﻿ILMath.pinv Method (InArray(Double), Nullable(Double))

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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: ILNumericsInArrayDouble
Input matrix.
tolerance (Optional)
Type: SystemNullableDouble
[Optional] Tolerance. Default: (null) - use default tolerance (see remarks).

#### Return Value

Type: RetArrayDouble
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(InArrayDouble, NullableDouble) 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]