

Java example source code file (LeastSquaresConverter.java)
The LeastSquaresConverter.java Java example source code/* * 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/LICENSE2.0 * * 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. * <br/> * 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. * <br/> * 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. * <br/> * 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. * <p> * The scalar objective function value is computed as: * <pre> * objective = ∑weight<sub>i(observation_{i}objective_{i})^{2} * </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° 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) in the even elements and 1.0/(15.0^{2}) 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 * @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. * <p> * The scalar objective function value is computed as: * <pre> * objective = y<sup>Ty with y = scale×(observationobjective) * </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} */ 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; } } Other Java examples (source code examples)Here is a short list of links related to this Java LeastSquaresConverter.java source code file: 
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