﻿DoubleSymPDTriDiagFact Class

# DoubleSymPDTriDiagFact Class

Class DoubleSymPDTriDiagFact represents the LDL' factorization of a symmetric, positive definite, tridiagonal matrix of double-precision floating point numbers.
Inheritance Hierarchy
SystemObject
CenterSpace.NMath.CoreDoubleSymPDTriDiagFact

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

The DoubleSymPDTriDiagFact type exposes the following members.

Constructors
NameDescription
DoubleSymPDTriDiagFact(DoubleTriDiagMatrix)
Constructs a DoubleSymPDTriDiagFact instance by factoring the given matrix. By default the condition number for the matrix will not be computed and will not be available from the ConditionNumber method.
DoubleSymPDTriDiagFact(DoubleTriDiagMatrix, Boolean)
Constructs an DoubleSymPDTriDiagFact instance by factoring the given matrix, optionally estimating the condition number of the 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 equations, compute determinants, inverses, and so on; otherwise false.
IsPositiveDefinite
Gets a boolean value which is true if the matrix is positive definite and the factorization may be used to solve equations, compute determinants, inverses, and so on; otherwise false.
Rows
Gets the number of rows in the matrix represented by the factorization.
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Methods
NameDescription
Clone
Creates a deep copy of this factorization.
ConditionNumber
Computes an estimate of the reciprocal of the condition number of a given matrix in the 1-norm.
Determinant
Computes the determinant of the factored matrix.
Factor(DoubleTriDiagMatrix)
Factors the matrix A so that self represents the LDL' factorization of A. By default the condition number for the matrix will not be computed and will not be available from the ConditionNumber method.
Factor(DoubleTriDiagMatrix, Boolean)
Factors the matrix A so that self represents the LDL' factorization of A. By default the condition number for the matrix will not be computed and will not be available from the ConditionNumber method.
Inverse
Computes the inverse of the factored matrix.
Solve(DoubleMatrix)
Uses this LDL' factorization to solve the linear system AX = B.
Solve(DoubleVector)
Uses the LDL' factorization of self to solve the linear system Ax = b.
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Remarks
The factorization has the form:
`A = LDL'`
where D is diagonal and L is unit lower bidiagonal (L' is the transpose of the matrix L).