Libraries.Compute.MatrixTransform.HessenbergDecomposition Documentation

A Hessenberg decomposition is a matrix decomposition of a matrix A into a unitary orthogonal matrix P and a Hessenberg matrix H such that: A = P*H*P^(T) This was adapted from the same model in Apache Commons, but was expanded upon to simplify the library and add a variety of helper actions that were missing. More information about this class can be found on its documentation page HessenbergTransformer: https://commons.apache.org/proper/commons-math/javadocs/api-3.6.1/index.html For more information: https://en.wikipedia.org/wiki/Hessenberg_matrix For more information: https://mathworld.wolfram.com/HessenbergDecomposition.html

Example Code

use Libraries.Compute.Matrix
use Libraries.Compute.MatrixTransform.HessenbergDecomposition

class Main
    action Main
        Matrix matrix
        matrix:Fill(3, 3, 5.0)
        HessenbergDecomposition calc
        calc:Calculate(matrix)
        output calc:GetHessenbergMatrix():ToText()
    end
end

Inherits from: Libraries.Language.Object

Actions Documentation

Calculate(Libraries.Compute.Matrix matrix)

precisionEpsilon = 1.0*math:RaiseToPower(10, -p)

Parameters

Compare(Libraries.Language.Object object)

This action compares two object hash codes and returns an integer. The result is larger if this hash code is larger than the object passed as a parameter, smaller, or equal. In this case, -1 means smaller, 0 means equal, and 1 means larger. This action was changed in Quorum 7 to return an integer, instead of a CompareResult object, because the previous implementation was causing efficiency issues.

Parameters

Return

integer: The Compare result, Smaller, Equal, or Larger.

Example

Object o
Object t
integer result = o:Compare(t) //1 (larger), 0 (equal), or -1 (smaller)

Equals(Libraries.Language.Object object)

This action determines if two objects are equal based on their hash code values.

Parameters

Return

boolean: True if the hash codes are equal and false if they are not equal.

Example

use Libraries.Language.Object
use Libraries.Language.Types.Text
Object o
Text t
boolean result = o:Equals(t)

GetHashCode()

This action gets the hash code for an object.

Return

integer: The integer hash code of the object.

Example

Object o
integer hash = o:GetHashCode()

GetHessenbergMatrix()

This matrix represents the hessenberg matrix (H)

Return

Libraries.Compute.Matrix:

GetOriginalMatrix()

Compute Householder transformation.

Return

Libraries.Compute.Matrix:

GetOrthogonalMatrix()

Return

Libraries.Compute.Matrix

GetOrthogonalTransposedMatrix()

Double division avoids possible underflow

Return

Libraries.Compute.Matrix: