Class SingularValueDecomposition

Singular Value Decomposition for a rectangular matrix.

Inheritance

System.Object

SingularValueDecomposition

Implements

ISolverMatrixDecomposition<System.Double>

Namespace: ISynergy.Framework.Mathematics.Decompositions

Assembly: ISynergy.Framework.Mathematics.dll

Syntax

public sealed class SingularValueDecomposition : ICloneable, ISolverMatrixDecomposition<double>

Remarks

For an m-by-n matrix A with m >= n, the singular value decomposition is an m-by-n orthogonal matrix U, an n-by-n diagonal matrix S, and an n-by-n orthogonal matrix V so that A = U * S * V'. The singular values, sigma[k] = S[k,k], are ordered so that sigma[0] >= sigma[1] >= ... >= sigma[n-1].

The singular value decomposition always exists, so the constructor will never fail. The matrix condition number and the effective numerical rank can be computed from this decomposition.

WARNING! Please be aware that if A has less rows than columns, it is better to compute the decomposition on the transpose of A and then swap the left and right eigenvectors. If the routine is computed on A directly, the diagonal of singular values may contain one or more zeros. The identity A = U * S * V' may still hold, however. To overcome this problem, pass true to the autoTranspose argument of the class constructor.

This routine computes the economy decomposition of A.

Constructors

SingularValueDecomposition(Double[,])

Constructs a new singular value decomposition.

Declaration

public SingularValueDecomposition(double[, ] value)

Parameters

Type	Name	Description
System.Double[,]	value	The matrix to be decomposed.

SingularValueDecomposition(Double[,], Boolean, Boolean)

Constructs a new singular value decomposition.

Declaration

public SingularValueDecomposition(double[, ] value, bool computeLeftSingularVectors, bool computeRightSingularVectors)

Parameters

Type	Name	Description
System.Double[,]	value	The matrix to be decomposed.
System.Boolean	computeLeftSingularVectors	Pass true if the left singular vector matrix U should be computed. Pass false otherwise. Default is true.
System.Boolean	computeRightSingularVectors	Pass true if the right singular vector matrix V should be computed. Pass false otherwise. Default is true.

SingularValueDecomposition(Double[,], Boolean, Boolean, Boolean)

Constructs a new singular value decomposition.

Declaration

public SingularValueDecomposition(double[, ] value, bool computeLeftSingularVectors, bool computeRightSingularVectors, bool autoTranspose)

Parameters

Type	Name	Description
System.Double[,]	value	The matrix to be decomposed.
System.Boolean	computeLeftSingularVectors	Pass true if the left singular vector matrix U should be computed. Pass false otherwise. Default is true.
System.Boolean	computeRightSingularVectors	Pass true if the right singular vector matrix V should be computed. Pass false otherwise. Default is true.
System.Boolean	autoTranspose	Pass true to automatically transpose the value matrix in case JAMA's assumptions about the dimensionality of the matrix are violated. Pass false otherwise. Default is false.

SingularValueDecomposition(Double[,], Boolean, Boolean, Boolean, Boolean)

Constructs a new singular value decomposition.

Declaration

public SingularValueDecomposition(double[, ] value, bool computeLeftSingularVectors, bool computeRightSingularVectors, bool autoTranspose, bool inPlace)

Parameters

Type	Name	Description
System.Double[,]	value	The matrix to be decomposed.
System.Boolean	computeLeftSingularVectors	Pass true if the left singular vector matrix U should be computed. Pass false otherwise. Default is true.
System.Boolean	computeRightSingularVectors	Pass true if the right singular vector matrix V should be computed. Pass false otherwise. Default is true.
System.Boolean	autoTranspose	Pass true to automatically transpose the value matrix in case JAMA's assumptions about the dimensionality of the matrix are violated. Pass false otherwise. Default is false.
System.Boolean	inPlace	Pass true to perform the decomposition in place. The matrix value will be destroyed in the process, resulting in less memory comsumption.

Properties

AbsoluteDeterminant

Returns the absolute value of the matrix determinant.

Declaration

public double AbsoluteDeterminant { get; }

Property Value

Type	Description
System.Double

Condition

Returns the condition number max(S) / min(S).

Declaration

public double Condition { get; }

Property Value

Type	Description
System.Double

Diagonal

Gets the one-dimensional array of singular values.

Declaration

public double[] Diagonal { get; }

Property Value

Type	Description
System.Double[]

DiagonalMatrix

Returns the block diagonal matrix of singular values.

Declaration

public double[, ] DiagonalMatrix { get; }

Property Value

Type	Description
System.Double[,]

IsSingular

Gets whether the decomposed matrix is singular.

Declaration

public bool IsSingular { get; }

Property Value

Type	Description
System.Boolean

LeftSingularVectors

Returns the U matrix of Singular Vectors.

Declaration

public double[, ] LeftSingularVectors { get; }

Property Value

Type	Description
System.Double[,]

LogDeterminant

Returns the log of the absolute value for the matrix determinant.

Declaration

public double LogDeterminant { get; }

Property Value

Type	Description
System.Double

LogPseudoDeterminant

Returns the log of the pseudo-determinant for the matrix.

Declaration

public double LogPseudoDeterminant { get; }

Property Value

Type	Description
System.Double

Ordering

Returns the ordering in which the singular values have been sorted.

Declaration

public int[] Ordering { get; }

Property Value

Type	Description
System.Int32[]

PseudoDeterminant

Returns the pseudo-determinant for the matrix.

Declaration

public double PseudoDeterminant { get; }

Property Value

Type	Description
System.Double

Rank

Returns the effective numerical matrix rank.

Declaration

public int Rank { get; }

Property Value

Type	Description
System.Int32	Number of non-negligible singular values.

RightSingularVectors

Returns the V matrix of Singular Vectors.

Declaration

public double[, ] RightSingularVectors { get; }

Property Value

Type	Description
System.Double[,]

Threshold

Returns the singularity threshold.

Declaration

public double Threshold { get; }

Property Value

Type	Description
System.Double

TwoNorm

Returns the Two norm.

Declaration

public double TwoNorm { 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()

Computes the (pseudo-)inverse of the matrix given to the Singular value decomposition.

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[])

Solves a linear equation system of the form Ax = b.

Declaration

public double[] Solve(double[] value)

Parameters

Type	Name	Description
System.Double[]	value	The b from the equation Ax = b.

Returns

Type	Description
System.Double[]	The x from equation Ax = b.

Solve(Double[,])

Solves a linear equation system of the form AX = B.

Declaration

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

Parameters

Type	Name	Description
System.Double[,]	value	Parameter B from the equation AX = B.

Returns

Type	Description
System.Double[,]	The solution X from equation AX = B.

SolveForDiagonal(Double[])

Solves a linear equation system of the form AX = B.

Declaration

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

Parameters

Type	Name	Description
System.Double[]	value	Parameter B from the equation AX = B.

Returns

Type	Description
System.Double[,]	The solution X from equation AX = B.

SolveTranspose(Double[])

Solves a linear equation system of the form xA = b.

Declaration

public double[] SolveTranspose(double[] value)

Parameters

Type	Name	Description
System.Double[]	value	The b from the equation xA = b.

Returns

Type	Description
System.Double[]	The x from equation Ax = b.

SolveTranspose(Double[,])

Solves a linear equation system of the form AX = B.

Declaration

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

Parameters

Type	Name	Description
System.Double[,]	value	Parameter B from the equation AX = B.

Returns

Type	Description
System.Double[,]	The solution X from equation AX = B.

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)