esys.downunder.splitinversioncostfunctions Package

Classes

class esys.downunder.splitinversioncostfunctions.ArithmeticTuple(*args)

Tuple supporting inplace update x+=y and scaling x=a*y where x,y is an ArithmeticTuple and a is a float.

Example of usage:

from esys.escript import Data
from numpy import array
a=eData(...)
b=array([1.,4.])
x=ArithmeticTuple(a,b)
y=5.*x
__init__(*args)

Initializes object with elements args.

Parameters

args – tuple of objects that support inplace add (x+=y) and scaling (x=a*y)

class esys.downunder.splitinversioncostfunctions.Data

Represents a collection of datapoints. It is used to store the values of a function. For more details please consult the c++ class documentation.

__init__((object)arg1) → None

__init__( (object)arg1, (object)value [, (object)p2 [, (object)p3 [, (object)p4]]]) -> None

conjugate((Data)arg1)Data
copy((Data)arg1, (Data)other) → None :

Make this object a copy of other

note

The two objects will act independently from now on. That is, changing other after this call will not change this object and vice versa.

copy( (Data)arg1) -> Data :
note

In the no argument form, a new object will be returned which is an independent copy of this object.

copyWithMask((Data)arg1, (Data)other, (Data)mask) → None :

Selectively copy values from other Data.Datapoints which correspond to positive values in mask will be copied from other

Parameters
  • other (Data) – source of values

  • mask (Scalar Data) –

delay((Data)arg1) → Data :

Convert this object into lazy representation

dump((Data)arg1, (str)fileName) → None :

Save the data as a netCDF file

Parameters

fileName (string) –

expand((Data)arg1) → None :

Convert the data to expanded representation if it is not expanded already.

getDomain((Data)arg1) → Domain :
Return type

Domain

getFunctionSpace((Data)arg1) → FunctionSpace :
Return type

FunctionSpace

getNumberOfDataPoints((Data)arg1) → int :
Return type

int

Returns

Number of datapoints in the object

getRank((Data)arg1) → int :
Returns

the number of indices required to address a component of a datapoint

Return type

positive int

getShape((Data)arg1) → tuple :

Returns the shape of the datapoints in this object as a python tuple. Scalar data has the shape ()

Return type

tuple

getTagNumber((Data)arg1, (object)dpno) → int :

Return tag number for the specified datapoint

Return type

int

Parameters

dpno (int) – datapoint number

getTupleForDataPoint((Data)arg1, (object)dataPointNo) → object :
Returns

Value of the specified datapoint

Return type

tuple

Parameters

dataPointNo (int) – datapoint to access

getTupleForGlobalDataPoint((Data)arg1, (object)procNo, (object)dataPointNo) → object :

Get a specific datapoint from a specific process

Return type

tuple

Parameters
  • procNo (positive int) – MPI rank of the process

  • dataPointNo (int) – datapoint to access

getX((Data)arg1) → Data :

Returns the spatial coordinates of the spatial nodes. :rtype: Data

hasInf((Data)arg1) → bool :

Returns return true if data contains +-Inf. [Note that for complex values, hasNaN and hasInf are not mutually exclusive.]

hasNaN((Data)arg1) → bool :

Returns return true if data contains NaN. [Note that for complex values, hasNaN and hasInf are not mutually exclusive.]

imag((Data)arg1)Data
internal_maxGlobalDataPoint((Data)arg1) → tuple :

Please consider using getSupLocator() from pdetools instead.

internal_minGlobalDataPoint((Data)arg1) → tuple :

Please consider using getInfLocator() from pdetools instead.

interpolate((Data)arg1, (FunctionSpace)functionspace) → Data :

Interpolate this object’s values into a new functionspace.

interpolateTable((Data)arg1, (object)table, (object)Amin, (object)Astep, (Data)B, (object)Bmin, (object)Bstep[, (object)undef=1e+50[, (object)check_boundaries=False]]) → Data :
Creates a new Data object by interpolating using the source data (which are

looked up in table) A must be the outer dimension on the table

param table

two dimensional collection of values

param Amin

The base of locations in table

type Amin

float

param Astep

size of gap between each item in the table

type Astep

float

param undef

upper bound on interpolated values

type undef

float

param B

Scalar representing the second coordinate to be mapped into the table

type B

Data

param Bmin

The base of locations in table for 2nd dimension

type Bmin

float

param Bstep

size of gap between each item in the table for 2nd dimension

type Bstep

float

param check_boundaries

if true, then values outside the boundaries will be rejected. If false, then boundary values will be used.

raise RuntimeError(DataException)

if the coordinates do not map into the table or if the interpolated value is above undef

rtype

Data

interpolateTable( (Data)arg1, (object)table, (object)Amin, (object)Astep [, (object)undef=1e+50 [, (object)check_boundaries=False]]) -> Data

isComplex((Data)arg1) → bool :
Return type

bool

Returns

True if this Data stores complex values.

isConstant((Data)arg1) → bool :
Return type

bool

Returns

True if this Data is an instance of DataConstant

Note

This does not mean the data is immutable.

isEmpty((Data)arg1) → bool :

Is this object an instance of DataEmpty

Return type

bool

Note

This is not the same thing as asking if the object contains datapoints.

isExpanded((Data)arg1) → bool :
Return type

bool

Returns

True if this Data is expanded.

isLazy((Data)arg1) → bool :
Return type

bool

Returns

True if this Data is lazy.

isProtected((Data)arg1) → bool :

Can this instance be modified. :rtype: bool

isReady((Data)arg1) → bool :
Return type

bool

Returns

True if this Data is not lazy.

isTagged((Data)arg1) → bool :
Return type

bool

Returns

True if this Data is expanded.

nonuniformInterpolate((Data)arg1, (object)in, (object)out, (object)check_boundaries) → Data :

1D interpolation with non equally spaced points

nonuniformSlope((Data)arg1, (object)in, (object)out, (object)check_boundaries) → Data :

1D interpolation of slope with non equally spaced points

phase((Data)arg1)Data
promote((Data)arg1) → None
real((Data)arg1)Data
replaceInf((Data)arg1, (object)value) → None :

Replaces +-Inf values with value. [Note, for complex Data, both real and imaginary components are replaced even if only one part is Inf].

replaceNaN((Data)arg1, (object)value) → None :

Replaces NaN values with value. [Note, for complex Data, both real and imaginary components are replaced even if only one part is NaN].

resolve((Data)arg1) → None :

Convert the data to non-lazy representation.

setProtection((Data)arg1) → None :

Disallow modifications to this data object

Note

This method does not allow you to undo protection.

setTaggedValue((Data)arg1, (object)tagKey, (object)value) → None :

Set the value of tagged Data.

param tagKey

tag to update

type tagKey

int

setTaggedValue( (Data)arg1, (str)name, (object)value) -> None :
param name

tag to update

type name

string

param value

value to set tagged data to

type value

object which acts like an array, tuple or list

setToZero((Data)arg1) → None :

After this call the object will store values of the same shape as before but all components will be zero.

setValueOfDataPoint((Data)arg1, (object)dataPointNo, (object)value) → None

setValueOfDataPoint( (Data)arg1, (object)arg2, (object)arg3) -> None

setValueOfDataPoint( (Data)arg1, (object)arg2, (object)arg3) -> None :

Modify the value of a single datapoint.

param dataPointNo

type dataPointNo

int

param value

type value

float or an object which acts like an array, tuple or list

warning

Use of this operation is discouraged. It prevents some optimisations from operating.

tag((Data)arg1) → None :

Convert data to tagged representation if it is not already tagged or expanded

toListOfTuples((Data)arg1[, (object)scalarastuple=False]) → object :

Return the datapoints of this object in a list. Each datapoint is stored as a tuple.

Parameters

scalarastuple – if True, scalar data will be wrapped as a tuple. True => [(0), (1), (2)]; False => [0, 1, 2]

class esys.downunder.splitinversioncostfunctions.ForwardModel

An abstract forward model that can be plugged into a cost function. Subclasses need to implement getDefect(), getGradient(), and possibly getArguments() and ‘getCoordinateTransformation’.

__init__()

Initialize self. See help(type(self)) for accurate signature.

getArguments(x)
getCoordinateTransformation()
getDefect(x, *args)
getGradient(x, *args)
class esys.downunder.splitinversioncostfunctions.FunctionJob(fn, *args, **kwargs)

Takes a python function (with only self and keyword params) to be called as the work method

__init__(fn, *args, **kwargs)

It ignores all of its parameters, except that, it requires the following as keyword arguments

Variables
  • domain – Domain to be used as the basis for all Data and PDEs in this Job.

  • jobid – sequence number of this job. The first job has id=1

work()

Need to be overloaded for the job to actually do anthing. A return value of True indicates this job thinks it is done. A return value of False indicates work still to be done

class esys.downunder.splitinversioncostfunctions.Job(*args, **kwargs)

Describes a sequence of work to be carried out in a subworld. The instances of this class used in the subworlds will be constructed by the system. To do specific work, this class should be subclassed and the work() (and possibly __init__ methods overloaded). The majority of the work done by the job will be in the overloaded work() method. The work() method should retrieve values from the outside using importValue() and pass values to the rest of the system using exportValue(). The rest of the methods should be considered off limits.

__init__(*args, **kwargs)

It ignores all of its parameters, except that, it requires the following as keyword arguments

Variables
  • domain – Domain to be used as the basis for all Data and PDEs in this Job.

  • jobid – sequence number of this job. The first job has id=1

clearExports()

Remove exported values from the map

clearImports()

Remove imported values from their map

declareImport(name)

Adds name to the list of imports

exportValue(name, v)

Make value v available to other Jobs under the label name. name must have already been registered with the SplitWorld instance. For use inside the work() method.

Variables
  • name – registered label for exported value

  • v – value to be imported

importValue(name)

For use inside the work() method.

Variables

name – label for imported value.

setImportValue(name, v)

Use to make a value available to the job (ie called from outside the job)

Variables
  • name – label used to identify this import

  • v – value to be imported

work()

Need to be overloaded for the job to actually do anthing. A return value of True indicates this job thinks it is done. A return value of False indicates work still to be done

class esys.downunder.splitinversioncostfunctions.Mapping(*args)

An abstract mapping class to map level set functions m to physical parameters p.

__init__(*args)

Initialize self. See help(type(self)) for accurate signature.

getDerivative(m)

returns the value for the derivative of the mapping for m

getInverse(s)

returns the value of the inverse of the mapping for physical parameter p

getTypicalDerivative()

returns a typical value for the derivative

getValue(m)

returns the value of the mapping for m

class esys.downunder.splitinversioncostfunctions.MeteredCostFunction

This an intrumented version of the CostFunction class. The function calls update statistical information. The actual work is done by the methods with corresponding name and a leading underscore. These functions need to be overwritten for a particular cost function implementation.

__init__()

the base constructor initializes the counters so subclasses should ensure the super class constructor is called.

getArguments(x)

returns precalculated values that are shared in the calculation of f(x) and grad f(x) and the Hessian operator

Note

The tuple returned by this call will be passed back to this CostFunction in other calls(eg: getGradient). Its contents are not specified at this level because no code, other than the CostFunction which created it, will be interacting with it. That is, the implementor can put whatever information they find useful in it.

Parameters

x (x-type) – location of derivative

Return type

tuple

getDualProduct(x, r)

returns the dual product of x and r

Return type

float

getGradient(x, *args)

returns the gradient of f at x using the precalculated values for x.

Parameters
  • x (x-type) – location of derivative

  • args – pre-calculated values for x from getArguments()

Return type

r-type

getInverseHessianApproximation(x, r, *args)

returns an approximative evaluation p of the inverse of the Hessian operator of the cost function for a given gradient r at a given location x: H(x) p = r

Note

In general it is assumed that the Hessian H(x) needs to be calculate in each call for a new location x. However, the solver may suggest that this is not required, typically when the iteration is close to completeness.

Parameters
  • x (x-type) – location of Hessian operator to be evaluated.

  • r (r-type) – a given gradient

  • args – pre-calculated values for x from getArguments()

Return type

x-type

getNorm(x)

returns the norm of x

Return type

float

getValue(x, *args)

returns the value f(x) using the precalculated values for x.

Parameters

x (x-type) – a solution approximation

Return type

float

resetCounters()

resets all statistical counters

class esys.downunder.splitinversioncostfunctions.SplitInversionCostFunction(numLevelSets=None, numModels=None, numMappings=None, splitworld=None, worldsinit_fn=None)

Class to define cost function J(m) for inversion with one or more forward models based on a multi-valued level set function m:

J(m) = J_reg(m) + sum_f mu_f * J_f(p)

where J_reg(m) is the regularization and cross gradient component of the cost function applied to a level set function m, J_f(p) are the data defect cost functions involving a physical forward model using the physical parameter(s) p and mu_f is the trade-off factor for model f.

A forward model depends on a set of physical parameters p which are constructed from components of the level set function m via mappings.

Example 1 (single forward model):

m=Mapping() f=ForwardModel() J=InversionCostFunction(Regularization(), m, f)

Example 2 (two forward models on a single valued level set)

m0=Mapping() m1=Mapping() f0=ForwardModel() f1=ForwardModel()

J=InversionCostFunction(Regularization(), mappings=[m0, m1], forward_models=[(f0, 0), (f1,1)])

Example 3 (two forward models on 2-valued level set)

m0=Mapping() m1=Mapping() f0=ForwardModel() f1=ForwardModel()

J=InversionCostFunction(Regularization(self.numLevelSets=2), mappings=[(m0,0), (m1,0)], forward_models=[(f0, 0), (f1,1)])

Note

If provides_inverse_Hessian_approximation is true, then the class provides an approximative inverse of the Hessian operator.

__init__(numLevelSets=None, numModels=None, numMappings=None, splitworld=None, worldsinit_fn=None)

fill this in.

calculateGradient(vnames1, vnames2)

The gradient operation produces two components (designated (Y^,X) in the non-split version). vnames1 gives the variable name(s) where the first component should be stored. vnames2 gives the variable name(s) where the second component should be stored.

static calculatePropertiesHelper(self, m, mappings)

returns a list of the physical properties from a given level set function m using the mappings of the cost function.

Parameters

m (Data) – level set function

Return type

list of Data

calculateValue(vname)
createLevelSetFunction(*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.

static createLevelSetFunctionHelper(self, regularization, mappings, *props)

Returns an object (init-ed) with 0s. 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.

static formatMappings(mappings, numLevelSets)
static formatModels(forward_models, numMappings)
getComponentValues(m, *args)
getDomain()

returns the domain of the cost function

Return type

Domain

getForwardModel(idx=None)

returns the idx-th forward model.

Parameters

idx (int) – model index. If cost function contains one model only idx can be omitted.

static getModelArgs(self, fwdmodels)

Attempts to import the arguments for forward models, if they are not available, Computes and exports them

getNumTradeOffFactors()

returns the number of trade-off factors being used including the trade-off factors used in the regularization component.

Return type

int

getProperties(m, return_list=False)

returns a list of the physical properties from a given level set function m using the mappings of the cost function.

Parameters
  • m (Data) – level set function

  • return_list (bool) – if True a list is returned.

Return type

list of Data

getRegularization()

returns the regularization

Return type

Regularization

getTradeOffFactors(mu=None)

returns a list of the trade-off factors.

Return type

list of float

getTradeOffFactorsModels()

returns the trade-off factors for the forward models

Return type

float or list of float

provides_inverse_Hessian_approximation = True
setPoint()
setTradeOffFactors(mu=None)

sets the trade-off factors for the forward model and regularization terms.

Parameters

mu (list of float) – list of trade-off factors.

setTradeOffFactorsModels(mu=None)

sets the trade-off factors for the forward model components.

Parameters

mu (float in case of a single model or a list of float with the length of the number of models.) – list of the trade-off factors. If not present ones are used.

setTradeOffFactorsRegularization(mu=None, mu_c=None)

sets the trade-off factors for the regularization component of the cost function, see Regularization for details.

Parameters
  • mu – trade-off factors for the level-set variation part

  • mu_c – trade-off factors for the cross gradient variation part

static subworld_setMu_model(self, **args)
updateHessian()

notifies the class that the Hessian operator needs to be updated.

static update_point_helper(self, newpoint)

Call within a subworld to set ‘current_point’ to newpoint and update all the cached args info

Functions

esys.downunder.splitinversioncostfunctions.inner(arg0, arg1)

Inner product of the two arguments. The inner product is defined as:

out=Sigma_s arg0[s]*arg1[s]

where s runs through arg0.Shape.

arg0 and arg1 must have the same shape.

Parameters
  • arg0 (numpy.ndarray, escript.Data, Symbol, float, int) – first argument

  • arg1 (numpy.ndarray, escript.Data, Symbol, float, int) – second argument

Returns

the inner product of arg0 and arg1 at each data point

Return type

numpy.ndarray, escript.Data, Symbol, float depending on the input

Raises

ValueError – if the shapes of the arguments are not identical

esys.downunder.splitinversioncostfunctions.updateHessianWorker(self, **kwargs)

Others

Packages