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

Deprecated.

As of 3.1 (to be removed in 4.0).

@Deprecated
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 constructs the Jacobian matrix of the function argument in method optimize and assumes that the rows of that matrix iterate on the model functions while the columns iterate on the parameters; thus, the numbers of rows is equal to the dimension of the Target while the number of columns is equal to the dimension of the InitialGuess.

Since:

1.2

Method Summary

Modifier and Type	Method and Description
double[][]	computeCovariances(double[] params, double threshold) Deprecated. Get the covariance matrix of the optimized parameters.
double[]	computeSigma(double[] params, double covarianceSingularityThreshold) Deprecated. Computes an estimate of the standard deviation of the parameters.
double	getChiSquare() Deprecated. 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() Deprecated. As of 3.1. Please use computeCovariances(double[],double) instead.
double[][]	getCovariances(double threshold) Deprecated. As of 3.1. Please use computeCovariances(double[],double) instead.
int	getJacobianEvaluations() Deprecated.
double	getRMS() Deprecated. Get the Root Mean Square value.
RealMatrix	getWeightSquareRoot() Deprecated. Gets the square-root of the weight matrix.
double[]	guessParametersErrors() Deprecated. as of version 3.1, computeSigma(double[],double) should be used instead. It should be emphasized that guessParametersErrors and computeSigma are not strictly equivalent.
PointVectorValuePair	optimize(int maxEval, DifferentiableMultivariateVectorFunction f, double[] target, double[] weights, double[] startPoint) Deprecated. As of 3.1. Please use optimize(int,MultivariateDifferentiableVectorFunction,OptimizationData...) instead.
PointVectorValuePair	optimize(int maxEval, MultivariateDifferentiableVectorFunction f, double[] target, double[] weights, double[] startPoint) Deprecated. As of 3.1. Please use optimize(int,MultivariateDifferentiableVectorFunction,OptimizationData...) instead.

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

getConvergenceChecker, getEvaluations, getMaxEvaluations, getStartPoint, getTarget, getWeight

Methods inherited from class java.lang.Object

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

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

getConvergenceChecker, getEvaluations, getMaxEvaluations

Method Detail

getJacobianEvaluations

public int getJacobianEvaluations()

Deprecated.

Returns:

the number of evaluations of the Jacobian function.

getRMS

public double getRMS()

Deprecated.

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()

Deprecated.

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()

Deprecated.

Gets the square-root of the weight matrix.

Returns:

the square-root of the weight matrix.

Since:

3.1

getCovariances

@Deprecated
public double[][] getCovariances()

Deprecated. As of 3.1. Please use computeCovariances(double[],double) instead.

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

@Deprecated
public double[][] getCovariances(double threshold)

Deprecated. As of 3.1. Please use computeCovariances(double[],double) instead.

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).

computeCovariances

public double[][] computeCovariances(double[] params,
                                     double threshold)

Deprecated.

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).

Since:

3.1

guessParametersErrors

@Deprecated
public double[] guessParametersErrors()

Deprecated. as of version 3.1, computeSigma(double[],double) should be used instead. It should be emphasized that guessParametersErrors and computeSigma are not strictly equivalent.

Returns an estimate of the standard deviation of each parameter. The returned values are the so-called (asymptotic) standard errors on the parameters, defined as sd(a[i]) = sqrt(S / (n - m) * C[i][i]), where a[i] is the optimized value of the i-th parameter, S is the minimized value of the sum of squares objective function (as returned by getChiSquare()), n is the number of observations, m is the number of parameters and C is the covariance matrix.

See also Wikipedia, or MathWorld, equations (34) and (35) for a particular case.

Returns:

an estimate of the standard deviation of the optimized parameters

Throws:

SingularMatrixException - if the covariance 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.

computeSigma

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

Deprecated.

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.

Since:

3.1

optimize

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

Deprecated. As of 3.1. Please use optimize(int,MultivariateDifferentiableVectorFunction,OptimizationData...) instead.

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.

optimize

@Deprecated
public PointVectorValuePair optimize(int maxEval,
                                                 MultivariateDifferentiableVectorFunction f,
                                                 double[] target,
                                                 double[] weights,
                                                 double[] startPoint)

Deprecated. As of 3.1. Please use optimize(int,MultivariateDifferentiableVectorFunction,OptimizationData...) instead.

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

Parameters:

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.

maxEval - Maximum number of function evaluations.

Returns:

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

Throws:

DimensionMismatchException - if the start point dimension is wrong.

TooManyEvaluationsException - if the maximal number of evaluations is exceeded.

NullArgumentException - if any argument is null.