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QRT Class

A class which encapsulates the functionality of the QR decomposition.

Any real square matrix A (m x n) may be decomposed as A = QR where Q is an orthogonal matrix (its columns are orthogonal unit vectors meaning QTQ = I) and R is an upper triangular matrix (also called right triangular matrix).

Inheritance Hierarchy
SystemObject
  Altaxo.Calc.LinearAlgebra.FactorizationQRT
    Altaxo.Calc.LinearAlgebra.FactorizationGramSchmidtT

Namespace: Altaxo.Calc.LinearAlgebra.Factorization
Assembly: AltaxoCore (in AltaxoCore.dll) Version: 4.8.3261.0 (4.8.3261.0)
Syntax
C#
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public abstract class QR<T> : ISolver<T>
where T : struct, new(), IEquatable<T>, IFormattable

Type Parameters

T
Supported data types are double, single, Altaxo.Calc.LinearAlgebra.Complex, and Altaxo.Calc.LinearAlgebra.Complex32.

The QRT type exposes the following members.

Constructors
 NameDescription
Protected methodQRTInitializes a new instance of the QRT class
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Properties
 NameDescription
Public propertyDeterminant Gets the absolute determinant value of the matrix for which the QR matrix was computed.
Public propertyIsFullRank Gets a value indicating whether the matrix is full rank or not.
Public propertyQ Gets or sets orthogonal Q matrix
Public propertyR Gets the upper triangular factor R.
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Methods
 NameDescription
Public methodEqualsDetermines whether the specified object is equal to the current object.
(Inherited from Object)
Protected methodFinalizeAllows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection.
(Inherited from Object)
Public methodGetHashCodeServes as the default hash function.
(Inherited from Object)
Public methodGetTypeGets the Type of the current instance.
(Inherited from Object)
Protected methodMemberwiseCloneCreates a shallow copy of the current Object.
(Inherited from Object)
Public methodSolve(MatrixT) Solves a system of linear equations, AX = B, with A QR factorized.
Public methodSolve(VectorT) Solves a system of linear equations, Ax = b, with A QR factorized.
Public methodSolve(MatrixT, MatrixT) Solves a system of linear equations, AX = B, with A QR factorized.
Public methodSolve(VectorT, VectorT) Solves a system of linear equations, Ax = b, with A QR factorized.
Public methodToStringReturns a string that represents the current object.
(Inherited from Object)
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Fields
 NameDescription
Protected fieldFullR 
Protected fieldMethod 
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Remarks
The computation of the QR decomposition is done at construction time by Householder transformation. If a factorization is performed, the resulting Q matrix is an m x m matrix and the R matrix is an m x n matrix. If a factorization is performed, the resulting Q matrix is an m x n matrix and the R matrix is an n x n matrix.
See Also