Fit linear models in Futhark with a robustness towards ill-conditioned problems. Model parameters are estimated by solving the linear least squares equations based on a pivoting QR-decomposition. It is well suited for small, numerically unstable problems.

This package seeks to match the output of lm in the R language. Therefore, the QR-decomposition and parts of the least squares solver is a 1:1 translation of sequential FORTRAN routines from the famous LINPACK library (see linpack.fut).

The QR-decomposition is rank revealing, meaning we obtain the rank of the regressor matrix, X. The rank is used to ensure a meaningful fit: if the problem is ill-conditioned so that (at least for numerical work) the regressor matrix is rank deficient, parameters will be dropped accordingly until this is no longer the case. It should be possible to extend this to also output the condition number of X, or at least an estimate of this---untested sample code can be found in lm.fut.