﻿FloatLUFact Class   # FloatLUFact Class

Class FloatLUFact represents the LU factorization of a matrix of floating point numbers. Inheritance Hierarchy
SystemObject
CenterSpace.NMath.CoreFloatLUFact

Namespace: CenterSpace.NMath.Core
Assembly: NMath (in NMath.dll) Version: 7.4 Syntax
```[SerializableAttribute]
public class FloatLUFact : ICloneable```

The FloatLUFact type exposes the following members. Constructors
NameDescription FloatLUFact Constructs a FloatLUFact instance by factoring the given matrix.
Top Properties
NameDescription Cols Gets the number of columns in the matrix represented by the factorization. IsGood Gets a boolean value which is true if the matrix factorization succeeded and the factorization may be used to solve eqations, compute determinants, inverses, and so on; otherwise false. IsSingular Gets a boolean value which is true if the matrix factored is singular; otherwise, false. L Gets the lower triangular matrix L from the factorization PA = LU, where A is the matrix that was factored. P Gets the permutation matrix P from the factorization PA = LU, where A is the matrix that was factored. Pivots Gets an array of pivot indices. The row i was interchanged with row Pivots[i]. Rows Gets the number of rows in the matrix represented by the factorization. U Gets the upper triangular matrix U from the factorization PA = LU, where A is the matrix that was factored.
Top Methods
NameDescription Clone Creates a deep copy of this factorization. ConditionNumber Computes the reciprocal of the condition number of a given matrix in the specified norm type. Determinant Computes the determinant of the factored matrix. Factor Factors the matrix A so that self represents the LU factorization of A. Inverse Computes the inverse of the factored matrix. Solve(FloatMatrix) Uses this LU factorization to solve the linear system AX = B. Solve(FloatVector) Uses the LU factorization of self to solve the linear system Ax = b. SolveInPlace(FloatMatrix) Uses this LU factorization to solve the linear system AX = B. SolveInPlace(FloatVector) Uses the LU factorization of self to solve the linear system Ax = b.
Top Remarks
LU factorization is a procedure for decomposing an matrix into a product of a lower triangular matrix and an upper triangular matrix. Given a matrix A, instances of the FloatLUFact class factor A as follows:
C#
`PA = LU`
where P is a permutation matrix, L is a lower triangular matrix with ones on the diagonal, and U is an upper triangular matrix.
A FloatLUFact instance is constructed by supplying a matrix to factor. An existing instance can be used to factor other matrices with the provided Factor() method. Read-only properties provide access to the permutation matrix P, lower triangular matrix L, and upper triangular matrix U. See Also

#### Reference

CenterSpace.NMath.Core Namespace