Namespaces

Types in MathNet.Numerics.LinearAlgebra.Factorization

Type QR<T>

Namespace MathNet.Numerics.LinearAlgebra.Factorization

Interfaces ISolver<T>

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).

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.

Methods

Properties

Public Methods

bool Equals(object obj)

int GetHashCode()

Type GetType()

Matrix<T> Solve(Matrix<T> input)

Solves a system of linear equations, , with A QR factorized.
Parameters
Matrix<T> input

The right hand side Matrix`1 , .

Return
Matrix<T>

The left hand side Matrix`1 , .

void Solve(Matrix<T> input, Matrix<T> result)

Solves a system of linear equations, , with A QR factorized.
Parameters
Matrix<T> input

The right hand side Matrix`1 , .

Matrix<T> result

The left hand side Matrix`1 , .

Vector<T> Solve(Vector<T> input)

Solves a system of linear equations, , with A QR factorized.
Parameters
Vector<T> input

The right hand side vector, .

Return
Vector<T>

The left hand side Vector`1 , .

void Solve(Vector<T> input, Vector<T> result)

Solves a system of linear equations, , with A QR factorized.
Parameters
Vector<T> input

The right hand side vector, .

Vector<T> result

The left hand side Matrix`1 , .

string ToString()

Public Properties

T Determinant get;

Gets the absolute determinant value of the matrix for which the QR matrix was computed.

bool IsFullRank get;

Gets a value indicating whether the matrix is full rank or not.
Value:

Matrix<T> Q get; set;

Gets or sets orthogonal Q matrix

Matrix<T> R get;

Gets the upper triangular factor R.