ILu |
LU decomposition of a rectangular matrix.
Namespace: Altaxo.Calc.LinearAlgebra
Assembly: AltaxoCore (in AltaxoCore.dll) Version: 4.8.3261.0 (4.8.3261.0)
SyntaxC#
public interface ILuDecomposition
The ILuDecomposition type exposes the following members.
Properties| Name | Description | |
|---|---|---|
 | Determinant | Returns the determinant of the matrix. |
| IsNonSingular | Returns if the matrix is non-singular. |
| LowerTriangularFactor | Returns the lower triangular factor L with A=LU. |
| PivotPermutationVector | Returns the pivot permuation vector. |
| UpperTriangularFactor | Returns the lower triangular factor L with A=LU. |
Methods
Remarks
For an m-by-n matrix A with m >= n, the LU decomposition is an m-by-n
unit lower triangular matrix L, an n-by-n upper triangular matrix U,
and a permutation vector piv of length m so that A(piv)=L*U.
If m < n, then L is m-by-m and U is m-by-n.
The LU decompostion with pivoting always exists, even if the matrix is
singular, so the constructor will never fail. The primary use of the
LU decomposition is in the solution of square systems of simultaneous
linear equations. This will fail if IsNonSingular returns .
See Also