net.finmath.optimizer

Class LevenbergMarquardt

java.lang.Object

net.finmath.optimizer.LevenbergMarquardt

All Implemented Interfaces:

java.io.Serializable, java.lang.Cloneable, OptimizerInterface

public abstract class LevenbergMarquardt
extends java.lang.Object
implements java.io.Serializable, java.lang.Cloneable, OptimizerInterface

This class implements a parallel Levenberg Marquardt non-linear least-squares fit algorithm.

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.

The Levenberg-Marquardt solver is implemented in using multi-threading. The calculation of the derivatives (in case a specific implementation of setDerivatives(double[] parameters, double[][] derivatives) is not provided) may be performed in parallel by setting the parameter numberOfThreads.

To use the solver inherit from it and implement the objective function as setValues(double[] parameters, double[] values) where values has to be set to the value of the objective functions for the given parameters.
You may also provide an a derivative for your objective function by additionally overriding the function setDerivatives(double[] parameters, double[][] derivatives), otherwise the solver will calculate the derivative via finite differences.

To reject a point, it is allowed to set an element of values to Double.NaN in the implementation of setValues(double[] parameters, double[] values). Put differently: The solver handles NaN values in values as an error larger than the current one (regardless of the current error) and rejects the point.
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.

The following simple example finds a solution for the equation

Sample linear system of equations.

0.0 * x1 + 1.0 * x2 = 5.0

2.0 * x1 + 1.0 * x2 = 10.0

 
 	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();
 
 

See the example in the main method below.

The class can be initialized to use a multi-threaded valuation. If initialized this way the implementation of setValues 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.

Note: Iteration steps will be logged (java.util.logging) with LogLevel.FINE

See Also:

Serialized Form

Nested Class Summary

Nested classes/interfaces inherited from interface net.finmath.optimizer.OptimizerInterface

OptimizerInterface.ObjectiveFunction

Constructor Summary

Constructors

Constructor and Description
LevenbergMarquardt() Create a Levenberg-Marquardt solver.
LevenbergMarquardt(double[] initialParameters, double[] targetValues, int maxIteration, java.util.concurrent.ExecutorService executorService) Create a Levenberg-Marquardt solver.
LevenbergMarquardt(double[] initialParameters, double[] targetValues, int maxIteration, int numberOfThreads) Create a Levenberg-Marquardt solver.
LevenbergMarquardt(int numberOfThreads) Create a Levenberg-Marquardt solver.
LevenbergMarquardt(java.util.List<java.lang.Number> initialParameters, java.util.List<java.lang.Number> targetValues, int maxIteration, java.util.concurrent.ExecutorService executorService) Create a Levenberg-Marquardt solver.
LevenbergMarquardt(java.util.List<java.lang.Number> initialParameters, java.util.List<java.lang.Number> targetValues, int maxIteration, int numberOfThreads) Create a Levenberg-Marquardt solver.

Method Summary

Modifier and Type	Method and Description
LevenbergMarquardt	clone() Create a clone of this LevenbergMarquardt optimizer.
double[]	getBestFitParameters() Get the best fit parameter vector.
LevenbergMarquardt	getCloneWithModifiedTargetValues(double[] newTargetVaues, double[] newWeights, boolean isUseBestParametersAsInitialParameters) Create a clone of this LevenbergMarquardt optimizer with a new vector for the target values and weights.
LevenbergMarquardt	getCloneWithModifiedTargetValues(java.util.List<java.lang.Number> newTargetVaues, java.util.List<java.lang.Number> newWeights, boolean isUseBestParametersAsInitialParameters) Create a clone of this LevenbergMarquardt optimizer with a new vector for the target values and weights.
int	getIterations() Get the number of iterations.
double	getMeanSquaredError(double[] value)
double	getRootMeanSquaredError()
static void	main(java.lang.String[] args)
void	run() Runs the optimization.
void	setDerivatives(double[] parameters, double[][] derivatives) The derivative of the objective function.
void	setErrorMeanSquaredCurrent(double errorMeanSquaredCurrent)
LevenbergMarquardt	setErrorTolerance(double errorTolerance) Set the error tolerance.
LevenbergMarquardt	setInitialParameters(double[] initialParameters) Set the initial parameters for the solver.
LevenbergMarquardt	setMaxIteration(int maxIteration) Set the maximum number of iterations to be performed until the solver gives up.
LevenbergMarquardt	setParameterSteps(double[] parameterSteps) Set the parameter step for the solver.
LevenbergMarquardt	setTargetValues(double[] targetValues) Set the target values for the solver.
abstract void	setValues(double[] parameters, double[] values) The objective function.
LevenbergMarquardt	setWeights(double[] weights) Set the weight for the objective function.

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

LevenbergMarquardt

public LevenbergMarquardt(double[] initialParameters,
                          double[] targetValues,
                          int maxIteration,
                          java.util.concurrent.ExecutorService executorService)

Create a Levenberg-Marquardt solver.

Parameters:

initialParameters - Initial value for the parameters where the solver starts its search.

targetValues - Target values to achieve.

maxIteration - Maximum number of iterations.

executorService - Executor to be used for concurrent valuation of the derivatives. This is only performed if setDerivative is not overwritten. Warning: The implementation of setValues has to be thread safe!

LevenbergMarquardt

public LevenbergMarquardt(double[] initialParameters,
                          double[] targetValues,
                          int maxIteration,
                          int numberOfThreads)

Create a Levenberg-Marquardt solver.

Parameters:

initialParameters - Initial value for the parameters where the solver starts its search.

targetValues - Target values to achieve.

maxIteration - Maximum number of iterations.

numberOfThreads - Maximum number of threads. Warning: If this number is larger than one, the implementation of setValues has to be thread safe!

LevenbergMarquardt

public LevenbergMarquardt(java.util.List<java.lang.Number> initialParameters,
                          java.util.List<java.lang.Number> targetValues,
                          int maxIteration,
                          java.util.concurrent.ExecutorService executorService)

Create a Levenberg-Marquardt solver.

Parameters:

initialParameters - List of initial values for the parameters where the solver starts its search.

targetValues - List of target values to achieve.

maxIteration - Maximum number of iterations.

executorService - Executor to be used for concurrent valuation of the derivatives. This is only performed if setDerivative is not overwritten. Warning: The implementation of setValues has to be thread safe!

LevenbergMarquardt

public LevenbergMarquardt(java.util.List<java.lang.Number> initialParameters,
                          java.util.List<java.lang.Number> targetValues,
                          int maxIteration,
                          int numberOfThreads)

Create a Levenberg-Marquardt solver.

Parameters:

initialParameters - Initial value for the parameters where the solver starts its search.

targetValues - Target values to achieve.

maxIteration - Maximum number of iterations.

numberOfThreads - Maximum number of threads. Warning: If this number is larger than one, the implementation of setValues has to be thread safe!

LevenbergMarquardt

public LevenbergMarquardt()

Create a Levenberg-Marquardt solver.

LevenbergMarquardt

public LevenbergMarquardt(int numberOfThreads)

Create a Levenberg-Marquardt solver.

Parameters:

numberOfThreads - Maximum number of threads. Warning: If this number is larger than one, the implementation of setValues has to be thread safe!

Method Detail

main

public static void main(java.lang.String[] args)
                 throws SolverException,
                        java.lang.CloneNotSupportedException

Throws:

SolverException

java.lang.CloneNotSupportedException

setInitialParameters

public LevenbergMarquardt setInitialParameters(double[] initialParameters)

Set the initial parameters for the solver.

Parameters:

initialParameters - The initial parameters.

Returns:

A self reference.

setParameterSteps

public LevenbergMarquardt setParameterSteps(double[] parameterSteps)

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.

Parameters:

parameterSteps - The parameter step.

Returns:

A self reference.

setTargetValues

public LevenbergMarquardt setTargetValues(double[] targetValues)

Set the target values for the solver. The solver will solver the equation weights * objectiveFunction = targetValues.

Parameters:

targetValues - The target values.

Returns:

A self reference.

setMaxIteration

public LevenbergMarquardt setMaxIteration(int maxIteration)

Set the maximum number of iterations to be performed until the solver gives up.

Parameters:

maxIteration - The maximum number of iterations.

Returns:

A self reference.

setWeights

public LevenbergMarquardt setWeights(double[] weights)

Set the weight for the objective function.

Parameters:

weights - The weights for the objective function.

Returns:

A self reference.

setErrorTolerance

public LevenbergMarquardt setErrorTolerance(double errorTolerance)

Set the error tolerance. The solver considers the solution "found" if the error is not improving by this given error tolerance.

Parameters:

errorTolerance - The error tolerance.

Returns:

A self reference.

getBestFitParameters

public double[] getBestFitParameters()

Description copied from interface: OptimizerInterface

Get the best fit parameter vector.

Specified by:

getBestFitParameters in interface OptimizerInterface

Returns:

The best fit parameter.

getRootMeanSquaredError

public double getRootMeanSquaredError()

Specified by:

getRootMeanSquaredError in interface OptimizerInterface

Returns:

the the root mean square error of achieved with the the best fit parameter

setErrorMeanSquaredCurrent

public void setErrorMeanSquaredCurrent(double errorMeanSquaredCurrent)

Parameters:

errorMeanSquaredCurrent - the errorMeanSquaredCurrent to set

getIterations

public int getIterations()

Description copied from interface: OptimizerInterface

Get the number of iterations.

Specified by:

getIterations in interface OptimizerInterface

Returns:

The number of iterations required

setValues

public abstract void setValues(double[] parameters,
                               double[] values)
                        throws SolverException

The objective function. Override this method to implement your custom function.

Parameters:

parameters - Input value. The parameter vector.

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 cause() method.

setDerivatives

public void setDerivatives(double[] parameters,
                           double[][] derivatives)
                    throws SolverException

The derivative of the objective function. You may override this method if you like to implement your own derivative.

Parameters:

parameters - Input value. The parameter vector.

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 cause() method.

run

public void run()
         throws SolverException

Description copied from interface: OptimizerInterface

Runs the optimization.

Specified by:

run in interface OptimizerInterface

Throws:

SolverException - Thrown if the valuation fails, specific cause may be available via the cause() method.

getMeanSquaredError

public double getMeanSquaredError(double[] value)

clone

public LevenbergMarquardt clone()
                         throws java.lang.CloneNotSupportedException

Create a clone of this LevenbergMarquardt optimizer. The clone will use the same objective function than this implementation, i.e., the implementation of setValues(double[], double[]) and that of setDerivatives(double[], double[][]) is reused.

Overrides:

clone in class java.lang.Object

Throws:

java.lang.CloneNotSupportedException

getCloneWithModifiedTargetValues

public LevenbergMarquardt getCloneWithModifiedTargetValues(double[] newTargetVaues,
                                                           double[] newWeights,
                                                           boolean isUseBestParametersAsInitialParameters)
                                                    throws java.lang.CloneNotSupportedException

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 setValues(double[], double[]) and that of 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 done().

Parameters:

newTargetVaues - New array of target values.

newWeights - New array of weights.

isUseBestParametersAsInitialParameters - If true and this optimizer is done(), then the clone will use this.getBestFitParameters() as initial parameters.

Returns:

A new LevenbergMarquardt optimizer, cloning this one except modified target values and weights.

Throws:

java.lang.CloneNotSupportedException - Thrown if this optimizer cannot be cloned.

getCloneWithModifiedTargetValues

public LevenbergMarquardt getCloneWithModifiedTargetValues(java.util.List<java.lang.Number> newTargetVaues,
                                                           java.util.List<java.lang.Number> newWeights,
                                                           boolean isUseBestParametersAsInitialParameters)
                                                    throws java.lang.CloneNotSupportedException

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 setValues(double[], double[]) and that of 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 done().

Parameters:

newTargetVaues - New list of target values.

newWeights - New list of weights.

isUseBestParametersAsInitialParameters - If true and this optimizer is done(), then the clone will use this.getBestFitParameters() as initial parameters.

Returns:

A new LevenbergMarquardt optimizer, cloning this one except modified target values and weights.

Throws:

java.lang.CloneNotSupportedException - Thrown if this optimizer cannot be cloned.