run_pm_dmo_NFW_fixed_timestep.md

In this example we will use create IC that sample a **NFW profile** and evolve it for 1Gyr with gravity computed using several layers of a **refined particle-mesh (PM)**.

![density map and acceleration of a NFW mock profile with 7 stacked PLACEHIGHRESREGION PM components](NFW_PM_fixed_timestep.png)

Here is a first benefit of a modular code: since in `hotwheels `PM is a self-contained module, we can instantiate it an arbitrary number of times. So one can stack seven [PLACEHIGHRESREGION](https://wwwmpa.mpa-garching.mpg.de/gadget4/03_simtypes/) 
 on smaller and smaller regions (a sort of refined mesh) on top of a sampled NFW halo  and use PM-only to **get accurate force down to a kpc** (see image).


Note that to run this module you need access to hotwheels **core, IO, PM,** and **integrate** components. Note that `hotwheels` do not provide parameter or config files. It is up to the user to initalise its sub-library components and connect them.

```python
import numpy as np, os, matplotlib as plt
from hotwheels_core import *
from hotwheels_pm import *
from hotwheels_integrate import *
from hotwheels_io import *

#
# step 1: config of components
#
# at this stage we do not allocate any resource, we just
# pass the right config parameters to the constructors
# in order to compile the underlying C libraries.
#

#call MPI_Init()
mpi = hwc.MPI().init()
#configure my malloc with 2GB
mym = MyMalloc(alloc_bytes=int(2e9))
#configure the default particle SoA with 1e5 particles
p = SoA(maxpart=int(1e5), mem=mym)
#add the particle soa to the multi-type particle SoAs
soas = SoAs(p, mem=mym)
# configure the timestep class to go from 0 to 1 Gyr
# note: G=43007.1 in units of length=kpc, velocity=km/s, mass = 1e10Msun
# if G=43007.1, masses are in 1e10Msun/h, and radii are in ckpc/h, then this
# constant converts from Gyr to internal units. Not much to comment about it
gyr_to_cu = 3.086e+16 / (1e9 * 3600 * 24 * 365)
ts = integrate.FixedTimeStep(soas, G=43007.1, t_from=0., t_to=1. * gyr_to_cu, MPI=mpi)
ic = NFWIC(rs=100., rho0=1e-6, rs_factor=10.) #init the build of a NFW profile with R<10rs, (note that mass is in units of 1e10Msun)
# init a refined PM grids with 7 stacked PLACEHIRESREGION at smaller and smaller scales
# note that PM needs the time-step integrator class TS to attach its DriftTable and kick callbacks
pm = SuperHiResPM(soas=soas, mem=mym, TS=ts, MPI=mpi, pmgrid=128, grids=8, dt_displacement_factor=0.25)
#configure to compile all modules in the current folder
build = make.Build('./', mpi, pm, ts, mym, *soas.values())
#configure generate SoA headers
headers = OnTheFly(build.build_name, *build.components, generate_user_c=True)

#
# step 2: build SoAs headers and compile C files
#


if mpi.rank == 0: #master rank compile and build headers
    headers.write()
    build.compile()


#
# step 3: allocate resources (e.g. MPI, MyMalloc, and allocations within it)
#

with (utils.Panic(Build=build) as panic, #attach panic handler to C calls
      utils.Timer(Build=build) as timer, #attach timer handler to C calls
      build.enter(debug=mpi.rank == 0), #parse the compiled object files
      mpi.enter(pm), #attach MPI init info to PM module
      mym.enter(*build.components), #actually allocates the 2GB of ram
      p, #allocate the particle data stracture in the MyMalloc area
      ic.enter(p, mpi.ranks, p.get_maxpart()), #sample the NFW in the particle SoA `p` fields
      pm, #call pm_init() the PM regions
      ts #compute DriftTables if necessary
      ):

        pm.compute_accelerations() #first acc computation


        #
        # step 4: the actual run
        #


        while ts.time < ts.time_end: #main run.c loop

            ts.find_timesteps() #integrator will find timesteps
            #integrator will call halfstep kick, including PM registered drift and kick callbacks
            ts.do_first_halfstep_kick()
            ts.drift() #integretor will drift
            pm.compute_accelerations() #accelerations
            #integrator will call halfstep kick, including PM registered drift and kick callbacks
            ts.do_second_halfstep_kick()
            
            if mpi.rank == 0 and steps % 10 == 0: #sometimes, master rank will do a plot
                f, ax = plt.subplots(1)
                ax.hist2d(p['pos'][:, 0], p['pos'][:, 1], bins=128)
                ax.set_aspect('equal')
                pat = os.path.join(os.getenv('HW_BUILD', '.'), 'snap%d_rank%d.png' % (steps, mpi.rank))
                f.savefig(pat, bbox_inches='tight', dpi=200)
                plt.close(f)


print('simualtion finished')