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adapted old Levenberg-Marquardt estimator to new top level optimizers API 

git-svn-id: https://svn.apache.org/repos/asf/commons/proper/math/trunk@754727 13f79535-47bb-0310-9956-ffa450edef68
This commit is contained in:
Luc Maisonobe 2009-03-15 19:11:02 +00:00
parent 3a0df1ba48
commit c37f06ed3a
16 changed files with 1811 additions and 3330 deletions
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12
src/java/org/apache/commons/math/optimization/VectorialDifferentiableOptimizer.java
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@ -60,7 +60,17 @@ public interface VectorialDifferentiableOptimizer extends Serializable {
* </p>
* @return number of evaluations of the objective function
*/
int getEvaluations();
int getEvaluations();
/** Get the number of evaluations of the objective function jacobian .
* <p>
* The number of evaluation correspond to the last call to the
* {@link #optimize(ObjectiveFunction, GoalType, double[]) optimize}
* method. It is 0 if the method has not been called yet.
* </p>
* @return number of evaluations of the objective function jacobian
*/
int getJacobianEvaluations();
/** Set the convergence checker.
* @param checker object to use to check for convergence

312
src/java/org/apache/commons/math/optimization/general/AbstractEstimator.java
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@ -1,312 +0,0 @@
/*
* 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 java.util.Arrays;
import org.apache.commons.math.linear.InvalidMatrixException;
import org.apache.commons.math.linear.MatrixUtils;
import org.apache.commons.math.linear.RealMatrix;
import org.apache.commons.math.linear.decomposition.LUDecompositionImpl;
import org.apache.commons.math.optimization.OptimizationException;
/**
* Base class for implementing estimators.
* <p>This base class handles the boilerplates methods associated to thresholds
* settings, jacobian and error estimation.</p>
* @version $Revision$ $Date$
* @since 1.2
*
*/
public abstract class AbstractEstimator implements Estimator {
/** Default maximal number of cost evaluations allowed. */
public static final int DEFAULT_MAX_COST_EVALUATIONS = 100;
/**
* Build an abstract estimator for least squares problems.
* <p>The maximal number of cost evaluations allowed is set
* to its default value {@link #DEFAULT_MAX_COST_EVALUATIONS}.</p>
*/
protected AbstractEstimator() {
setMaxCostEval(DEFAULT_MAX_COST_EVALUATIONS);
}
/**
* Set the maximal number of cost evaluations allowed.
*
* @param maxCostEval maximal number of cost evaluations allowed
* @see #estimate
*/
public final void setMaxCostEval(int maxCostEval) {
this.maxCostEval = maxCostEval;
}
/**
* Get the number of cost evaluations.
*
* @return number of cost evaluations
* */
public final int getCostEvaluations() {
return costEvaluations;
}
/**
* Get the number of jacobian evaluations.
*
* @return number of jacobian evaluations
* */
public final int getJacobianEvaluations() {
return jacobianEvaluations;
}
/**
* Update the jacobian matrix.
*/
protected void updateJacobian() {
incrementJacobianEvaluationsCounter();
Arrays.fill(jacobian, 0);
for (int i = 0, index = 0; i < rows; i++) {
WeightedMeasurement wm = measurements[i];
double factor = -Math.sqrt(wm.getWeight());
for (int j = 0; j < cols; ++j) {
jacobian[index++] = factor * wm.getPartial(parameters[j]);
}
}
}
/**
* Increment the jacobian evaluations counter.
*/
protected final void incrementJacobianEvaluationsCounter() {
++jacobianEvaluations;
}
/**
* Update the residuals array and cost function value.
* @exception OptimizationException if the number of cost evaluations
* exceeds the maximum allowed
*/
protected void updateResidualsAndCost()
throws OptimizationException {
if (++costEvaluations > maxCostEval) {
throw new OptimizationException("maximal number of evaluations exceeded ({0})",
maxCostEval);
}
cost = 0;
for (int i = 0, index = 0; i < rows; i++, index += cols) {
WeightedMeasurement wm = measurements[i];
double residual = wm.getResidual();
residuals[i] = Math.sqrt(wm.getWeight()) * residual;
cost += wm.getWeight() * residual * residual;
}
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 estimator as follows: if
* <em>c</em> if the criterion, and <em>n</em> is the number of
* measurements, then the RMS is <em>sqrt (c/n)</em>.
*
* @param problem estimation problem
* @return RMS value
*/
public double getRMS(EstimationProblem problem) {
WeightedMeasurement[] wm = problem.getMeasurements();
double criterion = 0;
for (int i = 0; i < wm.length; ++i) {
double residual = wm[i].getResidual();
criterion += wm[i].getWeight() * residual * residual;
}
return Math.sqrt(criterion / wm.length);
}
/**
* Get the Chi-Square value.
* @param problem estimation problem
* @return chi-square value
*/
public double getChiSquare(EstimationProblem problem) {
WeightedMeasurement[] wm = problem.getMeasurements();
double chiSquare = 0;
for (int i = 0; i < wm.length; ++i) {
double residual = wm[i].getResidual();
chiSquare += residual * residual / wm[i].getWeight();
}
return chiSquare;
}
/**
* Get the covariance matrix of unbound estimated parameters.
* @param problem estimation problem
* @return covariance matrix
* @exception OptimizationException if the covariance matrix
* cannot be computed (singular problem)
*/
public double[][] getCovariances(EstimationProblem problem)
throws OptimizationException {
// set up the jacobian
updateJacobian();
// compute transpose(J).J, avoiding building big intermediate matrices
final int rows = problem.getMeasurements().length;
final int cols = problem.getUnboundParameters().length;
final int max = cols * rows;
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 < max; k += cols) {
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 unbound estimated parameters.
* <p>Guessing is covariance-based, it only gives rough order of magnitude.</p>
* @param problem estimation problem
* @return errors in estimated parameters
* @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(EstimationProblem problem)
throws OptimizationException {
int m = problem.getMeasurements().length;
int p = problem.getUnboundParameters().length;
if (m <= p) {
throw new OptimizationException(
"no degrees of freedom ({0} measurements, {1} parameters)",
m, p);
}
double[] errors = new double[problem.getUnboundParameters().length];
final double c = Math.sqrt(getChiSquare(problem) / (m - p));
double[][] covar = getCovariances(problem);
for (int i = 0; i < errors.length; ++i) {
errors[i] = Math.sqrt(covar[i][i]) * c;
}
return errors;
}
/**
* Initialization of the common parts of the estimation.
* <p>This method <em>must</em> be called at the start
* of the {@link #estimate(EstimationProblem) estimate}
* method.</p>
* @param problem estimation problem to solve
*/
protected void initializeEstimate(EstimationProblem problem) {
// reset counters
costEvaluations = 0;
jacobianEvaluations = 0;
// retrieve the equations and the parameters
measurements = problem.getMeasurements();
parameters = problem.getUnboundParameters();
// arrays shared with the other private methods
rows = measurements.length;
cols = parameters.length;
jacobian = new double[rows * cols];
residuals = new double[rows];
cost = Double.POSITIVE_INFINITY;
}
/**
* Solve an estimation problem.
*
* <p>The method should set the parameters of the problem to several
* trial values until it reaches convergence. If this method returns
* normally (i.e. without throwing an exception), then the best
* estimate of the parameters can be retrieved from the problem
* itself, through the {@link EstimationProblem#getAllParameters
* EstimationProblem.getAllParameters} method.</p>
*
* @param problem estimation problem to solve
* @exception OptimizationException if the problem cannot be solved
*
*/
public abstract void estimate(EstimationProblem problem)
throws OptimizationException;
/** Array of measurements. */
protected WeightedMeasurement[] measurements;
/** Array of parameters. */
protected EstimatedParameter[] parameters;
/**
* 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 LevenbergMarquardtEstimator
* Levenberg-Marquardt estimator} 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;
/** Residuals array.
* <p>This array is in canonical form just after the calls to
* {@link #updateJacobian()}, but may be modified by the solver
* in the derived class (the {@link LevenbergMarquardtEstimator
* Levenberg-Marquardt estimator} does this).</p>
*/
protected double[] residuals;
/** Cost value (square root of the sum of the residuals). */
protected double cost;
/** Maximal allowed number of cost evaluations. */
private int maxCostEval;
/** Number of cost evaluations. */
private int costEvaluations;
/** Number of jacobian evaluations. */
private int jacobianEvaluations;
}

36
src/java/org/apache/commons/math/optimization/general/AbstractLeastSquaresOptimizer.java
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@ -30,8 +30,8 @@ import org.apache.commons.math.optimization.VectorialDifferentiableOptimizer;
import org.apache.commons.math.optimization.VectorialPointValuePair;
/**
* Base class for implementing estimators.
* <p>This base class handles the boilerplates methods associated to thresholds
* 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 $Revision$ $Date$
* @since 1.2
@ -61,8 +61,8 @@ public abstract class AbstractLeastSquaresOptimizer implements VectorialDifferen
* 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 LevenbergMarquardtEstimator
* Levenberg-Marquardt estimator} does this).</p>
* in the derived class (the {@link LevenbergMarquardtOptimizer
* Levenberg-Marquardt optimizer} does this).</p>
*/
protected double[][] jacobian;
@ -87,6 +87,9 @@ public abstract class AbstractLeastSquaresOptimizer implements VectorialDifferen
/** 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;
@ -114,6 +117,11 @@ public abstract class AbstractLeastSquaresOptimizer implements VectorialDifferen
return objectiveEvaluations;
}
/** {@inheritDoc} */
public int getJacobianEvaluations() {
return jacobianEvaluations;
}
/** {@inheritDoc} */
public void setConvergenceChecker(VectorialConvergenceChecker checker) {
this.checker = checker;
@ -175,7 +183,8 @@ public abstract class AbstractLeastSquaresOptimizer implements VectorialDifferen
}
cost = 0;
for (int i = 0, index = 0; i < rows; i++, index += cols) {
final double residual = objective[i] - target[i];
final double residual = target[i] - objective[i];
residuals[i] = residual;
cost += weights[i] * residual * residual;
}
cost = Math.sqrt(cost);
@ -186,7 +195,7 @@ public abstract class AbstractLeastSquaresOptimizer implements VectorialDifferen
* 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 estimator as follows: if
* criterion that is minimized by the optimizer as follows: if
* <em>c</em> if the criterion, and <em>n</em> is the number of
* measurements, then the RMS is <em>sqrt (c/n)</em>.
*
@ -195,7 +204,7 @@ public abstract class AbstractLeastSquaresOptimizer implements VectorialDifferen
public double getRMS() {
double criterion = 0;
for (int i = 0; i < rows; ++i) {
final double residual = objective[i] - target[i];
final double residual = residuals[i];
criterion += weights[i] * residual * residual;
}
return Math.sqrt(criterion / rows);
@ -208,14 +217,14 @@ public abstract class AbstractLeastSquaresOptimizer implements VectorialDifferen
public double getChiSquare() {
double chiSquare = 0;
for (int i = 0; i < rows; ++i) {
final double residual = objective[i] - target[i];
final double residual = residuals[i];
chiSquare += residual * residual / weights[i];
}
return chiSquare;
}
/**
* Get the covariance matrix of unbound estimated parameters.
* Get the covariance matrix of optimized parameters.
* @return covariance matrix
* @exception ObjectiveException if the function jacobian cannot
* be evaluated
@ -231,12 +240,10 @@ public abstract class AbstractLeastSquaresOptimizer implements VectorialDifferen
// compute transpose(J).J, avoiding building big intermediate matrices
double[][] jTj = new double[cols][cols];
for (int i = 0; i < cols; ++i) {
final double[] ji = jacobian[i];
for (int j = i; j < cols; ++j) {
final double[] jj = jacobian[j];
double sum = 0;
for (int k = 0; k < rows; ++k) {
sum += ji[k] * jj[k];
sum += jacobian[k][i] * jacobian[k][j];
}
jTj[i][j] = sum;
jTj[j][i] = sum;
@ -255,9 +262,9 @@ public abstract class AbstractLeastSquaresOptimizer implements VectorialDifferen
}
/**
* Guess the errors in unbound estimated parameters.
* Guess the errors in optimized parameters.
* <p>Guessing is covariance-based, it only gives rough order of magnitude.</p>
* @return errors in estimated parameters
* @return errors in optimized parameters
* @exception ObjectiveException 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
@ -299,6 +306,7 @@ public abstract class AbstractLeastSquaresOptimizer implements VectorialDifferen
this.target = target;
this.weights = weights;
this.variables = startPoint.clone();
this.residuals = new double[target.length];
// arrays shared with the other private methods
rows = target.length;

124
src/java/org/apache/commons/math/optimization/general/EstimatedParameter.java
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@ -1,124 +0,0 @@
/*
* 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 java.io.Serializable;
/** This class represents the estimated parameters of an estimation problem.
*
* <p>The parameters of an estimation problem have a name, a value and
* a bound flag. The value of bound parameters is considered trusted
* and the solvers should not adjust them. On the other hand, the
* solvers should adjust the value of unbounds parameters until they
* satisfy convergence criterions specific to each solver.</p>
*
* @version $Revision$ $Date$
* @since 1.2
*
*/
public class EstimatedParameter
implements Serializable {
/** Simple constructor.
* Build an instance from a first estimate of the parameter,
* initially considered unbound.
* @param name name of the parameter
* @param firstEstimate first estimate of the parameter
*/
public EstimatedParameter(String name, double firstEstimate) {
this.name = name;
estimate = firstEstimate;
bound = false;
}
/** Simple constructor.
* Build an instance from a first estimate of the parameter and a
* bound flag
* @param name name of the parameter
* @param firstEstimate first estimate of the parameter
* @param bound flag, should be true if the parameter is bound
*/
public EstimatedParameter(String name,
double firstEstimate,
boolean bound) {
this.name = name;
estimate = firstEstimate;
this.bound = bound;
}
/** Copy constructor.
* Build a copy of a parameter
* @param parameter instance to copy
*/
public EstimatedParameter(EstimatedParameter parameter) {
name = parameter.name;
estimate = parameter.estimate;
bound = parameter.bound;
}
/** Set a new estimated value for the parameter.
* @param estimate new estimate for the parameter
*/
public void setEstimate(double estimate) {
this.estimate = estimate;
}
/** Get the current estimate of the parameter
* @return current estimate
*/
public double getEstimate() {
return estimate;
}
/** get the name of the parameter
* @return parameter name
*/
public String getName() {
return name;
}
/** Set the bound flag of the parameter
* @param bound this flag should be set to true if the parameter is
* bound (i.e. if it should not be adjusted by the solver).
*/
public void setBound(boolean bound) {
this.bound = bound;
}
/** Check if the parameter is bound
* @return true if the parameter is bound */
public boolean isBound() {
return bound;
}
/** Name of the parameter */
private String name;
/** Current value of the parameter */
protected double estimate;
/** Indicator for bound parameters
* (ie parameters that should not be estimated)
*/
private boolean bound;
/** Serializable version identifier */
private static final long serialVersionUID = -555440800213416949L;
}

65
src/java/org/apache/commons/math/optimization/general/EstimationProblem.java
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@ -1,65 +0,0 @@
/*
* 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;
/**
* This interface represents an estimation problem.
*
* <p>This interface should be implemented by all real estimation
* problems before they can be handled by the estimators through the
* {@link Estimator#estimate Estimator.estimate} method.</p>
*
* <p>An estimation problem, as seen by a solver is a set of
* parameters and a set of measurements. The parameters are adjusted
* during the estimation through the {@link #getUnboundParameters
* getUnboundParameters} and {@link EstimatedParameter#setEstimate
* EstimatedParameter.setEstimate} methods. The measurements both have
* a measured value which is generally fixed at construction and a
* theoretical value which depends on the model and hence varies as
* the parameters are adjusted. The purpose of the solver is to reduce
* the residual between these values, it can retrieve the measurements
* through the {@link #getMeasurements getMeasurements} method.</p>
*
* @see Estimator
* @see WeightedMeasurement
*
* @version $Revision$ $Date$
* @since 1.2
*
*/
public interface EstimationProblem {
/**
* Get the measurements of an estimation problem.
* @return measurements
*/
WeightedMeasurement[] getMeasurements();
/**
* Get the unbound parameters of the problem.
* @return unbound parameters
*/
EstimatedParameter[] getUnboundParameters();
/**
* Get all the parameters of the problem.
* @return parameters
*/
EstimatedParameter[] getAllParameters();
}

93
src/java/org/apache/commons/math/optimization/general/Estimator.java
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@ -1,93 +0,0 @@
/*
* 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.optimization.OptimizationException;
/**
* This interface represents solvers for estimation problems.
*
* <p>The classes which are devoted to solve estimation problems
* should implement this interface. The problems which can be handled
* should implement the {@link EstimationProblem} interface which
* gather all the information needed by the solver.</p>
*
* <p>The interface is composed only of the {@link #estimate estimate}
* method.</p>
*
* @see EstimationProblem
*
* @version $Revision$ $Date$
* @since 1.2
*
*/
public interface Estimator {
/**
* Solve an estimation problem.
*
* <p>The method should set the parameters of the problem to several
* trial values until it reaches convergence. If this method returns
* normally (i.e. without throwing an exception), then the best
* estimate of the parameters can be retrieved from the problem
* itself, through the {@link EstimationProblem#getAllParameters
* EstimationProblem.getAllParameters} method.</p>
*
* @param problem estimation problem to solve
* @exception OptimizationException if the problem cannot be solved
*
*/
void estimate(EstimationProblem problem)
throws OptimizationException;
/**
* 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 estimator as follows: if
* <em>c</em> is the criterion, and <em>n</em> is the number of
* measurements, then the RMS is <em>sqrt (c/n)</em>.
* @see #guessParametersErrors(EstimationProblem)
*
* @param problem estimation problem
* @return RMS value
*/
double getRMS(EstimationProblem problem);
/**
* Get the covariance matrix of estimated parameters.
* @param problem estimation problem
* @return covariance matrix
* @exception OptimizationException if the covariance matrix
* cannot be computed (singular problem)
*/
double[][] getCovariances(EstimationProblem problem)
throws OptimizationException;
/**
* Guess the errors in estimated parameters.
* @see #getRMS(EstimationProblem)
* @param problem estimation problem
* @return errors in estimated parameters
* @exception OptimizationException if the error cannot be guessed
*/
double[] guessParametersErrors(EstimationProblem problem)
throws OptimizationException;
}

227
src/java/org/apache/commons/math/optimization/general/GaussNewtonEstimator.java
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@ -1,227 +0,0 @@
/*
* 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 java.io.Serializable;
import org.apache.commons.math.linear.InvalidMatrixException;
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.RealVectorImpl;
import org.apache.commons.math.linear.decomposition.LUDecompositionImpl;
import org.apache.commons.math.optimization.OptimizationException;
/**
* 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 $Revision$ $Date$
* @since 1.2
*
*/
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 OptimizationException} 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>Math.abs(J<sub>n</sub> - J<sub>n-1</sub>) &lt;
* J<sub>n</sub> &times 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>Math.abs(J<sub>n</sub> - J<sub>n-1</sub>) &lt;
* J<sub>n</sub> &times 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 OptimizationException} is
* thrown.</p>
*
* @param problem estimation problem to solve
* @exception OptimizationException if the problem cannot be solved
*
* @see EstimationProblem
*
*/
public void estimate(EstimationProblem problem)
throws OptimizationException {
initializeEstimate(problem);
// work matrices
double[] grad = new double[parameters.length];
RealVectorImpl bDecrement = new RealVectorImpl(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 RealVectorImpl(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 OptimizationException("unable to solve: singular problem");
}
previous = cost;
updateResidualsAndCost();
} while ((getCostEvaluations() < 2) ||
(Math.abs(previous - cost) > (cost * steadyStateThreshold) &&
(Math.abs(cost) > convergence)));
}
}

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src/java/org/apache/commons/math/optimization/general/LevenbergMarquardtEstimator.java
View File

@ -1,873 +0,0 @@
/*
* 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 java.io.Serializable;
import java.util.Arrays;
import org.apache.commons.math.optimization.OptimizationException;
/**
* This class solves a least squares problem.
*
* <p>This implementation <em>should</em> work even for over-determined systems
* (i.e. systems having more variables than equations). Over-determined systems
* are solved by ignoring the variables which have the smallest impact according
* to their jacobian column norm. Only the rank of the matrix and some loop bounds
* are changed to implement this.</p>
*
* <p>The resolution engine is a simple translation of the MINPACK <a
* href="http://www.netlib.org/minpack/lmder.f">lmder</a> routine with minor
* changes. The changes include the over-determined resolution and the Q.R.
* decomposition which has been rewritten following the algorithm described in the
* P. Lascaux and R. Theodor book <i>Analyse num&eacute;rique matricielle
* appliqu&eacute;e &agrave; l'art de l'ing&eacute;nieur</i>, Masson 1986. The
* redistribution policy for MINPACK is available <a
* href="http://www.netlib.org/minpack/disclaimer">here</a>, for convenience, it
* is reproduced below.</p>
*
* <table border="0" width="80%" cellpadding="10" align="center" bgcolor="#E0E0E0">
* <tr><td>
* Minpack Copyright Notice (1999) University of Chicago.
* All rights reserved
* </td></tr>
* <tr><td>
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
* <ol>
* <li>Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.</li>
* <li>Redistributions in binary form must reproduce the above
* copyright notice, this list of conditions and the following
* disclaimer in the documentation and/or other materials provided
* with the distribution.</li>
* <li>The end-user documentation included with the redistribution, if any,
* must include the following acknowledgment:
* <code>This product includes software developed by the University of
* Chicago, as Operator of Argonne National Laboratory.</code>
* Alternately, this acknowledgment may appear in the software itself,
* if and wherever such third-party acknowledgments normally appear.</li>
* <li><strong>WARRANTY DISCLAIMER. THE SOFTWARE IS SUPPLIED "AS IS"
* WITHOUT WARRANTY OF ANY KIND. THE COPYRIGHT HOLDER, THE
* UNITED STATES, THE UNITED STATES DEPARTMENT OF ENERGY, AND
* THEIR EMPLOYEES: (1) DISCLAIM ANY WARRANTIES, EXPRESS OR
* IMPLIED, INCLUDING BUT NOT LIMITED TO ANY IMPLIED WARRANTIES
* OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE, TITLE
* OR NON-INFRINGEMENT, (2) DO NOT ASSUME ANY LEGAL LIABILITY
* OR RESPONSIBILITY FOR THE ACCURACY, COMPLETENESS, OR
* USEFULNESS OF THE SOFTWARE, (3) DO NOT REPRESENT THAT USE OF
* THE SOFTWARE WOULD NOT INFRINGE PRIVATELY OWNED RIGHTS, (4)
* DO NOT WARRANT THAT THE SOFTWARE WILL FUNCTION
* UNINTERRUPTED, THAT IT IS ERROR-FREE OR THAT ANY ERRORS WILL
* BE CORRECTED.</strong></li>
* <li><strong>LIMITATION OF LIABILITY. IN NO EVENT WILL THE COPYRIGHT
* HOLDER, THE UNITED STATES, THE UNITED STATES DEPARTMENT OF
* ENERGY, OR THEIR EMPLOYEES: BE LIABLE FOR ANY INDIRECT,
* INCIDENTAL, CONSEQUENTIAL, SPECIAL OR PUNITIVE DAMAGES OF
* ANY KIND OR NATURE, INCLUDING BUT NOT LIMITED TO LOSS OF
* PROFITS OR LOSS OF DATA, FOR ANY REASON WHATSOEVER, WHETHER
* SUCH LIABILITY IS ASSERTED ON THE BASIS OF CONTRACT, TORT
* (INCLUDING NEGLIGENCE OR STRICT LIABILITY), OR OTHERWISE,
* EVEN IF ANY OF SAID PARTIES HAS BEEN WARNED OF THE
* POSSIBILITY OF SUCH LOSS OR DAMAGES.</strong></li>
* <ol></td></tr>
* </table>
* @author Argonne National Laboratory. MINPACK project. March 1980 (original fortran)
* @author Burton S. Garbow (original fortran)
* @author Kenneth E. Hillstrom (original fortran)
* @author Jorge J. More (original fortran)
* @version $Revision$ $Date$
* @since 1.2
*
*/
public class LevenbergMarquardtEstimator extends AbstractEstimator implements Serializable {
/**
* Build an estimator for least squares problems.
* <p>The default values for the algorithm settings are:
* <ul>
* <li>{@link #setInitialStepBoundFactor initial step bound factor}: 100.0</li>
* <li>{@link #setMaxCostEval maximal cost evaluations}: 1000</li>
* <li>{@link #setCostRelativeTolerance cost relative tolerance}: 1.0e-10</li>
* <li>{@link #setParRelativeTolerance parameters relative tolerance}: 1.0e-10</li>
* <li>{@link #setOrthoTolerance orthogonality tolerance}: 1.0e-10</li>
* </ul>
* </p>
*/
public LevenbergMarquardtEstimator() {
// set up the superclass with a default max cost evaluations setting
setMaxCostEval(1000);
// default values for the tuning parameters
setInitialStepBoundFactor(100.0);
setCostRelativeTolerance(1.0e-10);
setParRelativeTolerance(1.0e-10);
setOrthoTolerance(1.0e-10);
}
/**
* Set the positive input variable used in determining the initial step bound.
* This bound is set to the product of initialStepBoundFactor and the euclidean norm of diag*x if nonzero,
* or else to initialStepBoundFactor itself. In most cases factor should lie
* in the interval (0.1, 100.0). 100.0 is a generally recommended value
*
* @param initialStepBoundFactor initial step bound factor
* @see #estimate
*/
public void setInitialStepBoundFactor(double initialStepBoundFactor) {
this.initialStepBoundFactor = initialStepBoundFactor;
}
/**
* Set the desired relative error in the sum of squares.
*
* @param costRelativeTolerance desired relative error in the sum of squares
* @see #estimate
*/
public void setCostRelativeTolerance(double costRelativeTolerance) {
this.costRelativeTolerance = costRelativeTolerance;
}
/**
* Set the desired relative error in the approximate solution parameters.
*
* @param parRelativeTolerance desired relative error
* in the approximate solution parameters
* @see #estimate
*/
public void setParRelativeTolerance(double parRelativeTolerance) {
this.parRelativeTolerance = parRelativeTolerance;
}
/**
* Set the desired max cosine on the orthogonality.
*
* @param orthoTolerance desired max cosine on the orthogonality
* between the function vector and the columns of the jacobian
* @see #estimate
*/
public void setOrthoTolerance(double orthoTolerance) {
this.orthoTolerance = orthoTolerance;
}
/**
* Solve an estimation problem using the Levenberg-Marquardt algorithm.
* <p>The algorithm used is a modified Levenberg-Marquardt one, based
* on the MINPACK <a href="http://www.netlib.org/minpack/lmder.f">lmder</a>
* routine. The algorithm settings must have been set up before this method
* is called with the {@link #setInitialStepBoundFactor},
* {@link #setMaxCostEval}, {@link #setCostRelativeTolerance},
* {@link #setParRelativeTolerance} and {@link #setOrthoTolerance} methods.
* If these methods have not been called, the default values set up by the
* {@link #LevenbergMarquardtEstimator() constructor} will be used.</p>
* <p>The authors of the original fortran function are:</p>
* <ul>
* <li>Argonne National Laboratory. MINPACK project. March 1980</li>
* <li>Burton S. Garbow</li>
* <li>Kenneth E. Hillstrom</li>
* <li>Jorge J. More</li>
* </ul>
* <p>Luc Maisonobe did the Java translation.</p>
*
* @param problem estimation problem to solve
* @exception OptimizationException if convergence cannot be
* reached with the specified algorithm settings or if there are more variables
* than equations
* @see #setInitialStepBoundFactor
* @see #setCostRelativeTolerance
* @see #setParRelativeTolerance
* @see #setOrthoTolerance
*/
public void estimate(EstimationProblem problem)
throws OptimizationException {
initializeEstimate(problem);
// arrays shared with the other private methods
solvedCols = Math.min(rows, cols);
diagR = new double[cols];
jacNorm = new double[cols];
beta = new double[cols];
permutation = new int[cols];
lmDir = new double[cols];
// local variables
double delta = 0, xNorm = 0;
double[] diag = new double[cols];
double[] oldX = new double[cols];
double[] oldRes = new double[rows];
double[] work1 = new double[cols];
double[] work2 = new double[cols];
double[] work3 = new double[cols];
// evaluate the function at the starting point and calculate its norm
updateResidualsAndCost();
// outer loop
lmPar = 0;
boolean firstIteration = true;
while (true) {
// compute the Q.R. decomposition of the jacobian matrix
updateJacobian();
qrDecomposition();
// compute Qt.res
qTy(residuals);
// now we don't need Q anymore,
// so let jacobian contain the R matrix with its diagonal elements
for (int k = 0; k < solvedCols; ++k) {
int pk = permutation[k];
jacobian[k * cols + pk] = diagR[pk];
}
if (firstIteration) {
// scale the variables according to the norms of the columns
// of the initial jacobian
xNorm = 0;
for (int k = 0; k < cols; ++k) {
double dk = jacNorm[k];
if (dk == 0) {
dk = 1.0;
}
double xk = dk * parameters[k].getEstimate();
xNorm += xk * xk;
diag[k] = dk;
}
xNorm = Math.sqrt(xNorm);
// initialize the step bound delta
delta = (xNorm == 0) ? initialStepBoundFactor : (initialStepBoundFactor * xNorm);
}
// check orthogonality between function vector and jacobian columns
double maxCosine = 0;
if (cost != 0) {
for (int j = 0; j < solvedCols; ++j) {
int pj = permutation[j];
double s = jacNorm[pj];
if (s != 0) {
double sum = 0;
for (int i = 0, index = pj; i <= j; ++i, index += cols) {
sum += jacobian[index] * residuals[i];
}
maxCosine = Math.max(maxCosine, Math.abs(sum) / (s * cost));
}
}
}
if (maxCosine <= orthoTolerance) {
return;
}
// rescale if necessary
for (int j = 0; j < cols; ++j) {
diag[j] = Math.max(diag[j], jacNorm[j]);
}
// inner loop
for (double ratio = 0; ratio < 1.0e-4;) {
// save the state
for (int j = 0; j < solvedCols; ++j) {
int pj = permutation[j];
oldX[pj] = parameters[pj].getEstimate();
}
double previousCost = cost;
double[] tmpVec = residuals;
residuals = oldRes;
oldRes = tmpVec;
// determine the Levenberg-Marquardt parameter
determineLMParameter(oldRes, delta, diag, work1, work2, work3);
// compute the new point and the norm of the evolution direction
double lmNorm = 0;
for (int j = 0; j < solvedCols; ++j) {
int pj = permutation[j];
lmDir[pj] = -lmDir[pj];
parameters[pj].setEstimate(oldX[pj] + lmDir[pj]);
double s = diag[pj] * lmDir[pj];
lmNorm += s * s;
}
lmNorm = Math.sqrt(lmNorm);
// on the first iteration, adjust the initial step bound.
if (firstIteration) {
delta = Math.min(delta, lmNorm);
}
// evaluate the function at x + p and calculate its norm
updateResidualsAndCost();
// compute the scaled actual reduction
double actRed = -1.0;
if (0.1 * cost < previousCost) {
double r = cost / previousCost;
actRed = 1.0 - r * r;
}
// compute the scaled predicted reduction
// and the scaled directional derivative
for (int j = 0; j < solvedCols; ++j) {
int pj = permutation[j];
double dirJ = lmDir[pj];
work1[j] = 0;
for (int i = 0, index = pj; i <= j; ++i, index += cols) {
work1[i] += jacobian[index] * dirJ;
}
}
double coeff1 = 0;
for (int j = 0; j < solvedCols; ++j) {
coeff1 += work1[j] * work1[j];
}
double pc2 = previousCost * previousCost;
coeff1 = coeff1 / pc2;
double coeff2 = lmPar * lmNorm * lmNorm / pc2;
double preRed = coeff1 + 2 * coeff2;
double dirDer = -(coeff1 + coeff2);
// ratio of the actual to the predicted reduction
ratio = (preRed == 0) ? 0 : (actRed / preRed);
// update the step bound
if (ratio <= 0.25) {
double tmp =
(actRed < 0) ? (0.5 * dirDer / (dirDer + 0.5 * actRed)) : 0.5;
if ((0.1 * cost >= previousCost) || (tmp < 0.1)) {
tmp = 0.1;
}
delta = tmp * Math.min(delta, 10.0 * lmNorm);
lmPar /= tmp;
} else if ((lmPar == 0) || (ratio >= 0.75)) {
delta = 2 * lmNorm;
lmPar *= 0.5;
}
// test for successful iteration.
if (ratio >= 1.0e-4) {
// successful iteration, update the norm
firstIteration = false;
xNorm = 0;
for (int k = 0; k < cols; ++k) {
double xK = diag[k] * parameters[k].getEstimate();
xNorm += xK * xK;
}
xNorm = Math.sqrt(xNorm);
} else {
// failed iteration, reset the previous values
cost = previousCost;
for (int j = 0; j < solvedCols; ++j) {
int pj = permutation[j];
parameters[pj].setEstimate(oldX[pj]);
}
tmpVec = residuals;
residuals = oldRes;
oldRes = tmpVec;
}
// tests for convergence.
if (((Math.abs(actRed) <= costRelativeTolerance) &&
(preRed <= costRelativeTolerance) &&
(ratio <= 2.0)) ||
(delta <= parRelativeTolerance * xNorm)) {
return;
}
// tests for termination and stringent tolerances
// (2.2204e-16 is the machine epsilon for IEEE754)
if ((Math.abs(actRed) <= 2.2204e-16) && (preRed <= 2.2204e-16) && (ratio <= 2.0)) {
throw new OptimizationException("cost relative tolerance is too small ({0})," +
" no further reduction in the" +
" sum of squares is possible",
costRelativeTolerance);
} else if (delta <= 2.2204e-16 * xNorm) {
throw new OptimizationException("parameters relative tolerance is too small" +
" ({0}), no further improvement in" +
" the approximate solution is possible",
parRelativeTolerance);
} else if (maxCosine <= 2.2204e-16) {
throw new OptimizationException("orthogonality tolerance is too small ({0})," +
" solution is orthogonal to the jacobian",
orthoTolerance);
}
}
}
}
/**
* Determine the Levenberg-Marquardt parameter.
* <p>This implementation is a translation in Java of the MINPACK
* <a href="http://www.netlib.org/minpack/lmpar.f">lmpar</a>
* routine.</p>
* <p>This method sets the lmPar and lmDir attributes.</p>
* <p>The authors of the original fortran function are:</p>
* <ul>
* <li>Argonne National Laboratory. MINPACK project. March 1980</li>
* <li>Burton S. Garbow</li>
* <li>Kenneth E. Hillstrom</li>
* <li>Jorge J. More</li>
* </ul>
* <p>Luc Maisonobe did the Java translation.</p>
*
* @param qy array containing qTy
* @param delta upper bound on the euclidean norm of diagR * lmDir
* @param diag diagonal matrix
* @param work1 work array
* @param work2 work array
* @param work3 work array
*/
private void determineLMParameter(double[] qy, double delta, double[] diag,
double[] work1, double[] work2, double[] work3) {
// compute and store in x the gauss-newton direction, if the
// jacobian is rank-deficient, obtain a least squares solution
for (int j = 0; j < rank; ++j) {
lmDir[permutation[j]] = qy[j];
}
for (int j = rank; j < cols; ++j) {
lmDir[permutation[j]] = 0;
}
for (int k = rank - 1; k >= 0; --k) {
int pk = permutation[k];
double ypk = lmDir[pk] / diagR[pk];
for (int i = 0, index = pk; i < k; ++i, index += cols) {
lmDir[permutation[i]] -= ypk * jacobian[index];
}
lmDir[pk] = ypk;
}
// evaluate the function at the origin, and test
// for acceptance of the Gauss-Newton direction
double dxNorm = 0;
for (int j = 0; j < solvedCols; ++j) {
int pj = permutation[j];
double s = diag[pj] * lmDir[pj];
work1[pj] = s;
dxNorm += s * s;
}
dxNorm = Math.sqrt(dxNorm);
double fp = dxNorm - delta;
if (fp <= 0.1 * delta) {
lmPar = 0;
return;
}
// if the jacobian is not rank deficient, the Newton step provides
// a lower bound, parl, for the zero of the function,
// otherwise set this bound to zero
double sum2, parl = 0;
if (rank == solvedCols) {
for (int j = 0; j < solvedCols; ++j) {
int pj = permutation[j];
work1[pj] *= diag[pj] / dxNorm;
}
sum2 = 0;
for (int j = 0; j < solvedCols; ++j) {
int pj = permutation[j];
double sum = 0;
for (int i = 0, index = pj; i < j; ++i, index += cols) {
sum += jacobian[index] * work1[permutation[i]];
}
double s = (work1[pj] - sum) / diagR[pj];
work1[pj] = s;
sum2 += s * s;
}
parl = fp / (delta * sum2);
}
// calculate an upper bound, paru, for the zero of the function
sum2 = 0;
for (int j = 0; j < solvedCols; ++j) {
int pj = permutation[j];
double sum = 0;
for (int i = 0, index = pj; i <= j; ++i, index += cols) {
sum += jacobian[index] * qy[i];
}
sum /= diag[pj];
sum2 += sum * sum;
}
double gNorm = Math.sqrt(sum2);
double paru = gNorm / delta;
if (paru == 0) {
// 2.2251e-308 is the smallest positive real for IEE754
paru = 2.2251e-308 / Math.min(delta, 0.1);
}
// if the input par lies outside of the interval (parl,paru),
// set par to the closer endpoint
lmPar = Math.min(paru, Math.max(lmPar, parl));
if (lmPar == 0) {
lmPar = gNorm / dxNorm;
}
for (int countdown = 10; countdown >= 0; --countdown) {
// evaluate the function at the current value of lmPar
if (lmPar == 0) {
lmPar = Math.max(2.2251e-308, 0.001 * paru);
}
double sPar = Math.sqrt(lmPar);
for (int j = 0; j < solvedCols; ++j) {
int pj = permutation[j];
work1[pj] = sPar * diag[pj];
}
determineLMDirection(qy, work1, work2, work3);
dxNorm = 0;
for (int j = 0; j < solvedCols; ++j) {
int pj = permutation[j];
double s = diag[pj] * lmDir[pj];
work3[pj] = s;
dxNorm += s * s;
}
dxNorm = Math.sqrt(dxNorm);
double previousFP = fp;
fp = dxNorm - delta;
// if the function is small enough, accept the current value
// of lmPar, also test for the exceptional cases where parl is zero
if ((Math.abs(fp) <= 0.1 * delta) ||
((parl == 0) && (fp <= previousFP) && (previousFP < 0))) {
return;
}
// compute the Newton correction
for (int j = 0; j < solvedCols; ++j) {
int pj = permutation[j];
work1[pj] = work3[pj] * diag[pj] / dxNorm;
}
for (int j = 0; j < solvedCols; ++j) {
int pj = permutation[j];
work1[pj] /= work2[j];
double tmp = work1[pj];
for (int i = j + 1; i < solvedCols; ++i) {
work1[permutation[i]] -= jacobian[i * cols + pj] * tmp;
}
}
sum2 = 0;
for (int j = 0; j < solvedCols; ++j) {
double s = work1[permutation[j]];
sum2 += s * s;
}
double correction = fp / (delta * sum2);
// depending on the sign of the function, update parl or paru.
if (fp > 0) {
parl = Math.max(parl, lmPar);
} else if (fp < 0) {
paru = Math.min(paru, lmPar);
}
// compute an improved estimate for lmPar
lmPar = Math.max(parl, lmPar + correction);
}
}
/**
* Solve a*x = b and d*x = 0 in the least squares sense.
* <p>This implementation is a translation in Java of the MINPACK
* <a href="http://www.netlib.org/minpack/qrsolv.f">qrsolv</a>
* routine.</p>
* <p>This method sets the lmDir and lmDiag attributes.</p>
* <p>The authors of the original fortran function are:</p>
* <ul>
* <li>Argonne National Laboratory. MINPACK project. March 1980</li>
* <li>Burton S. Garbow</li>
* <li>Kenneth E. Hillstrom</li>
* <li>Jorge J. More</li>
* </ul>
* <p>Luc Maisonobe did the Java translation.</p>
*
* @param qy array containing qTy
* @param diag diagonal matrix
* @param lmDiag diagonal elements associated with lmDir
* @param work work array
*/
private void determineLMDirection(double[] qy, double[] diag,
double[] lmDiag, double[] work) {
// copy R and Qty to preserve input and initialize s
// in particular, save the diagonal elements of R in lmDir
for (int j = 0; j < solvedCols; ++j) {
int pj = permutation[j];
for (int i = j + 1; i < solvedCols; ++i) {
jacobian[i * cols + pj] = jacobian[j * cols + permutation[i]];
}
lmDir[j] = diagR[pj];
work[j] = qy[j];
}
// eliminate the diagonal matrix d using a Givens rotation
for (int j = 0; j < solvedCols; ++j) {
// prepare the row of d to be eliminated, locating the
// diagonal element using p from the Q.R. factorization
int pj = permutation[j];
double dpj = diag[pj];
if (dpj != 0) {
Arrays.fill(lmDiag, j + 1, lmDiag.length, 0);
}
lmDiag[j] = dpj;
// the transformations to eliminate the row of d
// modify only a single element of Qty
// beyond the first n, which is initially zero.
double qtbpj = 0;
for (int k = j; k < solvedCols; ++k) {
int pk = permutation[k];
// determine a Givens rotation which eliminates the
// appropriate element in the current row of d
if (lmDiag[k] != 0) {
double sin, cos;
double rkk = jacobian[k * cols + pk];
if (Math.abs(rkk) < Math.abs(lmDiag[k])) {
double cotan = rkk / lmDiag[k];
sin = 1.0 / Math.sqrt(1.0 + cotan * cotan);
cos = sin * cotan;
} else {
double tan = lmDiag[k] / rkk;
cos = 1.0 / Math.sqrt(1.0 + tan * tan);
sin = cos * tan;
}
// compute the modified diagonal element of R and
// the modified element of (Qty,0)
jacobian[k * cols + pk] = cos * rkk + sin * lmDiag[k];
double temp = cos * work[k] + sin * qtbpj;
qtbpj = -sin * work[k] + cos * qtbpj;
work[k] = temp;
// accumulate the tranformation in the row of s
for (int i = k + 1; i < solvedCols; ++i) {
double rik = jacobian[i * cols + pk];
temp = cos * rik + sin * lmDiag[i];
lmDiag[i] = -sin * rik + cos * lmDiag[i];
jacobian[i * cols + pk] = temp;
}
}
}
// store the diagonal element of s and restore
// the corresponding diagonal element of R
int index = j * cols + permutation[j];
lmDiag[j] = jacobian[index];
jacobian[index] = lmDir[j];
}
// solve the triangular system for z, if the system is
// singular, then obtain a least squares solution
int nSing = solvedCols;
for (int j = 0; j < solvedCols; ++j) {
if ((lmDiag[j] == 0) && (nSing == solvedCols)) {
nSing = j;
}
if (nSing < solvedCols) {
work[j] = 0;
}
}
if (nSing > 0) {
for (int j = nSing - 1; j >= 0; --j) {
int pj = permutation[j];
double sum = 0;
for (int i = j + 1; i < nSing; ++i) {
sum += jacobian[i * cols + pj] * work[i];
}
work[j] = (work[j] - sum) / lmDiag[j];
}
}
// permute the components of z back to components of lmDir
for (int j = 0; j < lmDir.length; ++j) {
lmDir[permutation[j]] = work[j];
}
}
/**
* Decompose a matrix A as A.P = Q.R using Householder transforms.
* <p>As suggested in the P. Lascaux and R. Theodor book
* <i>Analyse num&eacute;rique matricielle appliqu&eacute;e &agrave;
* l'art de l'ing&eacute;nieur</i> (Masson, 1986), instead of representing
* the Householder transforms with u<sub>k</sub> unit vectors such that:
* <pre>
* H<sub>k</sub> = I - 2u<sub>k</sub>.u<sub>k</sub><sup>t</sup>
* </pre>
* we use <sub>k</sub> non-unit vectors such that:
* <pre>
* H<sub>k</sub> = I - beta<sub>k</sub>v<sub>k</sub>.v<sub>k</sub><sup>t</sup>
* </pre>
* where v<sub>k</sub> = a<sub>k</sub> - alpha<sub>k</sub> e<sub>k</sub>.
* The beta<sub>k</sub> coefficients are provided upon exit as recomputing
* them from the v<sub>k</sub> vectors would be costly.</p>
* <p>This decomposition handles rank deficient cases since the tranformations
* are performed in non-increasing columns norms order thanks to columns
* pivoting. The diagonal elements of the R matrix are therefore also in
* non-increasing absolute values order.</p>
* @exception OptimizationException if the decomposition cannot be performed
*/
private void qrDecomposition() throws OptimizationException {
// initializations
for (int k = 0; k < cols; ++k) {
permutation[k] = k;
double norm2 = 0;
for (int index = k; index < jacobian.length; index += cols) {
double akk = jacobian[index];
norm2 += akk * akk;
}
jacNorm[k] = Math.sqrt(norm2);
}
// transform the matrix column after column
for (int k = 0; k < cols; ++k) {
// select the column with the greatest norm on active components
int nextColumn = -1;
double ak2 = Double.NEGATIVE_INFINITY;
for (int i = k; i < cols; ++i) {
double norm2 = 0;
int iDiag = k * cols + permutation[i];
for (int index = iDiag; index < jacobian.length; index += cols) {
double aki = jacobian[index];
norm2 += aki * aki;
}
if (Double.isInfinite(norm2) || Double.isNaN(norm2)) {
throw new OptimizationException(
"unable to perform Q.R decomposition on the {0}x{1} jacobian matrix",
rows, cols);
}
if (norm2 > ak2) {
nextColumn = i;
ak2 = norm2;
}
}
if (ak2 == 0) {
rank = k;
return;
}
int pk = permutation[nextColumn];
permutation[nextColumn] = permutation[k];
permutation[k] = pk;
// choose alpha such that Hk.u = alpha ek
int kDiag = k * cols + pk;
double akk = jacobian[kDiag];
double alpha = (akk > 0) ? -Math.sqrt(ak2) : Math.sqrt(ak2);
double betak = 1.0 / (ak2 - akk * alpha);
beta[pk] = betak;
// transform the current column
diagR[pk] = alpha;
jacobian[kDiag] -= alpha;
// transform the remaining columns
for (int dk = cols - 1 - k; dk > 0; --dk) {
int dkp = permutation[k + dk] - pk;
double gamma = 0;
for (int index = kDiag; index < jacobian.length; index += cols) {
gamma += jacobian[index] * jacobian[index + dkp];
}
gamma *= betak;
for (int index = kDiag; index < jacobian.length; index += cols) {
jacobian[index + dkp] -= gamma * jacobian[index];
}
}
}
rank = solvedCols;
}
/**
* Compute the product Qt.y for some Q.R. decomposition.
*
* @param y vector to multiply (will be overwritten with the result)
*/
private void qTy(double[] y) {
for (int k = 0; k < cols; ++k) {
int pk = permutation[k];
int kDiag = k * cols + pk;
double gamma = 0;
for (int i = k, index = kDiag; i < rows; ++i, index += cols) {
gamma += jacobian[index] * y[i];
}
gamma *= beta[pk];
for (int i = k, index = kDiag; i < rows; ++i, index += cols) {
y[i] -= gamma * jacobian[index];
}
}
}
/** Number of solved variables. */
private int solvedCols;
/** Diagonal elements of the R matrix in the Q.R. decomposition. */
private double[] diagR;
/** Norms of the columns of the jacobian matrix. */
private double[] jacNorm;
/** Coefficients of the Householder transforms vectors. */
private double[] beta;
/** Columns permutation array. */
private int[] permutation;
/** Rank of the jacobian matrix. */
private int rank;
/** Levenberg-Marquardt parameter. */
private double lmPar;
/** Parameters evolution direction associated with lmPar. */
private double[] lmDir;
/** Positive input variable used in determining the initial step bound. */
private double initialStepBoundFactor;
/** Desired relative error in the sum of squares. */
private double costRelativeTolerance;
/** Desired relative error in the approximate solution parameters. */
private double parRelativeTolerance;
/** Desired max cosine on the orthogonality between the function vector
* and the columns of the jacobian. */
private double orthoTolerance;
/** Serializable version identifier */
private static final long serialVersionUID = -5705952631533171019L;
}

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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 java.util.Arrays;
import org.apache.commons.math.optimization.ObjectiveException;
import org.apache.commons.math.optimization.OptimizationException;
import org.apache.commons.math.optimization.VectorialPointValuePair;
/**
* This class solves a least squares problem using the Levenberg-Marquardt algorithm.
*
* <p>This implementation <em>should</em> work even for over-determined systems
* (i.e. systems having more variables than equations). Over-determined systems
* are solved by ignoring the variables which have the smallest impact according
* to their jacobian column norm. Only the rank of the matrix and some loop bounds
* are changed to implement this.</p>
*
* <p>The resolution engine is a simple translation of the MINPACK <a
* href="http://www.netlib.org/minpack/lmder.f">lmder</a> routine with minor
* changes. The changes include the over-determined resolution and the Q.R.
* decomposition which has been rewritten following the algorithm described in the
* P. Lascaux and R. Theodor book <i>Analyse num&eacute;rique matricielle
* appliqu&eacute;e &agrave; l'art de l'ing&eacute;nieur</i>, Masson 1986. The
* redistribution policy for MINPACK is available <a
* href="http://www.netlib.org/minpack/disclaimer">here</a>, for convenience, it
* is reproduced below.</p>
*
* <table border="0" width="80%" cellpadding="10" align="center" bgcolor="#E0E0E0">
* <tr><td>
* Minpack Copyright Notice (1999) University of Chicago.
* All rights reserved
* </td></tr>
* <tr><td>
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
* <ol>
* <li>Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.</li>
* <li>Redistributions in binary form must reproduce the above
* copyright notice, this list of conditions and the following
* disclaimer in the documentation and/or other materials provided
* with the distribution.</li>
* <li>The end-user documentation included with the redistribution, if any,
* must include the following acknowledgment:
* <code>This product includes software developed by the University of
* Chicago, as Operator of Argonne National Laboratory.</code>
* Alternately, this acknowledgment may appear in the software itself,
* if and wherever such third-party acknowledgments normally appear.</li>
* <li><strong>WARRANTY DISCLAIMER. THE SOFTWARE IS SUPPLIED "AS IS"
* WITHOUT WARRANTY OF ANY KIND. THE COPYRIGHT HOLDER, THE
* UNITED STATES, THE UNITED STATES DEPARTMENT OF ENERGY, AND
* THEIR EMPLOYEES: (1) DISCLAIM ANY WARRANTIES, EXPRESS OR
* IMPLIED, INCLUDING BUT NOT LIMITED TO ANY IMPLIED WARRANTIES
* OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE, TITLE
* OR NON-INFRINGEMENT, (2) DO NOT ASSUME ANY LEGAL LIABILITY
* OR RESPONSIBILITY FOR THE ACCURACY, COMPLETENESS, OR
* USEFULNESS OF THE SOFTWARE, (3) DO NOT REPRESENT THAT USE OF
* THE SOFTWARE WOULD NOT INFRINGE PRIVATELY OWNED RIGHTS, (4)
* DO NOT WARRANT THAT THE SOFTWARE WILL FUNCTION
* UNINTERRUPTED, THAT IT IS ERROR-FREE OR THAT ANY ERRORS WILL
* BE CORRECTED.</strong></li>
* <li><strong>LIMITATION OF LIABILITY. IN NO EVENT WILL THE COPYRIGHT
* HOLDER, THE UNITED STATES, THE UNITED STATES DEPARTMENT OF
* ENERGY, OR THEIR EMPLOYEES: BE LIABLE FOR ANY INDIRECT,
* INCIDENTAL, CONSEQUENTIAL, SPECIAL OR PUNITIVE DAMAGES OF
* ANY KIND OR NATURE, INCLUDING BUT NOT LIMITED TO LOSS OF
* PROFITS OR LOSS OF DATA, FOR ANY REASON WHATSOEVER, WHETHER
* SUCH LIABILITY IS ASSERTED ON THE BASIS OF CONTRACT, TORT
* (INCLUDING NEGLIGENCE OR STRICT LIABILITY), OR OTHERWISE,
* EVEN IF ANY OF SAID PARTIES HAS BEEN WARNED OF THE
* POSSIBILITY OF SUCH LOSS OR DAMAGES.</strong></li>
* <ol></td></tr>
* </table>
* @author Argonne National Laboratory. MINPACK project. March 1980 (original fortran)
* @author Burton S. Garbow (original fortran)
* @author Kenneth E. Hillstrom (original fortran)
* @author Jorge J. More (original fortran)
* @version $Revision$ $Date$
* @since 2.0
*
*/
public class LevenbergMarquardtOptimizer extends AbstractLeastSquaresOptimizer {
/** Serializable version identifier */
private static final long serialVersionUID = 8851282236194244323L;
/** Number of solved variables. */
private int solvedCols;
/** Diagonal elements of the R matrix in the Q.R. decomposition. */
private double[] diagR;
/** Norms of the columns of the jacobian matrix. */
private double[] jacNorm;
/** Coefficients of the Householder transforms vectors. */
private double[] beta;
/** Columns permutation array. */
private int[] permutation;
/** Rank of the jacobian matrix. */
private int rank;
/** Levenberg-Marquardt parameter. */
private double lmPar;
/** Parameters evolution direction associated with lmPar. */
private double[] lmDir;
/** Positive input variable used in determining the initial step bound. */
private double initialStepBoundFactor;
/** Desired relative error in the sum of squares. */
private double costRelativeTolerance;
/** Desired relative error in the approximate solution parameters. */
private double parRelativeTolerance;
/** Desired max cosine on the orthogonality between the function vector
* and the columns of the jacobian. */
private double orthoTolerance;
/**
* Build an optimizer for least squares problems.
* <p>The default values for the algorithm settings are:
* <ul>
* <li>{@link #setInitialStepBoundFactor initial step bound factor}: 100.0</li>
* <li>{@link #setMaxCostEval maximal cost evaluations}: 1000</li>
* <li>{@link #setCostRelativeTolerance cost relative tolerance}: 1.0e-10</li>
* <li>{@link #setParRelativeTolerance parameters relative tolerance}: 1.0e-10</li>
* <li>{@link #setOrthoTolerance orthogonality tolerance}: 1.0e-10</li>
* </ul>
* </p>
*/
public LevenbergMarquardtOptimizer() {
// set up the superclass with a default max cost evaluations setting
setMaxEvaluations(1000);
// default values for the tuning parameters
setInitialStepBoundFactor(100.0);
setCostRelativeTolerance(1.0e-10);
setParRelativeTolerance(1.0e-10);
setOrthoTolerance(1.0e-10);
}
/**
* Set the positive input variable used in determining the initial step bound.
* This bound is set to the product of initialStepBoundFactor and the euclidean
* norm of diag*x if nonzero, or else to initialStepBoundFactor itself. In most
* cases factor should lie in the interval (0.1, 100.0). 100.0 is a generally
* recommended value.
*
* @param initialStepBoundFactor initial step bound factor
*/
public void setInitialStepBoundFactor(double initialStepBoundFactor) {
this.initialStepBoundFactor = initialStepBoundFactor;
}
/**
* Set the desired relative error in the sum of squares.
*
* @param costRelativeTolerance desired relative error in the sum of squares
*/
public void setCostRelativeTolerance(double costRelativeTolerance) {
this.costRelativeTolerance = costRelativeTolerance;
}
/**
* Set the desired relative error in the approximate solution parameters.
*
* @param parRelativeTolerance desired relative error
* in the approximate solution parameters
*/
public void setParRelativeTolerance(double parRelativeTolerance) {
this.parRelativeTolerance = parRelativeTolerance;
}
/**
* Set the desired max cosine on the orthogonality.
*
* @param orthoTolerance desired max cosine on the orthogonality
* between the function vector and the columns of the jacobian
*/
public void setOrthoTolerance(double orthoTolerance) {
this.orthoTolerance = orthoTolerance;
}
/** {@inheritDoc} */
protected VectorialPointValuePair doOptimize()
throws ObjectiveException, OptimizationException, IllegalArgumentException {
// arrays shared with the other private methods
solvedCols = Math.min(rows, cols);
diagR = new double[cols];
jacNorm = new double[cols];
beta = new double[cols];
permutation = new int[cols];
lmDir = new double[cols];
// local variables
double delta = 0, xNorm = 0;
double[] diag = new double[cols];
double[] oldX = new double[cols];
double[] oldRes = new double[rows];
double[] work1 = new double[cols];
double[] work2 = new double[cols];
double[] work3 = new double[cols];
// evaluate the function at the starting point and calculate its norm
updateResidualsAndCost();
// outer loop
lmPar = 0;
boolean firstIteration = true;
while (true) {
// compute the Q.R. decomposition of the jacobian matrix
updateJacobian();
qrDecomposition();
// compute Qt.res
qTy(residuals);
// now we don't need Q anymore,
// so let jacobian contain the R matrix with its diagonal elements
for (int k = 0; k < solvedCols; ++k) {
int pk = permutation[k];
jacobian[k][pk] = diagR[pk];
}
if (firstIteration) {
// scale the variables according to the norms of the columns
// of the initial jacobian
xNorm = 0;
for (int k = 0; k < cols; ++k) {
double dk = jacNorm[k];
if (dk == 0) {
dk = 1.0;
}
double xk = dk * variables[k];
xNorm += xk * xk;
diag[k] = dk;
}
xNorm = Math.sqrt(xNorm);
// initialize the step bound delta
delta = (xNorm == 0) ? initialStepBoundFactor : (initialStepBoundFactor * xNorm);
}
// check orthogonality between function vector and jacobian columns
double maxCosine = 0;
if (cost != 0) {
for (int j = 0; j < solvedCols; ++j) {
int pj = permutation[j];
double s = jacNorm[pj];
if (s != 0) {
double sum = 0;
for (int i = 0; i <= j; ++i) {
sum += jacobian[i][pj] * residuals[i];
}
maxCosine = Math.max(maxCosine, Math.abs(sum) / (s * cost));
}
}
}
if (maxCosine <= orthoTolerance) {
// convergence has been reached
return new VectorialPointValuePair(variables, objective);
}
// rescale if necessary
for (int j = 0; j < cols; ++j) {
diag[j] = Math.max(diag[j], jacNorm[j]);
}
// inner loop
for (double ratio = 0; ratio < 1.0e-4;) {
// save the state
for (int j = 0; j < solvedCols; ++j) {
int pj = permutation[j];
oldX[pj] = variables[pj];
}
double previousCost = cost;
double[] tmpVec = residuals;
residuals = oldRes;
oldRes = tmpVec;
// determine the Levenberg-Marquardt parameter
determineLMParameter(oldRes, delta, diag, work1, work2, work3);
// compute the new point and the norm of the evolution direction
double lmNorm = 0;
for (int j = 0; j < solvedCols; ++j) {
int pj = permutation[j];
lmDir[pj] = -lmDir[pj];
variables[pj] = oldX[pj] + lmDir[pj];
double s = diag[pj] * lmDir[pj];
lmNorm += s * s;
}
lmNorm = Math.sqrt(lmNorm);
// on the first iteration, adjust the initial step bound.
if (firstIteration) {
delta = Math.min(delta, lmNorm);
}
// evaluate the function at x + p and calculate its norm
updateResidualsAndCost();
// compute the scaled actual reduction
double actRed = -1.0;
if (0.1 * cost < previousCost) {
double r = cost / previousCost;
actRed = 1.0 - r * r;
}
// compute the scaled predicted reduction
// and the scaled directional derivative
for (int j = 0; j < solvedCols; ++j) {
int pj = permutation[j];
double dirJ = lmDir[pj];
work1[j] = 0;
for (int i = 0; i <= j; ++i) {
work1[i] += jacobian[i][pj] * dirJ;
}
}
double coeff1 = 0;
for (int j = 0; j < solvedCols; ++j) {
coeff1 += work1[j] * work1[j];
}
double pc2 = previousCost * previousCost;
coeff1 = coeff1 / pc2;
double coeff2 = lmPar * lmNorm * lmNorm / pc2;
double preRed = coeff1 + 2 * coeff2;
double dirDer = -(coeff1 + coeff2);
// ratio of the actual to the predicted reduction
ratio = (preRed == 0) ? 0 : (actRed / preRed);
// update the step bound
if (ratio <= 0.25) {
double tmp =
(actRed < 0) ? (0.5 * dirDer / (dirDer + 0.5 * actRed)) : 0.5;
if ((0.1 * cost >= previousCost) || (tmp < 0.1)) {
tmp = 0.1;
}
delta = tmp * Math.min(delta, 10.0 * lmNorm);
lmPar /= tmp;
} else if ((lmPar == 0) || (ratio >= 0.75)) {
delta = 2 * lmNorm;
lmPar *= 0.5;
}
// test for successful iteration.
if (ratio >= 1.0e-4) {
// successful iteration, update the norm
firstIteration = false;
xNorm = 0;
for (int k = 0; k < cols; ++k) {
double xK = diag[k] * variables[k];
xNorm += xK * xK;
}
xNorm = Math.sqrt(xNorm);
} else {
// failed iteration, reset the previous values
cost = previousCost;
for (int j = 0; j < solvedCols; ++j) {
int pj = permutation[j];
variables[pj] = oldX[pj];
}
tmpVec = residuals;
residuals = oldRes;
oldRes = tmpVec;
}
// tests for convergence.
if (((Math.abs(actRed) <= costRelativeTolerance) &&
(preRed <= costRelativeTolerance) &&
(ratio <= 2.0)) ||
(delta <= parRelativeTolerance * xNorm)) {
return new VectorialPointValuePair(variables, objective);
}
// tests for termination and stringent tolerances
// (2.2204e-16 is the machine epsilon for IEEE754)
if ((Math.abs(actRed) <= 2.2204e-16) && (preRed <= 2.2204e-16) && (ratio <= 2.0)) {
throw new OptimizationException("cost relative tolerance is too small ({0})," +
" no further reduction in the" +
" sum of squares is possible",
costRelativeTolerance);
} else if (delta <= 2.2204e-16 * xNorm) {
throw new OptimizationException("parameters relative tolerance is too small" +
" ({0}), no further improvement in" +
" the approximate solution is possible",
parRelativeTolerance);
} else if (maxCosine <= 2.2204e-16) {
throw new OptimizationException("orthogonality tolerance is too small ({0})," +
" solution is orthogonal to the jacobian",
orthoTolerance);
}
}
}
}
/**
* Determine the Levenberg-Marquardt parameter.
* <p>This implementation is a translation in Java of the MINPACK
* <a href="http://www.netlib.org/minpack/lmpar.f">lmpar</a>
* routine.</p>
* <p>This method sets the lmPar and lmDir attributes.</p>
* <p>The authors of the original fortran function are:</p>
* <ul>
* <li>Argonne National Laboratory. MINPACK project. March 1980</li>
* <li>Burton S. Garbow</li>
* <li>Kenneth E. Hillstrom</li>
* <li>Jorge J. More</li>
* </ul>
* <p>Luc Maisonobe did the Java translation.</p>
*
* @param qy array containing qTy
* @param delta upper bound on the euclidean norm of diagR * lmDir
* @param diag diagonal matrix
* @param work1 work array
* @param work2 work array
* @param work3 work array
*/
private void determineLMParameter(double[] qy, double delta, double[] diag,
double[] work1, double[] work2, double[] work3) {
// compute and store in x the gauss-newton direction, if the
// jacobian is rank-deficient, obtain a least squares solution
for (int j = 0; j < rank; ++j) {
lmDir[permutation[j]] = qy[j];
}
for (int j = rank; j < cols; ++j) {
lmDir[permutation[j]] = 0;
}
for (int k = rank - 1; k >= 0; --k) {
int pk = permutation[k];
double ypk = lmDir[pk] / diagR[pk];
for (int i = 0; i < k; ++i) {
lmDir[permutation[i]] -= ypk * jacobian[i][pk];
}
lmDir[pk] = ypk;
}
// evaluate the function at the origin, and test
// for acceptance of the Gauss-Newton direction
double dxNorm = 0;
for (int j = 0; j < solvedCols; ++j) {
int pj = permutation[j];
double s = diag[pj] * lmDir[pj];
work1[pj] = s;
dxNorm += s * s;
}
dxNorm = Math.sqrt(dxNorm);
double fp = dxNorm - delta;
if (fp <= 0.1 * delta) {
lmPar = 0;
return;
}
// if the jacobian is not rank deficient, the Newton step provides
// a lower bound, parl, for the zero of the function,
// otherwise set this bound to zero
double sum2, parl = 0;
if (rank == solvedCols) {
for (int j = 0; j < solvedCols; ++j) {
int pj = permutation[j];
work1[pj] *= diag[pj] / dxNorm;
}
sum2 = 0;
for (int j = 0; j < solvedCols; ++j) {
int pj = permutation[j];
double sum = 0;
for (int i = 0; i < j; ++i) {
sum += jacobian[i][pj] * work1[permutation[i]];
}
double s = (work1[pj] - sum) / diagR[pj];
work1[pj] = s;
sum2 += s * s;
}
parl = fp / (delta * sum2);
}
// calculate an upper bound, paru, for the zero of the function
sum2 = 0;
for (int j = 0; j < solvedCols; ++j) {
int pj = permutation[j];
double sum = 0;
for (int i = 0; i <= j; ++i) {
sum += jacobian[i][pj] * qy[i];
}
sum /= diag[pj];
sum2 += sum * sum;
}
double gNorm = Math.sqrt(sum2);
double paru = gNorm / delta;
if (paru == 0) {
// 2.2251e-308 is the smallest positive real for IEE754
paru = 2.2251e-308 / Math.min(delta, 0.1);
}
// if the input par lies outside of the interval (parl,paru),
// set par to the closer endpoint
lmPar = Math.min(paru, Math.max(lmPar, parl));
if (lmPar == 0) {
lmPar = gNorm / dxNorm;
}
for (int countdown = 10; countdown >= 0; --countdown) {
// evaluate the function at the current value of lmPar
if (lmPar == 0) {
lmPar = Math.max(2.2251e-308, 0.001 * paru);
}
double sPar = Math.sqrt(lmPar);
for (int j = 0; j < solvedCols; ++j) {
int pj = permutation[j];
work1[pj] = sPar * diag[pj];
}
determineLMDirection(qy, work1, work2, work3);
dxNorm = 0;
for (int j = 0; j < solvedCols; ++j) {
int pj = permutation[j];
double s = diag[pj] * lmDir[pj];
work3[pj] = s;
dxNorm += s * s;
}
dxNorm = Math.sqrt(dxNorm);
double previousFP = fp;
fp = dxNorm - delta;
// if the function is small enough, accept the current value
// of lmPar, also test for the exceptional cases where parl is zero
if ((Math.abs(fp) <= 0.1 * delta) ||
((parl == 0) && (fp <= previousFP) && (previousFP < 0))) {
return;
}
// compute the Newton correction
for (int j = 0; j < solvedCols; ++j) {
int pj = permutation[j];
work1[pj] = work3[pj] * diag[pj] / dxNorm;
}
for (int j = 0; j < solvedCols; ++j) {
int pj = permutation[j];
work1[pj] /= work2[j];
double tmp = work1[pj];
for (int i = j + 1; i < solvedCols; ++i) {
work1[permutation[i]] -= jacobian[i][pj] * tmp;
}
}
sum2 = 0;
for (int j = 0; j < solvedCols; ++j) {
double s = work1[permutation[j]];
sum2 += s * s;
}
double correction = fp / (delta * sum2);
// depending on the sign of the function, update parl or paru.
if (fp > 0) {
parl = Math.max(parl, lmPar);
} else if (fp < 0) {
paru = Math.min(paru, lmPar);
}
// compute an improved estimate for lmPar
lmPar = Math.max(parl, lmPar + correction);
}
}
/**
* Solve a*x = b and d*x = 0 in the least squares sense.
* <p>This implementation is a translation in Java of the MINPACK
* <a href="http://www.netlib.org/minpack/qrsolv.f">qrsolv</a>
* routine.</p>
* <p>This method sets the lmDir and lmDiag attributes.</p>
* <p>The authors of the original fortran function are:</p>
* <ul>
* <li>Argonne National Laboratory. MINPACK project. March 1980</li>
* <li>Burton S. Garbow</li>
* <li>Kenneth E. Hillstrom</li>
* <li>Jorge J. More</li>
* </ul>
* <p>Luc Maisonobe did the Java translation.</p>
*
* @param qy array containing qTy
* @param diag diagonal matrix
* @param lmDiag diagonal elements associated with lmDir
* @param work work array
*/
private void determineLMDirection(double[] qy, double[] diag,
double[] lmDiag, double[] work) {
// copy R and Qty to preserve input and initialize s
// in particular, save the diagonal elements of R in lmDir
for (int j = 0; j < solvedCols; ++j) {
int pj = permutation[j];
for (int i = j + 1; i < solvedCols; ++i) {
jacobian[i][pj] = jacobian[j][permutation[i]];
}
lmDir[j] = diagR[pj];
work[j] = qy[j];
}
// eliminate the diagonal matrix d using a Givens rotation
for (int j = 0; j < solvedCols; ++j) {
// prepare the row of d to be eliminated, locating the
// diagonal element using p from the Q.R. factorization
int pj = permutation[j];
double dpj = diag[pj];
if (dpj != 0) {
Arrays.fill(lmDiag, j + 1, lmDiag.length, 0);
}
lmDiag[j] = dpj;
// the transformations to eliminate the row of d
// modify only a single element of Qty
// beyond the first n, which is initially zero.
double qtbpj = 0;
for (int k = j; k < solvedCols; ++k) {
int pk = permutation[k];
// determine a Givens rotation which eliminates the
// appropriate element in the current row of d
if (lmDiag[k] != 0) {
double sin, cos;
double rkk = jacobian[k][pk];
if (Math.abs(rkk) < Math.abs(lmDiag[k])) {
double cotan = rkk / lmDiag[k];
sin = 1.0 / Math.sqrt(1.0 + cotan * cotan);
cos = sin * cotan;
} else {
double tan = lmDiag[k] / rkk;
cos = 1.0 / Math.sqrt(1.0 + tan * tan);
sin = cos * tan;
}
// compute the modified diagonal element of R and
// the modified element of (Qty,0)
jacobian[k][pk] = cos * rkk + sin * lmDiag[k];
double temp = cos * work[k] + sin * qtbpj;
qtbpj = -sin * work[k] + cos * qtbpj;
work[k] = temp;
// accumulate the tranformation in the row of s
for (int i = k + 1; i < solvedCols; ++i) {
double rik = jacobian[i][pk];
temp = cos * rik + sin * lmDiag[i];
lmDiag[i] = -sin * rik + cos * lmDiag[i];
jacobian[i][pk] = temp;
}
}
}
// store the diagonal element of s and restore
// the corresponding diagonal element of R
lmDiag[j] = jacobian[j][permutation[j]];
jacobian[j][permutation[j]] = lmDir[j];
}
// solve the triangular system for z, if the system is
// singular, then obtain a least squares solution
int nSing = solvedCols;
for (int j = 0; j < solvedCols; ++j) {
if ((lmDiag[j] == 0) && (nSing == solvedCols)) {
nSing = j;
}
if (nSing < solvedCols) {
work[j] = 0;
}
}
if (nSing > 0) {
for (int j = nSing - 1; j >= 0; --j) {
int pj = permutation[j];
double sum = 0;
for (int i = j + 1; i < nSing; ++i) {
sum += jacobian[i][pj] * work[i];
}
work[j] = (work[j] - sum) / lmDiag[j];
}
}
// permute the components of z back to components of lmDir
for (int j = 0; j < lmDir.length; ++j) {
lmDir[permutation[j]] = work[j];
}
}
/**
* Decompose a matrix A as A.P = Q.R using Householder transforms.
* <p>As suggested in the P. Lascaux and R. Theodor book
* <i>Analyse num&eacute;rique matricielle appliqu&eacute;e &agrave;
* l'art de l'ing&eacute;nieur</i> (Masson, 1986), instead of representing
* the Householder transforms with u<sub>k</sub> unit vectors such that:
* <pre>
* H<sub>k</sub> = I - 2u<sub>k</sub>.u<sub>k</sub><sup>t</sup>
* </pre>
* we use <sub>k</sub> non-unit vectors such that:
* <pre>
* H<sub>k</sub> = I - beta<sub>k</sub>v<sub>k</sub>.v<sub>k</sub><sup>t</sup>
* </pre>
* where v<sub>k</sub> = a<sub>k</sub> - alpha<sub>k</sub> e<sub>k</sub>.
* The beta<sub>k</sub> coefficients are provided upon exit as recomputing
* them from the v<sub>k</sub> vectors would be costly.</p>
* <p>This decomposition handles rank deficient cases since the tranformations
* are performed in non-increasing columns norms order thanks to columns
* pivoting. The diagonal elements of the R matrix are therefore also in
* non-increasing absolute values order.</p>
* @exception OptimizationException if the decomposition cannot be performed
*/
private void qrDecomposition() throws OptimizationException {
// initializations
for (int k = 0; k < cols; ++k) {
permutation[k] = k;
double norm2 = 0;
for (int i = 0; i < jacobian.length; ++i) {
double akk = jacobian[i][k];
norm2 += akk * akk;
}
jacNorm[k] = Math.sqrt(norm2);
}
// transform the matrix column after column
for (int k = 0; k < cols; ++k) {
// select the column with the greatest norm on active components
int nextColumn = -1;
double ak2 = Double.NEGATIVE_INFINITY;
for (int i = k; i < cols; ++i) {
double norm2 = 0;
for (int j = k; j < jacobian.length; ++j) {
double aki = jacobian[j][permutation[i]];
norm2 += aki * aki;
}
if (Double.isInfinite(norm2) || Double.isNaN(norm2)) {
throw new OptimizationException(
"unable to perform Q.R decomposition on the {0}x{1} jacobian matrix",
rows, cols);
}
if (norm2 > ak2) {
nextColumn = i;
ak2 = norm2;
}
}
if (ak2 == 0) {
rank = k;
return;
}
int pk = permutation[nextColumn];
permutation[nextColumn] = permutation[k];
permutation[k] = pk;
// choose alpha such that Hk.u = alpha ek
double akk = jacobian[k][pk];
double alpha = (akk > 0) ? -Math.sqrt(ak2) : Math.sqrt(ak2);
double betak = 1.0 / (ak2 - akk * alpha);
beta[pk] = betak;
// transform the current column
diagR[pk] = alpha;
jacobian[k][pk] -= alpha;
// transform the remaining columns
for (int dk = cols - 1 - k; dk > 0; --dk) {
double gamma = 0;
for (int j = k; j < jacobian.length; ++j) {
gamma += jacobian[j][pk] * jacobian[j][permutation[k + dk]];
}
gamma *= betak;
for (int j = k; j < jacobian.length; ++j) {
jacobian[j][permutation[k + dk]] -= gamma * jacobian[j][pk];
}
}
}
rank = solvedCols;
}
/**
* Compute the product Qt.y for some Q.R. decomposition.
*
* @param y vector to multiply (will be overwritten with the result)
*/
private void qTy(double[] y) {
for (int k = 0; k < cols; ++k) {
int pk = permutation[k];
double gamma = 0;
for (int i = k; i < rows; ++i) {
gamma += jacobian[i][pk] * y[i];
}
gamma *= beta[pk];
for (int i = k; i < rows; ++i) {
y[i] -= gamma * jacobian[i][pk];
}
}
}
}

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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 java.util.ArrayList;
import java.util.List;
/**
* Simple implementation of the {@link EstimationProblem
* EstimationProblem} interface for boilerplate data handling.
* <p>This class <em>only</em> handles parameters and measurements
* storage and unbound parameters filtering. It does not compute
* anything by itself. It should either be used with measurements
* implementation that are smart enough to know about the
* various parameters in order to compute the partial derivatives
* appropriately. Since the problem-specific logic is mainly related to
* the various measurements models, the simplest way to use this class
* is by extending it and using one internal class extending
* {@link WeightedMeasurement WeightedMeasurement} for each measurement
* type. The instances of the internal classes would have access to the
* various parameters and their current estimate.</p>
* @version $Revision$ $Date$
* @since 1.2
*/
public class SimpleEstimationProblem implements EstimationProblem {
/**
* Build an empty instance without parameters nor measurements.
*/
public SimpleEstimationProblem() {
parameters = new ArrayList<EstimatedParameter>();
measurements = new ArrayList<WeightedMeasurement>();
}
/**
* Get all the parameters of the problem.
* @return parameters
*/
public EstimatedParameter[] getAllParameters() {
return (EstimatedParameter[]) parameters.toArray(new EstimatedParameter[parameters.size()]);
}
/**
* Get the unbound parameters of the problem.
* @return unbound parameters
*/
public EstimatedParameter[] getUnboundParameters() {
// filter the unbound parameters
List<EstimatedParameter> unbound = new ArrayList<EstimatedParameter>(parameters.size());
for (EstimatedParameter p : parameters) {
if (! p.isBound()) {
unbound.add(p);
}
}
// convert to an array
return (EstimatedParameter[]) unbound.toArray(new EstimatedParameter[unbound.size()]);
}
/**
* Get the measurements of an estimation problem.
* @return measurements
*/
public WeightedMeasurement[] getMeasurements() {
return (WeightedMeasurement[]) measurements.toArray(new WeightedMeasurement[measurements.size()]);
}
/** Add a parameter to the problem.
* @param p parameter to add
*/
protected void addParameter(EstimatedParameter p) {
parameters.add(p);
}
/**
* Add a new measurement to the set.
* @param m measurement to add
*/
protected void addMeasurement(WeightedMeasurement m) {
measurements.add(m);
}
/** Estimated parameters. */
private final List<EstimatedParameter> parameters;
/** Measurements. */
private final List<WeightedMeasurement> measurements;
}

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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 java.io.Serializable;
/**
* This class represents measurements in estimation problems.
*
* <p>This abstract class implements all the methods needed to handle
* measurements in a general way. It defines neither the {@link
* #getTheoreticalValue getTheoreticalValue} nor the {@link
* #getPartial getPartial} methods, which should be defined by
* sub-classes according to the specific problem.</p>
*
* <p>The {@link #getTheoreticalValue getTheoreticalValue} and {@link
* #getPartial getPartial} methods must always use the current
* estimate of the parameters set by the solver in the problem. These
* parameters can be retrieved through the {@link
* EstimationProblem#getAllParameters
* EstimationProblem.getAllParameters} method if the measurements are
* independent of the problem, or directly if they are implemented as
* inner classes of the problem.</p>
*
* <p>The instances for which the <code>ignored</code> flag is set
* through the {@link #setIgnored setIgnored} method are ignored by the
* solvers. This can be used to reject wrong measurements at some
* steps of the estimation.</p>
*
* @see EstimationProblem
*
* @version $Revision$ $Date$
* @since 1.2
*
*/
public abstract class WeightedMeasurement implements Serializable {
/** Serializable version identifier. */
private static final long serialVersionUID = 4360046376796901941L;
/**
* Simple constructor.
* Build a measurement with the given parameters, and set its ignore
* flag to false.
* @param weight weight of the measurement in the least squares problem
* (two common choices are either to use 1.0 for all measurements, or to
* use a value proportional to the inverse of the variance of the measurement
* type)
*
* @param measuredValue measured value
*/
public WeightedMeasurement(double weight, double measuredValue) {
this.weight = weight;
this.measuredValue = measuredValue;
ignored = false;
}
/** Simple constructor.
*
* Build a measurement with the given parameters
*
* @param weight weight of the measurement in the least squares problem
* @param measuredValue measured value
* @param ignored true if the measurement should be ignored
*/
public WeightedMeasurement(double weight, double measuredValue,
boolean ignored) {
this.weight = weight;
this.measuredValue = measuredValue;
this.ignored = ignored;
}
/**
* Get the weight of the measurement in the least squares problem
*
* @return weight
*/
public double getWeight() {
return weight;
}
/**
* Get the measured value
*
* @return measured value
*/
public double getMeasuredValue() {
return measuredValue;
}
/**
* Get the residual for this measurement
* The residual is the measured value minus the theoretical value.
*
* @return residual
*/
public double getResidual() {
return measuredValue - getTheoreticalValue();
}
/**
* Get the theoretical value expected for this measurement
* <p>The theoretical value is the value expected for this measurement
* if the model and its parameter were all perfectly known.</p>
* <p>The value must be computed using the current estimate of the parameters
* set by the solver in the problem.</p>
*
* @return theoretical value
*/
public abstract double getTheoreticalValue();
/**
* Get the partial derivative of the {@link #getTheoreticalValue
* theoretical value} according to the parameter.
* <p>The value must be computed using the current estimate of the parameters
* set by the solver in the problem.</p>
*
* @param parameter parameter against which the partial derivative
* should be computed
* @return partial derivative of the {@link #getTheoreticalValue
* theoretical value}
*/
public abstract double getPartial(EstimatedParameter parameter);
/**
* Set the ignore flag to the specified value
* Setting the ignore flag to true allow to reject wrong
* measurements, which sometimes can be detected only rather late.
*
* @param ignored value for the ignore flag
*/
public void setIgnored(boolean ignored) {
this.ignored = ignored;
}
/**
* Check if this measurement should be ignored
*
* @return true if the measurement should be ignored
*/
public boolean isIgnored() {
return ignored;
}
/** Measurement weight. */
private final double weight;
/** Value of the measurements. */
private final double measuredValue;
/** Ignore measurement indicator. */
private boolean ignored;
}

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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 junit.framework.*;
public class EstimatedParameterTest
extends TestCase {
public EstimatedParameterTest(String name) {
super(name);
}
public void testConstruction() {
EstimatedParameter p1 = new EstimatedParameter("p1", 1.0);
assertTrue(p1.getName().equals("p1"));
checkValue(p1.getEstimate(), 1.0);
assertTrue(! p1.isBound());
EstimatedParameter p2 = new EstimatedParameter("p2", 2.0, true);
assertTrue(p2.getName().equals("p2"));
checkValue(p2.getEstimate(), 2.0);
assertTrue(p2.isBound());
}
public void testBound() {
EstimatedParameter p = new EstimatedParameter("p", 0.0);
assertTrue(! p.isBound());
p.setBound(true);
assertTrue(p.isBound());
p.setBound(false);
assertTrue(! p.isBound());
}
public void testEstimate() {
EstimatedParameter p = new EstimatedParameter("p", 0.0);
checkValue(p.getEstimate(), 0.0);
for (double e = 0.0; e < 10.0; e += 0.5) {
p.setEstimate(e);
checkValue(p.getEstimate(), e);
}
}
public static Test suite() {
return new TestSuite(EstimatedParameterTest.class);
}
private void checkValue(double value, double expected) {
assertTrue(Math.abs(value - expected) < 1.0e-10);
}
}

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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 java.util.ArrayList;
import java.util.HashSet;
import org.apache.commons.math.optimization.OptimizationException;
import junit.framework.Test;
import junit.framework.TestCase;
import junit.framework.TestSuite;
/**
* <p>Some of the unit tests are re-implementations of the MINPACK <a
* href="http://www.netlib.org/minpack/ex/file17">file17</a> and <a
* href="http://www.netlib.org/minpack/ex/file22">file22</a> test files.
* The redistribution policy for MINPACK is available <a
* href="http://www.netlib.org/minpack/disclaimer">here</a>, for
* convenience, it is reproduced below.</p>
* <table border="0" width="80%" cellpadding="10" align="center" bgcolor="#E0E0E0">
* <tr><td>
* Minpack Copyright Notice (1999) University of Chicago.
* All rights reserved
* </td></tr>
* <tr><td>
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
* <ol>
* <li>Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.</li>
* <li>Redistributions in binary form must reproduce the above
* copyright notice, this list of conditions and the following
* disclaimer in the documentation and/or other materials provided
* with the distribution.</li>
* <li>The end-user documentation included with the redistribution, if any,
* must include the following acknowledgment:
* <code>This product includes software developed by the University of
* Chicago, as Operator of Argonne National Laboratory.</code>
* Alternately, this acknowledgment may appear in the software itself,
* if and wherever such third-party acknowledgments normally appear.</li>
* <li><strong>WARRANTY DISCLAIMER. THE SOFTWARE IS SUPPLIED "AS IS"
* WITHOUT WARRANTY OF ANY KIND. THE COPYRIGHT HOLDER, THE
* UNITED STATES, THE UNITED STATES DEPARTMENT OF ENERGY, AND
* THEIR EMPLOYEES: (1) DISCLAIM ANY WARRANTIES, EXPRESS OR
* IMPLIED, INCLUDING BUT NOT LIMITED TO ANY IMPLIED WARRANTIES
* OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE, TITLE
* OR NON-INFRINGEMENT, (2) DO NOT ASSUME ANY LEGAL LIABILITY
* OR RESPONSIBILITY FOR THE ACCURACY, COMPLETENESS, OR
* USEFULNESS OF THE SOFTWARE, (3) DO NOT REPRESENT THAT USE OF
* THE SOFTWARE WOULD NOT INFRINGE PRIVATELY OWNED RIGHTS, (4)
* DO NOT WARRANT THAT THE SOFTWARE WILL FUNCTION
* UNINTERRUPTED, THAT IT IS ERROR-FREE OR THAT ANY ERRORS WILL
* BE CORRECTED.</strong></li>
* <li><strong>LIMITATION OF LIABILITY. IN NO EVENT WILL THE COPYRIGHT
* HOLDER, THE UNITED STATES, THE UNITED STATES DEPARTMENT OF
* ENERGY, OR THEIR EMPLOYEES: BE LIABLE FOR ANY INDIRECT,
* INCIDENTAL, CONSEQUENTIAL, SPECIAL OR PUNITIVE DAMAGES OF
* ANY KIND OR NATURE, INCLUDING BUT NOT LIMITED TO LOSS OF
* PROFITS OR LOSS OF DATA, FOR ANY REASON WHATSOEVER, WHETHER
* SUCH LIABILITY IS ASSERTED ON THE BASIS OF CONTRACT, TORT
* (INCLUDING NEGLIGENCE OR STRICT LIABILITY), OR OTHERWISE,
* EVEN IF ANY OF SAID PARTIES HAS BEEN WARNED OF THE
* POSSIBILITY OF SUCH LOSS OR DAMAGES.</strong></li>
* <ol></td></tr>
* </table>
* @author Argonne National Laboratory. MINPACK project. March 1980 (original fortran minpack tests)
* @author Burton S. Garbow (original fortran minpack tests)
* @author Kenneth E. Hillstrom (original fortran minpack tests)
* @author Jorge J. More (original fortran minpack tests)
* @author Luc Maisonobe (non-minpack tests and minpack tests Java translation)
*/
public class LevenbergMarquardtEstimatorTest
extends TestCase {
public LevenbergMarquardtEstimatorTest(String name) {
super(name);
}
public void testTrivial() throws OptimizationException {
LinearProblem problem =
new LinearProblem(new LinearMeasurement[] {
new LinearMeasurement(new double[] {2},
new EstimatedParameter[] {
new EstimatedParameter("p0", 0)
}, 3.0)
});
LevenbergMarquardtEstimator estimator = new LevenbergMarquardtEstimator();
estimator.estimate(problem);
assertEquals(0, estimator.getRMS(problem), 1.0e-10);
try {
estimator.guessParametersErrors(problem);
fail("an exception should have been thrown");
} catch (OptimizationException ee) {
// expected behavior
} catch (Exception e) {
fail("wrong exception caught");
}
assertEquals(1.5,
problem.getUnboundParameters()[0].getEstimate(),
1.0e-10);
}
public void testQRColumnsPermutation() throws OptimizationException {
EstimatedParameter[] x = {
new EstimatedParameter("p0", 0), new EstimatedParameter("p1", 0)
};
LinearProblem problem = new LinearProblem(new LinearMeasurement[] {
new LinearMeasurement(new double[] { 1.0, -1.0 },
new EstimatedParameter[] { x[0], x[1] },
4.0),
new LinearMeasurement(new double[] { 2.0 },
new EstimatedParameter[] { x[1] },
6.0),
new LinearMeasurement(new double[] { 1.0, -2.0 },
new EstimatedParameter[] { x[0], x[1] },
1.0)
});
LevenbergMarquardtEstimator estimator = new LevenbergMarquardtEstimator();
estimator.estimate(problem);
assertEquals(0, estimator.getRMS(problem), 1.0e-10);
assertEquals(7.0, x[0].getEstimate(), 1.0e-10);
assertEquals(3.0, x[1].getEstimate(), 1.0e-10);
}
public void testNoDependency() throws OptimizationException {
EstimatedParameter[] p = new EstimatedParameter[] {
new EstimatedParameter("p0", 0),
new EstimatedParameter("p1", 0),
new EstimatedParameter("p2", 0),
new EstimatedParameter("p3", 0),
new EstimatedParameter("p4", 0),
new EstimatedParameter("p5", 0)
};
LinearProblem problem = new LinearProblem(new LinearMeasurement[] {
new LinearMeasurement(new double[] {2}, new EstimatedParameter[] { p[0] }, 0.0),
new LinearMeasurement(new double[] {2}, new EstimatedParameter[] { p[1] }, 1.1),
new LinearMeasurement(new double[] {2}, new EstimatedParameter[] { p[2] }, 2.2),
new LinearMeasurement(new double[] {2}, new EstimatedParameter[] { p[3] }, 3.3),
new LinearMeasurement(new double[] {2}, new EstimatedParameter[] { p[4] }, 4.4),
new LinearMeasurement(new double[] {2}, new EstimatedParameter[] { p[5] }, 5.5)
});
LevenbergMarquardtEstimator estimator = new LevenbergMarquardtEstimator();
estimator.estimate(problem);
assertEquals(0, estimator.getRMS(problem), 1.0e-10);
for (int i = 0; i < p.length; ++i) {
assertEquals(0.55 * i, p[i].getEstimate(), 1.0e-10);
}
}
public void testOneSet() throws OptimizationException {
EstimatedParameter[] p = {
new EstimatedParameter("p0", 0),
new EstimatedParameter("p1", 0),
new EstimatedParameter("p2", 0)
};
LinearProblem problem = new LinearProblem(new LinearMeasurement[] {
new LinearMeasurement(new double[] { 1.0 },
new EstimatedParameter[] { p[0] },
1.0),
new LinearMeasurement(new double[] { -1.0, 1.0 },
new EstimatedParameter[] { p[0], p[1] },
1.0),
new LinearMeasurement(new double[] { -1.0, 1.0 },
new EstimatedParameter[] { p[1], p[2] },
1.0)
});
LevenbergMarquardtEstimator estimator = new LevenbergMarquardtEstimator();
estimator.estimate(problem);
assertEquals(0, estimator.getRMS(problem), 1.0e-10);
assertEquals(1.0, p[0].getEstimate(), 1.0e-10);
assertEquals(2.0, p[1].getEstimate(), 1.0e-10);
assertEquals(3.0, p[2].getEstimate(), 1.0e-10);
}
public void testTwoSets() throws OptimizationException {
EstimatedParameter[] p = {
new EstimatedParameter("p0", 0),
new EstimatedParameter("p1", 1),
new EstimatedParameter("p2", 2),
new EstimatedParameter("p3", 3),
new EstimatedParameter("p4", 4),
new EstimatedParameter("p5", 5)
};
double epsilon = 1.0e-7;
LinearProblem problem = new LinearProblem(new LinearMeasurement[] {
// 4 elements sub-problem
new LinearMeasurement(new double[] { 2.0, 1.0, 4.0 },
new EstimatedParameter[] { p[0], p[1], p[3] },
2.0),
new LinearMeasurement(new double[] { -4.0, -2.0, 3.0, -7.0 },
new EstimatedParameter[] { p[0], p[1], p[2], p[3] },
-9.0),
new LinearMeasurement(new double[] { 4.0, 1.0, -2.0, 8.0 },
new EstimatedParameter[] { p[0], p[1], p[2], p[3] },
2.0),
new LinearMeasurement(new double[] { -3.0, -12.0, -1.0 },
new EstimatedParameter[] { p[1], p[2], p[3] },
2.0),
// 2 elements sub-problem
new LinearMeasurement(new double[] { epsilon, 1.0 },
new EstimatedParameter[] { p[4], p[5] },
1.0 + epsilon * epsilon),
new LinearMeasurement(new double[] { 1.0, 1.0 },
new EstimatedParameter[] { p[4], p[5] },
2.0)
});
LevenbergMarquardtEstimator estimator = new LevenbergMarquardtEstimator();
estimator.estimate(problem);
assertEquals(0, estimator.getRMS(problem), 1.0e-10);
assertEquals( 3.0, p[0].getEstimate(), 1.0e-10);
assertEquals( 4.0, p[1].getEstimate(), 1.0e-10);
assertEquals(-1.0, p[2].getEstimate(), 1.0e-10);
assertEquals(-2.0, p[3].getEstimate(), 1.0e-10);
assertEquals( 1.0 + epsilon, p[4].getEstimate(), 1.0e-10);
assertEquals( 1.0 - epsilon, p[5].getEstimate(), 1.0e-10);
}
public void testNonInversible() throws OptimizationException {
EstimatedParameter[] p = {
new EstimatedParameter("p0", 0),
new EstimatedParameter("p1", 0),
new EstimatedParameter("p2", 0)
};
LinearMeasurement[] m = new LinearMeasurement[] {
new LinearMeasurement(new double[] { 1.0, 2.0, -3.0 },
new EstimatedParameter[] { p[0], p[1], p[2] },
1.0),
new LinearMeasurement(new double[] { 2.0, 1.0, 3.0 },
new EstimatedParameter[] { p[0], p[1], p[2] },
1.0),
new LinearMeasurement(new double[] { -3.0, -9.0 },
new EstimatedParameter[] { p[0], p[2] },
1.0)
};
LinearProblem problem = new LinearProblem(m);
LevenbergMarquardtEstimator estimator = new LevenbergMarquardtEstimator();
double initialCost = estimator.getRMS(problem);
estimator.estimate(problem);
assertTrue(estimator.getRMS(problem) < initialCost);
assertTrue(Math.sqrt(m.length) * estimator.getRMS(problem) > 0.6);
try {
estimator.getCovariances(problem);
fail("an exception should have been thrown");
} catch (OptimizationException ee) {
// expected behavior
} catch (Exception e) {
fail("wrong exception caught");
}
double dJ0 = 2 * (m[0].getResidual() * m[0].getPartial(p[0])
+ m[1].getResidual() * m[1].getPartial(p[0])
+ m[2].getResidual() * m[2].getPartial(p[0]));
double dJ1 = 2 * (m[0].getResidual() * m[0].getPartial(p[1])
+ m[1].getResidual() * m[1].getPartial(p[1]));
double dJ2 = 2 * (m[0].getResidual() * m[0].getPartial(p[2])
+ m[1].getResidual() * m[1].getPartial(p[2])
+ m[2].getResidual() * m[2].getPartial(p[2]));
assertEquals(0, dJ0, 1.0e-10);
assertEquals(0, dJ1, 1.0e-10);
assertEquals(0, dJ2, 1.0e-10);
}
public void testIllConditioned() throws OptimizationException {
EstimatedParameter[] p = {
new EstimatedParameter("p0", 0),
new EstimatedParameter("p1", 1),
new EstimatedParameter("p2", 2),
new EstimatedParameter("p3", 3)
};
LinearProblem problem1 = new LinearProblem(new LinearMeasurement[] {
new LinearMeasurement(new double[] { 10.0, 7.0, 8.0, 7.0 },
new EstimatedParameter[] { p[0], p[1], p[2], p[3] },
32.0),
new LinearMeasurement(new double[] { 7.0, 5.0, 6.0, 5.0 },
new EstimatedParameter[] { p[0], p[1], p[2], p[3] },
23.0),
new LinearMeasurement(new double[] { 8.0, 6.0, 10.0, 9.0 },
new EstimatedParameter[] { p[0], p[1], p[2], p[3] },
33.0),
new LinearMeasurement(new double[] { 7.0, 5.0, 9.0, 10.0 },
new EstimatedParameter[] { p[0], p[1], p[2], p[3] },
31.0)
});
LevenbergMarquardtEstimator estimator1 = new LevenbergMarquardtEstimator();
estimator1.estimate(problem1);
assertEquals(0, estimator1.getRMS(problem1), 1.0e-10);
assertEquals(1.0, p[0].getEstimate(), 1.0e-10);
assertEquals(1.0, p[1].getEstimate(), 1.0e-10);
assertEquals(1.0, p[2].getEstimate(), 1.0e-10);
assertEquals(1.0, p[3].getEstimate(), 1.0e-10);
LinearProblem problem2 = new LinearProblem(new LinearMeasurement[] {
new LinearMeasurement(new double[] { 10.0, 7.0, 8.1, 7.2 },
new EstimatedParameter[] { p[0], p[1], p[2], p[3] },
32.0),
new LinearMeasurement(new double[] { 7.08, 5.04, 6.0, 5.0 },
new EstimatedParameter[] { p[0], p[1], p[2], p[3] },
23.0),
new LinearMeasurement(new double[] { 8.0, 5.98, 9.89, 9.0 },
new EstimatedParameter[] { p[0], p[1], p[2], p[3] },
33.0),
new LinearMeasurement(new double[] { 6.99, 4.99, 9.0, 9.98 },
new EstimatedParameter[] { p[0], p[1], p[2], p[3] },
31.0)
});
LevenbergMarquardtEstimator estimator2 = new LevenbergMarquardtEstimator();
estimator2.estimate(problem2);
assertEquals(0, estimator2.getRMS(problem2), 1.0e-10);
assertEquals(-81.0, p[0].getEstimate(), 1.0e-8);
assertEquals(137.0, p[1].getEstimate(), 1.0e-8);
assertEquals(-34.0, p[2].getEstimate(), 1.0e-8);
assertEquals( 22.0, p[3].getEstimate(), 1.0e-8);
}
public void testMoreEstimatedParametersSimple() throws OptimizationException {
EstimatedParameter[] p = {
new EstimatedParameter("p0", 7),
new EstimatedParameter("p1", 6),
new EstimatedParameter("p2", 5),
new EstimatedParameter("p3", 4)
};
LinearProblem problem = new LinearProblem(new LinearMeasurement[] {
new LinearMeasurement(new double[] { 3.0, 2.0 },
new EstimatedParameter[] { p[0], p[1] },
7.0),
new LinearMeasurement(new double[] { 1.0, -1.0, 1.0 },
new EstimatedParameter[] { p[1], p[2], p[3] },
3.0),
new LinearMeasurement(new double[] { 2.0, 1.0 },
new EstimatedParameter[] { p[0], p[2] },
5.0)
});
LevenbergMarquardtEstimator estimator = new LevenbergMarquardtEstimator();
estimator.estimate(problem);
assertEquals(0, estimator.getRMS(problem), 1.0e-10);
}
public void testMoreEstimatedParametersUnsorted() throws OptimizationException {
EstimatedParameter[] p = {
new EstimatedParameter("p0", 2),
new EstimatedParameter("p1", 2),
new EstimatedParameter("p2", 2),
new EstimatedParameter("p3", 2),
new EstimatedParameter("p4", 2),
new EstimatedParameter("p5", 2)
};
LinearProblem problem = new LinearProblem(new LinearMeasurement[] {
new LinearMeasurement(new double[] { 1.0, 1.0 },
new EstimatedParameter[] { p[0], p[1] },
3.0),
new LinearMeasurement(new double[] { 1.0, 1.0, 1.0 },
new EstimatedParameter[] { p[2], p[3], p[4] },
12.0),
new LinearMeasurement(new double[] { 1.0, -1.0 },
new EstimatedParameter[] { p[4], p[5] },
-1.0),
new LinearMeasurement(new double[] { 1.0, -1.0, 1.0 },
new EstimatedParameter[] { p[3], p[2], p[5] },
7.0),
new LinearMeasurement(new double[] { 1.0, -1.0 },
new EstimatedParameter[] { p[4], p[3] },
1.0)
});
LevenbergMarquardtEstimator estimator = new LevenbergMarquardtEstimator();
estimator.estimate(problem);
assertEquals(0, estimator.getRMS(problem), 1.0e-10);
assertEquals(3.0, p[2].getEstimate(), 1.0e-10);
assertEquals(4.0, p[3].getEstimate(), 1.0e-10);
assertEquals(5.0, p[4].getEstimate(), 1.0e-10);
assertEquals(6.0, p[5].getEstimate(), 1.0e-10);
}
public void testRedundantEquations() throws OptimizationException {
EstimatedParameter[] p = {
new EstimatedParameter("p0", 1),
new EstimatedParameter("p1", 1)
};
LinearProblem problem = new LinearProblem(new LinearMeasurement[] {
new LinearMeasurement(new double[] { 1.0, 1.0 },
new EstimatedParameter[] { p[0], p[1] },
3.0),
new LinearMeasurement(new double[] { 1.0, -1.0 },
new EstimatedParameter[] { p[0], p[1] },
1.0),
new LinearMeasurement(new double[] { 1.0, 3.0 },
new EstimatedParameter[] { p[0], p[1] },
5.0)
});
LevenbergMarquardtEstimator estimator = new LevenbergMarquardtEstimator();
estimator.estimate(problem);
assertEquals(0, estimator.getRMS(problem), 1.0e-10);
assertEquals(2.0, p[0].getEstimate(), 1.0e-10);
assertEquals(1.0, p[1].getEstimate(), 1.0e-10);
}
public void testInconsistentEquations() throws OptimizationException {
EstimatedParameter[] p = {
new EstimatedParameter("p0", 1),
new EstimatedParameter("p1", 1)
};
LinearProblem problem = new LinearProblem(new LinearMeasurement[] {
new LinearMeasurement(new double[] { 1.0, 1.0 },
new EstimatedParameter[] { p[0], p[1] },
3.0),
new LinearMeasurement(new double[] { 1.0, -1.0 },
new EstimatedParameter[] { p[0], p[1] },
1.0),
new LinearMeasurement(new double[] { 1.0, 3.0 },
new EstimatedParameter[] { p[0], p[1] },
4.0)
});
LevenbergMarquardtEstimator estimator = new LevenbergMarquardtEstimator();
estimator.estimate(problem);
assertTrue(estimator.getRMS(problem) > 0.1);
}
public void testControlParameters() throws OptimizationException {
Circle circle = new Circle(98.680, 47.345);
circle.addPoint( 30.0, 68.0);
circle.addPoint( 50.0, -6.0);
circle.addPoint(110.0, -20.0);
circle.addPoint( 35.0, 15.0);
circle.addPoint( 45.0, 97.0);
checkEstimate(circle, 0.1, 10, 1.0e-14, 1.0e-16, 1.0e-10, false);
checkEstimate(circle, 0.1, 10, 1.0e-15, 1.0e-17, 1.0e-10, true);
checkEstimate(circle, 0.1, 5, 1.0e-15, 1.0e-16, 1.0e-10, true);
circle.addPoint(300, -300);
checkEstimate(circle, 0.1, 20, 1.0e-18, 1.0e-16, 1.0e-10, true);
}
private void checkEstimate(EstimationProblem problem,
double initialStepBoundFactor, int maxCostEval,
double costRelativeTolerance, double parRelativeTolerance,
double orthoTolerance, boolean shouldFail) {
try {
LevenbergMarquardtEstimator estimator = new LevenbergMarquardtEstimator();
estimator.setInitialStepBoundFactor(initialStepBoundFactor);
estimator.setMaxCostEval(maxCostEval);
estimator.setCostRelativeTolerance(costRelativeTolerance);
estimator.setParRelativeTolerance(parRelativeTolerance);
estimator.setOrthoTolerance(orthoTolerance);
estimator.estimate(problem);
assertTrue(! shouldFail);
} catch (OptimizationException ee) {
assertTrue(shouldFail);
} catch (Exception e) {
fail("wrong exception type caught");
}
}
public void testCircleFitting() throws OptimizationException {
Circle circle = new Circle(98.680, 47.345);
circle.addPoint( 30.0, 68.0);
circle.addPoint( 50.0, -6.0);
circle.addPoint(110.0, -20.0);
circle.addPoint( 35.0, 15.0);
circle.addPoint( 45.0, 97.0);
LevenbergMarquardtEstimator estimator = new LevenbergMarquardtEstimator();
estimator.estimate(circle);
assertTrue(estimator.getCostEvaluations() < 10);
assertTrue(estimator.getJacobianEvaluations() < 10);
double rms = estimator.getRMS(circle);
assertEquals(1.768262623567235, Math.sqrt(circle.getM()) * rms, 1.0e-10);
assertEquals(69.96016176931406, circle.getRadius(), 1.0e-10);
assertEquals(96.07590211815305, circle.getX(), 1.0e-10);
assertEquals(48.13516790438953, circle.getY(), 1.0e-10);
double[][] cov = estimator.getCovariances(circle);
assertEquals(1.839, cov[0][0], 0.001);
assertEquals(0.731, cov[0][1], 0.001);
assertEquals(cov[0][1], cov[1][0], 1.0e-14);
assertEquals(0.786, cov[1][1], 0.001);
double[] errors = estimator.guessParametersErrors(circle);
assertEquals(1.384, errors[0], 0.001);
assertEquals(0.905, errors[1], 0.001);
// add perfect measurements and check errors are reduced
double cx = circle.getX();
double cy = circle.getY();
double r = circle.getRadius();
for (double d= 0; d < 2 * Math.PI; d += 0.01) {
circle.addPoint(cx + r * Math.cos(d), cy + r * Math.sin(d));
}
estimator = new LevenbergMarquardtEstimator();
estimator.estimate(circle);
cov = estimator.getCovariances(circle);
assertEquals(0.004, cov[0][0], 0.001);
assertEquals(6.40e-7, cov[0][1], 1.0e-9);
assertEquals(cov[0][1], cov[1][0], 1.0e-14);
assertEquals(0.003, cov[1][1], 0.001);
errors = estimator.guessParametersErrors(circle);
assertEquals(0.004, errors[0], 0.001);
assertEquals(0.004, errors[1], 0.001);
}
public void testCircleFittingBadInit() throws OptimizationException {
Circle circle = new Circle(-12, -12);
double[][] points = new double[][] {
{-0.312967, 0.072366}, {-0.339248, 0.132965}, {-0.379780, 0.202724},
{-0.390426, 0.260487}, {-0.361212, 0.328325}, {-0.346039, 0.392619},
{-0.280579, 0.444306}, {-0.216035, 0.470009}, {-0.149127, 0.493832},
{-0.075133, 0.483271}, {-0.007759, 0.452680}, { 0.060071, 0.410235},
{ 0.103037, 0.341076}, { 0.118438, 0.273884}, { 0.131293, 0.192201},
{ 0.115869, 0.129797}, { 0.072223, 0.058396}, { 0.022884, 0.000718},
{-0.053355, -0.020405}, {-0.123584, -0.032451}, {-0.216248, -0.032862},
{-0.278592, -0.005008}, {-0.337655, 0.056658}, {-0.385899, 0.112526},
{-0.405517, 0.186957}, {-0.415374, 0.262071}, {-0.387482, 0.343398},
{-0.347322, 0.397943}, {-0.287623, 0.458425}, {-0.223502, 0.475513},
{-0.135352, 0.478186}, {-0.061221, 0.483371}, { 0.003711, 0.422737},
{ 0.065054, 0.375830}, { 0.108108, 0.297099}, { 0.123882, 0.222850},
{ 0.117729, 0.134382}, { 0.085195, 0.056820}, { 0.029800, -0.019138},
{-0.027520, -0.072374}, {-0.102268, -0.091555}, {-0.200299, -0.106578},
{-0.292731, -0.091473}, {-0.356288, -0.051108}, {-0.420561, 0.014926},
{-0.471036, 0.074716}, {-0.488638, 0.182508}, {-0.485990, 0.254068},
{-0.463943, 0.338438}, {-0.406453, 0.404704}, {-0.334287, 0.466119},
{-0.254244, 0.503188}, {-0.161548, 0.495769}, {-0.075733, 0.495560},
{ 0.001375, 0.434937}, { 0.082787, 0.385806}, { 0.115490, 0.323807},
{ 0.141089, 0.223450}, { 0.138693, 0.131703}, { 0.126415, 0.049174},
{ 0.066518, -0.010217}, {-0.005184, -0.070647}, {-0.080985, -0.103635},
{-0.177377, -0.116887}, {-0.260628, -0.100258}, {-0.335756, -0.056251},
{-0.405195, -0.000895}, {-0.444937, 0.085456}, {-0.484357, 0.175597},
{-0.472453, 0.248681}, {-0.438580, 0.347463}, {-0.402304, 0.422428},
{-0.326777, 0.479438}, {-0.247797, 0.505581}, {-0.152676, 0.519380},
{-0.071754, 0.516264}, { 0.015942, 0.472802}, { 0.076608, 0.419077},
{ 0.127673, 0.330264}, { 0.159951, 0.262150}, { 0.153530, 0.172681},
{ 0.140653, 0.089229}, { 0.078666, 0.024981}, { 0.023807, -0.037022},
{-0.048837, -0.077056}, {-0.127729, -0.075338}, {-0.221271, -0.067526}
};
for (int i = 0; i < points.length; ++i) {
circle.addPoint(points[i][0], points[i][1]);
}
LevenbergMarquardtEstimator estimator = new LevenbergMarquardtEstimator();
estimator.estimate(circle);
assertTrue(estimator.getCostEvaluations() < 15);
assertTrue(estimator.getJacobianEvaluations() < 10);
assertEquals( 0.030184491196225207, estimator.getRMS(circle), 1.0e-9);
assertEquals( 0.2922350065939634, circle.getRadius(), 1.0e-9);
assertEquals(-0.15173845023862165, circle.getX(), 1.0e-8);
assertEquals( 0.20750021499570379, circle.getY(), 1.0e-8);
}
public void testMath199() {
try {
QuadraticProblem problem = new QuadraticProblem();
problem.addPoint (0, -3.182591015485607, 0.0);
problem.addPoint (1, -2.5581184967730577, 4.4E-323);
problem.addPoint (2, -2.1488478161387325, 1.0);
problem.addPoint (3, -1.9122489313410047, 4.4E-323);
problem.addPoint (4, 1.7785661310051026, 0.0);
new LevenbergMarquardtEstimator().estimate(problem);
fail("an exception should have been thrown");
} catch (OptimizationException ee) {
// expected behavior
}
}
private static class LinearProblem implements EstimationProblem {
public LinearProblem(LinearMeasurement[] measurements) {
this.measurements = measurements;
}
public WeightedMeasurement[] getMeasurements() {
return measurements;
}
public EstimatedParameter[] getUnboundParameters() {
return getAllParameters();
}
public EstimatedParameter[] getAllParameters() {
HashSet<EstimatedParameter> set = new HashSet<EstimatedParameter>();
for (int i = 0; i < measurements.length; ++i) {
EstimatedParameter[] parameters = measurements[i].getParameters();
for (int j = 0; j < parameters.length; ++j) {
set.add(parameters[j]);
}
}
return (EstimatedParameter[]) set.toArray(new EstimatedParameter[set.size()]);
}
private LinearMeasurement[] measurements;
}
private static class LinearMeasurement extends WeightedMeasurement {
public LinearMeasurement(double[] factors, EstimatedParameter[] parameters,
double setPoint) {
super(1.0, setPoint);
this.factors = factors;
this.parameters = parameters;
}
public double getTheoreticalValue() {
double v = 0;
for (int i = 0; i < factors.length; ++i) {
v += factors[i] * parameters[i].getEstimate();
}
return v;
}
public double getPartial(EstimatedParameter parameter) {
for (int i = 0; i < parameters.length; ++i) {
if (parameters[i] == parameter) {
return factors[i];
}
}
return 0;
}
public EstimatedParameter[] getParameters() {
return parameters;
}
private double[] factors;
private EstimatedParameter[] parameters;
private static final long serialVersionUID = -3922448707008868580L;
}
private static class Circle implements EstimationProblem {
public Circle(double cx, double cy) {
this.cx = new EstimatedParameter("cx", cx);
this.cy = new EstimatedParameter("cy", cy);
points = new ArrayList<PointModel>();
}
public void addPoint(double px, double py) {
points.add(new PointModel(px, py));
}
public int getM() {
return points.size();
}
public WeightedMeasurement[] getMeasurements() {
return (WeightedMeasurement[]) points.toArray(new PointModel[points.size()]);
}
public EstimatedParameter[] getAllParameters() {
return new EstimatedParameter[] { cx, cy };
}
public EstimatedParameter[] getUnboundParameters() {
return new EstimatedParameter[] { cx, cy };
}
public double getPartialRadiusX() {
double dRdX = 0;
for (PointModel point : points) {
dRdX += point.getPartialDiX();
}
return dRdX / points.size();
}
public double getPartialRadiusY() {
double dRdY = 0;
for (PointModel point : points) {
dRdY += point.getPartialDiY();
}
return dRdY / points.size();
}
public double getRadius() {
double r = 0;
for (PointModel point : points) {
r += point.getCenterDistance();
}
return r / points.size();
}
public double getX() {
return cx.getEstimate();
}
public double getY() {
return cy.getEstimate();
}
private class PointModel extends WeightedMeasurement {
public PointModel(double px, double py) {
super(1.0, 0.0);
this.px = px;
this.py = py;
}
public double getPartial(EstimatedParameter parameter) {
if (parameter == cx) {
return getPartialDiX() - getPartialRadiusX();
} else if (parameter == cy) {
return getPartialDiY() - getPartialRadiusY();
}
return 0;
}
public double getCenterDistance() {
double dx = px - cx.getEstimate();
double dy = py - cy.getEstimate();
return Math.sqrt(dx * dx + dy * dy);
}
public double getPartialDiX() {
return (cx.getEstimate() - px) / getCenterDistance();
}
public double getPartialDiY() {
return (cy.getEstimate() - py) / getCenterDistance();
}
public double getTheoreticalValue() {
return getCenterDistance() - getRadius();
}
private double px;
private double py;
private static final long serialVersionUID = 1L;
}
private EstimatedParameter cx;
private EstimatedParameter cy;
private ArrayList<PointModel> points;
}
private static class QuadraticProblem extends SimpleEstimationProblem {
private EstimatedParameter a;
private EstimatedParameter b;
private EstimatedParameter c;
public QuadraticProblem() {
a = new EstimatedParameter("a", 0.0);
b = new EstimatedParameter("b", 0.0);
c = new EstimatedParameter("c", 0.0);
addParameter(a);
addParameter(b);
addParameter(c);
}
public void addPoint(double x, double y, double w) {
addMeasurement(new LocalMeasurement(x, y, w));
}
public double getA() {
return a.getEstimate();
}
public double getB() {
return b.getEstimate();
}
public double getC() {
return c.getEstimate();
}
public double theoreticalValue(double x) {
return ( (a.getEstimate() * x + b.getEstimate() ) * x + c.getEstimate());
}
private double partial(double x, EstimatedParameter parameter) {
if (parameter == a) {
return x * x;
} else if (parameter == b) {
return x;
} else {
return 1.0;
}
}
private class LocalMeasurement extends WeightedMeasurement {
private static final long serialVersionUID = 1555043155023729130L;
private final double x;
// constructor
public LocalMeasurement(double x, double y, double w) {
super(w, y);
this.x = x;
}
public double getTheoreticalValue() {
return theoreticalValue(x);
}
public double getPartial(EstimatedParameter parameter) {
return partial(x, parameter);
}
}
}
public static Test suite() {
return new TestSuite(LevenbergMarquardtEstimatorTest.class);
}
}

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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 java.awt.geom.Point2D;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.List;
import junit.framework.Test;
import junit.framework.TestCase;
import junit.framework.TestSuite;
import org.apache.commons.math.linear.DenseRealMatrix;
import org.apache.commons.math.linear.RealMatrix;
import org.apache.commons.math.optimization.ObjectiveException;
import org.apache.commons.math.optimization.OptimizationException;
import org.apache.commons.math.optimization.SimpleVectorialValueChecker;
import org.apache.commons.math.optimization.VectorialDifferentiableObjectiveFunction;
import org.apache.commons.math.optimization.VectorialPointValuePair;
/**
* <p>Some of the unit tests are re-implementations of the MINPACK <a
* href="http://www.netlib.org/minpack/ex/file17">file17</a> and <a
* href="http://www.netlib.org/minpack/ex/file22">file22</a> test files.
* The redistribution policy for MINPACK is available <a
* href="http://www.netlib.org/minpack/disclaimer">here</a>, for
* convenience, it is reproduced below.</p>
* <table border="0" width="80%" cellpadding="10" align="center" bgcolor="#E0E0E0">
* <tr><td>
* Minpack Copyright Notice (1999) University of Chicago.
* All rights reserved
* </td></tr>
* <tr><td>
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
* <ol>
* <li>Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.</li>
* <li>Redistributions in binary form must reproduce the above
* copyright notice, this list of conditions and the following
* disclaimer in the documentation and/or other materials provided
* with the distribution.</li>
* <li>The end-user documentation included with the redistribution, if any,
* must include the following acknowledgment:
* <code>This product includes software developed by the University of
* Chicago, as Operator of Argonne National Laboratory.</code>
* Alternately, this acknowledgment may appear in the software itself,
* if and wherever such third-party acknowledgments normally appear.</li>
* <li><strong>WARRANTY DISCLAIMER. THE SOFTWARE IS SUPPLIED "AS IS"
* WITHOUT WARRANTY OF ANY KIND. THE COPYRIGHT HOLDER, THE
* UNITED STATES, THE UNITED STATES DEPARTMENT OF ENERGY, AND
* THEIR EMPLOYEES: (1) DISCLAIM ANY WARRANTIES, EXPRESS OR
* IMPLIED, INCLUDING BUT NOT LIMITED TO ANY IMPLIED WARRANTIES
* OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE, TITLE
* OR NON-INFRINGEMENT, (2) DO NOT ASSUME ANY LEGAL LIABILITY
* OR RESPONSIBILITY FOR THE ACCURACY, COMPLETENESS, OR
* USEFULNESS OF THE SOFTWARE, (3) DO NOT REPRESENT THAT USE OF
* THE SOFTWARE WOULD NOT INFRINGE PRIVATELY OWNED RIGHTS, (4)
* DO NOT WARRANT THAT THE SOFTWARE WILL FUNCTION
* UNINTERRUPTED, THAT IT IS ERROR-FREE OR THAT ANY ERRORS WILL
* BE CORRECTED.</strong></li>
* <li><strong>LIMITATION OF LIABILITY. IN NO EVENT WILL THE COPYRIGHT
* HOLDER, THE UNITED STATES, THE UNITED STATES DEPARTMENT OF
* ENERGY, OR THEIR EMPLOYEES: BE LIABLE FOR ANY INDIRECT,
* INCIDENTAL, CONSEQUENTIAL, SPECIAL OR PUNITIVE DAMAGES OF
* ANY KIND OR NATURE, INCLUDING BUT NOT LIMITED TO LOSS OF
* PROFITS OR LOSS OF DATA, FOR ANY REASON WHATSOEVER, WHETHER
* SUCH LIABILITY IS ASSERTED ON THE BASIS OF CONTRACT, TORT
* (INCLUDING NEGLIGENCE OR STRICT LIABILITY), OR OTHERWISE,
* EVEN IF ANY OF SAID PARTIES HAS BEEN WARNED OF THE
* POSSIBILITY OF SUCH LOSS OR DAMAGES.</strong></li>
* <ol></td></tr>
* </table>
* @author Argonne National Laboratory. MINPACK project. March 1980 (original fortran minpack tests)
* @author Burton S. Garbow (original fortran minpack tests)
* @author Kenneth E. Hillstrom (original fortran minpack tests)
* @author Jorge J. More (original fortran minpack tests)
* @author Luc Maisonobe (non-minpack tests and minpack tests Java translation)
*/
public class LevenbergMarquardtOptimizerTest
extends TestCase {
public LevenbergMarquardtOptimizerTest(String name) {
super(name);
}
public void testTrivial() throws ObjectiveException, OptimizationException {
LinearProblem problem =
new LinearProblem(new double[][] { { 2 } }, new double[] { 3 });
LevenbergMarquardtOptimizer optimizer = new LevenbergMarquardtOptimizer();
VectorialPointValuePair optimum =
optimizer.optimize(problem, problem.target, new double[] { 1 }, new double[] { 0 });
assertEquals(0, optimizer.getRMS(), 1.0e-10);
try {
optimizer.guessParametersErrors();
fail("an exception should have been thrown");
} catch (OptimizationException ee) {
// expected behavior
} catch (Exception e) {
fail("wrong exception caught");
}
assertEquals(1.5, optimum.getPoint()[0], 1.0e-10);
}
public void testQRColumnsPermutation() throws ObjectiveException, OptimizationException {
LinearProblem problem =
new LinearProblem(new double[][] { { 1.0, -1.0 }, { 0.0, 2.0 }, { 1.0, -2.0 } },
new double[] { 4.0, 6.0, 1.0 });
LevenbergMarquardtOptimizer optimizer = new LevenbergMarquardtOptimizer();
VectorialPointValuePair optimum =
optimizer.optimize(problem, problem.target, new double[] { 1, 1, 1 }, new double[] { 0, 0 });
assertEquals(0, optimizer.getRMS(), 1.0e-10);
assertEquals(7.0, optimum.getPoint()[0], 1.0e-10);
assertEquals(3.0, optimum.getPoint()[1], 1.0e-10);
}
public void testNoDependency() throws ObjectiveException, OptimizationException {
LinearProblem problem = new LinearProblem(new double[][] {
{ 2, 0, 0, 0, 0, 0 },
{ 0, 2, 0, 0, 0, 0 },
{ 0, 0, 2, 0, 0, 0 },
{ 0, 0, 0, 2, 0, 0 },
{ 0, 0, 0, 0, 2, 0 },
{ 0, 0, 0, 0, 0, 2 }
}, new double[] { 0.0, 1.1, 2.2, 3.3, 4.4, 5.5 });
LevenbergMarquardtOptimizer optimizer = new LevenbergMarquardtOptimizer();
VectorialPointValuePair optimum =
optimizer.optimize(problem, problem.target, new double[] { 1, 1, 1, 1, 1, 1 },
new double[] { 0, 0, 0, 0, 0, 0 });
assertEquals(0, optimizer.getRMS(), 1.0e-10);
for (int i = 0; i < problem.target.length; ++i) {
assertEquals(0.55 * i, optimum.getPoint()[i], 1.0e-10);
}
}
public void testOneSet() throws ObjectiveException, OptimizationException {
LinearProblem problem = new LinearProblem(new double[][] {
{ 1, 0, 0 },
{ -1, 1, 0 },
{ 0, -1, 1 }
}, new double[] { 1, 1, 1});
LevenbergMarquardtOptimizer optimizer = new LevenbergMarquardtOptimizer();
VectorialPointValuePair optimum =
optimizer.optimize(problem, problem.target, new double[] { 1, 1, 1 }, new double[] { 0, 0, 0 });
assertEquals(0, optimizer.getRMS(), 1.0e-10);
assertEquals(1.0, optimum.getPoint()[0], 1.0e-10);
assertEquals(2.0, optimum.getPoint()[1], 1.0e-10);
assertEquals(3.0, optimum.getPoint()[2], 1.0e-10);
}
public void testTwoSets() throws ObjectiveException, OptimizationException {
double epsilon = 1.0e-7;
LinearProblem problem = new LinearProblem(new double[][] {
{ 2, 1, 0, 4, 0, 0 },
{ -4, -2, 3, -7, 0, 0 },
{ 4, 1, -2, 8, 0, 0 },
{ 0, -3, -12, -1, 0, 0 },
{ 0, 0, 0, 0, epsilon, 1 },
{ 0, 0, 0, 0, 1, 1 }
}, new double[] { 2, -9, 2, 2, 1 + epsilon * epsilon, 2});
LevenbergMarquardtOptimizer optimizer = new LevenbergMarquardtOptimizer();
VectorialPointValuePair optimum =
optimizer.optimize(problem, problem.target, new double[] { 1, 1, 1, 1, 1, 1 },
new double[] { 0, 0, 0, 0, 0, 0 });
assertEquals(0, optimizer.getRMS(), 1.0e-10);
assertEquals( 3.0, optimum.getPoint()[0], 1.0e-10);
assertEquals( 4.0, optimum.getPoint()[1], 1.0e-10);
assertEquals(-1.0, optimum.getPoint()[2], 1.0e-10);
assertEquals(-2.0, optimum.getPoint()[3], 1.0e-10);
assertEquals( 1.0 + epsilon, optimum.getPoint()[4], 1.0e-10);
assertEquals( 1.0 - epsilon, optimum.getPoint()[5], 1.0e-10);
}
public void testNonInversible() throws ObjectiveException, OptimizationException {
LinearProblem problem = new LinearProblem(new double[][] {
{ 1, 2, -3 },
{ 2, 1, 3 },
{ -3, 0, -9 }
}, new double[] { 1, 1, 1 });
LevenbergMarquardtOptimizer optimizer = new LevenbergMarquardtOptimizer();
optimizer.optimize(problem, problem.target, new double[] { 1, 1, 1 }, new double[] { 0, 0, 0 });
assertTrue(Math.sqrt(problem.target.length) * optimizer.getRMS() > 0.6);
try {
optimizer.getCovariances();
fail("an exception should have been thrown");
} catch (OptimizationException ee) {
// expected behavior
} catch (Exception e) {
fail("wrong exception caught");
}
}
public void testIllConditioned() throws ObjectiveException, OptimizationException {
LinearProblem problem1 = new LinearProblem(new double[][] {
{ 10.0, 7.0, 8.0, 7.0 },
{ 7.0, 5.0, 6.0, 5.0 },
{ 8.0, 6.0, 10.0, 9.0 },
{ 7.0, 5.0, 9.0, 10.0 }
}, new double[] { 32, 23, 33, 31 });
LevenbergMarquardtOptimizer optimizer = new LevenbergMarquardtOptimizer();
VectorialPointValuePair optimum1 =
optimizer.optimize(problem1, problem1.target, new double[] { 1, 1, 1, 1 },
new double[] { 0, 1, 2, 3 });
assertEquals(0, optimizer.getRMS(), 1.0e-10);
assertEquals(1.0, optimum1.getPoint()[0], 1.0e-10);
assertEquals(1.0, optimum1.getPoint()[1], 1.0e-10);
assertEquals(1.0, optimum1.getPoint()[2], 1.0e-10);
assertEquals(1.0, optimum1.getPoint()[3], 1.0e-10);
LinearProblem problem2 = new LinearProblem(new double[][] {
{ 10.00, 7.00, 8.10, 7.20 },
{ 7.08, 5.04, 6.00, 5.00 },
{ 8.00, 5.98, 9.89, 9.00 },
{ 6.99, 4.99, 9.00, 9.98 }
}, new double[] { 32, 23, 33, 31 });
VectorialPointValuePair optimum2 =
optimizer.optimize(problem2, problem2.target, new double[] { 1, 1, 1, 1 },
new double[] { 0, 1, 2, 3 });
assertEquals(0, optimizer.getRMS(), 1.0e-10);
assertEquals(-81.0, optimum2.getPoint()[0], 1.0e-8);
assertEquals(137.0, optimum2.getPoint()[1], 1.0e-8);
assertEquals(-34.0, optimum2.getPoint()[2], 1.0e-8);
assertEquals( 22.0, optimum2.getPoint()[3], 1.0e-8);
}
public void testMoreEstimatedParametersSimple() throws ObjectiveException, OptimizationException {
LinearProblem problem = new LinearProblem(new double[][] {
{ 3.0, 2.0, 0.0, 0.0 },
{ 0.0, 1.0, -1.0, 1.0 },
{ 2.0, 0.0, 1.0, 0.0 }
}, new double[] { 7.0, 3.0, 5.0 });
LevenbergMarquardtOptimizer optimizer = new LevenbergMarquardtOptimizer();
optimizer.optimize(problem, problem.target, new double[] { 1, 1, 1 },
new double[] { 7, 6, 5, 4 });
assertEquals(0, optimizer.getRMS(), 1.0e-10);
}
public void testMoreEstimatedParametersUnsorted() throws ObjectiveException, OptimizationException {
LinearProblem problem = new LinearProblem(new double[][] {
{ 1.0, 1.0, 0.0, 0.0, 0.0, 0.0 },
{ 0.0, 0.0, 1.0, 1.0, 1.0, 0.0 },
{ 0.0, 0.0, 0.0, 0.0, 1.0, -1.0 },
{ 0.0, 0.0, -1.0, 1.0, 0.0, 1.0 },
{ 0.0, 0.0, 0.0, -1.0, 1.0, 0.0 }
}, new double[] { 3.0, 12.0, -1.0, 7.0, 1.0 });
LevenbergMarquardtOptimizer optimizer = new LevenbergMarquardtOptimizer();
VectorialPointValuePair optimum =
optimizer.optimize(problem, problem.target, new double[] { 1, 1, 1, 1, 1 },
new double[] { 2, 2, 2, 2, 2, 2 });
assertEquals(0, optimizer.getRMS(), 1.0e-10);
assertEquals(3.0, optimum.getPointRef()[2], 1.0e-10);
assertEquals(4.0, optimum.getPointRef()[3], 1.0e-10);
assertEquals(5.0, optimum.getPointRef()[4], 1.0e-10);
assertEquals(6.0, optimum.getPointRef()[5], 1.0e-10);
}
public void testRedundantEquations() throws ObjectiveException, OptimizationException {
LinearProblem problem = new LinearProblem(new double[][] {
{ 1.0, 1.0 },
{ 1.0, -1.0 },
{ 1.0, 3.0 }
}, new double[] { 3.0, 1.0, 5.0 });
LevenbergMarquardtOptimizer optimizer = new LevenbergMarquardtOptimizer();
VectorialPointValuePair optimum =
optimizer.optimize(problem, problem.target, new double[] { 1, 1, 1 },
new double[] { 1, 1 });
assertEquals(0, optimizer.getRMS(), 1.0e-10);
assertEquals(2.0, optimum.getPointRef()[0], 1.0e-10);
assertEquals(1.0, optimum.getPointRef()[1], 1.0e-10);
}
public void testInconsistentEquations() throws ObjectiveException, OptimizationException {
LinearProblem problem = new LinearProblem(new double[][] {
{ 1.0, 1.0 },
{ 1.0, -1.0 },
{ 1.0, 3.0 }
}, new double[] { 3.0, 1.0, 4.0 });
LevenbergMarquardtOptimizer optimizer = new LevenbergMarquardtOptimizer();
optimizer.optimize(problem, problem.target, new double[] { 1, 1, 1 }, new double[] { 1, 1 });
assertTrue(optimizer.getRMS() > 0.1);
}
public void testInconsistentSizes() throws ObjectiveException, OptimizationException {
LinearProblem problem =
new LinearProblem(new double[][] { { 1, 0 }, { 0, 1 } }, new double[] { -1, 1 });
LevenbergMarquardtOptimizer optimizer = new LevenbergMarquardtOptimizer();
VectorialPointValuePair optimum =
optimizer.optimize(problem, problem.target, new double[] { 1, 1 }, new double[] { 0, 0 });
assertEquals(0, optimizer.getRMS(), 1.0e-10);
assertEquals(-1, optimum.getPoint()[0], 1.0e-10);
assertEquals(+1, optimum.getPoint()[1], 1.0e-10);
try {
optimizer.optimize(problem, problem.target,
new double[] { 1 },
new double[] { 0, 0 });
fail("an exception should have been thrown");
} catch (OptimizationException oe) {
// expected behavior
} catch (Exception e) {
fail("wrong exception caught");
}
try {
optimizer.optimize(problem, new double[] { 1 },
new double[] { 1 },
new double[] { 0, 0 });
fail("an exception should have been thrown");
} catch (ObjectiveException oe) {
// expected behavior
} catch (Exception e) {
fail("wrong exception caught");
}
}
public void testControlParameters() throws OptimizationException {
Circle circle = new Circle();
circle.addPoint( 30.0, 68.0);
circle.addPoint( 50.0, -6.0);
circle.addPoint(110.0, -20.0);
circle.addPoint( 35.0, 15.0);
circle.addPoint( 45.0, 97.0);
checkEstimate(circle, 0.1, 10, 1.0e-14, 1.0e-16, 1.0e-10, false);
checkEstimate(circle, 0.1, 10, 1.0e-15, 1.0e-17, 1.0e-10, true);
checkEstimate(circle, 0.1, 5, 1.0e-15, 1.0e-16, 1.0e-10, true);
circle.addPoint(300, -300);
checkEstimate(circle, 0.1, 20, 1.0e-18, 1.0e-16, 1.0e-10, true);
}
private void checkEstimate(VectorialDifferentiableObjectiveFunction problem,
double initialStepBoundFactor, int maxCostEval,
double costRelativeTolerance, double parRelativeTolerance,
double orthoTolerance, boolean shouldFail) {
try {
LevenbergMarquardtOptimizer optimizer = new LevenbergMarquardtOptimizer();
optimizer.setInitialStepBoundFactor(initialStepBoundFactor);
optimizer.setMaxEvaluations(maxCostEval);
optimizer.setCostRelativeTolerance(costRelativeTolerance);
optimizer.setParRelativeTolerance(parRelativeTolerance);
optimizer.setOrthoTolerance(orthoTolerance);
optimizer.optimize(problem, new double[] { 0, 0, 0, 0, 0 }, new double[] { 1, 1, 1, 1, 1 },
new double[] { 98.680, 47.345 });
assertTrue(! shouldFail);
} catch (OptimizationException ee) {
assertTrue(shouldFail);
} catch (ObjectiveException ee) {
assertTrue(shouldFail);
} catch (Exception e) {
fail("wrong exception type caught");
}
}
public void testCircleFitting() throws ObjectiveException, OptimizationException {
Circle circle = new Circle();
circle.addPoint( 30.0, 68.0);
circle.addPoint( 50.0, -6.0);
circle.addPoint(110.0, -20.0);
circle.addPoint( 35.0, 15.0);
circle.addPoint( 45.0, 97.0);
LevenbergMarquardtOptimizer optimizer = new LevenbergMarquardtOptimizer();
VectorialPointValuePair optimum =
optimizer.optimize(circle, new double[] { 0, 0, 0, 0, 0 }, new double[] { 1, 1, 1, 1, 1 },
new double[] { 98.680, 47.345 });
assertTrue(optimizer.getEvaluations() < 10);
assertTrue(optimizer.getJacobianEvaluations() < 10);
double rms = optimizer.getRMS();
assertEquals(1.768262623567235, Math.sqrt(circle.getN()) * rms, 1.0e-10);
Point2D.Double center = new Point2D.Double(optimum.getPointRef()[0], optimum.getPointRef()[1]);
assertEquals(69.96016176931406, circle.getRadius(center), 1.0e-10);
assertEquals(96.07590211815305, center.x, 1.0e-10);
assertEquals(48.13516790438953, center.y, 1.0e-10);
double[][] cov = optimizer.getCovariances();
assertEquals(1.839, cov[0][0], 0.001);
assertEquals(0.731, cov[0][1], 0.001);
assertEquals(cov[0][1], cov[1][0], 1.0e-14);
assertEquals(0.786, cov[1][1], 0.001);
double[] errors = optimizer.guessParametersErrors();
assertEquals(1.384, errors[0], 0.001);
assertEquals(0.905, errors[1], 0.001);
// add perfect measurements and check errors are reduced
double r = circle.getRadius(center);
for (double d= 0; d < 2 * Math.PI; d += 0.01) {
circle.addPoint(center.x + r * Math.cos(d), center.y + r * Math.sin(d));
}
double[] target = new double[circle.getN()];
Arrays.fill(target, 0.0);
double[] weights = new double[circle.getN()];
Arrays.fill(weights, 2.0);
optimum =
optimizer.optimize(circle, target, weights, new double[] { 98.680, 47.345 });
cov = optimizer.getCovariances();
assertEquals(0.0016, cov[0][0], 0.001);
assertEquals(3.2e-7, cov[0][1], 1.0e-9);
assertEquals(cov[0][1], cov[1][0], 1.0e-14);
assertEquals(0.0016, cov[1][1], 0.001);
errors = optimizer.guessParametersErrors();
assertEquals(0.002, errors[0], 0.001);
assertEquals(0.002, errors[1], 0.001);
}
public void testCircleFittingBadInit() throws ObjectiveException, OptimizationException {
Circle circle = new Circle();
double[][] points = new double[][] {
{-0.312967, 0.072366}, {-0.339248, 0.132965}, {-0.379780, 0.202724},
{-0.390426, 0.260487}, {-0.361212, 0.328325}, {-0.346039, 0.392619},
{-0.280579, 0.444306}, {-0.216035, 0.470009}, {-0.149127, 0.493832},
{-0.075133, 0.483271}, {-0.007759, 0.452680}, { 0.060071, 0.410235},
{ 0.103037, 0.341076}, { 0.118438, 0.273884}, { 0.131293, 0.192201},
{ 0.115869, 0.129797}, { 0.072223, 0.058396}, { 0.022884, 0.000718},
{-0.053355, -0.020405}, {-0.123584, -0.032451}, {-0.216248, -0.032862},
{-0.278592, -0.005008}, {-0.337655, 0.056658}, {-0.385899, 0.112526},
{-0.405517, 0.186957}, {-0.415374, 0.262071}, {-0.387482, 0.343398},
{-0.347322, 0.397943}, {-0.287623, 0.458425}, {-0.223502, 0.475513},
{-0.135352, 0.478186}, {-0.061221, 0.483371}, { 0.003711, 0.422737},
{ 0.065054, 0.375830}, { 0.108108, 0.297099}, { 0.123882, 0.222850},
{ 0.117729, 0.134382}, { 0.085195, 0.056820}, { 0.029800, -0.019138},
{-0.027520, -0.072374}, {-0.102268, -0.091555}, {-0.200299, -0.106578},
{-0.292731, -0.091473}, {-0.356288, -0.051108}, {-0.420561, 0.014926},
{-0.471036, 0.074716}, {-0.488638, 0.182508}, {-0.485990, 0.254068},
{-0.463943, 0.338438}, {-0.406453, 0.404704}, {-0.334287, 0.466119},
{-0.254244, 0.503188}, {-0.161548, 0.495769}, {-0.075733, 0.495560},
{ 0.001375, 0.434937}, { 0.082787, 0.385806}, { 0.115490, 0.323807},
{ 0.141089, 0.223450}, { 0.138693, 0.131703}, { 0.126415, 0.049174},
{ 0.066518, -0.010217}, {-0.005184, -0.070647}, {-0.080985, -0.103635},
{-0.177377, -0.116887}, {-0.260628, -0.100258}, {-0.335756, -0.056251},
{-0.405195, -0.000895}, {-0.444937, 0.085456}, {-0.484357, 0.175597},
{-0.472453, 0.248681}, {-0.438580, 0.347463}, {-0.402304, 0.422428},
{-0.326777, 0.479438}, {-0.247797, 0.505581}, {-0.152676, 0.519380},
{-0.071754, 0.516264}, { 0.015942, 0.472802}, { 0.076608, 0.419077},
{ 0.127673, 0.330264}, { 0.159951, 0.262150}, { 0.153530, 0.172681},
{ 0.140653, 0.089229}, { 0.078666, 0.024981}, { 0.023807, -0.037022},
{-0.048837, -0.077056}, {-0.127729, -0.075338}, {-0.221271, -0.067526}
};
double[] target = new double[points.length];
Arrays.fill(target, 0.0);
double[] weights = new double[points.length];
Arrays.fill(weights, 2.0);
for (int i = 0; i < points.length; ++i) {
circle.addPoint(points[i][0], points[i][1]);
}
LevenbergMarquardtOptimizer optimizer = new LevenbergMarquardtOptimizer();
optimizer.setConvergenceChecker(new SimpleVectorialValueChecker(1.0e-10, 1.0e-10));
VectorialPointValuePair optimum =
optimizer.optimize(circle, target, weights, new double[] { -12, -12 });
Point2D.Double center = new Point2D.Double(optimum.getPointRef()[0], optimum.getPointRef()[1]);
assertTrue(optimizer.getEvaluations() < 25);
assertTrue(optimizer.getJacobianEvaluations() < 20);
assertEquals( 0.043, optimizer.getRMS(), 1.0e-3);
assertEquals( 0.292235, circle.getRadius(center), 1.0e-6);
assertEquals(-0.151738, center.x, 1.0e-6);
assertEquals( 0.2075001, center.y, 1.0e-6);
}
public void testMath199() throws ObjectiveException, OptimizationException {
try {
QuadraticProblem problem = new QuadraticProblem();
problem.addPoint (0, -3.182591015485607);
problem.addPoint (1, -2.5581184967730577);
problem.addPoint (2, -2.1488478161387325);
problem.addPoint (3, -1.9122489313410047);
problem.addPoint (4, 1.7785661310051026);
new LevenbergMarquardtOptimizer().optimize(problem,
new double[] { 0, 0, 0, 0, 0 },
new double[] { 0.0, 4.4e-323, 1.0, 4.4e-323, 0.0 },
new double[] { 0, 0, 0 });
fail("an exception should have been thrown");
} catch (OptimizationException ee) {
// expected behavior
}
}
private static class LinearProblem implements VectorialDifferentiableObjectiveFunction {
private static final long serialVersionUID = 703247177355019415L;
final RealMatrix factors;
final double[] target;
public LinearProblem(double[][] factors, double[] target) {
this.factors = new DenseRealMatrix(factors);
this.target = target;
}
public double[][] jacobian(double[] variables, double[] value) {
return factors.getData();
}
public double[] objective(double[] variables) {
return factors.operate(variables);
}
}
private static class Circle implements VectorialDifferentiableObjectiveFunction {
private static final long serialVersionUID = -4711170319243817874L;
private ArrayList<Point2D.Double> points;
public Circle() {
points = new ArrayList<Point2D.Double>();
}
public void addPoint(double px, double py) {
points.add(new Point2D.Double(px, py));
}
public int getN() {
return points.size();
}
public double getRadius(Point2D.Double center) {
double r = 0;
for (Point2D.Double point : points) {
r += point.distance(center);
}
return r / points.size();
}
public double[][] jacobian(double[] variables, double[] value)
throws ObjectiveException, IllegalArgumentException {
int n = points.size();
Point2D.Double center = new Point2D.Double(variables[0], variables[1]);
// gradient of the optimal radius
double dRdX = 0;
double dRdY = 0;
for (Point2D.Double pk : points) {
double dk = pk.distance(center);
dRdX += (center.x - pk.x) / dk;
dRdY += (center.y - pk.y) / dk;
}
dRdX /= n;
dRdY /= n;
// jacobian of the radius residuals
double[][] jacobian = new double[n][2];
for (int i = 0; i < n; ++i) {
Point2D.Double pi = points.get(i);
double di = pi.distance(center);
jacobian[i][0] = (center.x - pi.x) / di - dRdX;
jacobian[i][1] = (center.y - pi.y) / di - dRdY;
}
return jacobian;
}
public double[] objective(double[] variables)
throws ObjectiveException, IllegalArgumentException {
Point2D.Double center = new Point2D.Double(variables[0], variables[1]);
double radius = getRadius(center);
double[] residuals = new double[points.size()];
for (int i = 0; i < residuals.length; ++i) {
residuals[i] = points.get(i).distance(center) - radius;
}
return residuals;
}
}
private static class QuadraticProblem implements VectorialDifferentiableObjectiveFunction {
private static final long serialVersionUID = -247096133023967957L;
private List<Double> x;
private List<Double> y;
public QuadraticProblem() {
x = new ArrayList<Double>();
y = new ArrayList<Double>();
}
public void addPoint(double x, double y) {
this.x.add(x);
this.y.add(y);
}
public double[][] jacobian(double[] variables, double[] value) {
double[][] jacobian = new double[x.size()][3];
for (int i = 0; i < jacobian.length; ++i) {
jacobian[i][0] = x.get(i) * x.get(i);
jacobian[i][1] = x.get(i);
jacobian[i][2] = 1.0;
}
return jacobian;
}
public double[] objective(double[] variables) {
double[] values = new double[x.size()];
for (int i = 0; i < values.length; ++i) {
values[i] = (variables[0] * x.get(i) + variables[1]) * x.get(i) + variables[2];
}
return values;
}
}
public static Test suite() {
return new TestSuite(LevenbergMarquardtOptimizerTest.class);
}
}

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src/test/org/apache/commons/math/optimization/general/MinpackTest.java
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src/test/org/apache/commons/math/optimization/general/WeightedMeasurementTest.java
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@ -1,124 +0,0 @@
/*
* 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 junit.framework.*;
public class WeightedMeasurementTest
extends TestCase {
public WeightedMeasurementTest(String name) {
super(name);
p1 = null;
p2 = null;
}
public void testConstruction() {
WeightedMeasurement m = new MyMeasurement(3.0, theoretical() + 0.1, this);
checkValue(m.getWeight(), 3.0);
checkValue(m.getMeasuredValue(), theoretical() + 0.1);
}
public void testIgnored() {
WeightedMeasurement m = new MyMeasurement(3.0, theoretical() + 0.1, this);
assertTrue(!m.isIgnored());
m.setIgnored(true);
assertTrue(m.isIgnored());
m.setIgnored(false);
assertTrue(!m.isIgnored());
}
public void testTheory() {
WeightedMeasurement m = new MyMeasurement(3.0, theoretical() + 0.1, this);
checkValue(m.getTheoreticalValue(), theoretical());
checkValue(m.getResidual(), 0.1);
double oldP1 = p1.getEstimate();
p1.setEstimate(oldP1 + m.getResidual() / m.getPartial(p1));
checkValue(m.getResidual(), 0.0);
p1.setEstimate(oldP1);
checkValue(m.getResidual(), 0.1);
double oldP2 = p2.getEstimate();
p2.setEstimate(oldP2 + m.getResidual() / m.getPartial(p2));
checkValue(m.getResidual(), 0.0);
p2.setEstimate(oldP2);
checkValue(m.getResidual(), 0.1);
}
public static Test suite() {
return new TestSuite(WeightedMeasurementTest.class);
}
public void setUp() {
p1 = new EstimatedParameter("p1", 1.0);
p2 = new EstimatedParameter("p2", 2.0);
}
public void tearDown() {
p1 = null;
p2 = null;
}
private void checkValue(double value, double expected) {
assertTrue(Math.abs(value - expected) < 1.0e-10);
}
private double theoretical() {
return 3 * p1.getEstimate() - p2.getEstimate();
}
private double partial(EstimatedParameter p) {
if (p == p1) {
return 3.0;
} else if (p == p2) {
return -1.0;
} else {
return 0.0;
}
}
private static class MyMeasurement
extends WeightedMeasurement {
public MyMeasurement(double weight, double measuredValue,
WeightedMeasurementTest testInstance) {
super(weight, measuredValue);
this.testInstance = testInstance;
}
public double getTheoreticalValue() {
return testInstance.theoretical();
}
public double getPartial(EstimatedParameter p) {
return testInstance.partial(p);
}
private transient WeightedMeasurementTest testInstance;
private static final long serialVersionUID = -246712922500792332L;
}
private EstimatedParameter p1;
private EstimatedParameter p2;
}