ILMathpinv Method (InArrayfcomplex, Nullablefcomplex)

ILNumerics Ultimate VS Documentation

ILNumerics - Technical Application Development

Moore-Penrose pseudo inverse of A.

[ILNumerics Computing Engine]

Namespace: ILNumerics
Assembly: ILNumerics.Computing (in ILNumerics.Computing.dll) Version: 5.5.0.0 (5.5.7503.3146)

Syntax

Copy

public static RetArray<fcomplex> pinv(
	InArray<fcomplex> A,
	Nullable<fcomplex> tolerance = null
)

Public Shared Function pinv ( 
	A As InArray(Of fcomplex),
	Optional tolerance As Nullable(Of fcomplex) = Nothing
) As RetArray(Of fcomplex)

Dim A As InArray(Of fcomplex)
Dim tolerance As Nullable(Of fcomplex)
Dim returnValue As RetArray(Of fcomplex)

returnValue = ILMath.pinv(A, tolerance)

Parameters

A: Type: ILNumericsInArrayfcomplex
Input matrix.
tolerance (Optional): Type: SystemNullablefcomplex
[Optional] Tolerance. Default: (null) - use default tolerance (see remarks).

Return Value

Type: RetArrayfcomplex
Pseudo inverse of input matrix A

Remarks

The function returns the pseudo inverse (Moore-Penrose pseudoinverse) of input matrix A. The return value will be of the same size as A.T. It will satisfy the following conditions:

A * pinv(A) * A = A
pinv(A) * A * pinv(A) = pinv(A)
pinv(A) * A is hermitian.
A * pinv(A) is hermitian.

pinv(InArrayfcomplex, Nullablefcomplex) relies on svd(InArraycomplex), utilizing native Lapack functions internally. Singular values less than tolerance will be set to zero. As default tolerance the following equation is used: \\ tolerance = length(A) * norm(A) * eps, where

length(A) - the longest dimension of A.
norm(A) being the largest singular value of A.
eps - the smallest number greater than one.

[ILNumerics Computing Engine]

Reference

ILMath Class

pinv Overload

ILNumerics Namespace

MathInternal.pinv(InArrayfcomplex, Nullablefcomplex)

MathInternal.svd(InArrayfcomplex)

Globalseps

MathInternal.norm(InArrayfcomplex, Single)