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
Version:
  $Id: AbstractLeastSquaresOptimizer.java 1422313 2012-12-15 18:53:41Z psteitz $

### Field Summary

Fields
`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)`.
`private static double` `DEFAULT_SINGULARITY_THRESHOLD` Deprecated. As of 3.1.
`private int` `jacobianEvaluations` Deprecated. Number of evaluations of the Jacobian.
`private MultivariateDifferentiableVectorFunction` `jF` Deprecated. Objective function derivatives.
`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.
`private RealMatrix` `weightMatrixSqrt` Deprecated. Square-root of the weight matrix.

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

`evaluations`

### Constructor Summary

Constructors
`protected` `AbstractLeastSquaresOptimizer()` Deprecated. See `SimpleValueChecker.SimpleValueChecker()`
`protected` `AbstractLeastSquaresOptimizer(ConvergenceChecker<PointVectorValuePair> checker)` Deprecated.

### Method Summary

Methods
`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.
`private RealMatrix` `squareRoot(RealMatrix m)` Deprecated. Computes the square-root of the weight matrix.
`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

#### DEFAULT_SINGULARITY_THRESHOLD

    @Deprecated
    private static final double DEFAULT_SINGULARITY_THRESHOLD

Deprecated. As of 3.1.
Singularity threshold (cf. `getCovariances(double)`).

See Also:
  Constant Field Values

#### 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).

#### jF

    private MultivariateDifferentiableVectorFunction jF

Deprecated.
Objective function derivatives.

#### jacobianEvaluations

    private int jacobianEvaluations

Deprecated.
Number of evaluations of the Jacobian.

#### weightMatrixSqrt

    private RealMatrix weightMatrixSqrt

Deprecated.
Square-root of the weight matrix.

### 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: W1/2 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 `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`.

#### 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 `∑weighti(objectivei - targeti)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,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

#### squareRoot

    private RealMatrix squareRoot(RealMatrix m)

Deprecated.
Computes the square-root of the weight matrix.

Parameters:
  `m` - Symmetric, positive-definite (weight) matrix.
Returns:
  the square-root of the weight matrix.