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//                                                                         //
//  Quadratic Monte Carlo Method                                           //
//                                                                         //
//  Burkhard Militzer                                    Berkeley 03-08-23 //
//                                                                         //
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(1) Compile our QMC code by typing "make"

machine:~/CMS_MC_test_03-08-23a> make
g++ -O3 -Wall -pedantic -funroll-loops  -DRING       Standard.C Main.C Form.C Timer.C PrintErrorBar.C  -lm -o ring
g++ -O3 -Wall -pedantic -funroll-loops  -DHARMONIC   Standard.C Main.C Form.C Timer.C PrintErrorBar.C  -lm -o harm
g++ -O3 -Wall -pedantic -funroll-loops  -DROSENBROCK Standard.C Main.C Form.C Timer.C PrintErrorBar.C  -lm -o rosen

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(2) Run test of harmonic potential in tcsh

set index = 58
set T = 0.01
set n = 6
set a = 1.5
harm -affine           n=$n a=$a T=${T} nBlocks=100000 > affine${index}_${T}_${n}_${a}.txt &
harm -qmc              n=$n a=$a T=${T} nBlocks=100000 > qmcLin${index}_${T}_${n}_${a}.txt &
harm -qmc    -Gaussian n=$n a=$a T=${T} nBlocks=100000 > qmcGau${index}_${T}_${n}_${a}.txt &

# Compare the output with the following results. The MC average of E should be close to 0.5*n*T = 0.03
 
grep "Fraction= 0.9" *58_*.txt
affine58_0.01_6_1.5.txt: Fraction= 0.9 n=  90000 E=     0.03000173 +-     0.00001369
qmcGau58_0.01_6_1.5.txt: Fraction= 0.9 n=  90000 E=     0.03003602 +-     0.00001169
qmcLin58_0.01_6_1.5.txt: Fraction= 0.9 n=  90000 E=     0.02999435 +-     0.00001152

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(3) Perform calculations for the ring potential, again with tcsh

machine:~/CMS_MC_test_03-08-23a> tcsh
set index = 57
set T = 0.01
set n = 6
set a = 1.5
set m = 6
set R = 1.0
ring -low -affine           m=$m n=$n a=$a T=${T} R=${R} nBlocks=100000 > affine${index}_${T}_${n}_${m}_${a}_${R}.txt &
ring -low -qmc              m=$m n=$n a=$a T=${T} R=${R} nBlocks=100000 > qmcLin${index}_${T}_${n}_${m}_${a}_${R}.txt &
ring -low -qmc    -Gaussian m=$m n=$n a=$a T=${T} R=${R} nBlocks=100000 > qmcGau${index}_${T}_${n}_${m}_${a}_${R}.txt &

# Compare the output with the following. The MC averages will not agree perfectly.

machine:~/CMS_MC_test_03-08-23a> grep "Fraction= 0.9" *57_*.txt
affine57_0.01_6_6_1.5_1.0.txt: Fraction= 0.9 n=  90000 E=    -0.00031481 +-     0.00007970
qmcGau57_0.01_6_6_1.5_1.0.txt: Fraction= 0.9 n=  90000 E=    -0.00030795 +-     0.00004486
qmcLin57_0.01_6_6_1.5_1.0.txt: Fraction= 0.9 n=  90000 E=    -0.00026504 +-     0.00003554

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(4) To evaluate the performance of our MODIFIED WALK moves, we recommend

machine:~/CMS_MC_test_03-08-23a> tcsh
set index = 199
set T = 1.0
foreach nWalkers (3 4 5 6 8 10 20) 
  set para = "T=$T nStepsPerBlock=1000 nBlocks=100000 nWalkers=${nWalkers}"
  foreach nMovers (3 4 5 6 10)
    foreach a (1.2 1.5 2.0 3.0)
      rosen -walk $para nMovers=$nMovers a=$a > walk${index}_${nWalkers}_${nMovers}_${a}.txt &
    end
  end
end

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(5) To understand the implementation of our QMC method, 
we recommend opening the file "MC.h" and reading the function 
PerformOneQuadraticMonteCarloSweep(...)