SingularValueDecomposition Class

Singular Value Decomposition for a rectangular matrix.

Inheritance Hierarchy

SystemObject
Accord.Math.DecompositionsSingularValueDecomposition

Namespace: Accord.Math.Decompositions
Assembly: Accord.Math (in Accord.Math.dll) Version: 3.8.0

Syntax

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[SerializableAttribute]
public sealed class SingularValueDecomposition : ICloneable, 
	ISolverMatrixDecomposition<double>

<SerializableAttribute>
Public NotInheritable Class SingularValueDecomposition
	Implements ICloneable, ISolverMatrixDecomposition(Of Double)

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The SingularValueDecomposition type exposes the following members.

Constructors

	Name	Description
	SingularValueDecomposition(Double)	Constructs a new singular value decomposition.
	SingularValueDecomposition(Double, Boolean, Boolean)	Constructs a new singular value decomposition.
	SingularValueDecomposition(Double, Boolean, Boolean, Boolean)	Constructs a new singular value decomposition.
	SingularValueDecomposition(Double, Boolean, Boolean, Boolean, Boolean)	Constructs a new singular value decomposition.

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Properties

	Name	Description
	AbsoluteDeterminant	Returns the absolute value of the matrix determinant.
	Condition	Returns the condition number max(S) / min(S).
	Diagonal	Gets the one-dimensional array of singular values.
	DiagonalMatrix	Returns the block diagonal matrix of singular values.
	IsSingular	Gets whether the decomposed matrix is singular.
	LeftSingularVectors	Returns the U matrix of Singular Vectors.
	LogDeterminant	Returns the log of the absolute value for the matrix determinant.
	LogPseudoDeterminant	Returns the log of the pseudo-determinant for the matrix.
	Ordering	Returns the ordering in which the singular values have been sorted.
	PseudoDeterminant	Returns the pseudo-determinant for the matrix.
	Rank	Returns the effective numerical matrix rank.
	RightSingularVectors	Returns the V matrix of Singular Vectors.
	Threshold	Returns the singularity threshold.
	TwoNorm	Returns the Two norm.

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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	Computes the (pseudo-)inverse of the matrix given to the Singular value decomposition.
	Reverse	Reverses the decomposition, reconstructing the original matrix X.
	Solve(Double)	Solves a linear equation system of the form AX = B.
	Solve(Double)	Solves a linear equation system of the form Ax = b.
	SolveForDiagonal	Solves a linear equation system of the form AX = B.
	SolveTranspose(Double)	Solves a linear equation system of the form AX = B.
	SolveTranspose(Double)	Solves a linear equation system of the form xA = b.
	ToString	Returns a string that represents the current object. (Inherited from Object.)

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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.)

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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.

Reference

Accord.Math.Decompositions Namespace