QRDecomposition Class

Members See Also

Represents the QR decomposition of a matrix.

Namespace: Extreme.Mathematics.LinearAlgebra
Assembly: Extreme.Numerics.Net40 (in Extreme.Numerics.Net40.dll) Version: 4.2.11333.0 (4.2.12253.0)

Syntax

C#
public class QRDecomposition : Decomposition, ILeastSquaresSolver

Visual Basic (Declaration)
Public Class QRDecomposition _ Inherits Decomposition _ Implements ILeastSquaresSolver

Visual C++
public ref class QRDecomposition : public Decomposition, ILeastSquaresSolver

F#
type QRDecomposition = class inherit Decomposition interface ILeastSquaresSolver end

Remarks

The QR decomposition of a matrix A rewrites the matrix in the form A= QR, where Q is an orthogonal matrix, and R is an upper-triangular matrix.

QRDecomposition can operate in two modes. In overwrite mode, the original matrix is overwritten by the decomposition. In preserve mode, the original matrix is preserved, and a new matrix is created to hold the decomposition. You can set the mode through the Overwrite property.

QRDecomposition inherits from LinearOperator. This means you can use it to solve systems of linear equations. You can solve for a single right-hand side, or for multiple right-hand sides using the Solve(DenseVector, Boolean) method. You can also calculate the determinant, the inverse, and an estimate for the EstimateConditionNumber()()()().

Inheritance Hierarchy

System..::..Object
  Extreme.Mathematics.LinearAlgebra..::..LinearOperator
    Extreme.Mathematics.LinearAlgebra..::..Decomposition
      Extreme.Mathematics.LinearAlgebra..::..QRDecomposition