NMath Reference Guide

## Double |

Class DoubleHermPDTriDiagFact represents the LDL' factorization of a Hermitian,
positive definite, tridiagonal matrix of complex double-precision floating point numbers.

Inheritance Hierarchy

Syntax

The DoubleHermPDTriDiagFact type exposes the following members.

Constructors

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

DoubleHermPDTriDiagFact(DoubleComplexTriDiagMatrix) | Constructs a DoubleHermPDTriDiagFact 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. | |

DoubleHermPDTriDiagFact(DoubleComplexTriDiagMatrix, Boolean) | Constructs a DoubleHermPDTriDiagFact instance by factoring the given matrix. |

Properties

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

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. |

Methods

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

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(DoubleComplexTriDiagMatrix) | 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(DoubleComplexTriDiagMatrix, Boolean) | Factors the matrix A so that self represents the LDL' factorization of A. | |

Inverse | Computes the inverse of the factored matrix. | |

Solve(DoubleComplexMatrix) | Uses this LDL' factorization to solve the linear system AX = B. | |

Solve(DoubleComplexVector) | Uses the LDL' factorization of self to solve the linear system Ax = b. |

Remarks

The factorization has the form:
where D is diagonal and L is unit lower bidiagonal (L'
is the conjugate transpose of the matrix L).

C#

A = LDL'

See Also