if self.__numLevelSets > 1:
self.__useDiagonalHessianApproximation = useDiagonalHessianApproximation
else:
self.__useDiagonalHessianApproximation = True
self._update_Hessian = True
self.__num_tradeoff_factors = numLevelSets + (
(numLevelSets - 1) * numLevelSets) // 2
self.setTradeOffFactors()
self.__vol_d = escript.vol(self.__domain)
def __init__(
self,
domain,
numLevelSets=1,
w0=None,
w1=None,
wc=None,
location_of_set_m=Data(),
useDiagonalHessianApproximation=False,
tol=1e-8,
coordinates=None,
scale=None,
scale_c=None,
):
"""
initialization.
:param domain: domain
:type domain: `Domain`
:param numLevelSets: number of level sets
:type numLevelSets: ``int``
:param w0: weighting factor for the m**2 term. If not set zero is assumed.
:type w0: ``Scalar`` if ``numLevelSets`` == 1 or `Data` object of shape
(``numLevelSets`` ,) if ``numLevelSets`` > 1
:param w1: weighting factor for the grad(m_i) terms. If not set zero is assumed
:type w1: ``Vector`` if ``numLevelSets`` == 1 or `Data` object of shape
(``numLevelSets`` , DIM) if ``numLevelSets`` > 1
:param wc: weighting factor for the cross gradient terms. If not set
zero is assumed. Used for the case if ``numLevelSets`` > 1
only. Only values ``wc[l,k]`` in the lower triangle (l<k)
are used.
:type wc: `Data` object of shape (``numLevelSets`` , ``numLevelSets``)
:param location_of_set_m: marks location of zero values of the level
set function ``m`` by a positive entry.
:type location_of_set_m: ``Scalar`` if ``numLevelSets`` == 1 or `Data`
object of shape (``numLevelSets`` ,) if ``numLevelSets`` > 1
:param useDiagonalHessianApproximation: if True cross gradient terms
between level set components are ignored when calculating
approximations of the inverse of the Hessian Operator.
This can speed-up the calculation of the inverse but may
lead to an increase of the number of iteration steps in the
inversion.
:type useDiagonalHessianApproximation: ``bool``
:param tol: tolerance when solving the PDE for the inverse of the
Hessian Operator
:type tol: positive ``float``
:param coordinates: defines coordinate system to be used
:type coordinates: ReferenceSystem` or `SpatialCoordinateTransformation`
:param scale: weighting factor for level set function variation terms.
If not set one is used.
:type scale: ``Scalar`` if ``numLevelSets`` == 1 or `Data` object of
shape (``numLevelSets`` ,) if ``numLevelSets`` > 1
:param scale_c: scale for the cross gradient terms. If not set
one is assumed. Used for the case if ``numLevelSets`` > 1
only. Only values ``scale_c[l,k]`` in the lower triangle
(l<k) are used.
:type scale_c: `Data` object of shape (``numLevelSets``,``numLevelSets``)
"""
if w0 is None and w1 is None:
raise ValueError("Values for w0 or for w1 must be given.")
if wc is None and numLevelSets > 1:
raise ValueError("Values for wc must be given.")
self.__pre_input = None
self.__pre_args = None
self.logger = logging.getLogger("inv.%s" % self.__class__.__name__)
self.__domain = domain
DIM = self.__domain.getDim()
self.__numLevelSets = numLevelSets
self.__trafo = makeTransformation(domain, coordinates)
self.__pde = LinearPDE(self.__domain, numEquations=self.__numLevelSets, numSolutions=self.__numLevelSets)
self.__pde.getSolverOptions().setTolerance(tol)
self.__pde.setSymmetryOn()
self.__pde.setValue(A=self.__pde.createCoefficient("A"), D=self.__pde.createCoefficient("D"))
try:
self.__pde.setValue(q=location_of_set_m)
except IllegalCoefficientValue:
raise ValueError("Unable to set location of fixed level set function.")
# =========== check the shape of the scales: ========================
if scale is None:
if numLevelSets == 1:
scale = 1.0
else:
scale = np.ones((numLevelSets,))
else:
scale = np.asarray(scale)
if numLevelSets == 1:
if scale.shape == ():
if not scale > 0:
raise ValueError("Value for scale must be positive.")
else:
raise ValueError("Unexpected shape %s for scale." % scale.shape)
else:
if scale.shape is (numLevelSets,):
if not min(scale) > 0:
raise ValueError("All values for scale must be positive.")
else:
raise ValueError("Unexpected shape %s for scale." % scale.shape)
if scale_c is None or numLevelSets < 2:
scale_c = np.ones((numLevelSets, numLevelSets))
else:
scale_c = np.asarray(scale_c)
if scale_c.shape == (numLevelSets, numLevelSets):
if not all([[scale_c[l, k] > 0.0 for l in range(k)] for k in range(1, numLevelSets)]):
raise ValueError("All values in the lower triangle of scale_c must be positive.")
else:
raise ValueError("Unexpected shape %s for scale." % scale_c.shape)
# ===== check the shape of the weights: =============================
if w0 is not None:
w0 = interpolate(w0, self.__pde.getFunctionSpaceForCoefficient("D"))
s0 = w0.getShape()
if numLevelSets == 1:
if not s0 == ():
raise ValueError("Unexpected shape %s for weight w0." % (s0,))
else:
if not s0 == (numLevelSets,):
raise ValueError("Unexpected shape %s for weight w0." % (s0,))
if not self.__trafo.isCartesian():
w0 *= self.__trafo.getVolumeFactor()
if not w1 is None:
w1 = interpolate(w1, self.__pde.getFunctionSpaceForCoefficient("A"))
s1 = w1.getShape()
if numLevelSets == 1:
if not s1 == (DIM,):
raise ValueError("Unexpected shape %s for weight w1." % (s1,))
else:
if not s1 == (numLevelSets, DIM):
raise ValueError("Unexpected shape %s for weight w1." % (s1,))
if not self.__trafo.isCartesian():
f = self.__trafo.getScalingFactors() ** 2 * self.__trafo.getVolumeFactor()
if numLevelSets == 1:
w1 *= f
else:
for i in range(numLevelSets):
w1[i, :] *= f
if numLevelSets == 1:
wc = None
else:
wc = interpolate(wc, self.__pde.getFunctionSpaceForCoefficient("A"))
sc = wc.getShape()
if not sc == (numLevelSets, numLevelSets):
raise ValueError("Unexpected shape %s for weight wc." % (sc,))
if not self.__trafo.isCartesian():
raise ValueError("Non-cartesian coordinates for cross-gradient term is not supported yet.")
# ============= now we rescale weights: =============================
L2s = np.asarray(boundingBoxEdgeLengths(domain)) ** 2
L4 = 1 / np.sum(1 / L2s) ** 2
if numLevelSets == 1:
A = 0
if w0 is not None:
A = integrate(w0)
if w1 is not None:
A += integrate(inner(w1, 1 / L2s))
if A > 0:
f = scale / A
if w0 is not None:
w0 *= f
if w1 is not None:
w1 *= f
else:
raise ValueError("Non-positive weighting factor detected.")
else: # numLevelSets > 1
for k in range(numLevelSets):
A = 0
if w0 is not None:
A = integrate(w0[k])
if w1 is not None:
A += integrate(inner(w1[k, :], 1 / L2s))
if A > 0:
f = scale[k] / A
if w0 is not None:
w0[k] *= f
if w1 is not None:
w1[k, :] *= f
else:
raise ValueError("Non-positive weighting factor for level set component %d detected." % k)
# and now the cross-gradient:
if wc is not None:
for l in range(k):
A = integrate(wc[l, k]) / L4
if A > 0:
f = scale_c[l, k] / A
wc[l, k] *= f
# else:
# raise ValueError("Non-positive weighting factor for cross-gradient level set components %d and %d detected."%(l,k))
self.__w0 = w0
self.__w1 = w1
self.__wc = wc
self.__pde_is_set = False
if self.__numLevelSets > 1:
self.__useDiagonalHessianApproximation = useDiagonalHessianApproximation
else:
self.__useDiagonalHessianApproximation = True
self._update_Hessian = True
self.__num_tradeoff_factors = numLevelSets + ((numLevelSets - 1) * numLevelSets) // 2
self.setTradeOffFactors()
self.__vol_d = vol(self.__domain)
def __init__(self,
domain,
v_p,
wavelet,
source_tag,
source_vector=[1., 0.],
eps=0.,
delta=0.,
azimuth=0.,
dt=None,
p0=None,
v0=None,
absorption_zone=300 * U.m,
absorption_cut=1e-2,
lumping=True):
"""
initialize the HTI wave solver
:param domain: domain of the problem
:type domain: `Doamin`
:param v_p: vertical p-velocity field
:type v_p: `escript.Scalar`
:param v_s: vertical s-velocity field
:type v_s: `escript.Scalar`
:param wavelet: wavelet to describe the time evolution of source term
:type wavelet: `Wavelet`
:param source_tag: tag of the source location
:type source_tag: 'str' or 'int'
:param source_vector: source orientation vector
:param eps: first Thompsen parameter
:param azimuth: azimuth (rotation around verticle axis)
:param gamma: third Thompsen parameter
:param rho: density
:param dt: time step size. If not present a suitable time step size is calculated.
:param p0: initial solution (Q(t=0), P(t=0)). If not present zero is used.
:param v0: initial solution change rate. If not present zero is used.
:param absorption_zone: thickness of absorption zone
:param absorption_cut: boundary value of absorption decay factor
:param lumping: if True mass matrix lumping is being used. This is accelerates the computing but introduces some diffusion.
"""
DIM = domain.getDim()
f = createAbsorptionLayerFunction(v_p.getFunctionSpace().getX(),
absorption_zone, absorption_cut)
self.v2_p = v_p**2
self.v2_t = self.v2_p * escript.sqrt(1 + 2 * delta)
self.v2_n = self.v2_p * (1 + 2 * eps)
if p0 == None:
p0 = escript.Data(0., (2, ), escript.Solution(domain))
else:
p0 = escript.interpolate(p0, escript.Solution(domain))
if v0 == None:
v0 = escript.Data(0., (2, ), escript.Solution(domain))
else:
v0 = escript.interpolate(v0, escript.Solution(domain))
if dt == None:
dt = min(
min(escript.inf(domain.getSize() / escript.sqrt(self.v2_p)),
escript.inf(domain.getSize() / escript.sqrt(self.v2_t)),
escript.inf(domain.getSize() / escript.sqrt(self.v2_n))),
wavelet.getTimeScale()) * 0.2
super(SonicHTIWave, self).__init__(dt, u0=p0, v0=v0, t0=0.)
self.__wavelet = wavelet
self.__mypde = lpde.LinearPDESystem(domain)
if lumping:
self.__mypde.getSolverOptions().setSolverMethod(
lpde.SolverOptions.HRZ_LUMPING)
self.__mypde.setSymmetryOn()
self.__mypde.setValue(D=escript.kronecker(2),
X=self.__mypde.createCoefficient('X'))
self.__source_tag = source_tag
self.__r = escript.Vector(
0, escript.DiracDeltaFunctions(self.__mypde.getDomain()))
self.__r.setTaggedValue(self.__source_tag, source_vector)
def __init__(self,
domain,
v_p,
v_s,
wavelet,
source_tag,
source_vector=[0., 1.],
eps=0.,
delta=0.,
theta=0.,
rho=1.,
dt=None,
u0=None,
v0=None,
absorption_zone=300 * U.m,
absorption_cut=1e-2,
lumping=True):
"""
initialize the TTI wave solver
:param domain: domain of the problem
:type domain: `Domain`
:param v_p: vertical p-velocity field
:type v_p: `escript.Scalar`
:param v_s: vertical s-velocity field
:type v_s: `escript.Scalar`
:param wavelet: wavelet to describe the time evolution of source term
:type wavelet: `Wavelet`
:param source_tag: tag of the source location
:type source_tag: 'str' or 'int'
:param source_vector: source orientation vector
:param eps: first Thompsen parameter
:param delta: second Thompsen parameter
:param theta: tilting (in Rad)
:param rho: density
:param dt: time step size. If not present a suitable time step size is calculated.
:param u0: initial solution. If not present zero is used.
:param v0: initial solution change rate. If not present zero is used.
:param absorption_zone: thickness of absorption zone
:param absorption_cut: boundary value of absorption decay factor
:param lumping: if True mass matrix lumping is being used. This is accelerates the computing but introduces some diffusion.
"""
cos = escript.cos
sin = escript.sin
DIM = domain.getDim()
if not DIM == 2:
raise ValueError("Only 2D is supported.")
f = createAbsorptionLayerFunction(
escript.Function(domain).getX(), absorption_zone, absorption_cut)
v_p = v_p * f
v_s = v_s * f
if u0 == None:
u0 = escript.Vector(0., escript.Solution(domain))
else:
u0 = escript.interpolate(p0, escript.Solution(domain))
if v0 == None:
v0 = escript.Vector(0., escript.Solution(domain))
else:
v0 = escript.interpolate(v0, escript.Solution(domain))
if dt == None:
dt = min((1. / 5.) * min(escript.inf(domain.getSize() / v_p),
escript.inf(domain.getSize() / v_s)),
wavelet.getTimeScale())
super(TTIWave, self).__init__(dt, u0=u0, v0=v0, t0=0.)
self.__wavelet = wavelet
self.__mypde = lpde.LinearPDESystem(domain)
if lumping:
self.__mypde.getSolverOptions().setSolverMethod(
lpde.SolverOptions.HRZ_LUMPING)
self.__mypde.setSymmetryOn()
self.__mypde.setValue(D=rho * escript.kronecker(DIM),
X=self.__mypde.createCoefficient('X'))
self.__source_tag = source_tag
self.__r = escript.Vector(
0, escript.DiracDeltaFunctions(self.__mypde.getDomain()))
self.__r.setTaggedValue(self.__source_tag, source_vector)
c0_33 = v_p**2 * rho
c0_66 = v_s**2 * rho
c0_11 = (1 + 2 * eps) * c0_33
c0_13 = escript.sqrt(2 * c0_33 * (c0_33 - c0_66) * delta +
(c0_33 - c0_66)**2) - c0_66
self.c11 = c0_11 * cos(theta)**4 - 2 * c0_13 * cos(
theta)**4 + 2 * c0_13 * cos(theta)**2 + c0_33 * sin(
theta)**4 - 4 * c0_66 * cos(theta)**4 + 4 * c0_66 * cos(
theta)**2
self.c13 = -c0_11 * cos(theta)**4 + c0_11 * cos(
theta)**2 + c0_13 * sin(theta)**4 + c0_13 * cos(
theta)**4 - c0_33 * cos(theta)**4 + c0_33 * cos(
theta)**2 + 4 * c0_66 * cos(theta)**4 - 4 * c0_66 * cos(
theta)**2
self.c16 = (-2 * c0_11 * cos(theta)**2 - 4 * c0_13 * sin(theta)**2 +
2 * c0_13 + 2 * c0_33 * sin(theta)**2 - 8 * c0_66 *
sin(theta)**2 + 4 * c0_66) * sin(theta) * cos(theta) / 2
self.c33 = c0_11 * sin(theta)**4 - 2 * c0_13 * cos(
theta)**4 + 2 * c0_13 * cos(theta)**2 + c0_33 * cos(
theta)**4 - 4 * c0_66 * cos(theta)**4 + 4 * c0_66 * cos(
theta)**2
self.c36 = (2 * c0_11 * cos(theta)**2 - 2 * c0_11 +
4 * c0_13 * sin(theta)**2 - 2 * c0_13 +
2 * c0_33 * cos(theta)**2 + 8 * c0_66 * sin(theta)**2 -
4 * c0_66) * sin(theta) * cos(theta) / 2
self.c66 = -c0_11 * cos(theta)**4 + c0_11 * cos(
theta)**2 + 2 * c0_13 * cos(theta)**4 - 2 * c0_13 * cos(
theta)**2 - c0_33 * cos(theta)**4 + c0_33 * cos(
theta)**2 + c0_66 * sin(theta)**4 + 3 * c0_66 * cos(
theta)**4 - 2 * c0_66 * cos(theta)**2
def __init__(self,
domain,
v_p,
v_s,
wavelet,
source_tag,
source_vector=[1., 0., 0.],
eps=0.,
gamma=0.,
delta=0.,
rho=1.,
dt=None,
u0=None,
v0=None,
absorption_zone=None,
absorption_cut=1e-2,
lumping=True,
disable_fast_assemblers=False):
"""
initialize the VTI wave solver
:param domain: domain of the problem
:type domain: `Domain`
:param v_p: vertical p-velocity field
:type v_p: `escript.Scalar`
:param v_s: vertical s-velocity field
:type v_s: `escript.Scalar`
:param wavelet: wavelet to describe the time evolution of source term
:type wavelet: `Wavelet`
:param source_tag: tag of the source location
:type source_tag: 'str' or 'int'
:param source_vector: source orientation vector
:param eps: first Thompsen parameter
:param delta: second Thompsen parameter
:param gamma: third Thompsen parameter
:param rho: density
:param dt: time step size. If not present a suitable time step size is calculated.
:param u0: initial solution. If not present zero is used.
:param v0: initial solution change rate. If not present zero is used.
:param absorption_zone: thickness of absorption zone
:param absorption_cut: boundary value of absorption decay factor
:param lumping: if True mass matrix lumping is being used. This is accelerates the computing but introduces some diffusion.
:param disable_fast_assemblers: if True, forces use of slower and more general PDE assemblers
"""
DIM = domain.getDim()
self.fastAssembler = hasattr(
domain, "createAssembler") and not disable_fast_assemblers
f = createAbsorptionLayerFunction(v_p.getFunctionSpace().getX(),
absorption_zone, absorption_cut)
v_p = v_p * f
v_s = v_s * f
if u0 == None:
u0 = escript.Vector(0., escript.Solution(domain))
else:
u0 = escript.interpolate(p0, escript.Solution(domain))
if v0 == None:
v0 = escript.Vector(0., escript.Solution(domain))
else:
v0 = escript.interpolate(v0, escript.Solution(domain))
if dt == None:
dt = min((1. / 5.) * min(escript.inf(domain.getSize() / v_p),
escript.inf(domain.getSize() / v_s)),
wavelet.getTimeScale())
super(HTIWave, self).__init__(dt, u0=u0, v0=v0, t0=0.)
self.__wavelet = wavelet
self.c33 = v_p**2 * rho
self.c44 = v_s**2 * rho
self.c11 = (1 + 2 * eps) * self.c33
self.c66 = (1 + 2 * gamma) * self.c44
self.c13 = escript.sqrt(2 * self.c33 * (self.c33 - self.c44) * delta +
(self.c33 - self.c44)**2) - self.c44
self.c23 = self.c33 - 2 * self.c66
if self.fastAssembler:
C = [("c11", self.c11), ("c23", self.c23), ("c13", self.c13),
("c33", self.c33), ("c44", self.c44), ("c66", self.c66)]
if "speckley" in domain.getDescription().lower():
C = [(n, escript.interpolate(d,
escript.ReducedFunction(domain)))
for n, d in C]
self.__mypde = lpde.WavePDE(domain, C)
else:
self.__mypde = lpde.LinearPDESystem(domain)
self.__mypde.setValue(X=self.__mypde.createCoefficient('X'))
if lumping:
self.__mypde.getSolverOptions().setSolverMethod(
lpde.SolverOptions.HRZ_LUMPING)
self.__mypde.setSymmetryOn()
self.__mypde.setValue(D=rho * escript.kronecker(DIM))
self.__source_tag = source_tag
if DIM == 2:
source_vector = [source_vector[0], source_vector[2]]
self.__r = escript.Vector(
0, escript.DiracDeltaFunctions(self.__mypde.getDomain()))
self.__r.setTaggedValue(self.__source_tag, source_vector)
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()
def RegionalCalculation(reg_mask):
"""
Calculates the "regional" from the entire FEILDS model excluding the
selected region and outputs gravity at the specified altitude...
see above for the "residual"
"""
# read in a gravity data grid to define data computation space
G_DATA = os.path.join(DATADIR,'Final_BouguerTC_UC15K_qrtdeg.nc')
FS=ReducedFunction(dom)
nValues=[NX, NY, 1]
first = [0, 0, cell_at_altitude]
multiplier = [1, 1, 1]
reverse = [0, 0, 0]
byteorder = BYTEORDER_NATIVE
gdata = readBinaryGrid(G_DATA, FS, shape=(),
fill=-999999, byteOrder=byteorder,
dataType=DATATYPE_FLOAT32, first=first, numValues=nValues,
multiplier=multiplier, reverse=reverse)
print("Grid successfully read")
# get the masking and units sorted out for the data-space
g_mask = whereNonZero(gdata+999999)
gdata=gdata*g_mask * GRAV_UNITS
# if people choose to have air in their region we exclude it from the
# specified gravity calculation region
if h_top < 0.:
reg_mask = reg_mask+mask_air
live_model = initial_model* whereNonPositive(reg_mask)
dead_model = initial_model* wherePositive(reg_mask)
if UseMean is True:
# calculate the mean density within the selected region
BackgroundDensity = integrate(dead_model)/integrate(wherePositive(reg_mask))
print("Density mean for selected region equals = %s"%BackgroundDensity)
live_model = live_model + BackgroundDensity * wherePositive(reg_mask)
# create mapping
rho_mapping = DensityMapping(dom, rho0=live_model)
# invert sign of gravity field to account for escript's coordinate system
gdata = -GRAV_UNITS * gdata
# turn the scalars into vectors (vertical direction)
d=kronecker(DIM)[DIM-1]
w=safeDiv(1., g_mask)
gravity_model=GravityModel(dom, w*d, gdata*d, fixPotentialAtBottom=False, coordinates=COORDINATES)
gravity_model.rescaleWeights(rho_scale=rho_mapping.getTypicalDerivative())
phi,_ = gravity_model.getArguments(live_model)
g_init = -gravity_model.getCoordinateTransformation().getGradient(phi)
g_init = interpolate(g_init, gdata.getFunctionSpace())
print("Computed gravity: %s"%(g_init[2]))
fn=os.path.join(OUTPUTDIR,'regional-gravity')
if SiloOutput is True:
saveSilo(fn, density=live_model, gravity_init=g_init, g_initz=-g_init[2], gravitymask=g_mask, modelmask=reg_mask)
print('SILO file written with the following fields: density (kg/m^3), gravity vector (m/s^2), gz (m/s^2), gravitymask, modelmask')
# to compare calculated data against input dataset.
# Not used by default but should work if the input dataset is correct
#gslice = g_init[2]*wherePositive(g_mask)
#g_dash = integrate(gslice)/integrate(wherePositive(g_mask))
#gdataslice = gdata*wherePositive(g_mask)
#gdata_dash = integrate(gdataslice)/integrate(wherePositive(g_mask))
#misfit=(gdataslice-gdata_dash)-(gslice-g_dash)
saveDataCSV(fn+".csv", mask=g_mask, gz=-g_init[2], Long=datacoords[0], Lat=datacoords[1], h=datacoords[2])
print('CSV file written with the following fields: Longitude (degrees) Latitude (degrees), h (100km), gz (m/s^2)')
def getGradient(self, rho, Hx, g_Hx):
"""
Returns the gradient of the defect with respect to resistivity.
:param rho: a suggestion for resistivity
:type rho: ``Data`` of shape ()
:param Hx: magnetic field
:type Hx: ``Data`` of shape (2,)
:param g_Hx: gradient of magnetic field
:type g_Hx: ``Data`` of shape (2,2)
"""
pde = self.setUpPDE()
DIM = self.getDomain().getDim()
x = g_Hx.getFunctionSpace().getX()
Hx = escript.interpolate(Hx, x.getFunctionSpace())
u0 = Hx[0]
u1 = Hx[1]
u00 = g_Hx[0, 0]
u10 = g_Hx[1, 0]
u01 = g_Hx[0, 1]
u11 = g_Hx[1, 1]
A = pde.getCoefficient('A')
D = pde.getCoefficient('D')
Y = pde.getCoefficient('Y')
X = pde.getCoefficient('X')
for i in range(DIM):
A[0, i, 0, i] = rho
A[1, i, 1, i] = rho
f = self._omega_mu
D[0, 1] = f
D[1, 0] = -f
Z = self._Z
scale = 1. / (u0**2 + u1**2)
scale2 = scale**2
scale *= self._weight
scale2 *= rho * self._weight
rho_scale = rho * scale
gscale = u01**2 + u11**2
Y[0] = scale2 * ((Z[0] * u01 + Z[1] * u11) *
(u0**2 - u1**2) + 2 * u0 * u1 *
(Z[0] * u11 - Z[1] * u01) - rho * u0 * gscale)
Y[1] = scale2 * ((Z[0] * u11 - Z[1] * u01) *
(u1**2 - u0**2) + 2 * u0 * u1 *
(Z[0] * u01 + Z[1] * u11) - rho * u1 * gscale)
X[0, 1] = rho_scale * (-Z[0] * u0 + Z[1] * u1 + rho * u01)
X[1, 1] = rho_scale * (-Z[0] * u1 - Z[1] * u0 + rho * u11)
pde.setValue(A=A, D=D, X=X, Y=Y)
g = escript.grad(pde.getSolution())
Hstarr_x = g[0, 0]
Hstari_x = g[1, 0]
Hstarr_z = g[0, 1]
Hstari_z = g[1, 1]
return -scale*(u0*(Z[0]*u01+Z[1]*u11)+u1*(Z[0]*u11-Z[1]*u01)-rho*gscale)\
- Hstarr_x*u00 - Hstarr_z*u01 - Hstari_x*u10 - Hstari_z*u11
