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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.math.optimization;
import org.apache.commons.math.FunctionEvaluationException;
import org.apache.commons.math.MathRuntimeException;
import org.apache.commons.math.analysis.MultivariateRealFunction;
import org.apache.commons.math.analysis.MultivariateVectorialFunction;
import org.apache.commons.math.exception.util.LocalizedFormats;
import org.apache.commons.math.linear.RealMatrix;
/** This class converts {@link MultivariateVectorialFunction vectorial
* objective functions} to {@link MultivariateRealFunction 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 MultivariateRealFunction} 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 MultivariateRealFunction
* @see MultivariateVectorialFunction
* @version $Revision: 1070725 $ $Date: 2011-02-15 02:31:12 +0100 (mar. 15 févr. 2011) $
* @since 2.0
*/
public class LeastSquaresConverter implements MultivariateRealFunction {
/** Underlying vectorial function. */
private final MultivariateVectorialFunction 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 MultivariateVectorialFunction 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>
* <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>
* <p>
* The array computed by the objective function, the observations array and the
* weights array must have consistent sizes or a {@link FunctionEvaluationException} 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 IllegalArgumentException if the observations vector and the weights
* vector dimensions don't match (objective function dimension is checked only when
* the {@link #value(double[])} method is called)
*/
public LeastSquaresConverter(final MultivariateVectorialFunction function,
final double[] observations, final double[] weights)
throws IllegalArgumentException {
if (observations.length != weights.length) {
throw MathRuntimeException.createIllegalArgumentException(
LocalizedFormats.DIMENSIONS_MISMATCH_SIMPLE,
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>
* <p>
* The array computed by the objective function, the observations array and the
* the scaling matrix must have consistent sizes or a {@link FunctionEvaluationException}
* 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
* @exception IllegalArgumentException if the observations vector and the scale
* matrix dimensions don't match (objective function dimension is checked only when
* the {@link #value(double[])} method is called)
*/
public LeastSquaresConverter(final MultivariateVectorialFunction function,
final double[] observations, final RealMatrix scale)
throws IllegalArgumentException {
if (observations.length != scale.getColumnDimension()) {
throw MathRuntimeException.createIllegalArgumentException(
LocalizedFormats.DIMENSIONS_MISMATCH_SIMPLE,
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) throws FunctionEvaluationException {
// compute residuals
final double[] residuals = function.value(point);
if (residuals.length != observations.length) {
throw new FunctionEvaluationException(point,LocalizedFormats.DIMENSIONS_MISMATCH_SIMPLE,
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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