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Copyright 2003, Landmark Graphics and others.
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at

    http://www.apache.org/licenses/LICENSE-2.0

Unless required by applicable law or agreed to in writing, software
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WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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package edu.mines.jtk.opt;

/**
 * Implement a non-linear transform and its linearizations
 * for a non-linear optimization.
 *
 * @author W.S. Harlan
 */

public interface Transform {
    /**
     * Non-linear transform: data = f(model).
     *
     * @param data  Output.  Initial values are ignored.
     * @param model Input. Unchanged.
     */
    void forwardNonlinear(Vect data, VectConst model);

    /**
     * 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.]
     *
     * @param data           Output.  Initial values are ignored.
     * @param model          Perturbation to reference model.
     * @param modelReference The reference model for the linearized operator.
     */
    void forwardLinearized(Vect data, VectConst 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.]
     *
     * @param data           Input for transpose operation.
     * @param model          Output.  The transpose will be added to this vector.
     * @param modelReference The reference model for the linearized operator.
     */
    void addTranspose(VectConst data, 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.
     *
     * @param model          The model to be multiplied.
     * @param modelReference The reference model for the linearized operators.
     */
    void inverseHessian(Vect model, VectConst modelReference);

    /**
     * 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.
     *
     * @param dataError This is the original data minus the modeled data.
     */
    void adjustRobustErrors(Vect dataError);
}