Pseudo-invert (Moore-Penrose) a matrix. More...

Functions
AFAPI array	pinverse (const array &in, const double tol=1E-6, const matProp options=AF_MAT_NONE)
	C++ Interface to pseudo-invert (Moore-Penrose) a matrix. More...

AFAPI af_err	af_pinverse (af_array *out, const af_array in, const double tol, const af_mat_prop options)
	C Interface to pseudo-invert (Moore-Penrose) a matrix. More...

Detailed Description

Pseudo-invert (Moore-Penrose) a matrix.

This function calculates the Moore-Penrose pseudoinverse of a matrix \(A\), using af::svd at its core. If \(A\) is of size \(M \times N\), then its pseudoinverse \(A^+\) will be of size \(N \times M\).

This calculation can be batched if the input array is three or four-dimensional \((M \times N \times P \times Q\), with \(Q=1\) for only three dimensions \()\). Each \(M \times N\) slice along the third dimension will have its own pseudoinverse, for a total of \(P \times Q\) pseudoinverses in the output array \((N \times M \times P \times Q)\).

Below is an example snippet of its usage. In this example, we have a matrix \(A\) and compute its pseudoinverse \(A^+\). This condition must hold: \(AA^+A=A\), given that the two matrices are pseudoinverses of each other (in fact, this is one of the Moore-Penrose conditions):

    float hA[] = {0, 1, 2, 3, 4, 5};
    array A(3, 2, hA);
    //  0.0000     3.0000
    //  1.0000     4.0000
    //  2.0000     5.0000
 
    array Apinv = pinverse(A);
    // -0.7778    -0.1111     0.5556
    //  0.2778     0.1111    -0.0556
 
    array MustBeA = matmul(A, Apinv, A);
    //  0.0000     3.0000
    //  1.0000     4.0000
    //  2.0000     5.0000

Function Documentation

◆ af_pinverse()

AFAPI af_err af_pinverse	(	af_array *	out,
		const af_array	in,
		const double	tol,
		const af_mat_prop	options
	)

C Interface to pseudo-invert (Moore-Penrose) a matrix.

Currently uses the SVD-based approach.

Parameter tol is not the actual lower threshold, but it is passed in as a parameter to the calculation of the actual threshold relative to the shape and contents of in.

Suggested parameters for tol: 1e-6 for single precision and 1e-12 for double precision.

Parameters

[out]	out	pseudo-inverse matrix
[in]	in	input matrix
[in]	tol	defines the lower threshold for singular values from SVD
[in]	options	must be AF_MAT_NONE (more options might be supported in the future)

Returns: AF_SUCCESS, if function returns successfully, else an af_err code is given

◆ pinverse()

AFAPI array pinverse	(	const array &	in,
		const double	tol = `1E-6`,
		const matProp	options = `AF_MAT_NONE`
	)

C++ Interface to pseudo-invert (Moore-Penrose) a matrix.