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The Apache Commons Math project is a library of lightweight, self-contained mathematics and statistics components addressing the most common practical problems not immediately available in the Java programming language or commons-lang.
/*
* 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;
}
}