NMath Reference Guide

## Double |

Class DoubleComplexLUFact represents the LU factorization of a matrix
of DoubleComplex numbers.

Inheritance Hierarchy

Syntax

The DoubleComplexLUFact type exposes the following members.

Constructors

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

DoubleComplexLUFact | Constructs a DoubleComplexLUFact 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 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. |

Methods

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

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. |

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:
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.

C#

PA = LU

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.

See Also