C# Class YAMP.Numerics.SingularValueDecomposition

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

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Public Methods

Method	Description
Condition ( ) : double	Two norm condition number
GetU ( ) : MatrixValue	Return the left singular vectors
GetV ( ) : MatrixValue	Return the right singular vectors
Norm2 ( ) : double	Two norm
Rank ( ) : int	Effective numerical matrix rank
SingularValueDecomposition ( MatrixValue Arg ) : System	Construct the singular value decomposition

Method Details

Condition() public method

Two norm condition number

public Condition ( ) : double
return	double

GetU() public method

Return the left singular vectors

public GetU ( ) : MatrixValue
return	YAMP.MatrixValue

GetV() public method

Return the right singular vectors

public GetV ( ) : MatrixValue
return	YAMP.MatrixValue

Norm2() public method

Two norm

public Norm2 ( ) : double
return	double

Rank() public method

Effective numerical matrix rank

public Rank ( ) : int
return	int

SingularValueDecomposition() public method

Construct the singular value decomposition

public SingularValueDecomposition ( MatrixValue Arg ) : System
Arg	YAMP.MatrixValue	Rectangular matrix
return	System