LinAlgExtensions

Consistent interface for QR-Factorization

Pseudo-Inverse Factorization

For sparse matrices A, there is currently algorithm implemented to calculate pinv(A) * rhs and pinv(A)' * rhs for arbitrary right hand sides rhs.

An algorithm is provided, which uses two QR-Factorizations. Without considering the column- and row permutation, which complicate the description it is as follows:

If `A = Q * R` where `R` has maximal rank (identical to the rank of `A`)

and `R' = q * r`

We have A = Q * r' * q' and pinv(A) = q * inv(r)' * Q'.

usage:

pin = pinvfact(A)

    x = pin \ rhs

Random test matrices

randorth: orthogonal columns or rows

randrealsv: arbitrary shape matrices with gibven singular values

randsparse: sparse random matrix with given shape and rank