MatrixMathSingularValueDecomposition Class

Class to calculate the singular value decomposition.

Inheritance Hierarchy

SystemObject
Altaxo.Calc.LinearAlgebraMatrixMathSingularValueDecomposition

Namespace: Altaxo.Calc.LinearAlgebra
Assembly: AltaxoCore (in AltaxoCore.dll) Version: 4.8.3572.0 (4.8.3572.0)

Syntax

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public class SingularValueDecomposition : ISingularValueDecomposition

The MatrixMathSingularValueDecomposition type exposes the following members.

Constructors

	Name	Description
	MatrixMathSingularValueDecomposition	Creates a singular value decomposition of matrix a, resulting in matrix a itself.

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Properties

	Name	Description
	Condition	Gets the condition number of the matrix, defined as the ratio of the largest singular value to the smallest.
	Diagonal	Gets the array of singular values.
	HatDiagonal	Returns the Hat diagonal. The hat diagonal is the diagonal of the Hat matrix, which is defined as `T -1 T T H = X (X X) X = U U`
	Norm2	Gets the 2-norm of the matrix, which is the largest singular value.
	Rank	Gets the rank of the matrix, which is the number of singular values greater than a small threshold.
	U	Gets the left singular vectors matrix.
	V	Gets the right singular vectors matrix.

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Methods

	Name	Description
	Backsubstitution(Double, Double)	Solves A·X = B for a vector X, where A is specified by A=USV'. U, S, and V are results of the decomposition.
	Backsubstitution(IReadOnlyListDouble, IVectorDouble)	Solves A·X = B for a vector X, where A is specified by A=USV'. U, S, and V are results of the decomposition.
	BuildHatDiagonal	Builds the diagonal of the hat matrix for the current singular value decomposition.
	ChopSingularValues	Sets all singular values, that are lesser than relativeThreshold*(maximum singular value), to zero.
	ComputeSingularValueDecomposition	Creates a singular value decomposition of matrix a, resulting in matrix a itself.
	Equals	Determines whether the specified object is equal to the current object. (Inherited from Object)
	Finalize	Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection. (Inherited from Object)
	GetCovariances	Calculates the covariance matrix Cov(i,j)= (X'X)^(-1) = SUM_over_k( V[i,k]*V[j,k]/s[k]^2). If s[k] is zero, 1/s[k]^2 will be set to zero. If the singular value decomposition was used to make a linear fit, this is the variance-covariance matrix of the fitting parameters.
	GetHashCode	Serves as the default hash function. (Inherited from Object)
	GetType	Gets the Type of the current instance. (Inherited from Object)
	MemberwiseClone	Creates a shallow copy of the current Object. (Inherited from Object)
	Solve	Solves the equation A x = B and returns x.
	ToString	Returns a string that represents the current object. (Inherited from Object)

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Remarks

Adapted from Lutz Roeders Mapack library.

Some properties of the singular value decomposition:
             X - the matrix to decompose, U w V' - the decomposition.
            
                   -1
             (X' X)    = V (1/w^2) V'  (usually called covariance matrix)
            
                                    -1
             Hat matrix H = X  (X' X)  X' = U U'

Reference

Altaxo.Calc.LinearAlgebra Namespace