org.hipparchus.optim.nonlinear.scalar

## Class LeastSquaresConverter

• All Implemented Interfaces:
MultivariateFunction

public class LeastSquaresConverter
extends Object
implements MultivariateFunction
This class converts 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 Detail

• #### LeastSquaresConverter

public LeastSquaresConverter(MultivariateVectorFunction function,
double[] observations)
Builds a simple converter for uncorrelated residuals with identical weights.
Parameters:
function - vectorial residuals function to wrap
observations - observations to be compared to objective function to compute residuals
• #### LeastSquaresConverter

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

The scalar objective function value is computed as:

objective = ∑weighti(observationi-objectivei)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/(0.012) in the even elements and 1.0/(15.02) 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 MathIllegalArgumentException will be triggered while computing the scalar objective.

Parameters:
function - vectorial residuals function to wrap
observations - observations to be compared to objective function to compute residuals
weights - weights to apply to the residuals
Throws:
MathIllegalArgumentException - 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)
• #### LeastSquaresConverter

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

The scalar objective function value is computed as:

objective = yTy with y = scale×(observation-objective)

The array computed by the objective function, the observations array and the the scaling matrix must have consistent sizes or a MathIllegalArgumentException will be triggered while computing the scalar objective.

Parameters:
function - vectorial residuals function to wrap
observations - observations to be compared to objective function to compute residuals
scale - scaling matrix
Throws:
MathIllegalArgumentException - 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)