x = A \ b; in Matlab

x = A \ b;

1. Is A square?
   no => use QR to solve least squares problem.
2. Is A triangular or permuted triangular?
   yes => sparse triangular solve
3. Is A symmetric with positive diagonal elements?
   yes => attempt Cholesky after symmetric minimum degree.
4. Otherwise
   => use LU on A (:, colamd(A))