SingularValueDecomposition<T> Class

public abstract class SingularValueDecomposition<T> : Decomposition<T>

Public MustInherit Class SingularValueDecomposition(Of T)
	Inherits Decomposition(Of T)

generic<typename T>
public ref class SingularValueDecomposition abstract : public Decomposition<T>

[<AbstractClassAttribute>]
type SingularValueDecomposition<'T> = 
    class
        inherit Decomposition<'T>
    end

Inheritance

Object  →  LinearOperator<T>  →  Decomposition<T>  →  SingularValueDecomposition<T>

Type Parameters

T

The singular value decomposition (SVD) of a matrix A rewrites the matrix in the form A= USV^T, where U and V are orthogonal matrices, and S is a diagonal matrix whose diagonal contains the singular values of the matrix.

QRDecomposition<T> can operate in two modes. In overwrite mode, the original matrix is overwritten by the decomposition. In preserve mode, the original matrix is preserved, and a new matrix is created to hold the decomposition. You can set the mode through the Overwrite property.

SingularValueDecomposition<T> inherits from LinearOperator<T>. This means you can use it to solve systems of linear equations. You can solve for a single right-hand side, or for multiple right-hand sides using the Solve(Vector<T>) method. You can also calculate the determinant, the inverse, and an estimate for the EstimateConditionNumber().

In addition, the SingularValueDecomposition<T> class provides some unique methods. The GetPseudoInverse() method calculates the pseudo-inverse of the matrix. This is a matrix A⁺ such that AA⁺A = A.

The managed implementation of the singular value decomposition is based on the LINPACK routine DSVDC. The native version uses the LAPACK routine ?GESDD.

Reference