ArrayFire: pinverse (original) (raw)

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

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);

array Apinv = pinverse(A);

array MustBeA = matmul(A, Apinv, A);

◆ af_pinverse()

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

Returns

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

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.

This function is not supported in GFOR.

Parameters

Returns

pseudo-inverse matrix