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Commons Math example source code file (AbstractLeastSquaresOptimizer.java)

This example Commons Math source code file (AbstractLeastSquaresOptimizer.java) is included in the DevDaily.com "Java Source Code Warehouse" project. The intent of this project is to help you "Learn Java by Example" TM.

Java - Commons Math tags/keywords

abstractleastsquaresoptimizer, differentiablemultivariatevectorialfunction, differentiablemultivariatevectorialoptimizer, functionevaluationexception, functionevaluationexception, illegalargumentexception, illegalargumentexception, invalidmatrixexception, optimizationexception, optimizationexception, realmatrix, vectorialconvergencechecker, vectorialconvergencechecker, vectorialpointvaluepair

The Commons Math AbstractLeastSquaresOptimizer.java 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/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.general;

import org.apache.commons.math.FunctionEvaluationException;
import org.apache.commons.math.MaxEvaluationsExceededException;
import org.apache.commons.math.MaxIterationsExceededException;
import org.apache.commons.math.analysis.DifferentiableMultivariateVectorialFunction;
import org.apache.commons.math.analysis.MultivariateMatrixFunction;
import org.apache.commons.math.linear.InvalidMatrixException;
import org.apache.commons.math.linear.LUDecompositionImpl;
import org.apache.commons.math.linear.MatrixUtils;
import org.apache.commons.math.linear.RealMatrix;
import org.apache.commons.math.optimization.OptimizationException;
import org.apache.commons.math.optimization.SimpleVectorialValueChecker;
import org.apache.commons.math.optimization.VectorialConvergenceChecker;
import org.apache.commons.math.optimization.DifferentiableMultivariateVectorialOptimizer;
import org.apache.commons.math.optimization.VectorialPointValuePair;

/**
 * Base class for implementing least squares optimizers.
 * <p>This base class handles the boilerplate methods associated to thresholds
 * settings, jacobian and error estimation.</p>
 * @version $Revision: 925812 $ $Date: 2010-03-21 11:49:31 -0400 (Sun, 21 Mar 2010) $
 * @since 1.2
 *
 */
public abstract class AbstractLeastSquaresOptimizer implements DifferentiableMultivariateVectorialOptimizer {

    /** Default maximal number of iterations allowed. */
    public static final int DEFAULT_MAX_ITERATIONS = 100;

    /** Convergence checker. */
    protected VectorialConvergenceChecker checker;

    /**
     * Jacobian matrix.
     * <p>This matrix is in canonical form just after the calls to
     * {@link #updateJacobian()}, but may be modified by the solver
     * in the derived class (the {@link LevenbergMarquardtOptimizer
     * Levenberg-Marquardt optimizer} does this).</p>
     */
    protected double[][] jacobian;

    /** Number of columns of the jacobian matrix. */
    protected int cols;

    /** Number of rows of the jacobian matrix. */
    protected int rows;

    /**
     * Target value for the objective functions at optimum.
     * @since 2.1
     */
    protected double[] targetValues;

    /**
     * Weight for the least squares cost computation.
     * @since 2.1
     */
    protected double[] residualsWeights;

    /** Current point. */
    protected double[] point;

    /** Current objective function value. */
    protected double[] objective;

    /** Current residuals. */
    protected double[] residuals;

    /** Cost value (square root of the sum of the residuals). */
    protected double cost;

    /** Maximal number of iterations allowed. */
    private int maxIterations;

    /** Number of iterations already performed. */
    private int iterations;

    /** Maximal number of evaluations allowed. */
    private int maxEvaluations;

    /** Number of evaluations already performed. */
    private int objectiveEvaluations;

    /** Number of jacobian evaluations. */
    private int jacobianEvaluations;

    /** Objective function. */
    private DifferentiableMultivariateVectorialFunction function;

    /** Objective function derivatives. */
    private MultivariateMatrixFunction jF;

    /** Simple constructor with default settings.
     * <p>The convergence check is set to a {@link SimpleVectorialValueChecker}
     * and the maximal number of evaluation is set to its default value.</p>
     */
    protected AbstractLeastSquaresOptimizer() {
        setConvergenceChecker(new SimpleVectorialValueChecker());
        setMaxIterations(DEFAULT_MAX_ITERATIONS);
        setMaxEvaluations(Integer.MAX_VALUE);
    }

    /** {@inheritDoc} */
    public void setMaxIterations(int maxIterations) {
        this.maxIterations = maxIterations;
    }

    /** {@inheritDoc} */
    public int getMaxIterations() {
        return maxIterations;
    }

    /** {@inheritDoc} */
    public int getIterations() {
        return iterations;
    }

    /** {@inheritDoc} */
    public void setMaxEvaluations(int maxEvaluations) {
        this.maxEvaluations = maxEvaluations;
    }

    /** {@inheritDoc} */
    public int getMaxEvaluations() {
        return maxEvaluations;
    }

    /** {@inheritDoc} */
    public int getEvaluations() {
        return objectiveEvaluations;
    }

    /** {@inheritDoc} */
    public int getJacobianEvaluations() {
        return jacobianEvaluations;
    }

    /** {@inheritDoc} */
    public void setConvergenceChecker(VectorialConvergenceChecker convergenceChecker) {
        this.checker = convergenceChecker;
    }

    /** {@inheritDoc} */
    public VectorialConvergenceChecker getConvergenceChecker() {
        return checker;
    }

    /** Increment the iterations counter by 1.
     * @exception OptimizationException if the maximal number
     * of iterations is exceeded
     */
    protected void incrementIterationsCounter()
        throws OptimizationException {
        if (++iterations > maxIterations) {
            throw new OptimizationException(new MaxIterationsExceededException(maxIterations));
        }
    }

    /**
     * Update the jacobian matrix.
     * @exception FunctionEvaluationException if the function jacobian
     * cannot be evaluated or its dimension doesn't match problem dimension
     */
    protected void updateJacobian() throws FunctionEvaluationException {
        ++jacobianEvaluations;
        jacobian = jF.value(point);
        if (jacobian.length != rows) {
            throw new FunctionEvaluationException(point, "dimension mismatch {0} != {1}",
                                                  jacobian.length, rows);
        }
        for (int i = 0; i < rows; i++) {
            final double[] ji = jacobian[i];
            final double factor = -Math.sqrt(residualsWeights[i]);
            for (int j = 0; j < cols; ++j) {
                ji[j] *= factor;
            }
        }
    }

    /**
     * Update the residuals array and cost function value.
     * @exception FunctionEvaluationException if the function cannot be evaluated
     * or its dimension doesn't match problem dimension or maximal number of
     * of evaluations is exceeded
     */
    protected void updateResidualsAndCost()
        throws FunctionEvaluationException {

        if (++objectiveEvaluations > maxEvaluations) {
            throw new FunctionEvaluationException(new MaxEvaluationsExceededException(maxEvaluations),
                                                  point);
        }
        objective = function.value(point);
        if (objective.length != rows) {
            throw new FunctionEvaluationException(point, "dimension mismatch {0} != {1}",
                                                  objective.length, rows);
        }
        cost = 0;
        int index = 0;
        for (int i = 0; i < rows; i++) {
            final double residual = targetValues[i] - objective[i];
            residuals[i] = residual;
            cost += residualsWeights[i] * residual * residual;
            index += cols;
        }
        cost = Math.sqrt(cost);

    }

    /**
     * Get the Root Mean Square value.
     * Get the Root Mean Square value, i.e. the root of the arithmetic
     * mean of the square of all weighted residuals. This is related to the
     * criterion that is minimized by the optimizer as follows: if
     * <em>c if the criterion, and n is the number of
     * measurements, then the RMS is <em>sqrt (c/n).
     *
     * @return RMS value
     */
    public double getRMS() {
        double criterion = 0;
        for (int i = 0; i < rows; ++i) {
            final double residual = residuals[i];
            criterion += residualsWeights[i] * residual * residual;
        }
        return Math.sqrt(criterion / rows);
    }

    /**
     * Get the Chi-Square value.
     * @return chi-square value
     */
    public double getChiSquare() {
        double chiSquare = 0;
        for (int i = 0; i < rows; ++i) {
            final double residual = residuals[i];
            chiSquare += residual * residual / residualsWeights[i];
        }
        return chiSquare;
    }

    /**
     * Get the covariance matrix of optimized parameters.
     * @return covariance matrix
     * @exception FunctionEvaluationException if the function jacobian cannot
     * be evaluated
     * @exception OptimizationException if the covariance matrix
     * cannot be computed (singular problem)
     */
    public double[][] getCovariances()
        throws FunctionEvaluationException, OptimizationException {

        // set up the jacobian
        updateJacobian();

        // compute transpose(J).J, avoiding building big intermediate matrices
        double[][] jTj = new double[cols][cols];
        for (int i = 0; i < cols; ++i) {
            for (int j = i; j < cols; ++j) {
                double sum = 0;
                for (int k = 0; k < rows; ++k) {
                    sum += jacobian[k][i] * jacobian[k][j];
                }
                jTj[i][j] = sum;
                jTj[j][i] = sum;
            }
        }

        try {
            // compute the covariances matrix
            RealMatrix inverse =
                new LUDecompositionImpl(MatrixUtils.createRealMatrix(jTj)).getSolver().getInverse();
            return inverse.getData();
        } catch (InvalidMatrixException ime) {
            throw new OptimizationException("unable to compute covariances: singular problem");
        }

    }

    /**
     * Guess the errors in optimized parameters.
     * <p>Guessing is covariance-based, it only gives rough order of magnitude.

* @return errors in optimized parameters * @exception FunctionEvaluationException if the function jacobian cannot b evaluated * @exception OptimizationException if the covariances matrix cannot be computed * or the number of degrees of freedom is not positive (number of measurements * lesser or equal to number of parameters) */ public double[] guessParametersErrors() throws FunctionEvaluationException, OptimizationException { if (rows <= cols) { throw new OptimizationException( "no degrees of freedom ({0} measurements, {1} parameters)", rows, cols); } double[] errors = new double[cols]; final double c = Math.sqrt(getChiSquare() / (rows - cols)); double[][] covar = getCovariances(); for (int i = 0; i < errors.length; ++i) { errors[i] = Math.sqrt(covar[i][i]) * c; } return errors; } /** {@inheritDoc} */ public VectorialPointValuePair optimize(final DifferentiableMultivariateVectorialFunction f, final double[] target, final double[] weights, final double[] startPoint) throws FunctionEvaluationException, OptimizationException, IllegalArgumentException { if (target.length != weights.length) { throw new OptimizationException("dimension mismatch {0} != {1}", target.length, weights.length); } // reset counters iterations = 0; objectiveEvaluations = 0; jacobianEvaluations = 0; // store least squares problem characteristics function = f; jF = f.jacobian(); targetValues = target.clone(); residualsWeights = weights.clone(); this.point = startPoint.clone(); this.residuals = new double[target.length]; // arrays shared with the other private methods rows = target.length; cols = point.length; jacobian = new double[rows][cols]; cost = Double.POSITIVE_INFINITY; return doOptimize(); } /** Perform the bulk of optimization algorithm. * @return the point/value pair giving the optimal value for objective function * @exception FunctionEvaluationException if the objective function throws one during * the search * @exception OptimizationException if the algorithm failed to converge * @exception IllegalArgumentException if the start point dimension is wrong */ protected abstract VectorialPointValuePair doOptimize() throws FunctionEvaluationException, OptimizationException, IllegalArgumentException; }

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