﻿DoubleSymSemiPDFact Class   # DoubleSymSemiPDFact Class

Given a real symmetric, positive semidefinite matrix A, class DoubleSymSemiPDFact performs a Cholesky factorization with complete pivoting. In the following ' denotes matrix transposition. The form of the factorization is: P'AP = U'U if upper is specified, and P'AP = LL' if lower is specified. where P is a permutation matrix, and U and L are upper and lower triangular matrices, respectively. The algorithm does not attempt to check if the matrix A is positive semidefinite. Inheritance Hierarchy
SystemObject
CenterSpace.NMath.CoreDoubleSymSemiPDFact

Namespace:  CenterSpace.NMath.Core
Assembly:  NMath (in NMath.dll) Version: 7.4 Syntax
`public class DoubleSymSemiPDFact`

The DoubleSymSemiPDFact type exposes the following members. Constructors
NameDescription DoubleSymSemiPDFact
Computes the Cholesky factorization with complete pivoting of a symmetric positive semidefinite matrix.
Top Properties
NameDescription CholeskyFactor
Gets the upper triangular matrix U or the lower triangular matrix L in the factorization P'AP = U'U, upper triangular specified. P'AP = LL', lower triangular specified. IsGood
Gets a boolean value which is true if the matrix factorization succeeded and the factorization may be used to solve equations. If this property returns false, any attempt to use the factorization to solve equations using the Solve methods will throw an exception. Order
Gets the order. This is equal to the number of rows and columns of the factored symmetric A. It is also the number of rows and columns in the Cholesky factor U, if upper is specified, or L, if lower is specified. P
Gets the permutation matrix P in the factorization P'AP = U'U, upper triangular specified. P'AP = LL', lower triangular specified. Pivots
Gets an array of pivot indices. The row i is interchanged with row Pivots[i]. Rank
Gets the rank of the factored matrix. This is the number of linearly independent columns of the factored matrix A. Using the Solve method should only be attempted when the rank is equal to the order of the factored symmeteric matrix A. Tolerance
Gets the value of the tolerance used in the factorization algorithm. The algorithm terminates at the (k-1)th step, if the pivot is less than or equal to
`Tolerance`
. UpperOrLowerFactors
Gets the upper of lower factors property.
Top Methods
NameDescription Solve(DoubleMatrix)
Solves the linear system AX = B using the Cholesky factorization for A. The factorization must be checked using the IsGood property before solving. An execption will be thrown when the IsGood property is false and this method is invoked. Solve(DoubleVector)
Solves the linear system Ax = b using the Cholesky factorization for A. The factorization must be checked using the IsGood property before solving. An execption will be thrown when the IsGood property is false and a solve is attempted by calling this function.
Top See Also