ILNumerics - Technical Application Development
Assembly: ILNumerics.Computing (in ILNumerics.Computing.dll) Version: 5.5.0.0 (5.5.7503.3146)
Pseudo inverse of input matrix A
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:
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
public static RetArray<double> pinv( InArray<double> A, Nullable<double> tolerance = null )
Parameters
- A
- Type: ILNumerics.InArray<Double>
Input matrix. - tolerance (Optional)
- Type: System.Nullable<Double>
[Optional] Tolerance. Default: (null) - use default tolerance (see remarks).
Return Value
Type: RetArray<Double>Pseudo inverse of input matrix A
Remarks
- A * pinv(A) * A = A
- pinv(A) * A * pinv(A) = pinv(A)
- pinv(A) * A is hermitian.
- A * pinv(A) is hermitian.
- 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]
See Also
Reference
MathInternal.pinv(InArray<Double>, Nullable<Double>)
MathInternal.svd(InArray<Double>)
MathInternal.norm(InArray<Double>, Double)