LevenbergMarquardt.java
/*
* (c) Copyright Christian P. Fries, Germany. Contact: email@christian-fries.de.
*
* Created on 16.06.2006
*/
package net.finmath.optimizer;
import java.io.Serializable;
import java.util.Arrays;
import java.util.List;
import java.util.Vector;
import java.util.concurrent.Callable;
import java.util.concurrent.ExecutionException;
import java.util.concurrent.ExecutorService;
import java.util.concurrent.Executors;
import java.util.concurrent.Future;
import java.util.concurrent.FutureTask;
import java.util.logging.Level;
import java.util.logging.Logger;
import net.finmath.functions.LinearAlgebra;
/**
* This class implements a parallel Levenberg-Marquardt non-linear least-squares fit
* algorithm.
*
* <p>
* The solver minimizes \( || f ||_{L_{2}} \) for a function \( f:\mathbb{R}^n \rightarrow \mathbb{R}^m \).
* The solver requires the calculation of a Jacobi-matrix \( J = \frac{\mathrm{d}f}{\mathrm{d}x} \). The iteration steps
* are then defined by
* \[
* \Delta x = H_{\lambda}^{-1} J^T f
* \]
* where \( H_{\lambda} \) is a regularized approximation of the Hessian matrix.
* The solver supports two different regularizations. For <code>RegularizationMethod.LEVENBERG</code> the solver uses
* \( H_{\lambda} = J^T J + \lambda I \). For <code>RegularizationMethod.LEVENBERG_MARQUARDT</code> the solver uses
* \( H_{\lambda} = J^T J + \lambda \text{diag}(J^T J) \).
* </p>
*
* <p>
* The design avoids the need to define the objective function as a
* separate class. The objective function is defined by overriding a class
* method, see the sample code below.
* </p>
* <p>
* The Levenberg-Marquardt solver is implemented in using multi-threading.
* The calculation of the derivatives (in case a specific implementation of
* {@code setDerivatives(double[] parameters, double[][] derivatives)} is not
* provided) may be performed in parallel by setting the parameter <code>numberOfThreads</code>.
* </p>
*
* <p>
* To use the solver inherit from it and implement the objective function as
* {@code setValues(double[] parameters, double[] values)} where values has
* to be set to the value of the objective functions for the given parameters.
* <br>
* You may also provide an a derivative for your objective function by
* additionally overriding the function {@code setDerivatives(double[] parameters, double[][] derivatives)},
* otherwise the solver will calculate the derivative via finite differences.
* </p>
* <p>
* To reject a point, it is allowed to set an element of <code>values</code> to {@link java.lang.Double#NaN}
* in the implementation of {@code setValues(double[] parameters, double[] values)}.
* Put differently: The solver handles NaN values in <code>values</code> as an error larger than
* the current one (regardless of the current error) and rejects the point.
* <br>
* Note, however, that is is an error if the initial parameter guess results in an NaN value.
* That is, the solver should be initialized with an initial parameter in an admissible region.
* </p>
*
* The following simple example finds a solution for the equation <br>
* <table>
* <caption>Sample linear system of equations.</caption>
* <tr><td>
* 0.0 * x<sub>1</sub> + 1.0 * x<sub>2</sub> = 5.0
* </td></tr>
* <tr><td>
* 2.0 * x<sub>1</sub> + 1.0 * x<sub>2</sub> = 10.0
* </td></tr>
* </table>
*
* <pre>
* <code>
* LevenbergMarquardt optimizer = new LevenbergMarquardt() {
* // Override your objective function here
* public void setValues(double[] parameters, double[] values) {
* values[0] = parameters[0] * 0.0 + parameters[1];
* values[1] = parameters[0] * 2.0 + parameters[1];
* }
* };
*
* // Set solver parameters
* optimizer.setInitialParameters(new double[] { 0, 0 });
* optimizer.setWeights(new double[] { 1, 1 });
* optimizer.setMaxIteration(100);
* optimizer.setTargetValues(new double[] { 5, 10 });
*
* optimizer.run();
*
* double[] bestParameters = optimizer.getBestFitParameters();
* </code>
* </pre>
*
* See the example in the main method below.
*
* <p>
* The class can be initialized to use a multi-threaded valuation. If initialized
* this way the implementation of <code>setValues</code> must be thread-safe.
* The solver will evaluate the gradient of the value vector in parallel, i.e.,
* use as many threads as the number of parameters.
* </p>
*
* Note: Iteration steps will be logged (java.util.logging) with LogLevel.FINE
*
* @author Christian Fries
* @version 1.6
*/
public abstract class LevenbergMarquardt implements Serializable, Cloneable, Optimizer {
private static final long serialVersionUID = 4560864869394838155L;
/**
* The regularization method used to invert the approximation of the
* Hessian matrix.
*
* @author Christian Fries
*/
public enum RegularizationMethod {
/**
* The Hessian approximated and regularized as
* \( H_{\lambda} = J^T J + \lambda I \).
*/
LEVENBERG,
/**
* The Hessian approximated and regularized as
* \( H_{\lambda} = J^T J + \lambda \text{diag}(J^T J) \).
*/
LEVENBERG_MARQUARDT
}
private final RegularizationMethod regularizationMethod;
private double[] initialParameters = null;
private double[] parameterSteps = null;
private double[] targetValues = null;
private double[] weights = null;
private int maxIteration = 100;
private double lambda = 0.001;
private double lambdaDivisor = 3.0;
private double lambdaMultiplicator = 2.0;
private double errorRootMeanSquaredTolerance = 0.0; // by default we solve upto machine presicion
private int iteration = 0;
private double[] parameterTest = null;
private double[] parameterIncrement = null;
private double[] valueTest = null;
private double[] parameterCurrent = null;
private double[] valueCurrent = null;
private double[][] derivativeCurrent = null;
private double errorMeanSquaredCurrent = Double.POSITIVE_INFINITY;
private double errorRootMeanSquaredChange = Double.POSITIVE_INFINITY;
private boolean isParameterCurrentDerivativeValid = false;
// These members will be updated in each iteration. These are members to prevent repeated memory allocation.
private double[][] hessianMatrix = null;
private double[] beta = null;
/*
* Used for multi-threadded calculation of the derivative.
* The use may provide its own executor. If not and numberOfThreads > 1
* we will temporarily create an executor with the specified number of threads.
* Note: If an executor was provided upon construction, it will not receive a shutdown when done.
*/
private int numberOfThreads = 1;
private ExecutorService executor = null;
private boolean executorShutdownWhenDone = true;
private final Logger logger = Logger.getLogger("net.finmath");
// A simple test
public static void main(final String[] args) throws SolverException, CloneNotSupportedException {
final LevenbergMarquardt optimizer = new LevenbergMarquardt() {
private static final long serialVersionUID = -282626938650139518L;
// Override your objective function here
@Override
public void setValues(final double[] parameters, final double[] values) {
values[0] = parameters[0] * 0.0 + parameters[1];
values[1] = parameters[0] * 2.0 + parameters[1];
}
};
// Set solver parameters
optimizer.setInitialParameters(new double[] { 0, 0 });
optimizer.setWeights(new double[] { 1, 1 });
optimizer.setMaxIteration(100);
optimizer.setTargetValues(new double[] { 5, 10 });
optimizer.run();
final double[] bestParameters = optimizer.getBestFitParameters();
System.out.println("The solver for problem 1 required " + optimizer.getIterations() + " iterations. The best fit parameters are:");
for (int i = 0; i < bestParameters.length; i++) {
System.out.println("\tparameter[" + i + "]: " + bestParameters[i]);
}
/*
* Creating a clone, continuing the search with new target values.
* Note that we do not re-define the setValues method.
*/
final Optimizer optimizer2 = optimizer.getCloneWithModifiedTargetValues(new double[] { 5.1, 10.2 }, new double[] { 1, 1 }, true);
optimizer2.run();
final double[] bestParameters2 = optimizer2.getBestFitParameters();
System.out.println("The solver for problem 2 required " + optimizer2.getIterations() + " iterations. The best fit parameters are:");
for (int i = 0; i < bestParameters2.length; i++) {
System.out.println("\tparameter[" + i + "]: " + bestParameters2[i]);
}
}
/**
* Create a Levenberg-Marquardt solver.
*
* @param regularizationMethod The regularization method to use. See {@link RegularizationMethod}.
* @param initialParameters Initial value for the parameters where the solver starts its search.
* @param targetValues Target values to achieve.
* @param maxIteration Maximum number of iterations.
* @param executorService Executor to be used for concurrent valuation of the derivatives. This is only performed if setDerivative is not overwritten. <i>Warning</i>: The implementation of setValues has to be thread safe!
*/
public LevenbergMarquardt(final RegularizationMethod regularizationMethod, final double[] initialParameters, final double[] targetValues, final int maxIteration, final ExecutorService executorService) {
super();
this.regularizationMethod = regularizationMethod;
this.initialParameters = initialParameters;
this.targetValues = targetValues;
this.maxIteration = maxIteration;
weights = new double[targetValues.length];
java.util.Arrays.fill(weights, 1.0);
executor = executorService;
executorShutdownWhenDone = (executorService == null);
numberOfThreads = 1;
}
/**
* Create a Levenberg-Marquardt solver.
*
* @param initialParameters Initial value for the parameters where the solver starts its search.
* @param targetValues Target values to achieve.
* @param maxIteration Maximum number of iterations.
* @param executorService Executor to be used for concurrent valuation of the derivatives. This is only performed if setDerivative is not overwritten. <i>Warning</i>: The implementation of setValues has to be thread safe!
*/
public LevenbergMarquardt(final double[] initialParameters, final double[] targetValues, final int maxIteration, final ExecutorService executorService) {
this(RegularizationMethod.LEVENBERG_MARQUARDT,
initialParameters, targetValues, maxIteration, executorService);
}
/**
* Create a Levenberg-Marquardt solver.
*
* @param regularizationMethod The regularization method to use. See {@link RegularizationMethod}.
* @param initialParameters Initial value for the parameters where the solver starts its search.
* @param targetValues Target values to achieve.
* @param maxIteration Maximum number of iterations.
* @param numberOfThreads Maximum number of threads. <i>Warning</i>: If this number is larger than one, the implementation of setValues has to be thread safe!
*/
public LevenbergMarquardt(final RegularizationMethod regularizationMethod, final double[] initialParameters, final double[] targetValues, final int maxIteration, final int numberOfThreads) {
this(regularizationMethod, initialParameters, targetValues, maxIteration, null);
this.numberOfThreads = numberOfThreads;
}
/**
* Create a Levenberg-Marquardt solver.
*
* @param initialParameters Initial value for the parameters where the solver starts its search.
* @param targetValues Target values to achieve.
* @param maxIteration Maximum number of iterations.
* @param numberOfThreads Maximum number of threads. <i>Warning</i>: If this number is larger than one, the implementation of setValues has to be thread safe!
*/
public LevenbergMarquardt(final double[] initialParameters, final double[] targetValues, final int maxIteration, final int numberOfThreads) {
this(RegularizationMethod.LEVENBERG_MARQUARDT, initialParameters, targetValues, maxIteration, numberOfThreads);
}
/**
* Create a Levenberg-Marquardt solver.
*
* @param initialParameters List of initial values for the parameters where the solver starts its search.
* @param targetValues List of target values to achieve.
* @param maxIteration Maximum number of iterations.
* @param executorService Executor to be used for concurrent valuation of the derivatives. This is only performed if setDerivative is not overwritten. <i>Warning</i>: The implementation of setValues has to be thread safe!
*/
public LevenbergMarquardt(final List<Number> initialParameters, final List<Number> targetValues, final int maxIteration, final ExecutorService executorService) {
this(numberListToDoubleArray(initialParameters), numberListToDoubleArray(targetValues), maxIteration, executorService);
}
/**
* Create a Levenberg-Marquardt solver.
*
* @param initialParameters Initial value for the parameters where the solver starts its search.
* @param targetValues Target values to achieve.
* @param maxIteration Maximum number of iterations.
* @param numberOfThreads Maximum number of threads. <i>Warning</i>: If this number is larger than one, the implementation of setValues has to be thread safe!
*/
public LevenbergMarquardt(final List<Number> initialParameters, final List<Number> targetValues, final int maxIteration, final int numberOfThreads) {
this(initialParameters, targetValues, maxIteration, null);
this.numberOfThreads = numberOfThreads;
}
/**
* Create a Levenberg-Marquardt solver.
*/
public LevenbergMarquardt() {
super();
regularizationMethod = RegularizationMethod.LEVENBERG_MARQUARDT;
}
/**
* Convert a list of numbers to an array of doubles.
*
* @param listOfNumbers A list of numbers.
* @return A corresponding array of doubles executing <code>doubleValue()</code> on each element.
*/
private static double[] numberListToDoubleArray(final List<Number> listOfNumbers) {
final double[] arrayOfDoubles = new double[listOfNumbers.size()];
for(int i=0; i<arrayOfDoubles.length; i++) {
arrayOfDoubles[i] = listOfNumbers.get(i).doubleValue();
}
return arrayOfDoubles;
}
/**
* Create a Levenberg-Marquardt solver.
*
* @param numberOfThreads Maximum number of threads. <i>Warning</i>: If this number is larger than one, the implementation of setValues has to be thread safe!
*/
public LevenbergMarquardt(final int numberOfThreads) {
super();
regularizationMethod = RegularizationMethod.LEVENBERG_MARQUARDT;
this.numberOfThreads = numberOfThreads;
}
/**
* Set the initial parameters for the solver.
*
* @param initialParameters The initial parameters.
* @return A self reference.
*/
public LevenbergMarquardt setInitialParameters(final double[] initialParameters) {
if(done()) {
throw new UnsupportedOperationException("Solver cannot be modified after it has run.");
}
this.initialParameters = initialParameters;
return this;
}
/**
* Set the parameter step for the solver.
* The parameter step is used to evaluate the derivatives via
* finite differences, if analytic derivatives are not provided.
*
* @param parameterSteps The parameter step.
* @return A self reference.
*/
public LevenbergMarquardt setParameterSteps(final double[] parameterSteps) {
if(done()) {
throw new UnsupportedOperationException("Solver cannot be modified after it has run.");
}
this.parameterSteps = parameterSteps;
return this;
}
/**
* Set the target values for the solver. The solver will solver the
* equation weights * objectiveFunction = targetValues.
*
* @param targetValues The target values.
* @return A self reference.
*/
public LevenbergMarquardt setTargetValues(final double[] targetValues) {
if(done()) {
throw new UnsupportedOperationException("Solver cannot be modified after it has run.");
}
this.targetValues = targetValues;
return this;
}
/**
* Set the maximum number of iterations to be performed until the solver
* gives up.
*
* @param maxIteration The maximum number of iterations.
* @return A self reference.
*/
public LevenbergMarquardt setMaxIteration(final int maxIteration) {
if(done()) {
throw new UnsupportedOperationException("Solver cannot be modified after it has run.");
}
this.maxIteration = maxIteration;
return this;
}
/**
* Set the weight for the objective function.
*
* @param weights The weights for the objective function.
* @return A self reference.
*/
public LevenbergMarquardt setWeights(final double[] weights) {
if(done()) {
throw new UnsupportedOperationException("Solver cannot be modified after it has run.");
}
this.weights = weights;
return this;
}
/**
* Set the error tolerance. The solver considers the solution "found"
* if the error is not improving by this given error tolerance.
*
* @param errorTolerance The error tolerance.
* @return A self reference.
*/
public LevenbergMarquardt setErrorTolerance(final double errorTolerance) {
if(done()) {
throw new UnsupportedOperationException("Solver cannot be modified after it has run.");
}
errorRootMeanSquaredTolerance = errorTolerance;
return this;
}
/**
* Get the parameter λ used in the Tikhonov-like regularization of the Hessian matrix,
* that is the \( \lambda \) in \( H + \lambda \diag H \).
*
* @return the parameter \( \lambda \).
*/
public double getLambda() {
return lambda;
}
/**
* Set the parameter λ used in the Tikhonov-like regularization of the Hessian matrix,
* that is the \( \lambda \) in \( H + \lambda \diag H \).
*
* @param lambda the lambda to set
* @return Self reference to this optimizer.
*/
public LevenbergMarquardt setLambda(final double lambda) {
this.lambda = lambda;
return this;
}
/**
* Get the multiplicator applied to lambda if the inversion of regularized
* Hessian fails, that is, if \( H + \lambda \diag H \) is not invertable.
*
* @return the lambdaMultiplicator
*/
public double getLambdaMultiplicator() {
return lambdaMultiplicator;
}
/**
* Set the multiplicator applied to lambda if the inversion of regularized
* Hessian fails, that is, if \( H + \lambda \diag H \) is not invertable.
*
* This will make lambda larger, hence let the stepping move slower.
*
* @param lambdaMultiplicator the lambdaMultiplicator to set. Should be > 1.
*/
public void setLambdaMultiplicator(final double lambdaMultiplicator) {
if(lambdaMultiplicator <= 1.0) {
throw new IllegalArgumentException("Parameter lambdaMultiplicator is required to be > 1.");
}
this.lambdaMultiplicator = lambdaMultiplicator;
}
/**
* Get the divisor applied to lambda (for the next iteration) if the inversion of regularized
* Hessian succeeds, that is, if \( H + \lambda \diag H \) is invertable.
*
* @return the lambdaDivisor
*/
public double getLambdaDivisor() {
return lambdaDivisor;
}
/**
* Set the divisor applied to lambda (for the next iteration) if the inversion of regularized
* Hessian succeeds, that is, if \( H + \lambda \diag H \) is invertable.
*
* This will make lambda smaller, hence let the stepping move faster.
*
* @param lambdaDivisor the lambdaDivisor to set. Should be > 1.
*/
public void setLambdaDivisor(final double lambdaDivisor) {
if(lambdaDivisor <= 1.0) {
throw new IllegalArgumentException("Parameter lambdaDivisor is required to be > 1.");
}
this.lambdaDivisor = lambdaDivisor;
}
@Override
public double[] getBestFitParameters() {
return parameterCurrent;
}
@Override
public double getRootMeanSquaredError() {
return Math.sqrt(errorMeanSquaredCurrent);
}
@Override
public int getIterations() {
return iteration;
}
/**
* The objective function. Override this method to implement your custom
* function.
*
* @param parameters Input value. The parameter vector.
* @param values Output value. The vector of values f(i,parameters), i=1,...,n
* @throws SolverException Thrown if the valuation fails, specific cause may be available via the <code>cause()</code> method.
*/
public abstract void setValues(double[] parameters, double[] values) throws SolverException;
/**
* The derivative of the objective function. You may override this method
* if you like to implement your own derivative.
*
* @param parameters Input value. The parameter vector.
* @param derivatives Output value, where derivatives[i][j] is d(value(j)) / d(parameters(i)
* @throws SolverException Thrown if the valuation fails, specific cause may be available via the <code>cause()</code> method.
*/
public void setDerivatives(final double[] parameters, final double[][] derivatives) throws SolverException {
// Calculate new derivatives. Note that this method is called only with
// parameters = parameterCurrent, so we may use valueCurrent.
final Vector<Future<double[]>> valueFutures = new Vector<>(parameterCurrent.length);
for (int parameterIndex = 0; parameterIndex < parameterCurrent.length; parameterIndex++) {
final double[] parametersNew = parameters.clone();
final double[] derivative = derivatives[parameterIndex];
final int workerParameterIndex = parameterIndex;
final Callable<double[]> worker = new Callable<double[]>() {
@Override
public double[] call() {
double parameterFiniteDifference;
if(parameterSteps != null) {
parameterFiniteDifference = parameterSteps[workerParameterIndex];
}
else {
/*
* Try to adaptively set a parameter shift. Note that in some
* applications it may be important to set parameterSteps.
* appropriately.
*/
parameterFiniteDifference = (Math.abs(parametersNew[workerParameterIndex]) + 1) * 1E-8;
}
// Shift parameter value
parametersNew[workerParameterIndex] += parameterFiniteDifference;
// Calculate derivative as (valueUpShift - valueCurrent) / parameterFiniteDifference
try {
setValues(parametersNew, derivative);
} catch (final Exception e) {
logger.severe("Valuation failed with exeption " + e.getMessage() + "\n" + e.getStackTrace());
// We signal an exception to calculate the derivative as NaN
Arrays.fill(derivative, Double.NaN);
}
for (int valueIndex = 0; valueIndex < valueCurrent.length; valueIndex++) {
derivative[valueIndex] -= valueCurrent[valueIndex];
derivative[valueIndex] /= parameterFiniteDifference;
if(Double.isNaN(derivative[valueIndex])) {
derivative[valueIndex] = 0.0;
}
}
return derivative;
}
};
if(executor != null) {
final Future<double[]> valueFuture = executor.submit(worker);
valueFutures.add(parameterIndex, valueFuture);
}
else {
final FutureTask<double[]> valueFutureTask = new FutureTask<>(worker);
valueFutureTask.run();
valueFutures.add(parameterIndex, valueFutureTask);
}
}
for (int parameterIndex = 0; parameterIndex < parameterCurrent.length; parameterIndex++) {
try {
derivatives[parameterIndex] = valueFutures.get(parameterIndex).get();
}
catch (final InterruptedException | ExecutionException e) {
throw new SolverException(e);
}
}
}
/**
* You may override this method to implement a custom stop condition.
*
* @return Stop condition.
*/
boolean done() {
// The solver terminates if...
return
// Maximum number of iterations is reached
(iteration > maxIteration)
||
// Error does not improve by more that the given error tolerance
(errorRootMeanSquaredChange <= errorRootMeanSquaredTolerance)
||
/*
* Lambda is infinite, i.e., no new point is acceptable.
* For example, this may happen if setValue repeatedly give contains invalid (NaN) values.
*/
Double.isInfinite(lambda);
}
@Override
public void run() throws SolverException {
// Create an executor for concurrent evaluation of derivatives
if(numberOfThreads > 1) {
if(executor == null) {
executor = Executors.newFixedThreadPool(numberOfThreads);
executorShutdownWhenDone = true;
}
}
try {
// Allocate memory
final int numberOfParameters = initialParameters.length;
final int numberOfValues = targetValues.length;
parameterTest = initialParameters.clone();
parameterIncrement = new double[numberOfParameters];
parameterCurrent = new double[numberOfParameters];
valueTest = new double[numberOfValues];
valueCurrent = new double[numberOfValues];
derivativeCurrent = new double[parameterCurrent.length][valueCurrent.length];
hessianMatrix = new double[parameterCurrent.length][parameterCurrent.length];
beta = new double[parameterCurrent.length];
iteration = 0;
while(true) {
// Count iterations
iteration++;
// Calculate values for test parameters
setValues(parameterTest, valueTest);
// Calculate error
final double errorMeanSquaredTest = getMeanSquaredError(valueTest);
/*
* Note: The following test will be false if errorMeanSquaredTest is NaN.
* That is: NaN is considered as a rejected point.
*/
if(errorMeanSquaredTest < errorMeanSquaredCurrent) {
errorRootMeanSquaredChange = Math.sqrt(errorMeanSquaredCurrent) - Math.sqrt(errorMeanSquaredTest);
// Accept point
System.arraycopy(parameterTest, 0, parameterCurrent, 0, parameterCurrent.length);
System.arraycopy(valueTest, 0, valueCurrent, 0, valueCurrent.length);
errorMeanSquaredCurrent = errorMeanSquaredTest;
// Derivative has to be recalculated
isParameterCurrentDerivativeValid = false;
// Decrease lambda (move faster)
lambda /= lambdaDivisor;
} else {
errorRootMeanSquaredChange = Math.sqrt(errorMeanSquaredTest) - Math.sqrt(errorMeanSquaredCurrent);
// Reject point, increase lambda (move slower)
lambda *= lambdaMultiplicator;
}
// Update a new parameter trial, if we are not done
if (!done()) {
updateParameterTest();
} else {
break;
}
// Log iteration
if (logger.isLoggable(Level.FINE))
{
String logString =
"Iteration: " + iteration +
"\tLambda=" + lambda +
"\tError Current (RMS):" + Math.sqrt(errorMeanSquaredCurrent) +
"\tError Change:" + errorRootMeanSquaredChange + "\t";
for (int i = 0; i < parameterCurrent.length; i++) {
logString += "[" + i + "] = " + parameterCurrent[i] + "\t";
}
logger.fine(logString);
}
}
}
finally {
// Shutdown executor if present.
if(executor != null && executorShutdownWhenDone) {
executor.shutdown();
executor = null;
}
}
}
public double getMeanSquaredError(final double[] value) {
double error = 0.0;
for (int valueIndex = 0; valueIndex < value.length; valueIndex++) {
final double deviation = value[valueIndex] - targetValues[valueIndex];
error += weights[valueIndex] * deviation * deviation;
}
return error/value.length;
}
/**
* Calculate a new parameter guess.
*
* @throws SolverException Thrown if the valuation fails, specific cause may be available via the <code>cause()</code> method.
*/
private void updateParameterTest() throws SolverException {
if (!isParameterCurrentDerivativeValid) {
this.setDerivatives(parameterCurrent, derivativeCurrent);
isParameterCurrentDerivativeValid = true;
}
/*
* We solve H \Delta x = b,
* where H = J^T J is the Hessian approximation and b = J^T (y-f(x)) and \Delta x is the parameterIncrement
*/
boolean hessianInvalid = true;
while (hessianInvalid && Double.isFinite(lambda)) {
hessianInvalid = false;
// Build matrix H (Hessian approximation), that is H = J^T J
for (int i = 0; i < parameterCurrent.length; i++) {
for (int j = i; j < parameterCurrent.length; j++) {
double hessianElement = 0.0;
for (int valueIndex = 0; valueIndex < valueCurrent.length; valueIndex++) {
hessianElement += weights[valueIndex] * derivativeCurrent[i][valueIndex] * derivativeCurrent[j][valueIndex];
}
if (i == j) {
if(regularizationMethod == RegularizationMethod.LEVENBERG) {
// RegularizationMethod.LEVENBERG - Regularization with a constant lambda
hessianElement += lambda;
}
else {
// RegularizationMethod.LEVENBERG_MARQUARDT - Regularization with a lambda time the diagonal of J^T J
if (hessianElement == 0.0) {
hessianElement = lambda;
}
else {
hessianElement *= 1 + lambda;
}
}
}
// The matrix is symmetric
hessianMatrix[i][j] = hessianElement;
hessianMatrix[j][i] = hessianElement;
}
}
// Build right hand side beta - gradient decent step: beta = J^T (y-f(x))
for (int i = 0; i < parameterCurrent.length; i++) {
double betaElement = 0.0;
final double[] derivativeCurrentSingleParam = derivativeCurrent[i];
for (int k = 0; k < valueCurrent.length; k++) {
betaElement += weights[k] * (targetValues[k] - valueCurrent[k]) * derivativeCurrentSingleParam[k];
}
beta[i] = betaElement;
}
try {
// Calculate new increment
// parameterIncrement = LinearAlgebra.solveLinearEquationSymmetric(hessianMatrix, beta);
parameterIncrement = LinearAlgebra.solveLinearEquationSVD(hessianMatrix, beta);
} catch (final Exception e) {
// Matrix not invertable, increase lambda
hessianInvalid = true;
lambda *= 16;
}
}
// Calculate new parameter
for (int i = 0; i < parameterCurrent.length; i++) {
parameterTest[i] = parameterCurrent[i] + parameterIncrement[i];
}
}
/**
* Create a clone of this LevenbergMarquardt optimizer.
*
* The clone will use the same objective function than this implementation,
* i.e., the implementation of {@link #setValues(double[], double[])} and
* that of {@link #setDerivatives(double[], double[][])} is reused.
*/
@Override
public LevenbergMarquardt clone() throws CloneNotSupportedException {
final LevenbergMarquardt clonedOptimizer = (LevenbergMarquardt)super.clone();
clonedOptimizer.isParameterCurrentDerivativeValid = false;
clonedOptimizer.iteration = 0;
clonedOptimizer.errorMeanSquaredCurrent = Double.POSITIVE_INFINITY;
clonedOptimizer.errorRootMeanSquaredChange = Double.POSITIVE_INFINITY;
return clonedOptimizer;
}
/**
* Create a clone of this LevenbergMarquardt optimizer with a new vector for the
* target values and weights.
*
* The clone will use the same objective function than this implementation,
* i.e., the implementation of {@link #setValues(double[], double[])} and
* that of {@link #setDerivatives(double[], double[][])} is reused.
*
* The initial values of the cloned optimizer will either be the original
* initial values of this object or the best parameters obtained by this
* optimizer, the latter is used only if this optimized signals a {@link #done()}.
*
* @param newTargetVaues New array of target values.
* @param newWeights New array of weights.
* @param isUseBestParametersAsInitialParameters If true and this optimizer is done(), then the clone will use this.{@link #getBestFitParameters()} as initial parameters.
* @return A new LevenbergMarquardt optimizer, cloning this one except modified target values and weights.
* @throws CloneNotSupportedException Thrown if this optimizer cannot be cloned.
*/
public LevenbergMarquardt getCloneWithModifiedTargetValues(final double[] newTargetVaues, final double[] newWeights, final boolean isUseBestParametersAsInitialParameters) throws CloneNotSupportedException {
final LevenbergMarquardt clonedOptimizer = clone();
clonedOptimizer.targetValues = newTargetVaues.clone(); // Defensive copy
clonedOptimizer.weights = newWeights.clone(); // Defensive copy
if(isUseBestParametersAsInitialParameters && this.done()) {
clonedOptimizer.initialParameters = this.getBestFitParameters();
}
return clonedOptimizer;
}
/**
* Create a clone of this LevenbergMarquardt optimizer with a new vector for the
* target values and weights.
*
* The clone will use the same objective function than this implementation,
* i.e., the implementation of {@link #setValues(double[], double[])} and
* that of {@link #setDerivatives(double[], double[][])} is reused.
*
* The initial values of the cloned optimizer will either be the original
* initial values of this object or the best parameters obtained by this
* optimizer, the latter is used only if this optimized signals a {@link #done()}.
*
* @param newTargetVaues New list of target values.
* @param newWeights New list of weights.
* @param isUseBestParametersAsInitialParameters If true and this optimizer is done(), then the clone will use this.{@link #getBestFitParameters()} as initial parameters.
* @return A new LevenbergMarquardt optimizer, cloning this one except modified target values and weights.
* @throws CloneNotSupportedException Thrown if this optimizer cannot be cloned.
*/
public LevenbergMarquardt getCloneWithModifiedTargetValues(final List<Number> newTargetVaues, final List<Number> newWeights, final boolean isUseBestParametersAsInitialParameters) throws CloneNotSupportedException {
final LevenbergMarquardt clonedOptimizer = clone();
clonedOptimizer.targetValues = numberListToDoubleArray(newTargetVaues);
clonedOptimizer.weights = numberListToDoubleArray(newWeights);
if(isUseBestParametersAsInitialParameters && this.done()) {
clonedOptimizer.initialParameters = this.getBestFitParameters();
}
return clonedOptimizer;
}
}