org.apache.commons.math3.optim.nonlinear.vector.jacobian

Class AbstractLeastSquaresOptimizer

java.lang.Object

org.apache.commons.math3.optim.BaseOptimizer<PAIR>

org.apache.commons.math3.optim.BaseMultivariateOptimizer<PointVectorValuePair>

org.apache.commons.math3.optim.nonlinear.vector.MultivariateVectorOptimizer

org.apache.commons.math3.optim.nonlinear.vector.JacobianMultivariateVectorOptimizer

org.apache.commons.math3.optim.nonlinear.vector.jacobian.AbstractLeastSquaresOptimizer

Direct Known Subclasses:

GaussNewtonOptimizer, LevenbergMarquardtOptimizer

public abstract class AbstractLeastSquaresOptimizer
extends JacobianMultivariateVectorOptimizer

Base class for implementing least-squares optimizers. It provides methods for error estimation.

Since:

3.1

Version:

$Id: AbstractLeastSquaresOptimizer.java 1443444 2013-02-07 12:41:36Z erans $

Field Summary

Fields inherited from class org.apache.commons.math3.optim.BaseOptimizer

evaluations, iterations

Constructor Summary

Constructors

Modifier	Constructor and Description
protected	AbstractLeastSquaresOptimizer(ConvergenceChecker<PointVectorValuePair> checker)

Method Summary

Methods

Modifier and Type	Method and Description
protected double	computeCost(double[] residuals) Computes the cost.
double[][]	computeCovariances(double[] params, double threshold) Get the covariance matrix of the optimized parameters.
protected double[]	computeResiduals(double[] objectiveValue) Computes the residuals.
double[]	computeSigma(double[] params, double covarianceSingularityThreshold) Computes an estimate of the standard deviation of the parameters.
protected RealMatrix	computeWeightedJacobian(double[] params) Computes the weighted Jacobian matrix.
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	getRMS() Gets the root-mean-square (RMS) value.
RealMatrix	getWeightSquareRoot() Gets the square-root of the weight matrix.
PointVectorValuePair	optimize(OptimizationData... optData) Stores data and performs the optimization.
protected void	parseOptimizationData(OptimizationData... optData) Scans the list of (required and optional) optimization data that characterize the problem.
protected void	setCost(double cost) Sets the cost.

Methods inherited from class org.apache.commons.math3.optim.nonlinear.vector.JacobianMultivariateVectorOptimizer

computeJacobian

Methods inherited from class org.apache.commons.math3.optim.nonlinear.vector.MultivariateVectorOptimizer

computeObjectiveValue, getTarget, getTargetSize, getWeight

Methods inherited from class org.apache.commons.math3.optim.BaseMultivariateOptimizer

getLowerBound, getStartPoint, getUpperBound

Methods inherited from class org.apache.commons.math3.optim.BaseOptimizer

doOptimize, getConvergenceChecker, getEvaluations, getIterations, getMaxEvaluations, getMaxIterations, incrementEvaluationCount, incrementIterationCount

Methods inherited from class java.lang.Object

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

Constructor Detail

AbstractLeastSquaresOptimizer

protected AbstractLeastSquaresOptimizer(ConvergenceChecker<PointVectorValuePair> checker)

Parameters:

checker - Convergence checker.

Method Detail

computeWeightedJacobian

protected RealMatrix computeWeightedJacobian(double[] params)

Computes the weighted Jacobian matrix.

Parameters:

params - Model parameters at which to compute the Jacobian.

Returns:

the weighted Jacobian: W^1/2 J.

Throws:

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

computeCost

protected double computeCost(double[] residuals)

Computes the cost.

Parameters:

residuals - Residuals.

Returns:

the cost.

See Also:

computeResiduals(double[])

getRMS

public double getRMS()

Gets the root-mean-square (RMS) value. The RMS 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:

the 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

getWeightSquareRoot

public RealMatrix getWeightSquareRoot()

Gets the square-root of the weight matrix.

Returns:

the square-root of the weight matrix.

setCost

protected void setCost(double cost)

Sets the cost.

Parameters:

cost - Cost value.

computeCovariances

public double[][] computeCovariances(double[] params,
                            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:

params - Model parameters.

threshold - Singularity threshold.

Returns:

the covariance matrix.

Throws:

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

computeSigma

public double[] computeSigma(double[] params,
                    double covarianceSingularityThreshold)

Computes an estimate of the standard deviation of the parameters. The returned values are the square root of the diagonal coefficients of the covariance matrix, sd(a[i]) ~= sqrt(C[i][i]), where a[i] is the optimized value of the i-th parameter, and C is the covariance matrix.

Parameters:

params - Model parameters.

covarianceSingularityThreshold - Singularity threshold (see computeCovariances).

Returns:

an estimate of the standard deviation of the optimized parameters

Throws:

SingularMatrixException - if the covariance matrix cannot be computed.

optimize

public PointVectorValuePair optimize(OptimizationData... optData)
                              throws TooManyEvaluationsException

Stores data and performs the optimization.
The list of parameters is open-ended so that sub-classes can extend it with arguments specific to their concrete implementations.
When the method is called multiple times, instance data is overwritten only when actually present in the list of arguments: when not specified, data set in a previous call is retained (and thus is optional in subsequent calls).
Important note: Subclasses must override BaseOptimizer.parseOptimizationData(OptimizationData[]) if they need to register their own options; but then, they must also call super.parseOptimizationData(optData) within that method.

Overrides:

optimize in class JacobianMultivariateVectorOptimizer

Parameters:

optData - Optimization data. In addition to those documented in JacobianMultivariateVectorOptimizer, this method will register the following data:

• Weight

Returns:

a point/value pair that satifies the convergence criteria.

Throws:

TooManyEvaluationsException - if the maximal number of evaluations is exceeded.

DimensionMismatchException - if the initial guess, target, and weight arguments have inconsistent dimensions.

computeResiduals

protected double[] computeResiduals(double[] objectiveValue)

Computes the residuals. The residual is the difference between the observed (target) values and the model (objective function) value. There is one residual for each element of the vector-valued function.

Parameters:

objectiveValue - Value of the the objective function. This is the value returned from a call to computeObjectiveValue (whose array argument contains the model parameters).

Returns:

the residuals.

Throws:

DimensionMismatchException - if params has a wrong length.

parseOptimizationData

protected void parseOptimizationData(OptimizationData... optData)

Scans the list of (required and optional) optimization data that characterize the problem. If the weight matrix is specified, the weightMatrixSqrt field is recomputed.

Overrides:

parseOptimizationData in class JacobianMultivariateVectorOptimizer

Parameters:

optData - Optimization data. The following data will be looked for:

• Weight