NMath Reference Guide

## Double |

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

Syntax

The DoubleSymSemiPDFact type exposes the following members.

Constructors

Name | Description | |
---|---|---|

DoubleSymSemiPDFact | Computes the Cholesky factorization with complete pivoting of a symmetric positive semidefinite matrix. |

Properties

Name | Description | |
---|---|---|

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 C# Tolerance | |

UpperOrLowerFactors | Gets the upper of lower factors property. |

Methods

Name | Description | |
---|---|---|

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. |

See Also