Class QrDecomposition

QR decomposition for a rectangular matrix.

Inheritance

System.Object

QrDecomposition

Implements

ISolverMatrixDecomposition<System.Double>

Namespace: ISynergy.Framework.Mathematics.Decompositions

Assembly: ISynergy.Framework.Mathematics.dll

Syntax

public sealed class QrDecomposition : ICloneable, ISolverMatrixDecomposition<double>

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 false.

Constructors

QrDecomposition(Double[,], Boolean, Boolean, Boolean)

Constructs a QR decomposition.

Declaration

public QrDecomposition(double[, ] value, bool transpose = false, bool economy = true, bool inPlace = false)

Parameters

Type	Name	Description
System.Double[,]	value	The matrix A to be decomposed.
System.Boolean	transpose	True if the decomposition should be performed on the transpose of A rather than A itself, false otherwise. Default is false.
System.Boolean	economy	True to perform the economy decomposition, where only .the information needed to solve linear systems is computed. If set to false, the full QR decomposition will be computed.
System.Boolean	inPlace	True if the decomposition should be done in place, overriding the given matrix value. Default is false.

Properties

Diagonal

Returns the diagonal of R.

Declaration

public double[] Diagonal { get; }

Property Value

Type	Description
System.Double[]

FullRank

Shows if the matrix A is of full rank.

Declaration

public bool FullRank { get; }

Property Value

Type	Description
System.Boolean	The value is true if R, and hence A, has full rank.

OrthogonalFactor

Returns the (economy-size) orthogonal factor Q.

Declaration

public double[, ] OrthogonalFactor { get; }

Property Value

Type	Description
System.Double[,]

UpperTriangularFactor

Returns the upper triangular factor R.

Declaration

public double[, ] UpperTriangularFactor { get; }

Property Value

Type	Description
System.Double[,]

Methods

Clone()

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

Declaration

public object Clone()

Returns

Type	Description
System.Object	A new object that is a copy of this instance.

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 methods.

Declaration

public double[, ] GetInformationMatrix()

Returns

Type	Description
System.Double[,]

Inverse()

Least squares solution of A * X = I

Declaration

public double[, ] Inverse()

Returns

Type	Description
System.Double[,]

Reverse()

Reverses the decomposition, reconstructing the original matrix X.

Declaration

public double[, ] Reverse()

Returns

Type	Description
System.Double[,]

Solve(Double[])

Least squares solution of A * X = B

Declaration

public double[] Solve(double[] value)

Parameters

Type	Name	Description
System.Double[]	value	Right-hand-side matrix with as many rows as A and any number of columns.

Returns

Type	Description
System.Double[]	A matrix that minimized the two norm of Q * R * X - B.

Exceptions

Type	Condition
System.ArgumentException	Matrix row dimensions must be the same.
System.InvalidOperationException	Matrix is rank deficient.

Solve(Double[,])

Least squares solution of A * X = B

Declaration

public double[, ] Solve(double[, ] value)

Parameters

Type	Name	Description
System.Double[,]	value	Right-hand-side matrix with as many rows as A and any number of columns.

Returns

Type	Description
System.Double[,]	A matrix that minimized the two norm of Q * R * X - B.

Exceptions

Type	Condition
System.ArgumentException	Matrix row dimensions must be the same.
System.InvalidOperationException	Matrix is rank deficient.

SolveTranspose(Double[,])

Least squares solution of X * A = B

Declaration

public double[, ] SolveTranspose(double[, ] value)

Parameters

Type	Name	Description
System.Double[,]	value	Right-hand-side matrix with as many columns as A and any number of rows.

Returns

Type	Description
System.Double[,]	A matrix that minimized the two norm of X * Q * R - B.

Exceptions

Type	Condition
System.ArgumentException	Matrix column dimensions must be the same.
System.InvalidOperationException	Matrix is rank deficient.

Implements

ISolverMatrixDecomposition<T>

Extension Methods

Matrix.Replace<T>(T, Object, Object)

Matrix.IsEqual(Object, Object, Decimal, Decimal)

EntityBaseExtensions.HasProperty(Object, String)

ArrayExtensions.Concatenate<T>(T, T[])

CollectionExtensions.FromHierarchy<TSource>(TSource, Func<TSource, TSource>, Func<TSource, Boolean>)

CollectionExtensions.FromHierarchy<TSource>(TSource, Func<TSource, TSource>)

ObjectExtensions.Clone<T>(T)

ObjectExtensions.To<T>(Object)

ObjectExtensions.To(Object, Type)

ObjectExtensions.HasMethod(Object, String)

ObjectExtensions.AddressOf<T>(T)

ReflectionExtensions.GetIdentityValue<T>(T)

ReflectionExtensions.GetIdentityValue<T, TResult>(T)

ReflectionExtensions.GetIdentityProperty<T>(T)

ReflectionExtensions.HasIdentityProperty<T>(T)

ReflectionExtensions.GetPropertyValue<T, TResult>(T, String, TResult)

ReflectionExtensions.GetPropertyInfo<T, TValue>(T, Expression<Func<T, TValue>>)

ReflectionExtensions.GetTitleValue<T>(T)

ReflectionExtensions.HasParentIdentityProperty<T>(T)

ReflectionExtensions.GetParentIdentityProperty<T>(T)

ReflectionExtensions.IsFreeApplication<T>(T)