public class LeastSquaresConverter extends Object implements MultivariateFunction
vectorial
objective functions
to scalar objective functions
when the goal is to minimize them.
This class is mostly used when the vectorial objective function represents a theoretical result computed from a point set applied to a model and the models point must be adjusted to fit the theoretical result to some reference observations. The observations may be obtained for example from physical measurements whether the model is built from theoretical considerations.
This class computes a possibly weighted squared sum of the residuals, which is
a scalar value. The residuals are the difference between the theoretical model
(i.e. the output of the vectorial objective function) and the observations. The
class implements the MultivariateFunction
interface and can therefore be
minimized by any optimizer supporting scalar objectives functions.This is one way
to perform a least square estimation. There are other ways to do this without using
this converter, as some optimization algorithms directly support vectorial objective
functions.
This class support combination of residuals with or without weights and correlations.
MultivariateFunction
,
MultivariateVectorFunction
Constructor and Description 

LeastSquaresConverter(MultivariateVectorFunction function,
double[] observations)
Build a simple converter for uncorrelated residuals with the same weight.

LeastSquaresConverter(MultivariateVectorFunction function,
double[] observations,
double[] weights)
Build a simple converter for uncorrelated residuals with the specific weights.

LeastSquaresConverter(MultivariateVectorFunction function,
double[] observations,
RealMatrix scale)
Build a simple converter for correlated residuals with the specific weights.

public LeastSquaresConverter(MultivariateVectorFunction function, double[] observations)
function
 vectorial residuals function to wrapobservations
 observations to be compared to objective function to compute residualspublic LeastSquaresConverter(MultivariateVectorFunction function, double[] observations, double[] weights)
The scalar objective function value is computed as:
objective = ∑weight_{i}(observation_{i}objective_{i})^{2}
Weights can be used for example to combine residuals with different standard deviations. As an example, consider a residuals array in which even elements are angular measurements in degrees with a 0.01° standard deviation and odd elements are distance measurements in meters with a 15m standard deviation. In this case, the weights array should be initialized with value 1.0/(0.01^{2}) in the even elements and 1.0/(15.0^{2}) in the odd elements (i.e. reciprocals of variances).
The array computed by the objective function, the observations array and the
weights array must have consistent sizes or a DimensionMismatchException
will be triggered while computing the scalar objective.
function
 vectorial residuals function to wrapobservations
 observations to be compared to objective function to compute residualsweights
 weights to apply to the residualsDimensionMismatchException
 if the observations vector and the weights
vector dimensions do not match (objective function dimension is checked only when
the value(double[])
method is called)public LeastSquaresConverter(MultivariateVectorFunction function, double[] observations, RealMatrix scale)
The scalar objective function value is computed as:
objective = y^{T}y with y = scale×(observationobjective)
The array computed by the objective function, the observations array and the
the scaling matrix must have consistent sizes or a DimensionMismatchException
will be triggered while computing the scalar objective.
function
 vectorial residuals function to wrapobservations
 observations to be compared to objective function to compute residualsscale
 scaling matrixDimensionMismatchException
 if the observations vector and the scale
matrix dimensions do not match (objective function dimension is checked only when
the value(double[])
method is called)public double value(double[] point)
value
in interface MultivariateFunction
point
 Point at which the function must be evaluated.Copyright © 20032012 The Apache Software Foundation. All Rights Reserved.