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/*
 * Licensed to the Apache Software Foundation (ASF) under one or more
 * contributor license agreements.  See the NOTICE file distributed with
 * this work for additional information regarding copyright ownership.
 * The ASF licenses this file to You 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
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 */

package org.apache.commons.math3.optim.nonlinear.scalar;

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
 * {@link MultivariateVectorFunction vectorial objective functions} to
 * {@link MultivariateFunction 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 {@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. *
* This class support combination of residuals with or without weights and correlations. * * @see MultivariateFunction * @see MultivariateVectorFunction * @since 2.0 */ public class LeastSquaresConverter implements MultivariateFunction { /** Underlying vectorial function. */ private final MultivariateVectorFunction function; /** Observations to be compared to objective function to compute residuals. */ private final double[] observations; /** Optional weights for the residuals. */ private final double[] weights; /** Optional scaling matrix (weight and correlations) for the residuals. */ private final RealMatrix scale; /** * Builds a simple converter for uncorrelated residuals with identical * weights. * * @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; } /** * Builds a simple converter for uncorrelated residuals with the * specified 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 {@link DimensionMismatchException} * will be triggered while computing the scalar objective. *

* * @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 * @throws 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; } /** * Builds a simple converter for correlated residuals with the * specified 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 {@link DimensionMismatchException} * will be triggered while computing the scalar objective. *

* * @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} */ 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; } }




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