Apache Commons Math 3.6.1 · org.apache.commons.math3.optim.nonlinear.scalar.LeastSquaresConverter

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.

Modifier and Type	Field and Description
private final MultivariateVectorFunction	function Underlying vectorial function.
private final double[]	observations Observations to be compared to objective function to compute residuals.
private final RealMatrix	scale Optional scaling matrix (weight and correlations) for the residuals.
private final double[]	weights Optional weights for the residuals.

Constructor Summary

Access	Constructor and Description
public	LeastSquaresConverter(final MultivariateVectorFunction vectorial residuals function to wrap function, final double[] observations to be compared to objective function to compute residuals observations) Builds a simple converter for uncorrelated residuals with identical weights.
public	LeastSquaresConverter(final MultivariateVectorFunction vectorial residuals function to wrap function, final double[] observations to be compared to objective function to compute residuals observations, final double[] weights to apply to the residuals weights) Builds a simple converter for uncorrelated residuals with the specified weights.
public	LeastSquaresConverter(final MultivariateVectorFunction vectorial residuals function to wrap function, final double[] observations to be compared to objective function to compute residuals observations, final RealMatrix scaling matrix scale) Builds a simple converter for correlated residuals with the specified weights.

Method Summary

Modifier and Type	Method and Description
public double	value(final double[] Point at which the function must be evaluated. point) Implements org.apache.commons.math3.analysis.MultivariateFunction.value. Compute the value for the function at the given point.

Inherited from java.lang.Object:: clone equals finalize getClass hashCode notify notifyAll toString wait wait wait

Field Detail

function	back to summary
private final MultivariateVectorFunction function Underlying vectorial function.

observations	back to summary
private final double[] observations Observations to be compared to objective function to compute residuals.

scale	back to summary
private final RealMatrix scale Optional scaling matrix (weight and correlations) for the residuals.

weights	back to summary
private final double[] weights Optional weights for the residuals.

Constructor Detail

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

LeastSquaresConverter

back to summary

public LeastSquaresConverter(final MultivariateVectorFunction function, final double[] observations)

Builds a simple converter for uncorrelated residuals with identical weights.

Parameters

function:MultivariateVectorFunction: vectorial residuals function to wrap
observations:double[]: observations to be compared to objective function to compute residuals

LeastSquaresConverter back to summary

LeastSquaresConverter	back to summary
public LeastSquaresConverter(final MultivariateVectorFunction function, final double[] observations, final double[] weights) Builds a simple converter for uncorrelated residuals with the specified 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/(0.01²) 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 `DimensionMismatchException` will be triggered while computing the scalar objective. Parameters function:MultivariateVectorFunction vectorial residuals function to wrap observations:double[] observations to be compared to objective function to compute residuals weights:double[] weights to apply to the residuals Exceptions DimensionMismatchException: 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(final MultivariateVectorFunction function, final double[] observations, final double[] weights)

Builds a simple converter for uncorrelated residuals with the specified 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/(0.01²) 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 DimensionMismatchException will be triggered while computing the scalar objective.

Parameters

function:MultivariateVectorFunction: vectorial residuals function to wrap
observations:double[]: observations to be compared to objective function to compute residuals
weights:double[]: weights to apply to the residuals

Exceptions

DimensionMismatchException:: 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 back to summary

LeastSquaresConverter	back to summary
public LeastSquaresConverter(final MultivariateVectorFunction function, final double[] observations, final RealMatrix scale) Builds a simple converter for correlated residuals with the specified weights. The scalar objective function value is computed as: objective = y^Ty 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 `DimensionMismatchException` will be triggered while computing the scalar objective. Parameters function:MultivariateVectorFunction vectorial residuals function to wrap observations:double[] observations to be compared to objective function to compute residuals scale:RealMatrix scaling matrix Exceptions DimensionMismatchException: 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 LeastSquaresConverter(final MultivariateVectorFunction function, final double[] observations, final RealMatrix scale)

Builds a simple converter for correlated residuals with the specified weights.

The scalar objective function value is computed as:

objective = y^Ty 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 DimensionMismatchException will be triggered while computing the scalar objective.

Parameters

function:MultivariateVectorFunction: vectorial residuals function to wrap
observations:double[]: observations to be compared to objective function to compute residuals
scale:RealMatrix: scaling matrix

Exceptions

DimensionMismatchException:: 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 Class LeastSquaresConverter

Field Summary

Constructor Summary

Method Summary

Field Detail

Constructor Detail

Method Detail