ILuDecomposition (FsODE)

FsODE

Documentation for 0.0.2

ILuDecomposition Type

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

LU decomposition of a rectangular matrix.

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 ILuDecomposition.IsNonSingular returns .

Instance members

Instance member	Description
`this.Determinant` Full Usage: `this.Determinant` Returns: `float` Modifiers: abstract	Returns the determinant of the matrix. Returns: `float`
`this.IsNonSingular` Full Usage: `this.IsNonSingular` Returns: `bool` Modifiers: abstract	Returns if the matrix is non-singular. Returns: `bool`
`this.LowerTriangularFactor` Full Usage: `this.LowerTriangularFactor` Returns: `IMapackMatrix` Modifiers: abstract	Returns the lower triangular factor `L` with `A=LU`. Returns: `IMapackMatrix`
`this.PivotPermutationVector` Full Usage: `this.PivotPermutationVector` Returns: `float[]` Modifiers: abstract	Returns the pivot permuation vector. Returns: `float[]`
`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` Matrix `X` so that `L * U * X = B`. Modifiers: abstract	Solves a set of equation systems of type `A * X = B`. rhs : `IMapackMatrix` Right hand side matrix with as many rows as `A` and any number of columns. Returns: `IMapackMatrix` Matrix `X` so that `L * U * X = B`.
`this.UpperTriangularFactor` Full Usage: `this.UpperTriangularFactor` Returns: `IMapackMatrix` Modifiers: abstract	Returns the lower triangular factor `L` with `A=LU`. Returns: `IMapackMatrix`