Emrys::StatisticalLinearization< InputSpace, OutputSpace, Scalar > Struct Template Reference

The statistical linearization of an output in an input, from statisticalLinearization(): the affine function of the input that best predicts the output in mean square, \( y \approx \bar y \boxplus H (x \boxminus \mu) \), and the covariance \( \Omega \) of what it leaves unexplained. More...

#include <EmrysFilter/Models/Condition.h>

Public Types
using	JacobianMatrix
	The Jacobian's type: output differences by input differences.
using	ErrorMatrix
	The error covariance's type: over the output's differences.

Public Attributes
JacobianMatrix	jacobian
	\( H = \Sigma_{xy}^T P^{-1} \): a row per difference coordinate of the output, a column per difference coordinate of the input
ErrorMatrix	errorCov
	\( \Omega = \Sigma_{yy} - H P H^T \): the covariance of the output given the input under the affine fit, from the other uncertain inputs and from the function's curvature

Detailed Description

template<typename InputSpace, typename OutputSpace, typename Scalar = double>
struct Emrys::StatisticalLinearization< InputSpace, OutputSpace, Scalar >

The statistical linearization of an output in an input, from statisticalLinearization(): the affine function of the input that best predicts the output in mean square, \( y \approx \bar y \boxplus H (x \boxminus \mu) \), and the covariance \( \Omega \) of what it leaves unexplained.

Template Parameters

InputSpace	space of the input
OutputSpace	space of the output

Member Typedef Documentation

ErrorMatrix

template<typename InputSpace, typename OutputSpace, typename Scalar = double>

using Emrys::StatisticalLinearization< InputSpace, OutputSpace, Scalar >::ErrorMatrix

Initial value:

internal::MatrixOf<
       Scalar,
       valueDimensionAtCompileTime<DifferenceSpace<OutputSpace>>,
       valueDimensionAtCompileTime<DifferenceSpace<OutputSpace>>,
       maxValueDimensionAtCompileTime<DifferenceSpace<OutputSpace>>,
       maxValueDimensionAtCompileTime<DifferenceSpace<OutputSpace>>>

The error covariance's type: over the output's differences.

JacobianMatrix

template<typename InputSpace, typename OutputSpace, typename Scalar = double>

using Emrys::StatisticalLinearization< InputSpace, OutputSpace, Scalar >::JacobianMatrix

Initial value:

internal::MatrixOf<
       Scalar,
       valueDimensionAtCompileTime<DifferenceSpace<OutputSpace>>,
       valueDimensionAtCompileTime<DifferenceSpace<InputSpace>>,
       maxValueDimensionAtCompileTime<DifferenceSpace<OutputSpace>>,
       maxValueDimensionAtCompileTime<DifferenceSpace<InputSpace>>>

The Jacobian's type: output differences by input differences.

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The documentation for this struct was generated from the following file:

• EmrysFilter/Models/Condition.h