Traction_change and fault_info (strike_dir, dip_dir, normal_dir orientation) in PyLith

Dear all,
I want to calculate the Coulomb stress (CFS) through the Traction_change on one fault in Pylith.
I checked the fault_info file (strike_dir,dip_dir, normal_dir), but it doesn’t seem to be consistent with the results of the direction value that I calculated according to my formula ( δ,dip angle; φ, strike angle; λ, slip angle; 1. normal_dir: x= sinδ×cosφ, y= -sinδ×sinφ, z= cosδ ; 2. strike_dir: x= sinφ, y= cosφ, z=0; 3. dip_dir: x= cosφ×cosδ, y= -sinφ×cosδ, z= sinδ)
In addition, if Traction_change_Z (TZ) on the fault is in the direction of fault opening, it should be projected on the normal and slip direction of the fault, and the CFS can be calculated by the formula : CFS = TX×cosλ + (TY+TZ×cosδ)×sinλ - μ×TZ×sinδ ? The result seems not be correct.

Thank you in advance.
Best regards

Fault slip and tractions changes are given in the fault coordinate system (along strike, up dip, fault normal). The strike_dir, dip_dir, and normal_dir give the components of the along-strike, up-dip, and fault normal directions in the global coordinate system. If you want to compute the Coulomb stress changes on the fault surface, then you do not need to rotate the traction vector.

Thank you so much
Best Regards