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The Apache Commons Math project is a library of lightweight, self-contained mathematics and statistics components addressing the most common practical problems not immediately available in the Java programming language or commons-lang.
/*
* 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.optimization.general;
import org.apache.commons.math3.exception.ConvergenceException;
import org.apache.commons.math3.exception.NullArgumentException;
import org.apache.commons.math3.exception.MathInternalError;
import org.apache.commons.math3.exception.util.LocalizedFormats;
import org.apache.commons.math3.linear.ArrayRealVector;
import org.apache.commons.math3.linear.BlockRealMatrix;
import org.apache.commons.math3.linear.DecompositionSolver;
import org.apache.commons.math3.linear.LUDecomposition;
import org.apache.commons.math3.linear.QRDecomposition;
import org.apache.commons.math3.linear.RealMatrix;
import org.apache.commons.math3.linear.SingularMatrixException;
import org.apache.commons.math3.optimization.ConvergenceChecker;
import org.apache.commons.math3.optimization.SimpleVectorValueChecker;
import org.apache.commons.math3.optimization.PointVectorValuePair;
/**
* Gauss-Newton least-squares solver.
*
* 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.
*
*
* @deprecated As of 3.1 (to be removed in 4.0).
* @since 2.0
*
*/
@Deprecated
public class GaussNewtonOptimizer extends AbstractLeastSquaresOptimizer {
/** Indicator for using LU decomposition. */
private final boolean useLU;
/**
* Simple constructor with default settings.
* The normal equations will be solved using LU decomposition and the
* convergence check is set to a {@link SimpleVectorValueChecker}
* with default tolerances.
* @deprecated See {@link SimpleVectorValueChecker#SimpleVectorValueChecker()}
*/
@Deprecated
public GaussNewtonOptimizer() {
this(true);
}
/**
* Simple constructor with default settings.
* The normal equations will be solved using LU decomposition.
*
* @param checker Convergence checker.
*/
public GaussNewtonOptimizer(ConvergenceChecker checker) {
this(true, checker);
}
/**
* Simple constructor with default settings.
* The convergence check is set to a {@link SimpleVectorValueChecker}
* with default tolerances.
*
* @param useLU If {@code true}, the normal equations will be solved
* using LU decomposition, otherwise they will be solved using QR
* decomposition.
* @deprecated See {@link SimpleVectorValueChecker#SimpleVectorValueChecker()}
*/
@Deprecated
public GaussNewtonOptimizer(final boolean useLU) {
this(useLU, new SimpleVectorValueChecker());
}
/**
* @param useLU If {@code true}, the normal equations will be solved
* using LU decomposition, otherwise they will be solved using QR
* decomposition.
* @param checker Convergence checker.
*/
public GaussNewtonOptimizer(final boolean useLU,
ConvergenceChecker checker) {
super(checker);
this.useLU = useLU;
}
/** {@inheritDoc} */
@Override
public PointVectorValuePair doOptimize() {
final ConvergenceChecker checker
= getConvergenceChecker();
// Computation will be useless without a checker (see "for-loop").
if (checker == null) {
throw new NullArgumentException();
}
final double[] targetValues = getTarget();
final int nR = targetValues.length; // Number of observed data.
final RealMatrix weightMatrix = getWeight();
// Diagonal of the weight matrix.
final double[] residualsWeights = new double[nR];
for (int i = 0; i < nR; i++) {
residualsWeights[i] = weightMatrix.getEntry(i, i);
}
final double[] currentPoint = getStartPoint();
final int nC = currentPoint.length;
// iterate until convergence is reached
PointVectorValuePair current = null;
int iter = 0;
for (boolean converged = false; !converged;) {
++iter;
// evaluate the objective function and its jacobian
PointVectorValuePair previous = current;
// Value of the objective function at "currentPoint".
final double[] currentObjective = computeObjectiveValue(currentPoint);
final double[] currentResiduals = computeResiduals(currentObjective);
final RealMatrix weightedJacobian = computeWeightedJacobian(currentPoint);
current = new PointVectorValuePair(currentPoint, currentObjective);
// build the linear problem
final double[] b = new double[nC];
final double[][] a = new double[nC][nC];
for (int i = 0; i < nR; ++i) {
final double[] grad = weightedJacobian.getRow(i);
final double weight = residualsWeights[i];
final double residual = currentResiduals[i];
// compute the normal equation
final double wr = weight * residual;
for (int j = 0; j < nC; ++j) {
b[j] += wr * grad[j];
}
// build the contribution matrix for measurement i
for (int k = 0; k < nC; ++k) {
double[] ak = a[k];
double wgk = weight * grad[k];
for (int l = 0; l < nC; ++l) {
ak[l] += wgk * grad[l];
}
}
}
try {
// solve the linearized least squares problem
RealMatrix mA = new BlockRealMatrix(a);
DecompositionSolver solver = useLU ?
new LUDecomposition(mA).getSolver() :
new QRDecomposition(mA).getSolver();
final double[] dX = solver.solve(new ArrayRealVector(b, false)).toArray();
// update the estimated parameters
for (int i = 0; i < nC; ++i) {
currentPoint[i] += dX[i];
}
} catch (SingularMatrixException e) {
throw new ConvergenceException(LocalizedFormats.UNABLE_TO_SOLVE_SINGULAR_PROBLEM);
}
// Check convergence.
if (previous != null) {
converged = checker.converged(iter, previous, current);
if (converged) {
cost = computeCost(currentResiduals);
// Update (deprecated) "point" field.
point = current.getPoint();
return current;
}
}
}
// Must never happen.
throw new MathInternalError();
}
}