Grid/HMC

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TODO: 
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i) Got mixed precision in 2f and EOFA force and action solves.
   But need mixed precision in the heatbath solve. Best for Fermop to have a "clone" method, to
   reduce the number of solver and action objects. Needed ideally for the EOFA heatbath.
   15% perhaps
   Combine with 2x trajectory length?

ii) Rational on EOFA HB  -- relax order
                         -- Test the approx as per David email

Resume / roll.sh 

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- 16^3 Currently 10 traj per hour

- EOFA use a different derivative solver from action solver
- EOFA fix Davids hack to the SchurRedBlack guessing

*** Reduce precision/tolerance  in EOFA with second CG param.                          (10% speed up)
*** Force gradient - reduced precision solve for the gradient                          (4/3x speedup)


*** Need a plan for gauge field update for mixed precision in HMC                      (2x speed up)
    -- Store the single prec action operator.
    -- Clone the gauge field from the operator function argument.
    -- Build the mixed precision operator dynamically from the passed operator and single prec clone.

*** Mixed precision CG into EOFA portion         
*** Further reduce precision in forces to 10^-6 ?

*** Overall: a 3x or so is still possible => 500s -> 160s and 20 traj per hour on 16^3.

- Use mixed precision CG in HMC                           
- SchurRedBlack.h: stop use of operator function; use LinearOperator or similar instead.
- Or make an OperatorFunction for mixed precision as a wrapper

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* Signed off 2+1f HMC with Hasenbush and strange RHMC 16^3 x 32 DWF Ls=16 Plaquette 0.5883 ish
* Signed off 2+1f HMC with Hasenbush and strange EOFA 16^3 x 32 DWF Ls=16 Plaquette 0.5883 ish
* Wilson plaquette cross checked against CPS and literature GwilsonFnone
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* RHMC: Timesteps & eigenranges matched from previous CPS 16^3 x 32 runs:
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Strange (m=0.04)  has eigenspan 
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16^3 done as 1+1+1 with separate PV's. 
/dirac1/archive/QCDOC/host/QCDDWF/DWF/2+1f/16nt32/IWASAKI/b2.13/ls16/M1_8/ms0.04/mu0.01/rhmc_multitimescale/evol5/work
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2+1f 16^3  - [ 4e^-4, 2.42 ]    for strange

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24^3 done as 1+1+1 at strange, and single quotient https://arxiv.org/pdf/0804.0473.pdf Eq 83,
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double lambda_low =   4.0000000000000002e-04 <- strange
double lambda_low =   1.0000000000000000e-02 <- pauli villars
And high = 2.5

Array bsn_mass[3] = { 
double bsn_mass[0] =   1.0000000000000000e+00
double bsn_mass[1] =   1.0000000000000000e+00
double bsn_mass[2] =   1.0000000000000000e+00
}
Array frm_mass[3] = { 
double frm_mass[0] =   4.0000000000000001e-02
double frm_mass[1] =   4.0000000000000001e-02
double frm_mass[2] =   4.0000000000000001e-02
}

***
32^3 
/dirac1/archive/QCDOC/host/QCDDWF/DWF/2+1f/32nt64/IWASAKI/b2.25/ls16/M1_8/ms0.03/mu0.004/evol6/work
***
Similar det scheme
double lambda_low =   4.0000000000000002e-04
double lambda_low =   1.0000000000000000e-02

Array bsn_mass[3] = { 
double bsn_mass[0] =   1.0000000000000000e+00
double bsn_mass[1] =   1.0000000000000000e+00
double bsn_mass[2] =   1.0000000000000000e+00
}
Array frm_mass[3] = { 
double frm_mass[0] =   3.0000000000000002e-02
double frm_mass[1] =   3.0000000000000002e-02
double frm_mass[2] =   3.0000000000000002e-02
}

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* Grid: Power method bounds check
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- Finding largest eigenvalue approx 25 not 2.5
- Conventions:

Grid MpcDagMpc based on:

   (Moo-Moe Mee^-1 Meo)^dag(Moo-Moe Mee^-1 Meo)

- with  Moo = 5-M5 = 3.2
- CPS use(d) Moo = 1
- Eigenrange in Grid is 3.2^2 rescaled so factor of 10 accounted for