Purpose

The module CovarianceMatrixLinearFunction computes the covariance matrix of a piecewise multi-linear function with values in an n-dimensional space (n ≤ 4) (represented as a list of n scalar-valued functions).

Also, an eigen analysis of the covariance matrix is performed.

Tips

Care about the bounding boxes and dimensions of the functions.

Windows

Default Panel

../../../Modules/ML/MLStochasticCollocation/mhelp/Images/Screenshots/CovarianceMatrixLinearFunction._default.png

Input Fields

This module has one base input. Connect here the function list to be examined. Multiple functions can be converted to a list using the SelectLinearFunction module. The module can work with any number of functions up to three. However, all the functions must have equal dimension and bounding box; otherwise the result will be wrong.

inputFunctions

name: inputFunctions, type: MLBase

Parameter Fields

Field Index

Apply: Trigger Eigenvector 2: Vector4 Scaled Eigenvector 2: Vector4
Auto apply: Bool Eigenvector 3: Vector4 Scaled Eigenvector 3: Vector4
Covariance Matrix: Matrix Eigenvector 4: Vector4 Scaled Eigenvector 4: Vector4
Eigenvalue 1: Double Expectation Value 1: Double  
Eigenvalue 2: Double Expectation Value 2: Double  
Eigenvalue 3: Double Expectation Value 3: Double  
Eigenvalue 4: Double Expectation Value 4: Double  
Eigenvector 1: Vector4 Scaled Eigenvector 1: Vector4  

Visible Fields

Covariance Matrix

name: covarMat, type: Matrix, persistent: no

Shows the covariance matrix.

This is a symmetric real n×n matrix. It is displayed as a 4×4 matrix, where in the case n<4, the empty parts are filled by ones in the diagonal and zeros elsewhere.

Expectation Value 1

name: expectation1, type: Double, persistent: no

Shows the expectation value of the first function.

Eigenvalue 1

name: eVal1, type: Double, persistent: no

Shows the first eigen value of the covariance matrix.

Eigenvector 1

name: eVec1, type: Vector4, persistent: no

Shows the first eigen vector of the covariance matrix.

Scaled Eigenvector 1

name: eVec1Scaled, type: Vector4, persistent: no

Shows the first eigen vector of the covariance matrix, scaled by the square of the eigen value.

Expectation Value 2

name: expectation2, type: Double, persistent: no

Shows the expectation value of the second function.

Eigenvalue 2

name: eVal2, type: Double, persistent: no

Shows the second eigen value of the covariance matrix.

Eigenvector 2

name: eVec2, type: Vector4, persistent: no

Shows the second eigen vector of the covariance matrix.

Scaled Eigenvector 2

name: eVec2Scaled, type: Vector4, persistent: no

Shows the second eigen vector of the covariance matrix, scaled by the square of the eigen value.

Expectation Value 3

name: expectation3, type: Double, persistent: no

Shows the expectation value of the third function.

Eigenvalue 3

name: eVal3, type: Double, persistent: no

Shows the third eigen value of the covariance matrix.

Eigenvector 3

name: eVec3, type: Vector4, persistent: no

Shows the third eigen vector of the covariance matrix.

Scaled Eigenvector 3

name: eVec3Scaled, type: Vector4, persistent: no

Shows the third eigen vector of the covariance matrix, scaled by the square of the eigen value.

Expectation Value 4

name: expectation4, type: Double, persistent: no

Shows the expectation value of the fourth function.

Eigenvalue 4

name: eVal4, type: Double, persistent: no

Shows the fourth eigen value of the covariance matrix.

Eigenvector 4

name: eVec4, type: Vector4, persistent: no

Shows the fourth eigen vector of the covariance matrix.

Scaled Eigenvector 4

name: eVec4Scaled, type: Vector4, persistent: no

Shows the fourth eigen vector of the covariance matrix, scaled by the square of the eigen value.

Auto apply

name: autoApply, type: Bool, default: FALSE

If checked, the module computes anew on any parameter or input change.

Apply

name: apply, type: Trigger

If pressed, the module computes anew.