I can't understand what you want to mean at all."stos()" is very clear and straightforward.
If you have any doubt about it, see its definition in "$HPEESOF_DIR/expressions/ael/network_fun.ael".
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PortZ={Z01, Z02}
Zs!=Z01, ZL!=Z02
S_Z01_ZL=stos(S, PortZ, {Z01, ZL})
S_Z01_ZL(1,1)==Gamma_in
S_Zs_ZL=stos(S, PortZ, {Zs, ZL})
S_Zs_ZL(1,1)!=Gamma_in
S_Zs_ZL(1,1)==Gamma_in_corrected
Zin is unique regardless of {Z01,Z02} values.
Zin is determined by only ZL.
Gamma_in is a reflection coefficient defined for Zin and Z01.
Gamma_in_corrected is a reflection coefficient defined for Zin and Zs.
=======================================================================
Again see
http://www.designers-guide.org/Forum/YaBB.pl?num=1266403928/24#24Try to calculate Gamma_in_corrected.
Show me plot result of this Gamma_in_corrected and S_new(1,1).
I think you can't understand S-parameters and Reference impedances at all.I think you should not use S-parameter formulation.You had better use AC analysis, although there are no difference between AC and SP analyses for me,
since they are both linear analysis.