AbstractLeastSquaresOptimizer (Apache Commons Math 3.6.1 API)

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

Field Summary

Fields
Modifier and Type	Field and Description
`protected int`	`cols` Deprecated. As of 3.1.
`protected double`	`cost` Deprecated. As of 3.1. Field to become "private" in 4.0. Please use `setCost(double)`.
`protected double[]`	`objective` Deprecated. As of 3.1.
`protected double[]`	`point` Deprecated. As of 3.1.
`protected int`	`rows` Deprecated. As of 3.1.
`protected double[][]`	`weightedResidualJacobian` Deprecated. As of 3.1. To be removed in 4.0. Please use `computeWeightedJacobian(double[])` instead.
`protected double[]`	`weightedResiduals` Deprecated. As of 3.1.

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

Constructor Summary

Constructors
Modifier	Constructor and Description
`protected`	`AbstractLeastSquaresOptimizer()` Deprecated. See `SimpleValueChecker.SimpleValueChecker()`
`protected`	`AbstractLeastSquaresOptimizer(ConvergenceChecker<PointVectorValuePair> checker)` Deprecated.

Method Summary

Methods
Modifier and Type	Method and Description
`protected double`	`computeCost(double[] residuals)` Deprecated. Computes the cost.
`double[][]`	`computeCovariances(double[] params, double threshold)` Deprecated. Get the covariance matrix of the optimized parameters.
`protected double[]`	`computeResiduals(double[] objectiveValue)` Deprecated. Computes the residuals.
`double[]`	`computeSigma(double[] params, double covarianceSingularityThreshold)` Deprecated. Computes an estimate of the standard deviation of the parameters.
`protected RealMatrix`	`computeWeightedJacobian(double[] params)` Deprecated. Computes the Jacobian matrix.
`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.
`protected PointVectorValuePair`	`optimizeInternal(int maxEval, MultivariateDifferentiableVectorFunction f, OptimizationData... optData)` Deprecated. As of 3.1. Override is necessary only until this class's generic argument is changed to `MultivariateDifferentiableVectorFunction`.
`protected void`	`setCost(double cost)` Deprecated. Sets the cost.
`protected void`	`setUp()` Deprecated. Method which a subclass must override whenever its internal state depend on the `input` parsed by this base class.
`protected void`	`updateJacobian()` Deprecated. As of 3.1. Please use `computeWeightedJacobian(double[])` instead.
`protected void`	`updateResidualsAndCost()` Deprecated. As of 3.1. Please use `computeResiduals(double[])`, `BaseAbstractMultivariateVectorOptimizer.computeObjectiveValue(double[])`, `computeCost(double[])` and `setCost(double)` instead.

Methods inherited from class org.apache.commons.math3.optimization.direct.BaseAbstractMultivariateVectorOptimizer
computeObjectiveValue, doOptimize, getConvergenceChecker, getEvaluations, getMaxEvaluations, getObjectiveFunction, getStartPoint, getTarget, getTargetRef, getWeight, getWeightRef, optimize, optimizeInternal, optimizeInternal

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
```
@Deprecated
protected double[][] weightedResidualJacobian
```
    Deprecated. As of 3.1. To be removed in 4.0. Please use computeWeightedJacobian(double[]) instead.
    
    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
```
@Deprecated
protected int cols
```
    Deprecated. As of 3.1.
    
    Number of columns of the jacobian matrix.
  - rows
```
@Deprecated
protected int rows
```
    Deprecated. As of 3.1.
    
    Number of rows of the jacobian matrix.
  - point
```
@Deprecated
protected double[] point
```
    Deprecated. As of 3.1.
    
    Current point.
  - objective
```
@Deprecated
protected double[] objective
```
    Deprecated. As of 3.1.
    
    Current objective function value.
  - weightedResiduals
```
@Deprecated
protected double[] weightedResiduals
```
    Deprecated. As of 3.1.
    
    Weighted residuals
  - cost
```
@Deprecated
protected double cost
```
    Deprecated. As of 3.1. Field to become "private" in 4.0. Please use setCost(double).
    
    Cost value (square root of the sum of the residuals).
- Constructor Detail
  - AbstractLeastSquaresOptimizer
```
@Deprecated
protected AbstractLeastSquaresOptimizer()
```
    Deprecated. See SimpleValueChecker.SimpleValueChecker()
    
    Simple constructor with default settings. The convergence check is set to a SimpleVectorValueChecker.
  - AbstractLeastSquaresOptimizer
```
protected AbstractLeastSquaresOptimizer(ConvergenceChecker<PointVectorValuePair> checker)
```
    Deprecated.
    
    Parameters:
    checker - Convergence checker.
- Method Detail
  - getJacobianEvaluations
```
public int getJacobianEvaluations()
```
    Deprecated.
    
    Returns:
    the number of evaluations of the Jacobian function.
  - updateJacobian
```
@Deprecated
protected void updateJacobian()
```
    Deprecated. As of 3.1. Please use computeWeightedJacobian(double[]) instead.
    
    Update the jacobian matrix.
    
    Throws:
    
    DimensionMismatchException - if the Jacobian dimension does not match problem dimension.
  - computeWeightedJacobian
```
protected RealMatrix computeWeightedJacobian(double[] params)
```
    Deprecated.
    
    Computes the 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.
    Since:
    
    3.1
  - updateResidualsAndCost
```
@Deprecated
protected void updateResidualsAndCost()
```
    Deprecated. As of 3.1. Please use computeResiduals(double[]), BaseAbstractMultivariateVectorOptimizer.computeObjectiveValue(double[]), computeCost(double[]) and setCost(double) instead.
    
    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.
  - computeCost
```
protected double computeCost(double[] residuals)
```
    Deprecated.
    
    Computes the cost.
    
    Parameters:
    residuals - Residuals.
    
    Returns:
    the cost.
    Since:
    
    3.1
    
    See Also:
    computeResiduals(double[])
  - 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
  - setCost
```
protected void setCost(double cost)
```
    Deprecated.
    
    Sets the cost.
    
    Parameters:
    cost - Cost value.
    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 J^TJ 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 J^TJ 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 ∑weight_i(objective_i - target_i)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 ∑weight_i(objective_i - target_i)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.
  - optimizeInternal
```
@Deprecated
protected PointVectorValuePair optimizeInternal(int maxEval,
                                               MultivariateDifferentiableVectorFunction f,
                                               OptimizationData... optData)
```
    Deprecated. As of 3.1. Override is necessary only until this class's generic argument is changed to MultivariateDifferentiableVectorFunction.
    
    Optimize an objective function. Optimization is considered to be a weighted least-squares minimization. The cost function to be minimized is ∑weight_i(objective_i - target_i)²
    Parameters:
    maxEval - Allowed number of evaluations of the objective function.
    f - Objective function.
    optData - Optimization data. The following data will be looked for:
    
    Target
    
    Weight
    
    InitialGuess
    Returns:
    the point/value pair giving the optimal value of the objective function.
    
    Throws:
    
    TooManyEvaluationsException - if the maximal number of evaluations is exceeded.
    
    DimensionMismatchException - if the target, and weight arguments have inconsistent dimensions.
    Since:
    
    3.1
    
    See Also:
    BaseAbstractMultivariateVectorOptimizer.optimizeInternal(int, org.apache.commons.math3.analysis.MultivariateVectorFunction,OptimizationData[])
  - setUp
```
protected void setUp()
```
    Deprecated.
    
    Method which a subclass must override whenever its internal state depend on the input parsed by this base class. It will be called after the parsing step performed in the optimize method and just before BaseAbstractMultivariateVectorOptimizer.doOptimize().
    
    Overrides:
    
    setUp in class BaseAbstractMultivariateVectorOptimizer<DifferentiableMultivariateVectorFunction>
  - computeResiduals
```
protected double[] computeResiduals(double[] objectiveValue)
```
    Deprecated.
    
    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.
    Since:
    
    3.1

Class AbstractLeastSquaresOptimizer

Field Summary

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

Constructor Summary

Method Summary

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

Methods inherited from class java.lang.Object

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

Field Detail

weightedResidualJacobian

cols

rows

point

objective

weightedResiduals

cost

Constructor Detail

AbstractLeastSquaresOptimizer

AbstractLeastSquaresOptimizer

Method Detail

getJacobianEvaluations

updateJacobian

computeWeightedJacobian

updateResidualsAndCost

computeCost

getRMS

getChiSquare

getWeightSquareRoot

setCost

getCovariances

getCovariances

computeCovariances

guessParametersErrors

computeSigma

optimize

optimize

optimizeInternal

setUp

computeResiduals