qmcpack/tests/heg/heg_14_gamma

These tests are for a 14 electron homogeneous electron gas at the gamma point.

The tests include:
  non-interacting          VMC (zero variance)
  non-interacting          DMC (zero variance)
  Slater-only              VMC ("Hartree-Fock")
  Slater-Jastrow           VMC (using older and recent input styles)
  Slater-Jastrow-Backflow  VMC
  Slater-Jastrow           DMC

The original files come from the 2012 QMCPACK school.  These were 
recovered from the old Google Code website as a tar file 
(qmcpack_tutorial.tar). The original output data (not included) was 
generated with QMCPACK SVN revision 5548 on 11 July 2012 by Jeremy 
McMinis.  The original runs include the calculation of the homogeneous 
pair correlation function, g(r).  The calculation of g(r) is retained 
in the current tests, but only the energy and its variance are checked 
at this time.  The original files were rerun using a recent build of 
SVN revision 6259 and were found to agree.  Subsequent runs of QMCPACK 
release versions 3.0.0 and 3.1.1 were also found to agree across 
multiple machines at ORNL.  

The backflow wavefunction in the original files had to be reoptimized 
because a cutoff larger than the Wigner-Seitz radius had been used 
originally (this was caught automatically by version 3.1.1).  Both 
SVN revision 6259 and the 3.1.1 release were capable of reoptimizing 
the backflow function (quartic optimizer, energy minization) to a 
similar degree of quality as the original in terms of energy and 
variance.  A more recent way of specifying HEG wavefunction input was 
added as a test as were Slater-only runs without an interaction as 
this provides an exact reference.  

Reference data was generated with runs the same overall length 
(blocks x steps) as those included in ./qmc-ref, but using 10x more 
blocks (8000) and 10x fewer steps.  Using more blocks reduced the 
statistical error of the error bars, but resulted in output data files 
that were too large to include in the QMCPACK distribution.  The 
reference values and error bars are therefore computed from the 8000 
block runs.  The included reference runs were confirmed to be 
consistent with the original higher block count runs.

Reference data from the high block count runs is found below (25 blocks 
excluded as equilibration from heg_SJ_dmc, 10 from all others):

                          LocalEnergy               Variance           ratio 
heg_NI      series 0   0.627711 +/- 0.000000   0.000000 +/- 0.000000   0.0000 
heg_NI_dmc  series 1   0.627711 +/- 0.000000   0.000000 +/- 0.000000   0.0000 
heg_HF      series 0  -0.812484 +/- 0.000027   0.193169 +/- 0.001852   0.2378 
heg_SJ      series 0  -1.073323 +/- 0.000027   0.024574 +/- 0.000018   0.0229 
heg_SJ_new  series 0  -1.073286 +/- 0.000027   0.024564 +/- 0.000034   0.0229
heg_SJB     series 0  -1.084963 +/- 0.000025   0.022667 +/- 0.000076   0.0209
heg_SJ_dmc  series 2  -1.110199 +/- 0.000032   0.022894 +/- 0.000006   0.0206  


For comparison, corresponding data for the lower block count reference 
data found in ./qmc-ref is:

>qmca -e 2 -q ev *scalar*
                          LocalEnergy               Variance           ratio 
heg_NI      series 0   0.627711 +/- 0.000000   0.000000 +/- 0.000000   0.0000 
heg_NI_dmc  series 1   0.627711 +/- 0.000000   0.000000 +/- 0.000000   0.0000 
heg_HF      series 0  -0.812480 +/- 0.000027   0.191245 +/- 0.000342   0.2354 
heg_SJ      series 0  -1.073379 +/- 0.000026   0.024530 +/- 0.000009   0.0229 
heg_SJ_new  series 0  -1.073333 +/- 0.000027   0.024553 +/- 0.000019   0.0229 
heg_SJB     series 0  -1.084968 +/- 0.000025   0.022614 +/- 0.000026   0.0208 
heg_SJ_dmc  series 2  -1.110158 +/- 0.000032   0.022906 +/- 0.000006   0.0206 

Tests input files were created by reducing the number of steps from 
the included reference by a factor of 10 for the "long" tests and by a 
further factor of 10 for the short tests.  A number of warmup steps 
was added to match the practice of excluding only the first two blocks 
within the ctest system (check_scalars.py -e 2 ...).  

Reference values for the mean local energy and variance were taken 
from the high block count reference runs.  Expected error bars were 
derived from the high block count data by multiplying the reference 
error bars by a factor of sqrt(10+1) and sqrt(100+1) for the long 
and short tests, respectively.  The factor of +1 accounts for the 
error bar intrinsic to the high block count runs.

The target means and error bars for long and short tests are:

                      refmean   referr    longerr   shorterr
heg_NI      energy    0.627711  0.000000  0.000001  0.000001  
            variance  0.000000  0.000000  0.000001  0.000001  
heg_NI_dmc  energy    0.627711  0.000000  0.000001  0.000001  
            variance  0.000000  0.000000  0.000001  0.000001  
heg_HF      energy   -0.812484  0.000027  0.000090  0.000271  
            variance  0.193169  0.001852  0.006142  0.018612  
heg_SJ      energy   -1.073323  0.000027  0.000090  0.000271  
            variance  0.024574  0.000018  0.000060  0.000181  
heg_SJ_new  energy   -1.073286  0.000027  0.000090  0.000271  
            variance  0.024564  0.000034  0.000113  0.000342  
heg_SJB     energy   -1.084963  0.000025  0.000083  0.000251  
            variance  0.022667  0.000076  0.000252  0.000764  
heg_SJ_dmc  energy   -1.110199  0.000032  0.000106  0.000322  
            variance  0.022894  0.000006  0.000020  0.000060  

Error bars from typical long and short runs are shown below:

Typical long run results:
>qmca -e 2 -q ev *long*scalar*
                               LocalEnergy               Variance           ratio 
heg_long_NI      series 0   0.627711 +/- 0.000000   0.000000 +/- 0.000000   0.0000 
heg_long_NI_dmc  series 1   0.627711 +/- 0.000000   0.000000 +/- 0.000000   0.0000 
heg_long_HF      series 0  -0.812621 +/- 0.000081   0.189785 +/- 0.000361   0.2335 
heg_long_SJ      series 0  -1.073216 +/- 0.000085   0.024582 +/- 0.000052   0.0229 
heg_long_SJ_new  series 0  -1.073202 +/- 0.000085   0.024605 +/- 0.000057   0.0229 
heg_long_SJB     series 0  -1.084962 +/- 0.000078   0.022531 +/- 0.000029   0.0208 
heg_long_SJ_dmc  series 2  -1.110036 +/- 0.000103   0.022899 +/- 0.000027   0.0206 

Typical short run results:
>qmca -e 2 -q ev *short*scalar*
                                LocalEnergy               Variance           ratio 
heg_short_NI      series 0   0.627711 +/- 0.000000   0.000000 +/- 0.000000   0.0000 
heg_short_NI_dmc  series 1   0.627711 +/- 0.000000   0.000000 +/- 0.000000   0.0000 
heg_short_HF      series 0  -0.812474 +/- 0.000310   0.189679 +/- 0.000867   0.2335 
heg_short_SJ      series 0  -1.073104 +/- 0.000273   0.024401 +/- 0.000075   0.0227 
heg_short_SJ_new  series 0  -1.073145 +/- 0.000277   0.024518 +/- 0.000086   0.0228 
heg_short_SJB     series 0  -1.085005 +/- 0.000256   0.022623 +/- 0.000234   0.0209 
heg_short_SJ_dmc  series 2  -1.110288 +/- 0.000459   0.022872 +/- 0.000066   0.0206 
  
Rough timings for the tests on an old (circa 2013) AMD system are:

>grep 'Total Exe' *long*.out
heg-long-NI.out:       Total Execution time = 9.4717e-01 secs
heg-long-NI-dmc.out:   Total Execution time = 2.2727e+00 secs
heg-long-HF.out:       Total Execution time = 2.0527e+02 secs
heg-long-SJ.out:       Total Execution time = 3.0473e+01 secs
heg-long-SJ-new.out:   Total Execution time = 2.8511e+01 secs
heg-long-SJB.out:      Total Execution time = 3.1974e+02 secs
heg-long-SJ-dmc.out:   Total Execution time = 3.8034e+02 secs

>grep 'Total Exe' *short*.out
heg-short-NI.out:      Total Execution time = 1.3245e-01 secs
heg-short-NI-dmc.out:  Total Execution time = 2.9920e-01 secs
heg-short-HF.out:      Total Execution time = 2.2165e+01 secs
heg-short-SJ.out:      Total Execution time = 4.4773e+00 secs
heg-short-SJ-new.out:  Total Execution time = 3.4323e+00 secs
heg-short-SJB.out:     Total Execution time = 3.3870e+01 secs
heg-short-SJ-dmc.out:  Total Execution time = 4.2180e+01 secs