IQrDecomposition Type

Namespace: Altaxo.Calc.LinearAlgebra
Assembly: AltaxoCore.Redist.dll
All Interfaces: IQrDecomposition

QR decomposition for a rectangular matrix.

For an m-by-n matrix A with m >= n, the QR decomposition is an m-by-n orthogonal matrix Q and an n-by-n upper triangular matrix R so that A = Q * R. The QR decompostion always exists, even if the matrix does not have full rank, so the constructor will never fail. The primary use of the QR decomposition is in the least squares solution of nonsquare systems of simultaneous linear equations. This will fail if IQrDecomposition.IsFullRank returns .

Instance members

Instance member Description

this.IsFullRank

Full Usage: this.IsFullRank

Returns: bool
Modifiers: abstract

Shows if the matrix A is of full rank.

Returns: bool

this.OrthogonalFactor

Full Usage: this.OrthogonalFactor

Returns: IMapackMatrix
Modifiers: abstract

Returns the orthogonal factor Q.

Returns: IMapackMatrix

this.Solve

Full Usage: this.Solve

Parameters:
    rhs : IMapackMatrix - Right-hand-side matrix with as many rows as A and any number of columns.

Returns: IMapackMatrix A matrix that minimized the two norm of Q * R * X - B.
Modifiers: abstract

Least squares solution of A * X = B

rhs : IMapackMatrix

Right-hand-side matrix with as many rows as A and any number of columns.

Returns: IMapackMatrix

A matrix that minimized the two norm of Q * R * X - B.

ArgumentException Matrix row dimensions must be the same.
InvalidOperationException Matrix is rank deficient.

this.UpperTriangularFactor

Full Usage: this.UpperTriangularFactor

Returns: IMapackMatrix
Modifiers: abstract

Returns the upper triangular factor R.

Returns: IMapackMatrix