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

java.lang.Object
  extended by org.apache.commons.math3.optim.BaseOptimizer<PAIR>
      extended by org.apache.commons.math3.optim.BaseMultivariateOptimizer<PointVectorValuePair>
          extended by org.apache.commons.math3.optim.nonlinear.vector.MultivariateVectorOptimizer
              extended by org.apache.commons.math3.optim.nonlinear.vector.JacobianMultivariateVectorOptimizer
                  extended by 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:
$Id$

Field Summary
 
Fields inherited from class org.apache.commons.math3.optim.BaseOptimizer
evaluations, iterations
 
Constructor Summary
protected AbstractLeastSquaresOptimizer(ConvergenceChecker<PointVectorValuePair> checker)
           
 
Method Summary
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 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: W1/2 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.

Overrides:
optimize in class JacobianMultivariateVectorOptimizer
Parameters:
optData - Optimization data. The following data will be looked for:
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.


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