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 * (the "License"); you may not use this file except in compliance with
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 *      http://www.apache.org/licenses/LICENSE-2.0
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package org.apache.commons.math3.optimization;

import org.apache.commons.math3.analysis.MultivariateFunction;
import org.apache.commons.math3.analysis.MultivariateVectorFunction;
import org.apache.commons.math3.exception.DimensionMismatchException;
import org.apache.commons.math3.linear.RealMatrix;

This class converts vectorial
objective functions to scalar objective functions when the goal is to minimize them. 

This class is mostly used when the vectorial objective function represents
a theoretical result computed from a point set applied to a model and
the models point must be adjusted to fit the theoretical result to some
reference observations. The observations may be obtained for example from
physical measurements whether the model is built from theoretical
considerations.

 This class computes a possibly weighted squared sum of the residuals, which is a scalar value. The residuals are the difference between the theoretical model (i.e. the output of the vectorial objective function) and the observations. The class implements the MultivariateFunction interface and can therefore be minimized by any optimizer supporting scalar objectives functions.This is one way to perform a least square estimation. There are other ways to do this without using this converter, as some optimization algorithms directly support vectorial objective functions. 

This class support combination of residuals with or without weights and correlations.

See Also:
MultivariateFunction
MultivariateVectorFunction
Deprecated:
As of 3.1 (to be removed in 4.0).
Since:
2.0/** This class converts {@link MultivariateVectorFunction vectorial
 * objective functions} to {@link MultivariateFunction scalar objective functions}
 * when the goal is to minimize them.
 * <p>
 * This class is mostly used when the vectorial objective function represents
 * a theoretical result computed from a point set applied to a model and
 * the models point must be adjusted to fit the theoretical result to some
 * reference observations. The observations may be obtained for example from
 * physical measurements whether the model is built from theoretical
 * considerations.
 * </p>
 * <p>
 * This class computes a possibly weighted squared sum of the residuals, which is
 * a scalar value. The residuals are the difference between the theoretical model
 * (i.e. the output of the vectorial objective function) and the observations. The
 * class implements the {@link MultivariateFunction} interface and can therefore be
 * minimized by any optimizer supporting scalar objectives functions.This is one way
 * to perform a least square estimation. There are other ways to do this without using
 * this converter, as some optimization algorithms directly support vectorial objective
 * functions.
 * </p>
 * <p>
 * This class support combination of residuals with or without weights and correlations.
 * </p>
  *
 * @see MultivariateFunction
 * @see MultivariateVectorFunction
 * @deprecated As of 3.1 (to be removed in 4.0).
 * @since 2.0
 */

@Deprecated
public class LeastSquaresConverter implements MultivariateFunction {

    
Underlying vectorial function. /** Underlying vectorial function. */
    private final MultivariateVectorFunction function;

    
Observations to be compared to objective function to compute residuals. /** Observations to be compared to objective function to compute residuals. */
    private final double[] observations;

    
Optional weights for the residuals. /** Optional weights for the residuals. */
    private final double[] weights;

    
Optional scaling matrix (weight and correlations) for the residuals. /** Optional scaling matrix (weight and correlations) for the residuals. */
    private final RealMatrix scale;

    
Build a simple converter for uncorrelated residuals with the same weight.
Params:
function – vectorial residuals function to wrap
observations – observations to be compared to objective function to compute residuals/** Build a simple converter for uncorrelated residuals with the same weight.
     * @param function vectorial residuals function to wrap
     * @param observations observations to be compared to objective function to compute residuals
     */
    public LeastSquaresConverter(final MultivariateVectorFunction function,
                                 final double[] observations) {
        this.function     = function;
        this.observations = observations.clone();
        this.weights      = null;
        this.scale        = null;
    }

    
Build a simple converter for uncorrelated residuals with the specific weights.

The scalar objective function value is computed as:
objective = ∑weighti(observationi-objectivei)2



Weights can be used for example to combine residuals with different standard
deviations. As an example, consider a residuals array in which even elements
are angular measurements in degrees with a 0.01° standard deviation and
odd elements are distance measurements in meters with a 15m standard deviation.
In this case, the weights array should be initialized with value
1.0/(0.012) in the even elements and 1.0/(15.02) in the
odd elements (i.e. reciprocals of variances).

 The array computed by the objective function, the observations array and the weights array must have consistent sizes or a DimensionMismatchException will be triggered while computing the scalar objective. 
Params:
function – vectorial residuals function to wrap
observations – observations to be compared to objective function to compute residuals
weights – weights to apply to the residuals
Throws:
DimensionMismatchException – if the observations vector and the weights vector dimensions do not match (objective function dimension is checked only when the value(double[]) method is called)/** Build a simple converter for uncorrelated residuals with the specific weights.
     * <p>
     * The scalar objective function value is computed as:
     * <pre>
     * objective = &sum;weight<sub>i</sub>(observation<sub>i</sub>-objective<sub>i</sub>)<sup>2</sup>
     * </pre>
     * </p>
     * <p>
     * Weights can be used for example to combine residuals with different standard
     * deviations. As an example, consider a residuals array in which even elements
     * are angular measurements in degrees with a 0.01&deg; standard deviation and
     * odd elements are distance measurements in meters with a 15m standard deviation.
     * In this case, the weights array should be initialized with value
     * 1.0/(0.01<sup>2</sup>) in the even elements and 1.0/(15.0<sup>2</sup>) in the
     * odd elements (i.e. reciprocals of variances).
     * </p>
     * <p>
     * The array computed by the objective function, the observations array and the
     * weights array must have consistent sizes or a {@link DimensionMismatchException}
     * will be triggered while computing the scalar objective.
     * </p>
     * @param function vectorial residuals function to wrap
     * @param observations observations to be compared to objective function to compute residuals
     * @param weights weights to apply to the residuals
     * @exception DimensionMismatchException if the observations vector and the weights
     * vector dimensions do not match (objective function dimension is checked only when
     * the {@link #value(double[])} method is called)
     */
    public LeastSquaresConverter(final MultivariateVectorFunction function,
                                 final double[] observations, final double[] weights) {
        if (observations.length != weights.length) {
            throw new DimensionMismatchException(observations.length, weights.length);
        }
        this.function     = function;
        this.observations = observations.clone();
        this.weights      = weights.clone();
        this.scale        = null;
    }

    
Build a simple converter for correlated residuals with the specific weights.

The scalar objective function value is computed as:
objective = yTy with y = scale×(observation-objective)


 The array computed by the objective function, the observations array and the the scaling matrix must have consistent sizes or a DimensionMismatchException will be triggered while computing the scalar objective. 
Params:
function – vectorial residuals function to wrap
observations – observations to be compared to objective function to compute residuals
scale – scaling matrix
Throws:
DimensionMismatchException – if the observations vector and the scale matrix dimensions do not match (objective function dimension is checked only when the value(double[]) method is called)/** Build a simple converter for correlated residuals with the specific weights.
     * <p>
     * The scalar objective function value is computed as:
     * <pre>
     * objective = y<sup>T</sup>y with y = scale&times;(observation-objective)
     * </pre>
     * </p>
     * <p>
     * The array computed by the objective function, the observations array and the
     * the scaling matrix must have consistent sizes or a {@link DimensionMismatchException}
     * will be triggered while computing the scalar objective.
     * </p>
     * @param function vectorial residuals function to wrap
     * @param observations observations to be compared to objective function to compute residuals
     * @param scale scaling matrix
     * @throws DimensionMismatchException if the observations vector and the scale
     * matrix dimensions do not match (objective function dimension is checked only when
     * the {@link #value(double[])} method is called)
     */
    public LeastSquaresConverter(final MultivariateVectorFunction function,
                                 final double[] observations, final RealMatrix scale) {
        if (observations.length != scale.getColumnDimension()) {
            throw new DimensionMismatchException(observations.length, scale.getColumnDimension());
        }
        this.function     = function;
        this.observations = observations.clone();
        this.weights      = null;
        this.scale        = scale.copy();
    }

    
{@inheritDoc} /** {@inheritDoc} */
    public double value(final double[] point) {
        // compute residuals
        final double[] residuals = function.value(point);
        if (residuals.length != observations.length) {
            throw new DimensionMismatchException(residuals.length, observations.length);
        }
        for (int i = 0; i < residuals.length; ++i) {
            residuals[i] -= observations[i];
        }

        // compute sum of squares
        double sumSquares = 0;
        if (weights != null) {
            for (int i = 0; i < residuals.length; ++i) {
                final double ri = residuals[i];
                sumSquares +=  weights[i] * ri * ri;
            }
        } else if (scale != null) {
            for (final double yi : scale.operate(residuals)) {
                sumSquares += yi * yi;
            }
        } else {
            for (final double ri : residuals) {
                sumSquares += ri * ri;
            }
        }

        return sumSquares;
    }
}