com.lgc.wsh.opt
Class LinearTransformWrapper

java.lang.Object
  com.lgc.wsh.opt.LinearTransformWrapper

All Implemented Interfaces:

Transform

public class LinearTransformWrapper
extends java.lang.Object
implements Transform

Wrap a LinearTransform as a non-linear Transform, by ignoring reference model.

Constructor Summary

LinearTransformWrapper(LinearTransform linearTransform)
Constructor.

Method Summary

void	addTranspose(VectConst data, Vect model, VectConst modelReference) The transpose of the linearized approximation of the forward transform for a small perturbation (model) to a reference model (modelReference): model = F' data.
void	adjustRobustErrors(Vect dataError) Apply any robust trimming of outliers, or scale all errors for an approximate L1 norm when squared.
void	forwardLinearized(Vect data, VectConst model, VectConst modelReference) A linearized approximation of the forward transform for a small perturbation (model) to a reference model (modelReference).
void	forwardNonlinear(Vect data, VectConst model) Non-linear transform: data = f(model).
void	inverseHessian(Vect model, VectConst modelReference) To speed convergence multiple a model by an approximate inverse Hessian.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

LinearTransformWrapper

public LinearTransformWrapper(LinearTransform linearTransform)

Constructor.

Parameters:

linearTransform - Wrap this as a general Transform

Method Detail

forwardNonlinear

public void forwardNonlinear(Vect data,
                             VectConst model)

Description copied from interface: Transform

Non-linear transform: data = f(model).

Specified by:

forwardNonlinear in interface Transform

Parameters:

data - Output. Initial values are ignored.

model - Input. Unchanged.

forwardLinearized

public void forwardLinearized(Vect data,
                              VectConst model,
                              VectConst modelReference)

Description copied from interface: Transform

A linearized approximation of the forward transform for a small perturbation (model) to a reference model (modelReference). The output data must be a linear function of the model perturbation. Linearized transform: data = F model ~= f(model + modelReference) - f(modelReference) [Do not add results to the existing model.]

Specified by:

forwardLinearized in interface Transform

Parameters:

data - Output. Initial values are ignored.

model - Perturbation to reference model.

modelReference - The reference model for the linearized operator.

addTranspose

public void addTranspose(VectConst data,
                         Vect model,
                         VectConst modelReference)

Description copied from interface: Transform

The transpose of the linearized approximation of the forward transform for a small perturbation (model) to a reference model (modelReference): model = F' data. Add the result to the existing model. [This transpose assumes a simple dot product, without the inverse covariance. I.e. data'F model = F' data model, for any arbitrary data or model.]

Specified by:

addTranspose in interface Transform

Parameters:

data - Input for transpose operation.

model - Output. The transpose will be added to this vector.

modelReference - The reference model for the linearized operator.

inverseHessian

public void inverseHessian(Vect model,
                           VectConst modelReference)

Description copied from interface: Transform

To speed convergence multiple a model by an approximate inverse Hessian. An empty implementation is equivalent to an identity and is also okay. The Hessian is equivalent to multiplying once by the linearized forward operation and then by the transpose. Your approximate inverse can greatly speed convergence by trying to diagonalize this Hessian, or at least balancing the diagonal. If this operation depends only on the model, then you may prefer to implement Vect.postCondition() on the model.

Specified by:

inverseHessian in interface Transform

Parameters:

model - The model to be multiplied.

modelReference - The reference model for the linearized operators.

adjustRobustErrors

public void adjustRobustErrors(Vect dataError)

Description copied from interface: Transform

Apply any robust trimming of outliers, or scale all errors for an approximate L1 norm when squared. This method should do nothing if you want a standard least-squares solution. Do not change the overall variance of the errors more than necessary.

Specified by:

adjustRobustErrors in interface Transform

Parameters:

dataError - This is the original data minus the modeled data.