no piv.                   - |A*x-b| =               0 - |x-x_true| =         80.0603
partial piv. (swap)       - |A*x-b| =     3.63842e-12 - |x-x_true| =         6.54865
partial piv. (indirect)   - |A*x-b| =      3.0003e-11 - |x-x_true| =         6.54865
scaled partial piv.       - |A*x-b| =      3.0003e-11 - |x-x_true| =         6.54865