FanCI tutorial

[AlexandreDeCamargo]

After getting from @RichRick1 a FCIDUMP file of a Hubbard model I am getting the values of the cost function, the residuals, the optimality and active_mask equal to zero when optimizing the AP1roG wavefunction. The solution found is:

x: [ 0.000e+00 0.000e+00 0.000e+00 0.000e+00 0.000e+00 0.000e+00 0.000e+00 0.000e+00 0.000e+00 3.000e+01]

Optimizing the pCCD+S wave function give me residuals near zero ($10^{-15}$ order) and a solution x:

x: [-1.334e+01 1.334e+01 ... -5.454e-14 3.000e+01]

[RichRick1]

@PaulWAyers I gave @AlexandreDeCamargo 6-site Hubbard model with U=10, so it's a strongly correlated system. I'd expect to have much higher projection error
@msricher is there any system for which AP1roG method will give a big error in energy?

[PaulWAyers]

AP1roG should be bad for attractive Hubbard and attractive Richardson.

[msricher]

I'm not sure. Is it possible to compare against the FCI energy?