org.apache.commons.math3.optimization.general

Class AbstractLeastSquaresOptimizer

java.lang.Object

org.apache.commons.math3.optimization.direct.BaseAbstractMultivariateVectorOptimizer<DifferentiableMultivariateVectorFunction>

org.apache.commons.math3.optimization.general.AbstractLeastSquaresOptimizer

All Implemented Interfaces:

BaseMultivariateVectorOptimizer<DifferentiableMultivariateVectorFunction>, BaseOptimizer<PointVectorValuePair>, DifferentiableMultivariateVectorOptimizer

Direct Known Subclasses:

GaussNewtonOptimizer, LevenbergMarquardtOptimizer

public abstract class AbstractLeastSquaresOptimizer
extends BaseAbstractMultivariateVectorOptimizer<DifferentiableMultivariateVectorFunction>
implements DifferentiableMultivariateVectorOptimizer

Base class for implementing least squares optimizers. It handles the boilerplate methods associated to thresholds settings, jacobian and error estimation.
This class uses the DifferentiableMultivariateVectorFunction.jacobian() of the function argument in method optimize and assumes that, in the matrix returned by the value method, the rows iterate on the model functions while the columns iterate on the parameters; thus, the numbers of rows is equal to the length of the target array while the number of columns is equal to the length of the startPoint array.

Since:

1.2

Version:

$Id: AbstractLeastSquaresOptimizer.java 1295552 2012-03-01 13:14:32Z erans $

Field Summary

Fields

Modifier and Type	Field and Description
protected int	cols Number of columns of the jacobian matrix.
protected double	cost Cost value (square root of the sum of the residuals).
protected double[]	objective Current objective function value.
protected double[]	point Current point.
protected int	rows Number of rows of the jacobian matrix.
protected double[][]	weightedResidualJacobian Jacobian matrix of the weighted residuals.
protected double[]	weightedResiduals Weighted residuals

Fields inherited from class org.apache.commons.math3.optimization.direct.BaseAbstractMultivariateVectorOptimizer

evaluations

Constructor Summary

Constructors

Modifier	Constructor and Description
protected	AbstractLeastSquaresOptimizer() Simple constructor with default settings.
protected	AbstractLeastSquaresOptimizer(ConvergenceChecker<PointVectorValuePair> checker)

Method Summary

Methods

Modifier and Type	Method and Description
double	getChiSquare() Get a Chi-Square-like value assuming the N residuals follow N distinct normal distributions centered on 0 and whose variances are the reciprocal of the weights.
double[][]	getCovariances() Get the covariance matrix of the optimized parameters.
double[][]	getCovariances(double threshold) Get the covariance matrix of the optimized parameters.
int	getJacobianEvaluations()
double	getRMS() Get the Root Mean Square value.
double[]	guessParametersErrors() Guess the errors in optimized parameters.
PointVectorValuePair	optimize(int maxEval, DifferentiableMultivariateVectorFunction f, double[] target, double[] weights, double[] startPoint) Optimize an objective function.
protected void	updateJacobian() Update the jacobian matrix.
protected void	updateResidualsAndCost() Update the residuals array and cost function value.

Methods inherited from class org.apache.commons.math3.optimization.direct.BaseAbstractMultivariateVectorOptimizer

computeObjectiveValue, doOptimize, getConvergenceChecker, getEvaluations, getMaxEvaluations, getStartPoint, getTargetRef, getWeightRef

Methods inherited from class java.lang.Object

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

Methods inherited from interface org.apache.commons.math3.optimization.BaseOptimizer

getConvergenceChecker, getEvaluations, getMaxEvaluations

Field Detail

weightedResidualJacobian

protected double[][] weightedResidualJacobian

Jacobian matrix of the weighted residuals. This matrix is in canonical form just after the calls to updateJacobian(), but may be modified by the solver in the derived class (the Levenberg-Marquardt optimizer does this).

cols

protected int cols

Number of columns of the jacobian matrix.

rows

protected int rows

Number of rows of the jacobian matrix.

point

protected double[] point

Current point.

objective

protected double[] objective

Current objective function value.

weightedResiduals

protected double[] weightedResiduals

Weighted residuals

cost

protected double cost

Cost value (square root of the sum of the residuals).

Constructor Detail

AbstractLeastSquaresOptimizer

protected AbstractLeastSquaresOptimizer()

Simple constructor with default settings. The convergence check is set to a SimpleVectorValueChecker.

AbstractLeastSquaresOptimizer

protected AbstractLeastSquaresOptimizer(ConvergenceChecker<PointVectorValuePair> checker)

Parameters:

checker - Convergence checker.

Method Detail

getJacobianEvaluations

public int getJacobianEvaluations()

Returns:

the number of evaluations of the Jacobian function.

updateJacobian

protected void updateJacobian()

Update the jacobian matrix.

Throws:

DimensionMismatchException - if the Jacobian dimension does not match problem dimension.

updateResidualsAndCost

protected void updateResidualsAndCost()

Update the residuals array and cost function value.

Throws:

DimensionMismatchException - if the dimension does not match the problem dimension.

TooManyEvaluationsException - if the maximal number of evaluations is exceeded.

getRMS

public double getRMS()

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 optimizer as follows: if c if the criterion, and n is the number of measurements, then the RMS is sqrt (c/n).

Returns:

RMS value

getChiSquare

public double getChiSquare()

Get a Chi-Square-like value assuming the N residuals follow N distinct normal distributions centered on 0 and whose variances are the reciprocal of the weights.

Returns:

chi-square value

getCovariances

public double[][] getCovariances()

Get the covariance matrix of the optimized parameters.

Returns:

the covariance matrix.

Throws:

SingularMatrixException - if the covariance matrix cannot be computed (singular problem).

See Also:

getCovariances(double)

getCovariances

public double[][] getCovariances(double threshold)

Get the covariance matrix of the optimized parameters.
Note that this operation involves the inversion of the JTJ matrix, where J is the Jacobian matrix. The threshold parameter is a way for the caller to specify that the result of this computation should be considered meaningless, and thus trigger an exception.

Parameters:

threshold - Singularity threshold.

Returns:

the covariance matrix.

Throws:

SingularMatrixException - if the covariance matrix cannot be computed (singular problem).

guessParametersErrors

public double[] guessParametersErrors()

Guess the errors in optimized parameters. Guessing is covariance-based: It only gives a rough order of magnitude.

Returns:

errors in optimized parameters

Throws:

SingularMatrixException - if the covariances matrix cannot be computed.

NumberIsTooSmallException - if the number of degrees of freedom is not positive, i.e. the number of measurements is less or equal to the number of parameters.

optimize

public PointVectorValuePair optimize(int maxEval,
                            DifferentiableMultivariateVectorFunction f,
                            double[] target,
                            double[] weights,
                            double[] startPoint)

Optimize an objective function. Optimization is considered to be a weighted least-squares minimization. The cost function to be minimized is ∑weighti(objectivei - targeti)2

Specified by:

optimize in interface BaseMultivariateVectorOptimizer<DifferentiableMultivariateVectorFunction>

Overrides:

optimize in class BaseAbstractMultivariateVectorOptimizer<DifferentiableMultivariateVectorFunction>

Parameters:

maxEval - Maximum number of function evaluations.

f - Objective function.

target - Target value for the objective functions at optimum.

weights - Weights for the least squares cost computation.

startPoint - Start point for optimization.

Returns:

the point/value pair giving the optimal value for objective function.