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QrDecomposition Class

QR decomposition for a rectangular matrix.
Inheritance Hierarchy

Namespace:  Accord.Math.Decompositions
Assembly:  Accord.Math (in Accord.Math.dll) Version: 3.7.0
public sealed class QrDecomposition : ICloneable, 
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The QrDecomposition type exposes the following members.

Public methodQrDecomposition
Constructs a QR decomposition.
Public propertyDiagonal
Returns the diagonal of R.
Public propertyFullRank
Shows if the matrix A is of full rank.
Public propertyOrthogonalFactor
Returns the (economy-size) orthogonal factor Q.
Public propertyUpperTriangularFactor
Returns the upper triangular factor R.
Public methodClone
Creates a new object that is a copy of the current instance.
Public methodEquals
Determines whether the specified object is equal to the current object.
(Inherited from Object.)
Public methodGetHashCode
Serves as the default hash function.
(Inherited from Object.)
Public methodGetInformationMatrix
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.
Public methodGetType
Gets the Type of the current instance.
(Inherited from Object.)
Public methodInverse
Least squares solution of A * X = I
Public methodReverse
Reverses the decomposition, reconstructing the original matrix X.
Public methodSolve(Double)
Least squares solution of A * X = B
Public methodSolve(Double)
Least squares solution of A * X = B
Public methodSolveTranspose
Least squares solution of X * A = B
Public methodToString
Returns a string that represents the current object.
(Inherited from Object.)
Extension Methods
Public Extension MethodHasMethod
Checks whether an object implements a method with the given name.
(Defined by ExtensionMethods.)
Public Extension MethodIsEqual
Compares two objects for equality, performing an elementwise comparison if the elements are vectors or matrices.
(Defined by Matrix.)
Public Extension MethodToT
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.)

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