  Magnetic field extrapolation is an important tool to study the
three-dimensional (3D) solar coronal magnetic field which is difficult to
directly measure. Various analytic models and numerical codes exist but their
results often drastically differ. Thus a critical comparison of the modeled
magnetic field lines with the observed coronal loops is strongly required to
establish the credibility of the model. Here we compare two different
non-potential extrapolation codes, a non-linear force-free field code
(CESE-MHD-NLFFF) and a non-force-free field (NFFF) code in modeling a solar
active region (AR) that has a sigmoidal configuration just before a major flare
erupted from the region. A 2D coronal-loop tracing and fitting method is
employed to study the 3D misalignment angles between the extrapolated magnetic
field lines and the EUV loops as imaged by SDO/AIA. It is found that the
CESE-MHD-NLFFF code with preprocessed magnetogram performs the best, outputting
a field which matches the coronal loops in the AR core imaged in AIA 94 {\AA}
with a misalignment angle of ~10 degree. This suggests that the CESE-MHD-NLFFF
code, even without using the information of coronal loops in constraining the
magnetic field, performs as good as some coronal-loop forward-fitting models.
For the loops as imaged by AIA 171 {\AA} in the outskirts of the AR, all the
codes including the potential-field give comparable results of mean
misalignment angle (~30 degree). Thus further improvement of the codes is
needed for a better reconstruction of the long loops enveloping the core
region.
