/*
* 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.estimation;
import java.io.Serializable;
import org.apache.commons.math.exception.util.LocalizedFormats;
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.linear.RealVector;
import org.apache.commons.math.linear.ArrayRealVector;
import org.apache.commons.math.util.FastMath;
/**
* This class implements a solver for estimation problems.
*
* <p>This class solves estimation problems using a weighted least
* squares criterion on the measurement residuals. It uses a
* Gauss-Newton algorithm.</p>
*
* @version $Revision: 990655 $ $Date: 2010-08-29 23:49:40 +0200 (dim. 29 août 2010) $
* @since 1.2
* @deprecated as of 2.0, everything in package org.apache.commons.math.estimation has
* been deprecated and replaced by package org.apache.commons.math.optimization.general
*
*/
@Deprecated
public class GaussNewtonEstimator extends AbstractEstimator implements Serializable {
/** Serializable version identifier */
private static final long serialVersionUID = 5485001826076289109L;
/** Default threshold for cost steady state detection. */
private static final double DEFAULT_STEADY_STATE_THRESHOLD = 1.0e-6;
/** Default threshold for cost convergence. */
private static final double DEFAULT_CONVERGENCE = 1.0e-6;
/** Threshold for cost steady state detection. */
private double steadyStateThreshold;
/** Threshold for cost convergence. */
private double convergence;
/** Simple constructor with default settings.
* <p>
* The estimator is built with default values for all settings.
* </p>
* @see #DEFAULT_STEADY_STATE_THRESHOLD
* @see #DEFAULT_CONVERGENCE
* @see AbstractEstimator#DEFAULT_MAX_COST_EVALUATIONS
*/
public GaussNewtonEstimator() {
this.steadyStateThreshold = DEFAULT_STEADY_STATE_THRESHOLD;
this.convergence = DEFAULT_CONVERGENCE;
}
/**
* Simple constructor.
*
* <p>This constructor builds an estimator and stores its convergence
* characteristics.</p>
*
* <p>An estimator is considered to have converged whenever either
* the criterion goes below a physical threshold under which
* improvements are considered useless or when the algorithm is
* unable to improve it (even if it is still high). The first
* condition that is met stops the iterations.</p>
*
* <p>The fact an estimator has converged does not mean that the
* model accurately fits the measurements. It only means no better
* solution can be found, it does not mean this one is good. Such an
* analysis is left to the caller.</p>
*
* <p>If neither conditions are fulfilled before a given number of
* iterations, the algorithm is considered to have failed and an
* {@link EstimationException} is thrown.</p>
*
* @param maxCostEval maximal number of cost evaluations allowed
* @param convergence criterion threshold below which we do not need
* to improve the criterion anymore
* @param steadyStateThreshold steady state detection threshold, the
* problem has converged has reached a steady state if
* <code>FastMath.abs(J<sub>n</sub> - J<sub>n-1</sub>) <
* J<sub>n</sub> × convergence</code>, where <code>J<sub>n</sub></code>
* and <code>J<sub>n-1</sub></code> are the current and preceding criterion
* values (square sum of the weighted residuals of considered measurements).
*/
public GaussNewtonEstimator(final int maxCostEval, final double convergence,
final double steadyStateThreshold) {
setMaxCostEval(maxCostEval);
this.steadyStateThreshold = steadyStateThreshold;
this.convergence = convergence;
}
/**
* Set the convergence criterion threshold.
* @param convergence criterion threshold below which we do not need
* to improve the criterion anymore
*/
public void setConvergence(final double convergence) {
this.convergence = convergence;
}
/**
* Set the steady state detection threshold.
* <p>
* The problem has converged has reached a steady state if
* <code>FastMath.abs(J<sub>n</sub> - J<sub>n-1</sub>) <
* J<sub>n</sub> × convergence</code>, where <code>J<sub>n</sub></code>
* and <code>J<sub>n-1</sub></code> are the current and preceding criterion
* values (square sum of the weighted residuals of considered measurements).
* </p>
* @param steadyStateThreshold steady state detection threshold
*/
public void setSteadyStateThreshold(final double steadyStateThreshold) {
this.steadyStateThreshold = steadyStateThreshold;
}
/**
* Solve an estimation problem using a least squares criterion.
*
* <p>This method set the unbound parameters of the given problem
* starting from their current values through several iterations. At
* each step, the unbound parameters are changed in order to
* minimize a weighted least square criterion based on the
* measurements of the problem.</p>
*
* <p>The iterations are stopped either when the criterion goes
* below a physical threshold under which improvement are considered
* useless or when the algorithm is unable to improve it (even if it
* is still high). The first condition that is met stops the
* iterations. If the convergence it not reached before the maximum
* number of iterations, an {@link EstimationException} is
* thrown.</p>
*
* @param problem estimation problem to solve
* @exception EstimationException if the problem cannot be solved
*
* @see EstimationProblem
*
*/
@Override
public void estimate(EstimationProblem problem)
throws EstimationException {
initializeEstimate(problem);
// work matrices
double[] grad = new double[parameters.length];
ArrayRealVector bDecrement = new ArrayRealVector(parameters.length);
double[] bDecrementData = bDecrement.getDataRef();
RealMatrix wGradGradT = MatrixUtils.createRealMatrix(parameters.length, parameters.length);
// iterate until convergence is reached
double previous = Double.POSITIVE_INFINITY;
do {
// build the linear problem
incrementJacobianEvaluationsCounter();
RealVector b = new ArrayRealVector(parameters.length);
RealMatrix a = MatrixUtils.createRealMatrix(parameters.length, parameters.length);
for (int i = 0; i < measurements.length; ++i) {
if (! measurements [i].isIgnored()) {
double weight = measurements[i].getWeight();
double residual = measurements[i].getResidual();
// compute the normal equation
for (int j = 0; j < parameters.length; ++j) {
grad[j] = measurements[i].getPartial(parameters[j]);
bDecrementData[j] = weight * residual * grad[j];
}
// build the contribution matrix for measurement i
for (int k = 0; k < parameters.length; ++k) {
double gk = grad[k];
for (int l = 0; l < parameters.length; ++l) {
wGradGradT.setEntry(k, l, weight * gk * grad[l]);
}
}
// update the matrices
a = a.add(wGradGradT);
b = b.add(bDecrement);
}
}
try {
// solve the linearized least squares problem
RealVector dX = new LUDecompositionImpl(a).getSolver().solve(b);
// update the estimated parameters
for (int i = 0; i < parameters.length; ++i) {
parameters[i].setEstimate(parameters[i].getEstimate() + dX.getEntry(i));
}
} catch(InvalidMatrixException e) {
throw new EstimationException(LocalizedFormats.UNABLE_TO_SOLVE_SINGULAR_PROBLEM);
}
previous = cost;
updateResidualsAndCost();
} while ((getCostEvaluations() < 2) ||
(FastMath.abs(previous - cost) > (cost * steadyStateThreshold) &&
(FastMath.abs(cost) > convergence)));
}
}