Accord.NET Framework

## QrDecomposition Class |

QR decomposition for a rectangular matrix.

Inheritance Hierarchy

SystemObject

Accord.Math.DecompositionsQrDecomposition

Accord.Math.DecompositionsQrDecomposition

Syntax

The QrDecomposition type exposes the following members.

Constructors

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

QrDecomposition | Constructs a QR decomposition. |

Properties

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

Diagonal | Returns the diagonal of R. | |

FullRank | Shows if the matrix A is of full rank. | |

OrthogonalFactor |
Returns the (economy-size) orthogonal factor Q.
| |

UpperTriangularFactor | Returns the upper triangular factor R. |

Methods

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

Clone |
Creates a new object that is a copy of the current instance.
| |

Equals | Determines whether the specified object is equal to the current object. (Inherited from Object.) | |

GetHashCode | Serves as the default hash function. (Inherited from Object.) | |

GetInformationMatrix |
Computes (Xt * X)^1 (the inverse of the covariance matrix). This
matrix can be used to determine standard errors for the coefficients when
solving a linear set of equations through any of the Solve(Double)
methods.
| |

GetType | Gets the Type of the current instance. (Inherited from Object.) | |

Inverse | Least squares solution of A * X = I | |

Reverse |
Reverses the decomposition, reconstructing the original matrix X.
| |

Solve(Double) | Least squares solution of A * X = B | |

Solve(Double) | Least squares solution of A * X = B | |

SolveTranspose | Least squares solution of X * A = B | |

ToString | Returns a string that represents the current object. (Inherited from Object.) |

Extension Methods

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

HasMethod |
Checks whether an object implements a method with the given name.
(Defined by ExtensionMethods.) | |

IsEqual |
Compares two objects for equality, performing an elementwise
comparison if the elements are vectors or matrices.
(Defined by Matrix.) | |

To(Type) | Overloaded.
Converts an object into another type, irrespective of whether
the conversion can be done at compile time or not. This can be
used to convert generic types to numeric types during runtime.
(Defined by ExtensionMethods.) | |

ToT | Overloaded.
Converts an object into another type, irrespective of whether
the conversion can be done at compile time or not. This can be
used to convert generic types to numeric types during runtime.
(Defined by ExtensionMethods.) |

Remarks

For an m-by-n matrix A with m >= n, the QR decomposition is an m-by-n orthogonal matrix Q and an n-by-n upper triangular matrix R so that A = Q * R.

The QR decomposition always exists, even if the matrix does not have full rank, so the constructor will never fail. The primary use of the QR decomposition is in the least squares solution of nonsquare systems of simultaneous linear equations. This will fail if FullRank returns .

See Also