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Diffstat (limited to 'src/main/java/org/apache/commons/math3/optim/nonlinear/scalar/LeastSquaresConverter.java')
-rw-r--r-- | src/main/java/org/apache/commons/math3/optim/nonlinear/scalar/LeastSquaresConverter.java | 186 |
1 files changed, 186 insertions, 0 deletions
diff --git a/src/main/java/org/apache/commons/math3/optim/nonlinear/scalar/LeastSquaresConverter.java b/src/main/java/org/apache/commons/math3/optim/nonlinear/scalar/LeastSquaresConverter.java new file mode 100644 index 0000000..4be1f12 --- /dev/null +++ b/src/main/java/org/apache/commons/math3/optim/nonlinear/scalar/LeastSquaresConverter.java @@ -0,0 +1,186 @@ +/* + * 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. + * <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</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 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>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 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; + } +} |