﻿DoubleComplexLUFact Class

# DoubleComplexLUFact Class

Class DoubleComplexLUFact represents the LU factorization of a matrix of DoubleComplex numbers.
Inheritance Hierarchy
SystemObject
CenterSpace.NMath.CoreDoubleComplexLUFact

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

The DoubleComplexLUFact type exposes the following members.

Constructors
NameDescription
DoubleComplexLUFact Constructs a DoubleComplexLUFact instance by factoring the given matrix.
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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.
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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(DoubleComplexMatrix) Uses this LU factorization to solve the linear system AX = B.
Solve(DoubleComplexVector) Uses the LU factorization of self to solve the linear system Ax = b.
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Remarks
LU factorization is a procedure for decomposing a matrix into a product of a lower triangular matrix and an upper triangular matrix. Given a matrix A, instances of the DoubleComplexLUFact 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 DoubleComplexLUFact 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.