NMath Reference Guide

## Double |

Class DoubleQRDecomp represents the QR decomposition of a general matrix.

Inheritance Hierarchy

Syntax

The DoubleQRDecomp type exposes the following members.

Constructors

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

DoubleQRDecomp | Default constructor. Constructs a DoubleQRDecomp instance of size zero by zero. | |

DoubleQRDecomp(DoubleMatrix) | Constructs a DoubleQRDecomp instance of a given matrix. | |

DoubleQRDecomp(DoubleMatrix, Boolean) | Constructs a DoubleQRDecomp instance of a given matrix. | |

DoubleQRDecomp(DoubleMatrix, Boolean, Boolean) | Constructs a DoubleQRDecomp instance of a given matrix. |

Properties

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

Cols | Gets the number of columns in the matrix that the decomposition represents. | |

P | Gets an explicit representation of the permutation matrix. | |

Pivoting | Whether the decomposition is pivoted or not. | |

Q | Gets an explicit representation of the orthogonal matrix Q. | |

QFull | Gets an explicit representation of the Q matrix in the full QR factorization. The matrix Q is m x m where m is the number of rows in the factored matrix. | |

R | Gets an explicit representation of the upper trapezoidal matrix R. | |

Rows | Gets the number of rows in the matrix that this decomposition represents. |

Methods

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

Clone | Creates a deep copy of this decomposition. | |

Factor | Builds a decomposition for the matrix A. | |

PTx | Computes the inner product of the transpose of the permutation matrix P and a given vector. | |

Px | Computes the inner product of the permutation matrix P and a given vector. | |

QM | Computes the inner product of the orthogonal matrix Q and a given matrix. | |

QTM | Computes the inner product of the transpose of the orthogonal matrix Q and a given matrix. | |

QTx | Computes the inner product of the transpose of the orthogonal matrix Q and a given vector. | |

Qx | Computes the inner product of the orthogonal matrix Q and s given vector. | |

RDiagonal | Returns the main diagonal of the upper trapezoidal matrix R. | |

RInvx | Computes the inner product of the inverse of the matrix R and a given vector. | |

RTInvx | Computes the inner product of the transpose of the inverse of the matrix R and a given vector. | |

RTx | Computes the inner product of the transpose of the matrix R and a given vector. | |

Rx | Computes the inner product of the matrix R and a given vector. |

Remarks

A QR decomposition is a representation of a matrix A of
the form
where P is a permutation matrix, Q is orthogonal, and R is
upper trapezoidal (upper triangular if A has more rows than columns and has
full rank).

C#

AP = QR

See Also