Extensive optimization of grids

I extensively optimized the Grid code. Specifically:

I removed many allocations that were showing up in profiling. This basically amounted to use in many more places std::array with size maxdim rather than std::vector, and rewriting overloads for some functions so that it is possible to pass a pair (pointer,size). In this way I can use them to act on vectors or arrays without other changes. I guess most of this code could be simplified using something similar to C++20 span to do the conversion, without replicating all functions.
In one case I used a small_vector. This is the number of neighbors (2^dim), which might be too large to fit in stack. The code will automatically place it on heap when dim>4
I cherry picked a number of functions that were showing up in the profiler and moved them to a locally defined separate class where the number of dimensions is known at compiler time (template<unsigned dimension_> class Accelerator). The code is a bit messy and probably I need to add more documentation.

I want to go back and revise the code before mering. Meanwhile I post the results that I could obtain on my INTEL macbook.

Test 1 - update

The first test is representative of cases where the PACE is relatively low, so that the cost is mostly in adding new Gaussians. Here I get a significant speedup (more than 50%). I see a significant speedup also in using sum_hills on a large file (not shown). I expect this to also help when restarting simulations with many Gaussians. The speedup is mostly in the Update phase, but from the timings it can be seen that also Calculating is faster.

Command:

plumed benchmark --nsteps 10000 --natoms 100

plumed.dat:

d1: DISTANCE ATOMS=1,2
d2: DISTANCE ATOMS=3,4
d3: DISTANCE ATOMS=5,6
c1: CUSTOM ARG=d1 FUNC=sin(x) PERIODIC=NO
c2: CUSTOM ARG=d2 FUNC=sin(x) PERIODIC=NO
c3: CUSTOM ARG=d3 FUNC=sin(x) PERIODIC=NO
METAD ARG=c1,c2,c3 HEIGHT=1.0 GRID_MIN=-1,-1,-1 GRID_MAX=+1,+1,+1 SIGMA=0.1,0.1,0.1 PACE=10

Results:

BENCH:  Kernel: /Users/bussi/plumed2/tmp/reference/lib/libplumedKernel.dylib
PLUMED:                                               Cycles        Total      Average      Minimum      Maximum
PLUMED:                                                    1     4.541843     4.541843     4.541843     4.541843
PLUMED: 1 Prepare dependencies                         10000     0.005873     0.000001     0.000000     0.000055
PLUMED: 2 Sharing data                                 10000     0.007854     0.000001     0.000000     0.000032
PLUMED: 3 Waiting for data                             10000     0.002283     0.000000     0.000000     0.000015
PLUMED: 4 Calculating (forward loop)                   10000     0.035392     0.000004     0.000002     0.000083
PLUMED: 5 Applying (backward loop)                     10000     0.008125     0.000001     0.000000     0.000019
PLUMED: 6 Update                                       10000     4.423286     0.000442     0.000000     0.011253
BENCH:  
BENCH:  Kernel: this
PLUMED:                                               Cycles        Total      Average      Minimum      Maximum
PLUMED:                                                    1     1.973595     1.973595     1.973595     1.973595
PLUMED: 1 Prepare dependencies                         10000     0.006112     0.000001     0.000000     0.000018
PLUMED: 2 Sharing data                                 10000     0.007715     0.000001     0.000000     0.000067
PLUMED: 3 Waiting for data                             10000     0.002298     0.000000     0.000000     0.000016
PLUMED: 4 Calculating (forward loop)                   10000     0.030407     0.000003     0.000002     0.000060
PLUMED: 5 Applying (backward loop)                     10000     0.008156     0.000001     0.000000     0.000027
PLUMED: 6 Update                                       10000     1.865217     0.000187     0.000000     0.007363

Test 2 - calculate

The second test is representative of cases where the PACE is larger so that the cost is mostly in evaluating the potential. Here the speedup is limited but measurable, and is in the Calculating phase.

Command

plumed benchmark --nsteps 100000 --natoms 100

plumed.dat:

d1: DISTANCE ATOMS=1,2
d2: DISTANCE ATOMS=3,4
d3: DISTANCE ATOMS=5,6
c1: CUSTOM ARG=d1 FUNC=sin(x) PERIODIC=NO
c2: CUSTOM ARG=d2 FUNC=sin(x) PERIODIC=NO
c3: CUSTOM ARG=d3 FUNC=sin(x) PERIODIC=NO

METAD ARG=c1,c2,c3 HEIGHT=1.0 GRID_MIN=-1,-1,-1 GRID_MAX=+1,+1,+1 SIGMA=0.1,0.1,0.1 PACE=100000

Results:

BENCH:  Kernel: /Users/bussi/plumed2/tmp/reference/lib/libplumedKernel.dylib
PLUMED:                                               Cycles        Total      Average      Minimum      Maximum
PLUMED:                                                    1     0.697111     0.697111     0.697111     0.697111
PLUMED: 1 Prepare dependencies                        100000     0.038268     0.000000     0.000000     0.000045
PLUMED: 2 Sharing data                                100000     0.057732     0.000001     0.000000     0.000095
PLUMED: 3 Waiting for data                            100000     0.014023     0.000000     0.000000     0.000034
PLUMED: 4 Calculating (forward loop)                  100000     0.258862     0.000003     0.000002     0.000148
PLUMED: 5 Applying (backward loop)                    100000     0.058995     0.000001     0.000000     0.000045
PLUMED: 6 Update                                      100000     0.025503     0.000000     0.000000     0.000064
BENCH:  
BENCH:  Kernel: this
PLUMED:                                               Cycles        Total      Average      Minimum      Maximum
PLUMED:                                                    1     0.642643     0.642643     0.642643     0.642643
PLUMED: 1 Prepare dependencies                        100000     0.040423     0.000000     0.000000     0.000054
PLUMED: 2 Sharing data                                100000     0.054178     0.000001     0.000000     0.000053
PLUMED: 3 Waiting for data                            100000     0.016572     0.000000     0.000000     0.000066
PLUMED: 4 Calculating (forward loop)                  100000     0.214136     0.000002     0.000002     0.000177
PLUMED: 5 Applying (backward loop)                    100000     0.055705     0.000001     0.000000     0.000043
PLUMED: 6 Update                                      100000     0.026816     0.000000     0.000000     0.000047

plumed / plumed2

Extensive optimization of grids #1030

Test 1 - update

Test 2 - calculate

Codecov Report