edu.mines.jtk.opt

Interface Transform

All Known Implementing Classes:

LinearTransformWrapper

public interface Transform

Implement a non-linear transform and its linearizations for a non-linear optimization.

Method Summary

Methods

Modifier and Type	Method and Description
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.

Method Detail

forwardNonlinear

void forwardNonlinear(Vect data,
                    VectConst model)

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

Parameters:

data - Output. Initial values are ignored.

model - Input. Unchanged.

forwardLinearized

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). 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.]

Parameters:

data - Output. Initial values are ignored.

model - Perturbation to reference model.

modelReference - The reference model for the linearized operator.

addTranspose

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. 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.]

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

void inverseHessian(Vect model,
                  VectConst modelReference)

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.

Parameters:

model - The model to be multiplied.

modelReference - The reference model for the linearized operators.

adjustRobustErrors

void adjustRobustErrors(Vect dataError)

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.

Parameters:

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