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Diffstat (limited to 'src/main/java/org/apache/commons/math3/optimization/LeastSquaresConverter.java')
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diff --git a/src/main/java/org/apache/commons/math3/optimization/LeastSquaresConverter.java b/src/main/java/org/apache/commons/math3/optimization/LeastSquaresConverter.java new file mode 100644 index 0000000..5ee9754 --- /dev/null +++ b/src/main/java/org/apache/commons/math3/optimization/LeastSquaresConverter.java @@ -0,0 +1,181 @@ +/* + * 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.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 {@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>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>This class support combination of residuals with or without weights and correlations. + * + * @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. */ + 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; + + /** + * 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. + * + * <p>The scalar objective function value is computed as: + * + * <pre> + * objective = ∑weight<sub>i</sub>(observation<sub>i</sub>-objective<sub>i</sub>)<sup>2</sup> + * </pre> + * + * <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</sup>) in the even elements and 1.0/(15.0<sup>2</sup>) in the odd + * elements (i.e. reciprocals of variances). + * + * <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. + * + * @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. + * + * <p>The scalar objective function value is computed as: + * + * <pre> + * objective = y<sup>T</sup>y with y = scale×(observation-objective) + * </pre> + * + * <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. + * + * @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; + } +} |