LUT Class |
A class which encapsulates the functionality of an LU factorization.
For a matrix A, the LU factorization is a pair of lower triangular matrix L and upper triangular matrix U so that A = L*U.
In the Math.NET implementation we also store a set of pivot elements for increased numerical stability. The pivot elements encode a permutation matrix P such that P*A = L*U.
Inheritance HierarchyNamespace: Altaxo.Calc.LinearAlgebra.Factorization
Assembly: AltaxoCore (in AltaxoCore.dll) Version: 4.8.3179.0 (4.8.3179.0)
SyntaxC#
public abstract class LU<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 LUT type exposes the following members.
ConstructorsProperties| Name | Description | |
|---|---|---|
 | Determinant | Gets the determinant of the matrix for which the LU factorization was computed. |
| L | Gets the lower triangular factor. |
| P | Gets the permutation applied to LU factorization. |
| U | Gets the upper triangular factor. |
Methods| Name | Description | |
|---|---|---|
 | Equals | Determines whether the specified object is equal to the current object. (Inherited from Object) |
 | Finalize | Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection. (Inherited from Object) |
| GetHashCode | Serves as the default hash function. (Inherited from Object) |
| GetType | Gets the Type of the current instance. (Inherited from Object) |
| Inverse | Returns the inverse of this matrix. The inverse is calculated using LU decomposition. |
| MemberwiseClone | Creates a shallow copy of the current Object. (Inherited from Object) |
| Solve(MatrixT) | Solves a system of linear equations, AX = B, with A LU factorized. |
| Solve(VectorT) | Solves a system of linear equations, Ax = b, with A LU factorized. |
| Solve(MatrixT, MatrixT) | Solves a system of linear equations, AX = B, with A LU factorized. |
| Solve(VectorT, VectorT) | Solves a system of linear equations, Ax = b, with A LU factorized. |
| ToString | Returns a string that represents the current object. (Inherited from Object) |
Fields
Remarks
The computation of the LU factorization is done at construction time.
See Also