def test_ys_from_p4s(nevents, nparticles):
p4s = ef.gen_random_events(nevents, nparticles, dim=4,
mass='random').reshape(nevents, nparticles, 4)
ys = 0.5 * np.log(
(p4s[..., 0] + p4s[..., 3]) / (p4s[..., 0] - p4s[..., 3]))
assert epsilon_diff(ys, ef.ys_from_p4s(p4s))
def test_coordinate_transforms(nevents, nparticles):
p4s = ef.gen_random_events(nevents, nparticles, dim=4,
mass='random').reshape(nevents, nparticles, 4)
ptyphims = ef.ptyphims_from_p4s(p4s)
new_p4s = ef.p4s_from_ptyphims(ptyphims)
assert epsilon_diff(p4s, new_p4s, 1e-11)
def test_etas_from_p4s(nevents, nparticles):
p4s = ef.gen_random_events(nevents, nparticles, dim=4,
mass='random').reshape(nevents, nparticles, 4)
p3tots = np.linalg.norm(p4s[..., 1:], axis=-1)
etas = 0.5 * np.log((p3tots + p4s[..., 3]) / (p3tots - p4s[..., 3]))
assert epsilon_diff(etas, ef.etas_from_p4s(p4s), 1e-13)
def test_efm_batch_compute(v, M, measure, normed):
events = ef.gen_random_events(2, M)
e = ef.EFM(v, measure=measure, normed=normed, coords='epxpypz')
r1 = [e.compute(event) for event in events]
r2 = e.batch_compute(events)
assert epsilon_percent(r1, r2, 10**-1)
def test_gen_random_events(nevents, nparticles, dim, mass):
if mass == 'array':
mass = np.random.rand(nevents, nparticles)
events = ef.gen_random_events(nevents, nparticles, dim=dim, mass=mass)
assert events.shape == (nevents, nparticles, dim)
if mass != 'random':
assert epsilon_diff(ef.ms_from_ps(events)**2, mass**2, 10**-13)
def test_ms_from_ps(dim, nevents, nparticles):
masses = np.random.rand(nevents, nparticles)
events = ef.gen_random_events(nevents, nparticles, mass=masses, dim=dim)
masses = masses.reshape(events.shape[:-1])
results = ef.ms_from_ps(events)
assert epsilon_diff(results, masses, 1e-10)
if dim == 4:
assert epsilon_diff(results, ef.ms_from_p4s(events), 1e-10)
def test_gen_random_events(nevents, nparticles, dim, mass):
if mass == 'array':
mass = np.random.rand(nevents, nparticles)
events = ef.gen_random_events(nevents, nparticles, dim=dim, mass=mass)
assert events.shape == (nevents, nparticles, dim)
if not (isinstance(mass, six.string_types) and mass == 'random'):
assert epsilon_diff(ef.ms_from_ps(events)**2, mass**2, 10**-13)
def test_batch_compute_vs_compute(measure, beta, kappa, normed):
if measure == 'hadr' and kappa == 'pf':
pytest.skip('hadr does not do pf')
if 'efm' in measure and beta != 2:
pytest.skip('only test efm when beta=2')
events = ef.gen_random_events(10, 15)
s = ef.EFPSet('d<=6', measure=measure, beta=beta, kappa=kappa, normed=normed)
r_batch = s.batch_compute(events)
r = np.asarray([s.compute(event) for event in events])
assert epsilon_percent(r_batch, r, 10**-14)
def test_shapes_from_p4s(method, nevents, nparticles):
events = ef.gen_random_events(nevents, nparticles, dim=4,
mass='random').reshape(
nevents, nparticles, 4)
event, particle = events[0], events[0, 0]
func = getattr(ef, method)
results = func(events)
assert epsilon_diff(results[0], func(event))
assert epsilon_diff(results[0, 0], func(particle))
def test_batch_compute_vs_compute(measure, beta, kappa, normed):
if measure == 'hadr' and kappa == 'pf':
pytest.skip('hadr does not do pf')
if kappa == 'pf' and normed:
pytest.skip('normed not supported with kappa=pf')
if ('efm' in measure) and (beta != 2):
pytest.skip('only beta=2 can use efm measure')
events = ef.gen_random_events(10, 15)
s = ef.EFPSet('d<=6', measure=measure, beta=beta, kappa=kappa, normed=normed)
r_batch = s.batch_compute(events, n_jobs=1)
r = np.asarray([s.compute(event) for event in events])
assert epsilon_percent(r_batch, r, 10**-14)
def test_C2D2C3(measure, beta, normed):
# skip the efm measures for beta other than 2
if ('efm' in measure) and (beta != 2):
pytest.skip('only beta=2 can use efm measure')
# generate a random event with 10 particles
event = ef.gen_random_events(1, 10, dim=4)
# specify the relevant graphs and EFPs to compute C1, D2, C3
line = ef.EFP([(0, 1)],
measure=measure,
coords='epxpypz',
beta=beta,
normed=True)(event)
triangle = ef.EFP([(0, 1), (0, 2), (1, 2)],
measure=measure,
coords='epxpypz',
beta=beta,
normed=True)(event)
kite = ef.EFP([(0, 1), (0, 2), (0, 3), (1, 2), (1, 3), (2, 3)],
measure=measure,
coords='epxpypz',
beta=beta,
normed=True)(event)
# determine the observables
C2val = triangle / line**2
D2val = triangle / line**3
C3val = kite * line / triangle**2
for strassen in [True, False]:
# skip strassen for EFM measures and hadr
if ('efm' in measure or measure == 'hadr') and strassen:
continue
D2 = ef.obs.D2(measure=measure,
beta=beta,
strassen=strassen,
normed=normed,
coords='epxpypz')
assert epsilon_diff(D2(event), D2val, 10**-10)
C2 = ef.obs.C2(measure=measure,
beta=beta,
strassen=strassen,
normed=normed,
coords='epxpypz')
assert epsilon_diff(C2(event), C2val, 10**-10)
C3 = ef.obs.C3(measure=measure, beta=beta, coords='epxpypz')
assert epsilon_diff(C3(event), C3val, 10**-10)
def test_efm_vs_efmset_compute(sigs, M, measure, normed):
efmset = ef.EFMSet(sigs, measure=measure, normed=normed, coords='epxpypz')
efms = [
ef.EFM(*sig, measure=measure, normed=normed, coords='epxpypz')
for sig in sigs
]
for event in ef.gen_random_events(2, M):
efm_dict = efmset.compute(event)
for sig, efm in zip(sigs, efms):
print(sig, np.max(np.abs(efm_dict[sig] - efm.compute(event))))
assert epsilon_percent(efm_dict[sig], efm.compute(event), 10**-10)
def test_pt2s_from_p4s(nevents, nparticles):
p4s = ef.gen_random_events(nevents, nparticles, dim=4,
mass='random').reshape(nevents, nparticles, 4)
pt2s = ef.pt2s_from_p4s(p4s)
slow_pt2s = []
for i in range(nevents):
event_pt2s = []
for j in range(nparticles):
event_pt2s.append(p4s[i, j, 1]**2 + p4s[i, j, 2]**2)
slow_pt2s.append(event_pt2s)
slow_pt2s = np.asarray(slow_pt2s)
assert epsilon_diff(slow_pt2s, pt2s)
def test_efm_vs_efmset_batch_compute(sigs, M, measure, normed):
efmset = ef.EFMSet(sigs, measure=measure, normed=normed, coords='epxpypz')
efms = [
ef.EFM(*sig, measure=measure, normed=normed, coords='epxpypz')
for sig in sigs
]
events = ef.gen_random_events(2, M)
efm_dict = efmset.batch_compute(events)
for sig, efm in zip(sigs, efms):
results = efm.batch_compute(events)
for i in range(len(events)):
assert epsilon_percent(efm_dict[i][sig], results[i], 10**-10)
def test_ms_from_p4s(nevents, nparticles):
p4s = ef.gen_random_events(nevents, nparticles, dim=4,
mass='random').reshape(nevents, nparticles, 4)
ms = ef.ms_from_p4s(p4s)
slow_ms = []
for i in range(nevents):
event_ms = []
for j in range(nparticles):
event_ms.append(
np.sqrt(p4s[i, j, 0]**2 - p4s[i, j, 1]**2 - p4s[i, j, 2]**2 -
p4s[i, j, 3]**2))
slow_ms.append(event_ms)
slow_ms = np.asarray(slow_ms)
assert epsilon_diff(slow_ms, ms)
def test_ys_from_pts_etas_ms(nevents, nparticles):
p4s = ef.gen_random_events(nevents, nparticles, dim=4,
mass='random').reshape(nevents, nparticles, 4)
ys = ef.ys_from_p4s(p4s)
y_primes = ef.ys_from_pts_etas_ms(ef.pts_from_p4s(p4s),
ef.etas_from_p4s(p4s),
ef.ms_from_p4s(p4s))
assert epsilon_diff(ys, y_primes, 1e-12)
# test cutoff
pts, ms = 1000 * np.random.rand(25), 10 * np.random.rand(25)
etas = np.random.choice([-1., 1.], size=25) * 100 * np.random.rand(25)
for c1, c2 in zip(np.linspace(20, 100, 5), 20 + 80 * np.random.rand(5)):
ys_c1 = ef.ys_from_pts_etas_ms(pts, etas, ms, _cutoff=c1)
ys_c2 = ef.ys_from_pts_etas_ms(pts, etas, ms, _cutoff=c2)
assert epsilon_diff(ys_c1, ys_c2, 1e-12)
def test_efms(v, measure, normed, M):
events = ef.gen_random_events(2, M)
e = ef.EFM(v, measure=measure, normed=normed, coords='epxpypz')
for event in events:
if measure == 'hadrefm':
zs = np.atleast_1d(ef.pts_from_p4s(event))
elif measure == 'eeefm':
zs = event[:, 0]
nhats = event / zs[:, np.newaxis]
if normed:
zs = zs / zs.sum()
e_ans = e.compute(event)
if v == 0:
assert epsilon_percent(e_ans, zs.sum(), 10**-13)
else:
s_ans = slow_efm(zs, nhats, v)
assert epsilon_percent(s_ans, e_ans, 10**-13)
def test_shapes_from_ptyphis(method, nevents, nparticles):
p4s = ef.gen_random_events(nevents, nparticles, dim=4,
mass='random').reshape(nevents, nparticles, 4)
ptyphims = ef.ptyphims_from_p4s(p4s)
func = getattr(ef, method)
if 'ms' in method:
for end in [3, 4]:
results = func(ptyphims[..., :end])
assert epsilon_diff(results[0], func(ptyphims[0, ..., :end]))
elif 'pids' in method:
ptyphims[..., 3] = (
np.random.choice([-1., 1.], size=(nevents, nparticles)) *
np.random.choice(list(
ef.utils.particle_utils.PARTICLE_MASSES.keys()),
size=(nevents, nparticles)))
results = func(ptyphims)
assert epsilon_diff(results[0], func(ptyphims[0]))
def test_sum_ptyphims(nparticles, scheme):
p4s = ef.gen_random_events(10, nparticles, dim=4, mass='random')
ptyphims = ef.ptyphims_from_p4s(p4s)
if scheme == 'escheme':
for ev_p4s, ev_ptyphims in zip(p4s, ptyphims):
tot = ef.p4s_from_ptyphims(
ef.sum_ptyphims(ev_ptyphims, scheme=scheme))
tot_p4 = ev_p4s.sum(axis=0)
assert epsilon_diff(tot, tot_p4, 10**-12)
elif scheme == 'ptscheme':
for ev_ptyphims in ptyphims:
tot = ef.sum_ptyphims(ev_ptyphims, scheme=scheme)
pt = ev_ptyphims[:, 0].sum()
y = np.sum(ev_ptyphims[:, 0] * ev_ptyphims[:, 1]) / pt
phi = np.sum(ev_ptyphims[:, 0] * ev_ptyphims[:, 2]) / pt
assert epsilon_diff(tot, np.array([pt, y, phi]), 10**-12)
def test_linear_relations(measure):
graphs ={# d=0
'dot': [],
# d=1
'line': [(0,1)],
# d=2
'dumbbell': [(0,1), (0,1)],
'wedge': [(0,1),(1,2)],
'linesqd' : [(0,1),(2,3)],
# d = 3
'tribell' : [(0,1),(0,1),(0,1)],
'triangle' : [(0,1),(1,2),(2,0)],
'asymwedge' : [(0,1),(0,1),(1,2)],
'birdfoot' : [(0,1),(0,2),(0,3)],
'chain' : [(0,1),(1,2),(2,3)],
'linedumbbell' : [(0,1),(2,3),(2,3)],
'linewedge' : [(0,1),(2,3),(3,4)],
'linecbd' : [(0,1),(2,3),(4,5)],
# d = 4
'quadbell' : [(0,1),(0,1),(0,1),(0,1)],
'doublewedge' : [(0,1),(0,1),(1,2),(1,2)],
'icecreamcone' : [(0,1),(0,1),(1,2),(2,0)],
'asymwedge2' : [(0,1),(0,1),(0,1),(1,2)],
'square' : [(0,1),(1,2),(2,3),(3,0)],
'flyswatter' : [(0,1),(1,2),(2,3),(3,1)],
'chain2mid' : [(0,1),(1,2),(1,2),(2,3)],
'chain2end' : [(0,1),(1,2),(2,3),(2,3)],
'asymbirdfoot' : [(0,1),(0,1),(1,2),(1,3)],
'bigbirdfoot' : [(0,1),(0,2),(0,3),(0,4)],
'dog' : [(0,1),(1,2),(2,3),(2,4)],
'bigchain' : [(0,1),(1,2),(2,3),(3,4)],
'dumbbellwedge' : [(0,1),(0,1),(2,3),(3,4)],
'triangleline' : [(0,1),(1,2),(2,0),(3,4)],
'dumbbellsqd' : [(0,1),(0,1),(2,3),(2,3)],
# d = 5
'pentagon' : [(0,1),(1,2),(2,3),(3,4),(4,0)],
'triangledumbbell': [(0,1),(0,1),(2,3),(3,4),(4,2)]
}
# pick a random event with 2 particles
event = ef.gen_random_events(1, 2, dim=4)
# compute the value of all of the EFPs on this event
d = {name: ef.EFP(graph, measure=measure, coords='epxpypz')(event) for name,graph in graphs.items()}
eps = 10**-8
# check that the identities in the EFM paper are valid (i.e. = 0)
assert epsilon_diff(2 * d['wedge'] - d['dumbbell'], 0, eps)
assert epsilon_diff(2 * d['triangle'], 0, eps)
assert epsilon_diff(d['tribell'] - 2 * d['asymwedge'], 0, eps)
assert epsilon_diff(2 * d['chain'] - d['linedumbbell'] - d['triangle'], 0, eps)
assert epsilon_diff(d['birdfoot'] + d['chain'] - d['asymwedge'], 0, eps)
# Four Dimensions
# pick a random event in 4 dimensions
event = ef.gen_random_events(1, 25, dim=4)
# compute the value of all of the EFPs on this event
d = {name: ef.EFP(graph, measure=measure, coords='epxpypz')(event) for name,graph in graphs.items()}
# check that the identity in the paper is valid (i.e. = 0)
assert epsilon_percent(6*d['pentagon'], 5*d['triangledumbbell'], 10**-11)
# count the number of leafless multigraphs (all or just connected) with degree d
ds = np.arange(11)
counts_all, counts_con = [], []
# for each degree, get the graphs with edges<=d and check whether they are leafless
for d in ds:
counts_all.append(np.sum([leafless(graph) for graph in ef.EFPSet(('d<=',d)).graphs()]))
counts_con.append(np.sum([leafless(graph) for graph in ef.EFPSet(('d<=',d), ('p==',1)).graphs()]))
# note: computed counts are cumulative, must take the difference to get individual d
counts_all = np.asarray(counts_all[1:]) - np.asarray(counts_all[:-1])
counts_con = np.asarray(counts_con[1:]) - np.asarray(counts_con[:-1])
# ensure agreement with the table in the paper
assert epsilon_diff(counts_all, [0,1,2,5,11,34,87,279,897,3129], eps)
assert epsilon_diff(counts_con, [0,1,2,4,9,26,68,217,718,2553], eps)
zs = (pts**kappa) / norm
thetas = np.asarray([[
(ys[i] - ys[j])**2 +
min(abs(phis[i] - phis[j]), 2 * np.pi - abs(phis[i] - phis[j]))**2
for i in range(M)
] for j in range(M)])**(beta / 2)
assert epsilon_diff(hzs, zs, 10**-13)
assert epsilon_diff(hthetas, thetas, 10**-13)
@pytest.mark.measure
@pytest.mark.parametrize('normed', [True, False])
@pytest.mark.parametrize('kappa', [0, .5, 1])
@pytest.mark.parametrize('beta', [.2, 1, 2])
@pytest.mark.parametrize('event', ef.gen_random_events(3, 15))
def test_measure_hadr_p4s(event, beta, kappa, normed):
M = len(event)
pTs = np.sqrt(event[:, 1]**2 + event[:, 2]**2)
ys = 0.5 * np.log(
(event[:, 0] + event[:, 3]) / (event[:, 0] - event[:, 3]))
phis = np.arctan2(event[:, 2], event[:, 1])
# compute using the energyflow package
hmeas = ef.Measure('hadr', beta, kappa, normed, 'epxpypz', True)
hzs, hthetas = hmeas.evaluate(event)
# compute naively
norm = 1 if not normed else np.sum(pTs**kappa)
zs = (pTs**kappa) / norm
thetas = np.asarray([[
def test_gen_random_events(nevents, nparticles, dim, mass):
events = ef.gen_random_events(nevents, nparticles, dim=dim, mass=mass)
assert events.shape == (nevents, nparticles, dim)
assert epsilon_diff(ef.ms_from_p4s(events)**2, mass**2, 10**-13)