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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.general;
import org.apache.commons.math.FunctionEvaluationException;
import org.apache.commons.math.exception.util.LocalizedFormats;
import org.apache.commons.math.linear.BlockRealMatrix;
import org.apache.commons.math.linear.DecompositionSolver;
import org.apache.commons.math.linear.InvalidMatrixException;
import org.apache.commons.math.linear.LUDecompositionImpl;
import org.apache.commons.math.linear.QRDecompositionImpl;
import org.apache.commons.math.linear.RealMatrix;
import org.apache.commons.math.optimization.OptimizationException;
import org.apache.commons.math.optimization.VectorialPointValuePair;
/**
* Gauss-Newton least-squares solver.
* <p>
* This class solve a least-square problem by solving the normal equations
* of the linearized problem at each iteration. Either LU decomposition or
* QR decomposition can be used to solve the normal equations. LU decomposition
* is faster but QR decomposition is more robust for difficult problems.
* </p>
*
* @version $Revision: 1073158 $ $Date: 2011-02-21 22:46:52 +0100 (lun. 21 févr. 2011) $
* @since 2.0
*
*/
public class GaussNewtonOptimizer extends AbstractLeastSquaresOptimizer {
/** Indicator for using LU decomposition. */
private final boolean useLU;
/** Simple constructor with default settings.
* <p>The convergence check is set to a {@link
* org.apache.commons.math.optimization.SimpleVectorialValueChecker}
* and the maximal number of evaluation is set to
* {@link AbstractLeastSquaresOptimizer#DEFAULT_MAX_ITERATIONS}.
* @param useLU if true, the normal equations will be solved using LU
* decomposition, otherwise they will be solved using QR decomposition
*/
public GaussNewtonOptimizer(final boolean useLU) {
this.useLU = useLU;
}
/** {@inheritDoc} */
@Override
public VectorialPointValuePair doOptimize()
throws FunctionEvaluationException, OptimizationException, IllegalArgumentException {
// iterate until convergence is reached
VectorialPointValuePair current = null;
for (boolean converged = false; !converged;) {
incrementIterationsCounter();
// evaluate the objective function and its jacobian
VectorialPointValuePair previous = current;
updateResidualsAndCost();
updateJacobian();
current = new VectorialPointValuePair(point, objective);
// build the linear problem
final double[] b = new double[cols];
final double[][] a = new double[cols][cols];
for (int i = 0; i < rows; ++i) {
final double[] grad = jacobian[i];
final double weight = residualsWeights[i];
final double residual = objective[i] - targetValues[i];
// compute the normal equation
final double wr = weight * residual;
for (int j = 0; j < cols; ++j) {
b[j] += wr * grad[j];
}
// build the contribution matrix for measurement i
for (int k = 0; k < cols; ++k) {
double[] ak = a[k];
double wgk = weight * grad[k];
for (int l = 0; l < cols; ++l) {
ak[l] += wgk * grad[l];
}
}
}
try {
// solve the linearized least squares problem
RealMatrix mA = new BlockRealMatrix(a);
DecompositionSolver solver = useLU ?
new LUDecompositionImpl(mA).getSolver() :
new QRDecompositionImpl(mA).getSolver();
final double[] dX = solver.solve(b);
// update the estimated parameters
for (int i = 0; i < cols; ++i) {
point[i] += dX[i];
}
} catch(InvalidMatrixException e) {
throw new OptimizationException(LocalizedFormats.UNABLE_TO_SOLVE_SINGULAR_PROBLEM);
}
// check convergence
if (previous != null) {
converged = checker.converged(getIterations(), previous, current);
}
}
// we have converged
return current;
}
}
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