﻿ JaggedQrDecomposition Class   # JaggedQrDecomposition Class

QR decomposition for a rectangular matrix. Inheritance Hierarchy
SystemObject
Accord.Math.DecompositionsJaggedQrDecomposition

Namespace:  Accord.Math.Decompositions
Assembly:  Accord.Math (in Accord.Math.dll) Version: 3.8.0 Syntax
```public sealed class JaggedQrDecomposition : ICloneable,
ISolverArrayDecomposition<double>```

The JaggedQrDecomposition type exposes the following members. Constructors
NameDescription JaggedQrDecomposition
Constructs a QR decomposition.
Top Properties
NameDescription Diagonal
Returns the diagonal of R. FullRank
Shows if the matrix A is of full rank. OrthogonalFactor
Returns the orthogonal factor Q. UpperTriangularFactor
Returns the upper triangular factor R.
Top Methods
NameDescription 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 SolveForDiagonal
Solves a set of equation systems of type A * X = B where B is a diagonal matrix. SolveTranspose
Least squares solution of X * A = B ToString
Returns a string that represents the current object.
(Inherited from Object.)
Top Extension Methods
NameDescription 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.) ToTOverloaded.
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.)
Top 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