Performance issue: h5 writing of AtomDiag object very slow

[the-hampel]

Writing an AtomDiag object into an h5 archive is very slow due to the unfortunate data layout. Especially, for sparse Hamiltonians with many sub-blocks, a few ~100k small datasets need to be written, making the h5 serialization very slow. This problem shows itself also when broadcasting an AtomDiag object, as the broadcast uses h5 for serialization.

Here is a minimal example for n orbitals with a sparse structure. For n<=5 this works fine and finishes in a few seconds. However, when running for n=6 or even n=7 solving the problem is very fast, but writting or bcast the object takes very long:

from triqs.gf import *
from triqs.operators import *
from triqs.utility import mpi
from h5 import HDFArchive
from triqs.atom_diag import *
from itertools import product
import numpy as np
from triqs.operators.util.hamiltonians import h_int_kanamori
import timeit

spin_names = ('up','dn')
n_orb = 6
orb_names = list(range(n_orb))
fops = [(sn,on) for sn, on in product(spin_names,orb_names)]

H = n('up',0) * n('dn',0)

# Split the Hilbert space automatically
start_time = timeit.default_timer()
ad = AtomDiag(H, fops)
mpi.report('time for AD: {:.2f} s'.format(timeit.default_timer() - start_time))

# this part takes very long especially with sparce Hamiltonians with many blocks
if mpi.is_master_node():
    start_time = timeit.default_timer()
    with HDFArchive('test.h5','w') as ar:
        ar['ad'] = ad
    mpi.report('time for h5 write: {:.2f} s'.format(timeit.default_timer() - start_time))

start_time = timeit.default_timer()
ad = mpi.bcast(ad)
mpi.report('time for h5 bcast: {:.2f} s'.format(timeit.default_timer() - start_time))

for example for n=7 the output looks like:

time for AD: 0.56 s
time for h5 write: 48.08 s
time for h5 bcast: 30.18 s

We should think about how to more efficiently serialize the atomdiag object. This is now done via h5:

triqs/python/triqs/atom_diag/atom_diag_desc.py

Line 58 in dd749a1

serializable = "h5",