class DispositionTypeParams(BaseModel):
allowChangeTimer = properties.Bool(
'Whether the agent can change the redial timer for this disposition.',
)
attempts = properties.Integer('Number of redial attempts.', )
timer = properties.Instance(
'Redial timer.',
instance_class=Timer,
)
useTimer = properties.Bool(
'Whether this disposition uses a redial timer.', )
class CustomField(BaseModel):
"""This represents optional data that can defined for specific mailbox
and filled when creating or updating a Conversation."""
field_name = properties.String(
'The name of the field; note that this may change if a field '
'is renamed, but the ``id`` will not.',
required=True,
)
field_type = properties.StringChoice(
'Type of the field.',
choices=[
'SINGLE_LINE',
'MULTI_LINE',
'DATA',
'NUMBER',
'DROPDOWN',
],
default='SINGLE_LINE',
required=True,
)
required = properties.Bool('Flag for UI to mark the field as required.', )
order = properties.Integer(
'Relative order of the custom field. Can be ``null`` or a number '
'between ``0`` and ``255``.',
min=0,
max=255,
)
options = properties.List(
'Field options',
prop=Option,
)
class BaseWaveform(properties.HasProperties):
hasInitialFields = properties.Bool(
"Does the waveform have initial fields?", default=False
)
offTime = properties.Float(
"off-time of the source", default=0.
)
eps = properties.Float(
"window of time within which the waveform is considered on",
default=1e-9
)
def __init__(self, **kwargs):
Utils.setKwargs(self, **kwargs)
def _assertMatchesPair(self, pair):
assert isinstance(self, pair), (
"Waveform object must be an instance of a %s "
"BaseWaveform class.".format(pair.__name__)
)
def eval(self, time):
raise NotImplementedError
def evalDeriv(self, time):
raise NotImplementedError # needed for E-formulation
class HasOptionalUnion(properties.HasProperties):
mybc = properties.Union(
'union of bool or color',
props=[properties.Bool(''),
properties.Color('')],
required=False,
)
class HasOptPropsUnion(properties.HasProperties):
mybc = properties.Union(
'union of bool or color',
props=[
properties.Bool('', required=False),
properties.Color('', required=False),
],
required=True,
)
class SimpleSmoothDeriv(BaseRegularization):
"""
Base Simple Smooth Regularization. This base class regularizes on the first
spatial derivative, not considering length scales, in the provided
orientation
**Optional Inputs**
:param BaseMesh mesh: SimPEG mesh
:param int nP: number of parameters
:param IdentityMap mapping: regularization mapping, takes the model from model space to the space you want to regularize in
:param numpy.ndarray mref: reference model
:param numpy.ndarray indActive: active cell indices for reducing the size of differential operators in the definition of a regularization mesh
:param numpy.ndarray cell_weights: cell weights
:param bool mrefInSmooth: include the reference model in the smoothness computation? (eg. look at Deriv of m (False) or Deriv of (m-mref) (True))
:param numpy.ndarray cell_weights: vector of cell weights (applied in all terms)
"""
def __init__(self, mesh, orientation='x', **kwargs):
self.orientation = orientation
assert self.orientation in ['x', 'y', 'z'
], ("Orientation must be 'x', 'y' or 'z'")
if self.orientation == 'y':
assert mesh.dim > 1, (
"Mesh must have at least 2 dimensions to regularize along the "
"y-direction")
elif self.orientation == 'z':
assert mesh.dim > 2, (
"Mesh must have at least 3 dimensions to regularize along the "
"z-direction")
super(SimpleSmoothDeriv, self).__init__(mesh=mesh, **kwargs)
mrefInSmooth = properties.Bool(
"include mref in the smoothness calculation?", default=False)
@property
def _multiplier_pair(self):
return 'alpha_{orientation}'.format(orientation=self.orientation)
@property
def W(self):
"""
Weighting matrix that takes the first spatial difference (no
length scales considered) in the specified orientation
"""
W = getattr(
self.regmesh, "cellDiff{orientation}Stencil".format(
orientation=self.orientation))
if self.cell_weights is not None:
Ave = getattr(self.regmesh, 'aveCC2F{}'.format(self.orientation))
W = (Utils.sdiag((Ave * self.cell_weights)**0.5) * W)
return W
class DomainConditionBoolean(DomainCondition):
"""This represents an integer query."""
value = properties.Bool(
'Boolean Value',
required=True,
)
def __str__(self):
"""Return a string usable as a query part in an API request."""
value = 'true' if self.value else 'false'
return '%s:%s' % (self.field_name, value)
class GlobalAEMSurvey(Survey.BaseSurvey, properties.HasProperties):
# This assumes a multiple sounding locations
rx_locations = properties.Array("Receiver locations ",
dtype=float,
shape=('*', 3))
src_locations = properties.Array("Source locations ",
dtype=float,
shape=('*', 3))
topo = properties.Array("Topography", dtype=float, shape=('*', 3))
half_switch = properties.Bool("Switch for half-space", default=False)
_pred = None
@Utils.requires('prob')
def dpred(self, m, f=None):
"""
Return predicted data.
Predicted data, (`_pred`) are computed when
self.prob.fields is called.
"""
if f is None:
f = self.prob.fields(m)
return self._pred
@property
def n_sounding(self):
"""
# of Receiver locations
"""
return self.rx_locations.shape[0]
def read_xyz_data(self, fname):
"""
Read csv file format
This is a place holder at this point
"""
pass
@property
def nD(self):
# Need to generalize this for the dual moment data
if getattr(self, '_nD', None) is None:
self._nD = self.nD_vec.sum()
return self._nD
class BaseSparse(BaseRegularization):
"""
Base class for building up the components of the Sparse Regularization
"""
def __init__(self, mesh, **kwargs):
self._stashedR = None
super(BaseSparse, self).__init__(mesh=mesh, **kwargs)
model = properties.Array("current model", dtype=float)
epsilon = properties.Float("Threshold value for the model norm",
default=1e-3,
required=True)
norm = properties.Array("norm used", dtype=float)
space = properties.String("By default inherit the objctive",
default='linear')
gradientType = properties.String("type of gradient", default='components')
scale = properties.Array(
"General nob for scaling",
dtype=float,
)
# Give the option to scale or not
scaledIRLS = properties.Bool("Scale the gradients of the IRLS norms",
default=True)
@properties.validator('scale')
def _validate_scale(self, change):
if change['value'] is not None:
# todo: residual size? we need to know the expected end shape
if self._nC_residual != '*':
assert len(change['value']) == self._nC_residual, (
'scale must be length {} not {}'.format(
self._nC_residual, len(change['value'])))
@property
def stashedR(self):
return self._stashedR
@stashedR.setter
def stashedR(self, value):
self._stashedR = value
class SearchConversation(BaseConversation):
"""This represents a conversation as returned by search results."""
mailbox_id = properties.Integer(
'The ID of the mailbox this conversation is in.',
required=True,
)
customer_name = properties.String(
'Name of the customer this conversation is regarding.',
required=True,
)
customer_email = properties.String(
'Email address of the customer',
required=True,
)
has_attachments = properties.Bool(
'``True`` when the conversation has at least one attachment.', )
class BaseWaveform(properties.HasProperties):
hasInitialFields = properties.Bool(
"Does the waveform have initial fields?", default=False)
offTime = properties.Float("off-time of the source", default=0.0)
eps = properties.Float(
"window of time within which the waveform is considered on",
default=1e-9)
def __init__(self, **kwargs):
setKwargs(self, **kwargs)
def eval(self, time):
raise NotImplementedError
def evalDeriv(self, time):
raise NotImplementedError # needed for E-formulation
class SparseDeriv(BaseSparse):
"""
Base Class for sparse regularization on first spatial derivatives
"""
def __init__(self, mesh, orientation='x', **kwargs):
self.orientation = orientation
super(SparseDeriv, self).__init__(mesh=mesh, **kwargs)
mrefInSmooth = properties.Bool(
"include mref in the smoothness calculation?", default=False)
@property
def _multiplier_pair(self):
return 'alpha_{orientation}'.format(orientation=self.orientation)
@property
def f_m(self):
return self.cellDiffStencil * (self.mapping * self.model)
@property
def cellDiffStencil(self):
return getattr(self.regmesh,
'cellDiff{}Stencil'.format(self.orientation))
@property
def W(self):
Ave = getattr(self.regmesh, 'aveCC2F{}'.format(self.orientation))
if getattr(self, 'model', None) is None:
R = Utils.speye(self.cellDiffStencil.shape[0])
else:
r = self.R(self.f_m) # , self.eps_q, self.norm)
R = Utils.sdiag(r)
if self.cell_weights is not None:
return (Utils.sdiag(
(self.gamma * (Ave * self.cell_weights))**0.5) * R *
self.cellDiffStencil)
return ((self.gamma)**0.5) * R * self.cellDiffStencil
def test_bool(self):
class BoolOpts(properties.HasProperties):
mybool = properties.Bool('My bool')
opt = BoolOpts(mybool=True)
assert opt.mybool is True
self.assertRaises(ValueError, lambda: setattr(opt, 'mybool', 'true'))
opt.mybool = False
assert opt.mybool is False
assert properties.Bool('').equal(True, True)
assert not properties.Bool('').equal(True, 1)
assert not properties.Bool('').equal(True, 'true')
json = properties.Bool.to_json(opt.mybool)
assert not json
assert not properties.Bool.from_json(json)
with self.assertRaises(ValueError):
properties.Bool.from_json({})
with self.assertRaises(ValueError):
properties.Bool.from_json('nope')
assert properties.Bool.from_json('true')
assert properties.Bool.from_json('y')
assert properties.Bool.from_json('Yes')
assert properties.Bool.from_json('ON')
assert not properties.Bool.from_json('false')
assert not properties.Bool.from_json('N')
assert not properties.Bool.from_json('no')
assert not properties.Bool.from_json('OFF')
self.assertEqual(opt.serialize(include_class=False), {'mybool': False})
assert BoolOpts.deserialize({'mybool': 'Y'}).mybool
assert BoolOpts._props['mybool'].deserialize(None) is None
assert properties.Bool('').equal(True, True)
assert not properties.Bool('').equal(True, 1)
assert not properties.Bool('').equal(True, 'true')
with self.assertRaises(ValueError):
BoolOpts._props['mybool'].assert_valid(opt, 'true')
opt.validate()
opt._backend['mybool'] = 'true'
with self.assertRaises(ValueError):
opt.validate()
class HasOptionalSet(properties.HasProperties):
myset = properties.Set('',
properties.Bool(''),
required=False,
observe_mutations=om)
class HasOptPropList(properties.HasProperties):
mylist = properties.List(
doc='',
prop=properties.Bool('', required=False),
default=properties.undefined,
)
class HasOptionalList(properties.HasProperties):
mylist = properties.List('',
properties.Bool(''),
required=False,
observe_mutations=om)
class HasOptPropTuple(properties.HasProperties):
mytuple = properties.Tuple(
doc='',
prop=properties.Bool('', required=False),
default=properties.undefined,
)
class HasOptionalTuple(properties.HasProperties):
mytuple = properties.Tuple('', properties.Bool(''), required=False)
class Base(properties.HasProperties):
check_accuracy = properties.Bool(
"check the accuracy of the solve?",
default = False
)
accuracy_tol = properties.Float(
"tolerance on the accuracy of the solver",
default=1e-6
)
def __init__(self, A):
self.A = A.tocsr()
def set_kwargs(self, ignore=None, **kwargs):
"""
Sets key word arguments (kwargs) that are present in the object,
throw an error if they don't exist.
"""
if ignore is None:
ignore = []
for attr in kwargs:
if attr in ignore:
continue
if hasattr(self, attr):
setattr(self, attr, kwargs[attr])
else:
raise Exception('{0!s} attr is not recognized'.format(attr))
@property
def _transposeClass(self):
return self.__class__
@property
def T(self):
if self._transposeClass is None:
raise Exception(
'The transpose for the {} class is not possible.'.format(
self.__name__
)
)
newS = self._transposeClass(self.A.T)
return newS
def _compute_accuracy(self, rhs, x):
nrm = np.linalg.norm(np.ravel(self.A*x - rhs), np.inf)
nrm_rhs = np.linalg.norm(np.ravel(rhs), np.inf)
if nrm_rhs > 0:
nrm /= nrm_rhs
if nrm > self.accuracy_tol:
msg = 'Accuracy on solve is above tolerance: {0:e} > {1:e}'.format(
nrm, self.accuracy_tol
)
raise Exception(msg)
def _solve(self, rhs):
n = self.A.shape[0]
assert rhs.size % n == 0, 'Incorrect shape of rhs.'
nrhs = rhs.size // n
if len(rhs.shape) == 1 or rhs.shape[1] == 1:
x = self._solve1(rhs)
else:
x = self._solveM(rhs)
if self.check_accuracy:
self._compute_accuracy(rhs, x)
if nrhs == 1:
return x.flatten()
elif nrhs > 1:
return x.reshape((n, nrhs), order='F')
def clean(self):
pass
def __mul__(self, val):
if type(val) is np.ndarray:
return self._solve(val)
raise TypeError('Can only multiply by a numpy array.')
@property
def is_real(self):
return self.A.dtype == float
@property
def is_symmetric(self):
return getattr(self, '_is_symmetric', False)
@is_symmetric.setter
def is_symmetric(self, value):
self._is_symmetric = value
@property
def is_hermitian(self):
if self.is_real and self.is_symmetric:
return True
else:
return getattr(self, '_is_hermitian', False)
@is_hermitian.setter
def is_hermitian(self, value):
self._is_hermitian = value
@property
def is_positive_definite(self):
return getattr(self, '_is_positive_definite', False)
@is_positive_definite.setter
def is_positive_definite(self, value):
self._is_positive_definite = value
class RichardsProblem(Problem.BaseTimeProblem):
"""docstring for RichardsProblem"""
modelMap = properties.Property("the mapping")
boundaryConditions = properties.Array("boundary conditions.")
initialConditions = properties.Array("boundary conditions.")
surveyPair = RichardsSurvey
mapPair = RichardsMap
debug = properties.Bool("Show all messages")
Solver = Solver
solverOpts = {}
def __init__(self, mesh, modelMap=None, **kwargs):
assert (isinstance(
modelMap,
self.mapPair)), ('modelMap must be a {} class not {}'.format(
self.mapPair.__class__.__name__, modelMap))
self.modelMap = modelMap
Problem.BaseTimeProblem.__init__(self, mesh, **kwargs)
def getBoundaryConditions(self, ii, u_ii):
if type(self.boundaryConditions) is np.ndarray:
return self.boundaryConditions
time = self.timeMesh.vectorCCx[ii]
return self.boundaryConditions(time, u_ii)
method = properties.StringChoice(
"Formulation used, See notes in Celia et al., 1990.",
choices=['mixed', 'head'])
doNewton = properties.Bool("Do a Newton iteration vs. a Picard iteration ",
default=False)
maxIterRootFinder = properties.Integer(
"Maximum iterations for rootFinder iteration.", default=30)
tolRootFinder = properties.Float(
"Maximum iterations for rootFinder iteration.", default=1e-4)
@properties.observer(['doNewton', 'maxIterRootFinder', 'tolRootFinder'])
def _on_root_finder_update(self, change):
"""
Setting doNewton will clear the rootFinder,
which will be reinitialized when called
"""
if hasattr(self, '_rootFinder'):
del self._rootFinder
@property
def rootFinder(self):
"""Root-finding Algorithm"""
if getattr(self, '_rootFinder', None) is None:
self._rootFinder = Optimization.NewtonRoot(
doLS=self.doNewton,
maxIter=self.maxIterRootFinder,
tol=self.tolRootFinder,
Solver=self.Solver)
return self._rootFinder
@Utils.timeIt
def fields(self, m):
tic = time.time()
u = list(range(self.nT + 1))
u[0] = self.initialConditions
for ii, dt in enumerate(self.timeSteps):
bc = self.getBoundaryConditions(ii, u[ii])
u[ii + 1] = self.rootFinder.root(
lambda hn1m, return_g=True: self.getResidual(
m, u[ii], hn1m, dt, bc, return_g=return_g),
u[ii])
if self.debug:
print("Solving Fields ({0:4d}/{1:d} - {2:3.1f}% Done) {3:d} "
"Iterations, {4:4.2f} seconds".format(
ii + 1, self.nT, 100.0 * (ii + 1) / self.nT,
self.rootFinder.iter,
time.time() - tic))
return u
@property
def Dz(self):
if self.mesh.dim == 1:
Dz = self.mesh.faceDivx
elif self.mesh.dim == 2:
Dz = sp.hstack((Utils.spzeros(
self.mesh.nC, self.mesh.vnF[0]), self.mesh.faceDivy),
format='csr')
elif self.mesh.dim == 3:
Dz = sp.hstack(
(Utils.spzeros(self.mesh.nC, self.mesh.vnF[0] +
self.mesh.vnF[1]), self.mesh.faceDivz),
format='csr')
return Dz
@Utils.timeIt
def diagsJacobian(self, m, hn, hn1, dt, bc):
DIV = self.mesh.faceDiv
GRAD = self.mesh.cellGrad
BC = self.mesh.cellGradBC
AV = self.mesh.aveF2CC.T
Dz = self.Dz
dT = self.modelMap.thetaDerivU(hn, m)
dT1 = self.modelMap.thetaDerivU(hn1, m)
K1 = self.modelMap.k(hn1, m)
dK1 = self.modelMap.kDerivU(hn1, m)
dKm1 = self.modelMap.kDerivM(hn1, m)
# 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)))
# The matrix that we are computing has the form:
#
# - - - - - -
# | Adiag | | h1 | | b1 |
# | Asub Adiag | | h2 | | b2 |
# | Asub Adiag | | h3 | = | b3 |
# | ... ... | | .. | | .. |
# | Asub Adiag | | hn | | bn |
# - - - - - -
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
return Asub, Adiag, B
@Utils.timeIt
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
@Utils.timeIt
def Jfull(self, m, f=None):
if f is None:
f = self.fields(m)
nn = len(f) - 1
Asubs, Adiags, Bs = list(range(nn)), list(range(nn)), list(range(nn))
for ii in range(nn):
dt = self.timeSteps[ii]
bc = self.getBoundaryConditions(ii, f[ii])
Asubs[ii], Adiags[ii], Bs[ii] = self.diagsJacobian(
m, f[ii], f[ii + 1], dt, bc)
Ad = sp.block_diag(Adiags)
zRight = Utils.spzeros((len(Asubs) - 1) * Asubs[0].shape[0],
Adiags[0].shape[1])
zTop = Utils.spzeros(Adiags[0].shape[0],
len(Adiags) * Adiags[0].shape[1])
As = sp.vstack((zTop, sp.hstack((sp.block_diag(Asubs[1:]), zRight))))
A = As + Ad
B = np.array(sp.vstack(Bs).todense())
Ainv = self.Solver(A, **self.solverOpts)
P = self.survey.evalDeriv(f, m)
AinvB = Ainv * B
z = np.zeros((self.mesh.nC, B.shape[1]))
zAinvB = np.vstack((z, AinvB))
J = P * zAinvB
return J
@Utils.timeIt
def Jvec(self, m, v, f=None):
if f is None:
f = self.fields(m)
JvC = list(range(len(f) -
1)) # Cell to hold each row of the long vector
# This is done via forward substitution.
bc = self.getBoundaryConditions(0, f[0])
temp, Adiag, B = self.diagsJacobian(m, f[0], f[1], self.timeSteps[0],
bc)
Adiaginv = self.Solver(Adiag, **self.solverOpts)
JvC[0] = Adiaginv * (B * v)
for ii in range(1, len(f) - 1):
bc = self.getBoundaryConditions(ii, f[ii])
Asub, Adiag, B = self.diagsJacobian(m, f[ii], f[ii + 1],
self.timeSteps[ii], bc)
Adiaginv = self.Solver(Adiag, **self.solverOpts)
JvC[ii] = Adiaginv * (B * v - Asub * JvC[ii - 1])
P = self.survey.evalDeriv(f, m)
return P * np.concatenate([np.zeros(self.mesh.nC)] + JvC)
@Utils.timeIt
def Jtvec(self, m, v, f=None):
if f is None:
f = self.field(m)
P = self.survey.evalDeriv(f, m)
PTv = P.T * v
# This is done via backward substitution.
minus = 0
BJtv = 0
for ii in range(len(f) - 1, 0, -1):
bc = self.getBoundaryConditions(ii - 1, f[ii - 1])
Asub, Adiag, B = self.diagsJacobian(m, f[ii - 1], f[ii],
self.timeSteps[ii - 1], bc)
# select the correct part of v
vpart = list(
range((ii) * Adiag.shape[0], (ii + 1) * Adiag.shape[0]))
AdiaginvT = self.Solver(Adiag.T, **self.solverOpts)
JTvC = AdiaginvT * (PTv[vpart] - minus)
minus = Asub.T * JTvC # this is now the super diagonal.
BJtv = BJtv + B.T * JTvC
return BJtv
class Update_IRLS(InversionDirective):
f_old = 0
f_min_change = 1e-2
beta_tol = 1e-1
beta_ratio_l2 = None
prctile = 100
chifact_start = 1.0
chifact_target = 1.0
# Solving parameter for IRLS (mode:2)
irls_iteration = 0
minGNiter = 1
max_irls_iterations = properties.Integer("maximum irls iterations",
default=20)
iterStart = 0
sphericalDomain = False
# Beta schedule
update_beta = properties.Bool("Update beta", default=True)
beta_search = properties.Bool("Do a beta serarch", default=False)
coolingFactor = properties.Float("Cooling factor", default=2.0)
coolingRate = properties.Integer("Cooling rate", default=1)
ComboObjFun = False
mode = 1
coolEpsOptimized = True
coolEps_p = True
coolEps_q = True
floorEps_p = 1e-8
floorEps_q = 1e-8
coolEpsFact = 1.2
silent = False
fix_Jmatrix = False
maxIRLSiters = deprecate_property(
max_irls_iterations,
"maxIRLSiters",
new_name="max_irls_iterations",
removal_version="0.15.0",
)
updateBeta = deprecate_property(update_beta,
"updateBeta",
new_name="update_beta",
removal_version="0.15.0")
betaSearch = deprecate_property(beta_search,
"betaSearch",
new_name="beta_search",
removal_version="0.15.0")
@property
def target(self):
if getattr(self, "_target", None) is None:
nD = 0
for survey in self.survey:
nD += survey.nD
self._target = nD * 0.5 * self.chifact_target
return self._target
@target.setter
def target(self, val):
self._target = val
@property
def start(self):
if getattr(self, "_start", None) is None:
if isinstance(self.survey, list):
self._start = 0
for survey in self.survey:
self._start += survey.nD * 0.5 * self.chifact_start
else:
self._start = self.survey.nD * 0.5 * self.chifact_start
return self._start
@start.setter
def start(self, val):
self._start = val
def initialize(self):
if self.mode == 1:
self.norms = []
for reg in self.reg.objfcts:
self.norms.append(reg.norms)
reg.norms = np.c_[2.0, 2.0, 2.0, 2.0]
reg.model = self.invProb.model
# Update the model used by the regularization
for reg in self.reg.objfcts:
reg.model = self.invProb.model
if self.sphericalDomain:
self.angleScale()
def endIter(self):
if self.sphericalDomain:
self.angleScale()
# Check if misfit is within the tolerance, otherwise scale beta
if np.all([
np.abs(1.0 - self.invProb.phi_d / self.target) > self.beta_tol,
self.update_beta,
self.mode != 1,
]):
ratio = self.target / self.invProb.phi_d
if ratio > 1:
ratio = np.mean([2.0, ratio])
else:
ratio = np.mean([0.75, ratio])
self.invProb.beta = self.invProb.beta * ratio
if np.all([self.mode != 1, self.beta_search]):
print("Beta search step")
# self.update_beta = False
# Re-use previous model and continue with new beta
self.invProb.model = self.reg.objfcts[0].model
self.opt.xc = self.reg.objfcts[0].model
self.opt.iter -= 1
return
elif np.all([self.mode == 1, self.opt.iter % self.coolingRate == 0]):
self.invProb.beta = self.invProb.beta / self.coolingFactor
phim_new = 0
for reg in self.reg.objfcts:
for comp, multipier in zip(reg.objfcts, reg.multipliers):
if multipier > 0:
phim_new += np.sum(comp.f_m**2.0 /
(comp.f_m**2.0 + comp.epsilon**2.0)
**(1 - comp.norm / 2.0))
# Update the model used by the regularization
phi_m_last = []
for reg in self.reg.objfcts:
reg.model = self.invProb.model
phi_m_last += [reg(self.invProb.model)]
# After reaching target misfit with l2-norm, switch to IRLS (mode:2)
if np.all([self.invProb.phi_d < self.start, self.mode == 1]):
self.startIRLS()
# Only update after GN iterations
if np.all([(self.opt.iter - self.iterStart) % self.minGNiter == 0,
self.mode != 1]):
if self.fix_Jmatrix:
print(">> Fix Jmatrix")
self.invProb.dmisfit.simulation.fix_Jmatrix = True
# Check for maximum number of IRLS cycles
if self.irls_iteration == self.max_irls_iterations:
if not self.silent:
print("Reach maximum number of IRLS cycles:" +
" {0:d}".format(self.max_irls_iterations))
self.opt.stopNextIteration = True
return
# Print to screen
for reg in self.reg.objfcts:
if reg.eps_p > self.floorEps_p and self.coolEps_p:
reg.eps_p /= self.coolEpsFact
# print('Eps_p: ' + str(reg.eps_p))
if reg.eps_q > self.floorEps_q and self.coolEps_q:
reg.eps_q /= self.coolEpsFact
# print('Eps_q: ' + str(reg.eps_q))
# Remember the value of the norm from previous R matrices
# self.f_old = self.reg(self.invProb.model)
self.irls_iteration += 1
# Reset the regularization matrices so that it is
# recalculated for current model. Do it to all levels of comboObj
for reg in self.reg.objfcts:
# If comboObj, go down one more level
for comp in reg.objfcts:
comp.stashedR = None
for dmis in self.dmisfit.objfcts:
if getattr(dmis, "stashedR", None) is not None:
dmis.stashedR = None
# Compute new model objective function value
f_change = np.abs(self.f_old - phim_new) / (self.f_old + 1e-12)
# Check if the function has changed enough
if np.all([
f_change < self.f_min_change,
self.irls_iteration > 1,
np.abs(1.0 - self.invProb.phi_d / self.target) <
self.beta_tol,
]):
print("Minimum decrease in regularization." + "End of IRLS")
self.opt.stopNextIteration = True
return
self.f_old = phim_new
self.update_beta = True
self.invProb.phi_m_last = self.reg(self.invProb.model)
def startIRLS(self):
if not self.silent:
print("Reached starting chifact with l2-norm regularization:" +
" Start IRLS steps...")
self.mode = 2
if getattr(self.opt, "iter", None) is None:
self.iterStart = 0
else:
self.iterStart = self.opt.iter
self.invProb.phi_m_last = self.reg(self.invProb.model)
# Either use the supplied epsilon, or fix base on distribution of
# model values
for reg in self.reg.objfcts:
if getattr(reg, "eps_p", None) is None:
reg.eps_p = np.percentile(
np.abs(reg.mapping * reg._delta_m(self.invProb.model)),
self.prctile)
if getattr(reg, "eps_q", None) is None:
reg.eps_q = np.percentile(
np.abs(reg.mapping * reg._delta_m(self.invProb.model)),
self.prctile)
# Re-assign the norms supplied by user l2 -> lp
for reg, norms in zip(self.reg.objfcts, self.norms):
reg.norms = norms
# Save l2-model
self.invProb.l2model = self.invProb.model.copy()
# Print to screen
for reg in self.reg.objfcts:
if not self.silent:
print("eps_p: " + str(reg.eps_p) + " eps_q: " + str(reg.eps_q))
def angleScale(self):
"""
Update the scales used by regularization for the
different block of models
"""
# Currently implemented for MVI-S only
max_p = []
for reg in self.reg.objfcts[0].objfcts:
eps_p = reg.epsilon
f_m = abs(reg.f_m)
max_p += [np.max(f_m)]
max_p = np.asarray(max_p).max()
max_s = [np.pi, np.pi]
for obj, var in zip(self.reg.objfcts[1:3], max_s):
obj.scales = np.ones(obj.scales.shape) * max_p / var
def validate(self, directiveList):
# check if a linear preconditioner is in the list, if not warn else
# assert that it is listed after the IRLS directive
dList = directiveList.dList
self_ind = dList.index(self)
lin_precond_ind = [isinstance(d, UpdatePreconditioner) for d in dList]
if any(lin_precond_ind):
assert lin_precond_ind.index(True) > self_ind, (
"The directive 'UpdatePreconditioner' must be after Update_IRLS "
"in the directiveList")
else:
warnings.warn(
"Without a Linear preconditioner, convergence may be slow. "
"Consider adding `Directives.UpdatePreconditioner` to your "
"directives list")
return True
class SimpleComboRegularization(ComboObjectiveFunction):
def __init__(self, mesh, objfcts=[], **kwargs):
super(SimpleComboRegularization, self).__init__(objfcts=objfcts,
multipliers=None)
self.regmesh = RegularizationMesh(mesh)
if "indActive" in kwargs.keys():
indActive = kwargs.pop("indActive")
self.regmesh.indActive = indActive
utils.setKwargs(self, **kwargs)
# link these attributes
linkattrs = [
"regmesh",
"indActive",
]
for attr in linkattrs:
val = getattr(self, attr)
if val is not None:
[setattr(fct, attr, val) for fct in self.objfcts]
# Properties
alpha_s = props.Float("smallness weight")
alpha_x = props.Float("weight for the first x-derivative")
alpha_y = props.Float("weight for the first y-derivative")
alpha_z = props.Float("weight for the first z-derivative")
alpha_xx = props.Float("weight for the second x-derivative")
alpha_yy = props.Float("weight for the second y-derivative")
alpha_zz = props.Float("weight for the second z-derivative")
counter = None
mref = props.Array("reference model")
mrefInSmooth = properties.Bool(
"include mref in the smoothness calculation?", default=False)
indActive = properties.Array("indices of active cells in the mesh",
dtype=(bool, int))
cell_weights = properties.Array(
"regularization weights applied at cell centers", dtype=float)
scale = properties.Float("function scaling applied inside the norm",
default=1.0)
regmesh = properties.Instance("regularization mesh",
RegularizationMesh,
required=True)
mapping = properties.Instance(
"mapping which is applied to model in the regularization",
maps.IdentityMap,
default=maps.IdentityMap(),
)
# Other properties and methods
@property
def nP(self):
"""
number of model parameters
"""
if getattr(self.mapping, "nP") != "*":
return self.mapping.nP
elif getattr(self.regmesh, "nC") != "*":
return self.regmesh.nC
else:
return "*"
@property
def _nC_residual(self):
"""
Shape of the residual
"""
nC = getattr(self.regmesh, "nC", None)
mapping = getattr(self, "mapping", None)
if nC != "*" and nC is not None:
return self.regmesh.nC
elif mapping is not None and mapping.shape[0] != "*":
return self.mapping.shape[0]
else:
return self.nP
def _delta_m(self, m):
if self.mref is None:
return m
return -self.mref + m # in case self.mref is Zero, returns type m
@property
def multipliers(self):
"""
Factors that multiply the objective functions that are summed together
to build to composite regularization
"""
return [
getattr(self, "{alpha}".format(alpha=objfct._multiplier_pair))
for objfct in self.objfcts
]
# Observers and Validators
@properties.validator("indActive")
def _cast_to_bool(self, change):
value = change["value"]
if value is not None:
if value.dtype != "bool": # cast it to a bool otherwise
tmp = value
value = np.zeros(self.regmesh.nC, dtype=bool)
value[tmp] = True
change["value"] = value
# update regmesh indActive
if getattr(self, "regmesh", None) is not None:
self.regmesh.indActive = utils.mkvc(value)
@properties.observer("indActive")
def _update_regmesh_indActive(self, change):
# update regmesh indActive
if getattr(self, "regmesh", None) is not None:
self.regmesh.indActive = change["value"]
@properties.observer("mref")
def _mirror_mref_to_objfctlist(self, change):
for fct in self.objfcts:
if getattr(fct, "mrefInSmooth", None) is not None:
if self.mrefInSmooth is False:
fct.mref = utils.Zero()
else:
fct.mref = change["value"]
else:
fct.mref = change["value"]
@properties.observer("mrefInSmooth")
def _mirror_mrefInSmooth_to_objfctlist(self, change):
for fct in self.objfcts:
if getattr(fct, "mrefInSmooth", None) is not None:
fct.mrefInSmooth = change["value"]
@properties.observer("indActive")
def _mirror_indActive_to_objfctlist(self, change):
value = change["value"]
if value is not None:
if value.dtype != "bool":
tmp = value
value = np.zeros(self.mesh.nC, dtype=bool)
value[tmp] = True
change["value"] = value
if getattr(self, "regmesh", None) is not None:
self.regmesh.indActive = value
for fct in self.objfcts:
fct.indActive = value
class SparseDeriv(BaseSparse):
"""
Base Class for sparse regularization on first spatial derivatives
"""
def __init__(self, mesh, orientation="x", **kwargs):
self.orientation = orientation
super(SparseDeriv, self).__init__(mesh=mesh, **kwargs)
mrefInSmooth = properties.Bool(
"include mref in the smoothness calculation?", default=False
)
# Give the option to scale or not
scaledIRLS = properties.Bool("Scale the gradients of the IRLS norms", default=True)
@utils.timeIt
def __call__(self, m):
"""
We use a weighted 2-norm objective function
.. math::
r(m) = \\frac{1}{2}
"""
if self.mrefInSmooth:
f_m = self._delta_m(m)
else:
f_m = m
if self.scale is None:
self.scale = np.ones(self.mapping.shape[0])
if self.space == "spherical":
Ave = getattr(self.regmesh, "aveCC2F{}".format(self.orientation))
if getattr(self, "model", None) is None:
R = utils.speye(self.cellDiffStencil.shape[0])
else:
r = self.R(self.f_m)
R = utils.sdiag(r)
if self.cell_weights is not None:
W = utils.sdiag((Ave * (self.scale * self.cell_weights)) ** 0.5) * R
else:
W = utils.sdiag((Ave * (self.scale * self.regmesh.vol)) ** 0.5) * R
theta = self.cellDiffStencil * (self.mapping * f_m)
dmdx = utils.mat_utils.coterminal(theta)
r = W * dmdx
else:
r = self.W * (self.mapping * f_m)
return 0.5 * r.dot(r)
def R(self, f_m):
# if R is stashed, return that instead
if getattr(self, "stashedR") is not None:
return self.stashedR
# Default
eta = np.ones_like(f_m)
if self.scaledIRLS:
# Eta scaling is important for mix-norms...do not mess with it
# Scale on l2-norm gradient: f_m.max()
maxVal = np.ones_like(f_m) * np.abs(f_m).max()
# Compute theoritical maximum gradients for p < 1
maxVal[self.norm < 1] = self.epsilon / np.sqrt(
1.0 - self.norm[self.norm < 1]
)
maxGrad = maxVal / (
maxVal ** 2.0 + (self.epsilon * self.length_scales) ** 2.0
) ** (1.0 - self.norm / 2.0)
# Scaling Factor
eta[maxGrad != 0] = np.abs(f_m).max() / maxGrad[maxGrad != 0]
# Scaled-IRLS weights
r = (
eta
/ (f_m ** 2.0 + (self.epsilon * self.length_scales) ** 2.0)
** (1.0 - self.norm / 2.0)
) ** 0.5
self.stashedR = r # stash on the first calculation
return r
@utils.timeIt
def deriv(self, m):
"""
The regularization is:
.. math::
R(m) = \\frac{1}{2}\mathbf{(m-m_\\text{ref})^\\top W^\\top
W(m-m_\\text{ref})}
So the derivative is straight forward:
.. math::
R(m) = \mathbf{W^\\top W (m-m_\\text{ref})}
"""
if self.mrefInSmooth:
model = self._delta_m(m)
else:
model = m
if self.scale is None:
self.scale = np.ones(self.mapping.shape[0])
if self.space == "spherical":
Ave = getattr(self.regmesh, "aveCC2F{}".format(self.orientation))
if getattr(self, "model", None) is None:
R = utils.speye(self.cellDiffStencil.shape[0])
else:
r = self.R(self.f_m)
R = utils.sdiag(r)
if self.cell_weights is not None:
W = utils.sdiag(((Ave * (self.scale * self.cell_weights))) ** 0.5) * R
else:
W = utils.sdiag((Ave * (self.scale * self.regmesh.vol)) ** 0.5) * R
theta = self.cellDiffStencil * (self.mapping * model)
dmdx = utils.mat_utils.coterminal(theta)
r = W * dmdx
else:
r = self.W * (self.mapping * model)
mD = self.mapping.deriv(model)
return mD.T * (self.W.T * r)
@property
def _multiplier_pair(self):
return "alpha_{orientation}".format(orientation=self.orientation)
@property
def f_m(self):
if self.mrefInSmooth:
f_m = self._delta_m(self.model)
else:
f_m = self.model
if self.space == "spherical":
theta = self.cellDiffStencil * (self.mapping * f_m)
dmdx = utils.mat_utils.coterminal(theta)
else:
if self.gradientType == "total":
Ave = getattr(self.regmesh, "aveCC2F{}".format(self.orientation))
dmdx = np.abs(
self.regmesh.aveFx2CC
* self.regmesh.cellDiffxStencil
* (self.mapping * f_m)
)
if self.regmesh.dim > 1:
dmdx += np.abs(
self.regmesh.aveFy2CC
* self.regmesh.cellDiffyStencil
* (self.mapping * f_m)
)
if self.regmesh.dim > 2:
dmdx += np.abs(
self.regmesh.aveFz2CC
* self.regmesh.cellDiffzStencil
* (self.mapping * f_m)
)
dmdx = Ave * dmdx
else:
dmdx = self.cellDiffStencil * (self.mapping * f_m)
return dmdx
@property
def cellDiffStencil(self):
return utils.sdiag(self.length_scales) * getattr(
self.regmesh, "cellDiff{}Stencil".format(self.orientation)
)
@property
def W(self):
Ave = getattr(self.regmesh, "aveCC2F{}".format(self.orientation))
if getattr(self, "model", None) is None:
R = utils.speye(self.cellDiffStencil.shape[0])
else:
r = self.R(self.f_m)
R = utils.sdiag(r)
if self.scale is None:
self.scale = np.ones(self.mapping.shape[0])
if self.cell_weights is not None:
return (
utils.sdiag((Ave * (self.scale * self.cell_weights)) ** 0.5)
* R
* self.cellDiffStencil
)
else:
return (
utils.sdiag((Ave * (self.scale * self.regmesh.vol)) ** 0.5)
* R
* self.cellDiffStencil
)
@property
def length_scales(self):
"""
Normalized cell based weighting
"""
Ave = getattr(self.regmesh, "aveCC2F{}".format(self.orientation))
if getattr(self, "_length_scales", None) is None:
index = "xyz".index(self.orientation)
length_scales = Ave * (
self.regmesh.Pac.T * self.regmesh.mesh.h_gridded[:, index]
)
self._length_scales = length_scales.min() / length_scales
return self._length_scales
@length_scales.setter
def length_scales(self, value):
self._length_scales = value
class ExpFitSurvey(Survey.BaseSurvey, properties.HasProperties):
time = properties.Array("Time channels (s) at current off-time",
dtype=float)
wave_type = properties.StringChoice(
"Source location",
default="stepoff",
choices=["stepoff", "general", "general_conv"])
moment_type = properties.StringChoice("Source moment type",
default="single",
choices=["single", "dual"])
n_pulse = properties.Integer("The number of pulses", default=1)
base_frequency = properties.Float("Base frequency (Hz)")
time_input_currents = properties.Array("Time for input currents",
dtype=float)
input_currents = properties.Array("Input currents", dtype=float)
t0 = properties.Float("End of the ramp")
use_lowpass_filter = properties.Bool("Switch for low pass filter",
default=False)
high_cut_frequency = properties.Float(
"High cut frequency for low pass filter (Hz)", default=1e5)
# Predicted data
_pred = None
# ------------- For dual moment ------------- #
time_dual_moment = properties.Array(
"Off-time channels (s) for the dual moment", dtype=float)
time_input_currents_dual_moment = properties.Array(
"Time for input currents (dual moment)", dtype=float)
input_currents_dual_moment = properties.Array(
"Input currents (dual moment)", dtype=float)
t0_dual_moment = properties.Array("End of the ramp", dtype=float)
base_frequency_dual_moment = properties.Float(
"Base frequency for the dual moment (Hz)")
xyz = properties.Array("sounding locations", dtype=float, shape=('*', '*'))
uncert = None
def __init__(self, **kwargs):
Survey.BaseSurvey.__init__(self, **kwargs)
@property
def n_time(self):
n_time = self.time.size
if self.moment_type == 'dual':
n_time += self.time_dual_moment.size
return n_time
@property
def n_sounding(self):
return self.xyz.shape[0]
@property
def nD(self):
"""
# of data
"""
return self.n_time * self.n_sounding
def eval(self, f):
return f
def set_uncertainty(self, dobs, perc=0.1, floor=0., floorIP=0.):
# TODO: need to consider dual moment
self.uncert = np.zeros((self.n_time, self.n_sounding))
self.dobs = dobs
dobs = dobs.reshape((self.n_time, self.n_sounding), order='F')
for itx in range(self.n_sounding):
ipind = dobs[:, itx] < 0.
# Set different uncertainty for stations having negative transients
if (ipind).sum() > 3:
ip = dobs[ipind, itx]
self.uncert[:, itx] = (perc * abs(dobs[:, itx]) +
abs(ip).max() * 10)
self.uncert[ipind, itx] = np.Inf
else:
self.uncert[:, itx] = perc * abs(dobs[:, itx]) + floor
self.uncert = Utils.mkvc(self.uncert)
return self.uncert
class BaseComboRegularization(ObjectiveFunction.ComboObjectiveFunction):
def __init__(self, mesh, objfcts=[], **kwargs):
super(BaseComboRegularization, self).__init__(objfcts=objfcts,
multipliers=None)
self.regmesh = RegularizationMesh(mesh)
Utils.setKwargs(self, **kwargs)
# link these attributes
linkattrs = ['regmesh', 'indActive', 'cell_weights', 'mapping']
for attr in linkattrs:
val = getattr(self, attr)
if val is not None:
[setattr(fct, attr, val) for fct in self.objfcts]
# Properties
alpha_s = Props.Float("smallness weight")
alpha_x = Props.Float("weight for the first x-derivative")
alpha_y = Props.Float("weight for the first y-derivative")
alpha_z = Props.Float("weight for the first z-derivative")
alpha_xx = Props.Float("weight for the second x-derivative")
alpha_yy = Props.Float("weight for the second y-derivative")
alpha_zz = Props.Float("weight for the second z-derivative")
counter = None
mref = Props.Array("reference model")
mrefInSmooth = properties.Bool(
"include mref in the smoothness calculation?", default=False)
indActive = properties.Array("indices of active cells in the mesh",
dtype=(bool, int))
cell_weights = properties.Array(
"regularization weights applied at cell centers", dtype=float)
regmesh = properties.Instance("regularization mesh",
RegularizationMesh,
required=True)
mapping = properties.Instance(
"mapping which is applied to model in the regularization",
Maps.IdentityMap,
default=Maps.IdentityMap())
# Other properties and methods
@property
def nP(self):
"""
number of model parameters
"""
if getattr(self.mapping, 'nP') != '*':
return self.mapping.nP
elif getattr(self.regmesh, 'nC') != '*':
return self.regmesh.nC
else:
return '*'
@property
def _nC_residual(self):
"""
Shape of the residual
"""
if getattr(self.regmesh, 'nC', None) != '*':
return self.regmesh.nC
elif getattr(self, 'mapping', None) != '*':
return self.mapping.shape[0]
else:
return self.nP
def _delta_m(self, m):
if self.mref is None:
return m
return (-self.mref + m) # in case self.mref is Zero, returns type m
@property
def multipliers(self):
"""
Factors that multiply the objective functions that are summed together
to build to composite regularization
"""
return [
getattr(self, '{alpha}'.format(alpha=objfct._multiplier_pair))
for objfct in self.objfcts
]
# Observers and Validators
@properties.validator('indActive')
def _cast_to_bool(self, change):
value = change['value']
if value is not None:
if value.dtype != 'bool': # cast it to a bool otherwise
tmp = value
value = np.zeros(self.regmesh.nC, dtype=bool)
value[tmp] = True
change['value'] = value
# update regmesh indActive
if getattr(self, 'regmesh', None) is not None:
self.regmesh.indActive = Utils.mkvc(value)
@properties.observer('indActive')
def _update_regmesh_indActive(self, change):
# update regmesh indActive
if getattr(self, 'regmesh', None) is not None:
self.regmesh.indActive = change['value']
@properties.validator('cell_weights')
def _validate_cell_weights(self, change):
if change['value'] is not None:
# todo: residual size? we need to know the expected end shape
if self._nC_residual != '*':
assert len(change['value']) == self._nC_residual, (
'cell_weights must be length {} not {}'.format(
self._nC_residual, len(change['value'])))
@properties.observer('mref')
def _mirror_mref_to_objfctlist(self, change):
for fct in self.objfcts:
if getattr(fct, 'mrefInSmooth', None) is not None:
if self.mrefInSmooth is False:
fct.mref = Utils.Zero()
else:
fct.mref = change['value']
else:
fct.mref = change['value']
@properties.observer('mrefInSmooth')
def _mirror_mrefInSmooth_to_objfctlist(self, change):
for fct in self.objfcts:
if getattr(fct, 'mrefInSmooth', None) is not None:
fct.mrefInSmooth = change['value']
@properties.observer('indActive')
def _mirror_indActive_to_objfctlist(self, change):
value = change['value']
if value is not None:
if value.dtype != 'bool':
tmp = value
value = np.zeros(self.mesh.nC, dtype=bool)
value[tmp] = True
change['value'] = value
if getattr(self, 'regmesh', None) is not None:
self.regmesh.indActive = value
for fct in self.objfcts:
fct.indActive = value
@properties.observer('cell_weights')
def _mirror_cell_weights_to_objfctlist(self, change):
for fct in self.objfcts:
fct.cell_weights = change['value']
@properties.observer('mapping')
def _mirror_mapping_to_objfctlist(self, change):
for fct in self.objfcts:
fct.mapping = change['value']
class BaseFDEM(BaseEM):
"""
Base frequency domain electromagnetic class
"""
sigma = properties.Complex(
"Electrical conductivity (S/m)",
default=1.0,
cast=True
)
frequency = properties.Float(
"Source frequency (Hz)",
default=1.,
min=0.0
)
quasistatic = properties.Bool(
"Use the quasi-static approximation and ignore displacement current?",
default=False
)
@properties.validator('sigma')
def _validate_real_part(self, change):
if not np.real(change['value']) > 0:
raise properties.ValidationError("The real part of sigma must be positive")
@property
def omega(self):
"""
Angular frequency
.. math::
\\omega = 2\\pi f
"""
return omega(self.frequency)
@property
def sigma_hat(self):
"""
conductivity with displacement current contribution
.. math::
\\hat{\\sigma} = \\sigma + i \\omega \\varepsilon
"""
sigma = sigma_hat(
self.frequency, self.sigma, epsilon=self.epsilon,
quasistatic=self.quasistatic
)
if np.all(np.imag(sigma) == 0):
sigma = np.real(sigma)
return sigma
@property
def wavenumber(self):
"""
Wavenumber of an electromagnetic wave in a medium with constant
physical properties
.. math::
k = \\sqrt{\\omega**2 \\mu \\varepsilon - i \\omega \\mu \\sigma}
"""
return wavenumber(
self.frequency, self.sigma, mu=self.mu, epsilon=self.epsilon,
quasistatic=self.quasistatic
)
@property
def skin_depth(self):
"""
Distance at which an em wave has decayed by a factor of :math:`1/e` in
a medium with constant physical properties
.. math::
\\sqrt{\\frac{2}{\\omega \\sigma \\mu}}
"""
return skin_depth(self.frequency, self.sigma, mu=self.mu)
class Sparse(BaseComboRegularization):
"""
The regularization is:
.. math::
R(m) = \\frac{1}{2}\mathbf{(m-m_\\text{ref})^\\top W^\\top R^\\top R
W(m-m_\\text{ref})}
where the IRLS weight
.. math::
R = \eta TO FINISH LATER!!!
So the derivative is straight forward:
.. math::
R(m) = \mathbf{W^\\top R^\\top R W (m-m_\\text{ref})}
The IRLS weights are recomputed after each beta solves.
It is strongly recommended to do a few Gauss-Newton iterations
before updating.
"""
def __init__(
self, mesh, alpha_s=1.0, alpha_x=1.0, alpha_y=1.0, alpha_z=1.0, **kwargs
):
objfcts = [
SparseSmall(mesh=mesh, **kwargs),
SparseDeriv(mesh=mesh, orientation="x", **kwargs),
]
if mesh.dim > 1:
objfcts.append(SparseDeriv(mesh=mesh, orientation="y", **kwargs))
if mesh.dim > 2:
objfcts.append(SparseDeriv(mesh=mesh, orientation="z", **kwargs))
super(Sparse, self).__init__(
mesh=mesh,
objfcts=objfcts,
alpha_s=alpha_s,
alpha_x=alpha_x,
alpha_y=alpha_y,
alpha_z=alpha_z,
**kwargs
)
# Utils.setKwargs(self, **kwargs)
# Properties
norms = properties.Array(
"Norms used to create the sparse regularization",
default=np.c_[2.0, 2.0, 2.0, 2.0],
shape={("*", "*")},
)
eps_p = properties.Float("Threshold value for the model norm", required=True)
eps_q = properties.Float(
"Threshold value for the model gradient norm", required=True
)
model = properties.Array("current model", dtype=float)
space = properties.String("type of model", default="linear")
gradientType = properties.String("type of gradient", default="components")
scales = properties.Array(
"General nob for scaling", default=np.c_[1.0, 1.0, 1.0, 1.0], shape={("*", "*")}
)
# Give the option to scale or not
scaledIRLS = properties.Bool("Scale the gradients of the IRLS norms", default=True)
# Save the l2 result during the IRLS
l2model = None
@properties.validator("norms")
def _validate_norms(self, change):
if change["value"].shape[0] == 1:
change["value"] = np.kron(
np.ones((self.regmesh.Pac.shape[1], 1)), change["value"]
)
elif change["value"].shape[0] > 1:
assert change["value"].shape[0] == self.regmesh.Pac.shape[1], (
"Vector of norms must be the size"
" of active model parameters ({})"
"The provided vector has length "
"{}".format(self.regmesh.Pac.shape[0], len(change["value"]))
)
# Observers
@properties.observer("norms")
def _mirror_norms_to_objfcts(self, change):
self.objfcts[0].norm = change["value"][:, 0]
for i, objfct in enumerate(self.objfcts[1:]):
Ave = getattr(objfct.regmesh, "aveCC2F{}".format(objfct.orientation))
objfct.norm = Ave * change["value"][:, i + 1]
@properties.observer("model")
def _mirror_model_to_objfcts(self, change):
for objfct in self.objfcts:
objfct.model = change["value"]
@properties.observer("eps_p")
def _mirror_eps_p_to_smallness(self, change):
for objfct in self.objfcts:
if isinstance(objfct, SparseSmall):
objfct.epsilon = change["value"]
@properties.observer("eps_q")
def _mirror_eps_q_to_derivs(self, change):
for objfct in self.objfcts:
if isinstance(objfct, SparseDeriv):
objfct.epsilon = change["value"]
@properties.observer("space")
def _mirror_space_to_objfcts(self, change):
for objfct in self.objfcts:
objfct.space = change["value"]
@properties.observer("gradientType")
def _mirror_gradientType_to_objfcts(self, change):
for objfct in self.objfcts:
objfct.gradientType = change["value"]
@properties.observer("scaledIRLS")
def _mirror_scaledIRLS_to_objfcts(self, change):
for objfct in self.objfcts:
objfct.scaledIRLS = change["value"]
@properties.validator("scales")
def _validate_scales(self, change):
if change["value"].shape[0] == 1:
change["value"] = np.kron(
np.ones((self.regmesh.Pac.shape[1], 1)), change["value"]
)
elif change["value"].shape[0] > 1:
assert change["value"].shape[0] == self.regmesh.Pac.shape[1], (
"Vector of scales must be the size"
" of active model parameters ({})"
"The provided vector has length "
"{}".format(self.regmesh.Pac.shape[0], len(change["value"]))
)
# Observers
@properties.observer("scales")
def _mirror_scale_to_objfcts(self, change):
for i, objfct in enumerate(self.objfcts):
objfct.scale = change["value"][:, i]
class HasProps2(properties.HasProperties):
my_list = properties.List('my list', properties.Bool(''))
five = properties.GettableProperty('five', default=5)
my_array = properties.Vector3Array('my array')
class BaseDCSimulation(BaseEMSimulation):
"""
Base DC Problem
"""
survey = properties.Instance("a DC survey object", Survey, required=True)
storeJ = properties.Bool("store the sensitivity matrix?", default=False)
_mini_survey = None
Ainv = None
_Jmatrix = None
gtgdiag = None
def __init__(self, *args, **kwargs):
miniaturize = kwargs.pop("miniaturize", False)
super().__init__(*args, **kwargs)
# Do stuff to simplify the forward and JTvec operation if number of dipole
# sources is greater than the number of unique pole sources
if miniaturize:
self._dipoles, self._invs, self._mini_survey = _mini_pole_pole(
self.survey)
def fields(self, m=None, calcJ=True):
if m is not None:
self.model = m
self._Jmatrix = None
f = self.fieldsPair(self)
if self.Ainv is not None:
self.Ainv.clean()
A = self.getA()
self.Ainv = self.solver(A, **self.solver_opts)
RHS = self.getRHS()
f[:, self._solutionType] = self.Ainv * RHS
return f
def getJ(self, m, f=None):
if self._Jmatrix is None:
if f is None:
f = self.fields(m)
self._Jmatrix = self._Jtvec(m, v=None, f=f).T
return self._Jmatrix
def dpred(self, m=None, f=None):
if self._mini_survey is not None:
# Temporarily set self.survey to self._mini_survey
survey = self.survey
self.survey = self._mini_survey
data = super().dpred(m=m, f=f)
if self._mini_survey is not None:
# reset survey
self.survey = survey
return self._mini_survey_data(data)
def getJtJdiag(self, m, W=None):
"""
Return the diagonal of JtJ
"""
if self.gtgdiag is None:
J = self.getJ(m)
if W is None:
W = np.ones(J.shape[0])
else:
W = W.diagonal()**2
diag = np.zeros(J.shape[1])
for i in range(J.shape[0]):
diag += (W[i]) * (J[i] * J[i])
self.gtgdiag = diag
return self.gtgdiag
def Jvec(self, m, v, f=None):
"""
Compute sensitivity matrix (J) and vector (v) product.
"""
if f is None:
f = self.fields(m)
if self.storeJ:
J = self.getJ(m, f=f)
return J.dot(v)
self.model = m
if self._mini_survey is not None:
survey = self._mini_survey
else:
survey = self.survey
Jv = []
for source in survey.source_list:
u_source = f[source, self._solutionType] # solution vector
dA_dm_v = self.getADeriv(u_source, v)
dRHS_dm_v = self.getRHSDeriv(source, v)
du_dm_v = self.Ainv * (-dA_dm_v + dRHS_dm_v)
for rx in source.receiver_list:
df_dmFun = getattr(f, "_{0!s}Deriv".format(rx.projField), None)
df_dm_v = df_dmFun(source, du_dm_v, v, adjoint=False)
Jv.append(rx.evalDeriv(source, self.mesh, f, df_dm_v))
Jv = np.hstack(Jv)
return self._mini_survey_data(Jv)
def Jtvec(self, m, v, f=None):
"""
Compute adjoint sensitivity matrix (J^T) and vector (v) product.
"""
if f is None:
f = self.fields(m)
self.model = m
if self.storeJ:
J = self.getJ(m, f=f)
return np.asarray(J.T.dot(v))
return self._Jtvec(m, v=v, f=f)
def _Jtvec(self, m, v=None, f=None):
"""
Compute adjoint sensitivity matrix (J^T) and vector (v) product.
Full J matrix can be computed by inputing v=None
"""
if self._mini_survey is not None:
survey = self._mini_survey
else:
survey = self.survey
if v is not None:
if isinstance(v, Data):
v = v.dobs
v = self._mini_survey_dataT(v)
v = Data(survey, v)
Jtv = np.zeros(m.size)
else:
# This is for forming full sensitivity matrix
Jtv = np.zeros((self.model.size, survey.nD), order="F")
istrt = int(0)
iend = int(0)
for source in survey.source_list:
u_source = f[source, self._solutionType].copy()
for rx in source.receiver_list:
# wrt f, need possibility wrt m
if v is not None:
PTv = rx.evalDeriv(source,
self.mesh,
f,
v[source, rx],
adjoint=True)
else:
# This is for forming full sensitivity matrix
PTv = rx.getP(self.mesh, rx.projGLoc(f)).toarray().T
df_duTFun = getattr(f, "_{0!s}Deriv".format(rx.projField),
None)
df_duT, df_dmT = df_duTFun(source, None, PTv, adjoint=True)
ATinvdf_duT = self.Ainv * df_duT
dA_dmT = self.getADeriv(u_source, ATinvdf_duT, adjoint=True)
dRHS_dmT = self.getRHSDeriv(source, ATinvdf_duT, adjoint=True)
du_dmT = -dA_dmT + dRHS_dmT
if v is not None:
Jtv += (df_dmT + du_dmT).astype(float)
else:
iend = istrt + rx.nD
if rx.nD == 1:
Jtv[:, istrt] = df_dmT + du_dmT
else:
Jtv[:, istrt:iend] = df_dmT + du_dmT
istrt += rx.nD
if v is not None:
return mkvc(Jtv)
else:
return (self._mini_survey_data(Jtv.T)).T
def getSourceTerm(self):
"""
Evaluates the sources, and puts them in matrix form
:rtype: tuple
:return: q (nC or nN, nSrc)
"""
if self._mini_survey is not None:
Srcs = self._mini_survey.source_list
else:
Srcs = self.survey.source_list
if self._formulation == "EB":
n = self.mesh.nN
elif self._formulation == "HJ":
n = self.mesh.nC
q = np.zeros((n, len(Srcs)), order="F")
for i, source in enumerate(Srcs):
q[:, i] = source.eval(self)
return q
@property
def deleteTheseOnModelUpdate(self):
toDelete = super(BaseDCSimulation, self).deleteTheseOnModelUpdate
if self._Jmatrix is not None:
toDelete += ["_Jmatrix"]
if self.gtgdiag is not None:
toDelete += ["gtgdiag"]
return toDelete
def _mini_survey_data(self, d_mini):
if self._mini_survey is not None:
out = d_mini[self._invs[0]] # AM
out[self._dipoles[0]] -= d_mini[self._invs[1]] # AN
out[self._dipoles[1]] -= d_mini[self._invs[2]] # BM
out[self._dipoles[0]
& self._dipoles[1]] += d_mini[self._invs[3]] # BN
else:
out = d_mini
return out
def _mini_survey_dataT(self, v):
if self._mini_survey is not None:
out = np.zeros(self._mini_survey.nD)
# Need to use ufunc.at because there could be repeated indices
# That need to be properly handled.
np.add.at(out, self._invs[0], v) # AM
np.subtract.at(out, self._invs[1], v[self._dipoles[0]]) # AN
np.subtract.at(out, self._invs[2], v[self._dipoles[1]]) # BM
np.add.at(out, self._invs[3],
v[self._dipoles[0] & self._dipoles[1]]) # BN
return out
else:
out = v
return out
class SparseSmall(BaseSparse):
"""
Sparse smallness regularization
**Inputs**
:param int norm: norm on the smallness
"""
_multiplier_pair = "alpha_s"
def __init__(self, mesh, **kwargs):
super(SparseSmall, self).__init__(mesh=mesh, **kwargs)
# Give the option to scale or not
scaledIRLS = properties.Bool("Scale the gradients of the IRLS norms", default=True)
@property
def f_m(self):
return self.mapping * self._delta_m(self.model)
@property
def W(self):
if getattr(self, "model", None) is None:
R = utils.speye(self.mapping.shape[0])
else:
r = self.R(self.f_m)
R = utils.sdiag(r)
if self.scale is None:
self.scale = np.ones(self.mapping.shape[0])
if self.cell_weights is not None:
return utils.sdiag((self.scale * self.cell_weights) ** 0.5) * R
else:
return utils.sdiag((self.scale * self.regmesh.vol) ** 0.5) * R
def R(self, f_m):
# if R is stashed, return that instead
if getattr(self, "stashedR") is not None:
return self.stashedR
# Default
eta = np.ones_like(f_m)
if self.scaledIRLS:
# Eta scaling is important for mix-norms...do not mess with it
# Scale on l2-norm gradient: f_m.max()
maxVal = np.ones_like(f_m) * np.abs(f_m).max()
# Compute theoritical maximum gradients for p < 1
maxVal[self.norm < 1] = self.epsilon / np.sqrt(
1.0 - self.norm[self.norm < 1]
)
maxGrad = maxVal / (maxVal ** 2.0 + self.epsilon ** 2.0) ** (
1.0 - self.norm / 2.0
)
# Scaling factor
eta[maxGrad != 0] = np.abs(f_m).max() / maxGrad[maxGrad != 0]
# Scaled IRLS weights
r = (eta / (f_m ** 2.0 + self.epsilon ** 2.0) ** (1.0 - self.norm / 2.0)) ** 0.5
self.stashedR = r # stash on the first calculation
return r
@utils.timeIt
def deriv(self, m):
"""
The regularization is:
.. math::
R(m) = \\frac{1}{2}\mathbf{(m-m_\\text{ref})^\\top W^\\top
W(m-m_\\text{ref})}
So the derivative is straight forward:
.. math::
R(m) = \mathbf{W^\\top W (m-m_\\text{ref})}
"""
mD = self.mapping.deriv(self._delta_m(m))
r = self.W * (self.mapping * (self._delta_m(m)))
return mD.T * (self.W.T * r)