Package wsh.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

      All Methods Instance Methods Abstract Methods 
      Modifier and Type Method 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.