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MInvCG has hard-coded isign internally, is this intentional? #89

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kostrzewa opened this issue Jul 7, 2017 · 4 comments
Open

MInvCG has hard-coded isign internally, is this intentional? #89

kostrzewa opened this issue Jul 7, 2017 · 4 comments

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@kostrzewa
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The multi-shift CG has isign hard-coded to +1 and -1 internally, is this intentional and sensible?

@martin-ueding
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Since the operator() takes an isign argument, I'd say that this is not sensible. The test case only tests one isign. The hard-coded default might be implicitly used in Chroma, so one has to be careful when actually using the isign.

@kostrzewa
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@bjoo Can we safely switch this to +-isign throughout without affecting you?

@bjoo
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bjoo commented Jul 7, 2017 via email

@kostrzewa
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Hi Balint,

sorry for taking so long to reply to this, it has been an unusually busy week.

The answer to your question is that yes, we solve

( M M^\dagger + shift_i ) psi_i = chi

The reason for this is basically one of convention. In tmLQCD, everything uses the hermitian Wilson Dirac operator plus a twisted quark mass (without gamma_5 then), so we have something like

Q_{+} = \gamma_5 ( M_w + i \mu \gamma_5 ) = \gamma_5 M_w + i\mu
Q_{-} = Q_{+}^\dagger = \gamma_5 ( M_w - i \mu \gamma_5 ) = \gamma_5 M_w - i\mu

And for reasons of convention, our nf=2 action is

exp{- \phi^dagger ( Q_{+} Q_{-} )^{-1} \phi }

where translating between QPhiX and tmLQCD, we have to insert appropriate factors of \gamma_5 but everything goes through smoothly with the definitions that we've made with the twisted mass addtitions to QPhiX as long as we solve the "isign=-1" system. ( M = M_w + i \mu \gamma_5, M^dag = M_w^dag - i \mu\gamma_5)

Now the situation for nf=2 (degenerate) also translates to the non-degenerate doublet or a single flavour of Wilson quarks and so we need to solve the shifted M.M^dagger system rather than the shifted M^dagger.M system.

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