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Hi,
In the density of states or the band structure calculations, VASP code can be made to write the contributions from different orbits (s,p,d..) or specific orbitals (1s,2s..). How does the code calculates mathematically the contributions from each orbital and each atom which are written in the output files?

I am not asking how to analyse it from the outputs, I just want to realise what are the approximations taken by VASP to arrive at this data.

Thanks

In the wiki article about the LORBIT INCAR tag some equations explain the projection used. There is also a reference if you want to know more details.