def test_EFN_masking(mask_val): n, m1, m2 = (50, 10, 20) input_dim = 3 X_train = [np.random.rand(n, m1), np.random.rand(n, m1, input_dim)] y_train = np.random.rand(n, 2) efn = archs.EFN(input_dim=input_dim, Phi_sizes=[10], F_sizes=[10], mask_val=mask_val) efn.fit(X_train, y_train, epochs=1) X_test = [np.random.rand(n, m2), np.random.rand(n, m2, input_dim)] X_test_mask = [ np.concatenate((X_test[0], mask_val * np.ones((n, 5))), axis=1), np.concatenate((X_test[1], mask_val * np.ones((n, 5, input_dim))), axis=1) ] assert epsilon_diff(efn.predict(X_test), efn.predict(X_test_mask), 10**-15) kf = K.function(inputs=efn.inputs, outputs=efn.latent) pure_mask = kf([0 * X_test[0] + mask_val, 0 * X_test[1] + mask_val])[0] assert epsilon_diff(pure_mask, 0, 10**-15)
def test_measure_hadrdot_ptyphi(event, beta, theta_eps, kappa, normed, kappa_normed_behavior): if normed and kappa == 'pf': pytest.skip() pTs = event[:, 0] ps = np.asarray([ pT * np.asarray( [np.cosh(y), np.cos(phi), np.sin(phi), np.sinh(y)]) for (pT, y, phi) in event ]) # compute using the energyflow package hmeas = ef.Measure('hadrdot', beta, kappa, normed, 'ptyphim', True, kappa_normed_behavior) hzs, hthetas = hmeas.evaluate(event) # compute naively norm = 1 if not normed else (np.sum(pTs**kappa) if kappa_normed_behavior == 'orig' else np.sum(pTs)**kappa) zs = (pTs**kappa) / norm if kappa != 'pf' else np.ones(len(pTs)) phats = np.asarray( [p / (pT if kappa != 'pf' else 1) for p, pT in zip(ps, pTs)]) thetas = np.asarray([[ 2 * abs(phti[0] * phtj[0] - np.dot(phti[1:], phtj[1:])) for phti in phats ] for phtj in phats])**(beta / 2) assert epsilon_diff(hzs, zs, 10**-13) assert epsilon_diff(hthetas, thetas, 10**-theta_eps)
def test_emd_equivalence(M1, M2, norm, R): gdim = 2 events1 = np.random.rand(nev, M1, gdim + 1) events2 = np.random.rand(nev, M2, gdim + 1) # test two different sets emds1 = np.zeros((nev, nev)) for i, ev1 in enumerate(events1): for j, ev2 in enumerate(events2): emds1[i, j] = emd.emd(ev1, ev2, R=R, norm=norm, gdim=gdim) emds2 = emd.emds(events1, events2, R=R, norm=norm, verbose=0, n_jobs=1, gdim=gdim) assert epsilon_diff(emds1, emds2, 10**-12) # test same set emds1 = np.zeros((nev, nev)) for i, ev1 in enumerate(events1): for j in range(i): emds1[i, j] = emd.emd(ev1, events1[j], R=R, norm=norm, gdim=gdim) emds1 += emds1.T emds2 = emd.emds(events1, R=R, norm=norm, verbose=0, n_jobs=1, gdim=gdim) assert epsilon_diff(emds1, emds2, 10**-12)
def test_periodic_phi(gdim, M): events = np.random.rand(nev, M, 1 + gdim) for phi_col in range(1, gdim + 1): emds1 = emd.emds_pot(events, R=1.0, gdim=gdim, n_jobs=1, verbose=0) events_c = np.copy(events) events_c[:, :, phi_col] += 2 * np.pi * np.random.randint( -10, 10, size=(nev, M)) emds2 = emd.emds_pot(events_c, R=1.0, gdim=gdim, periodic_phi=True, phi_col=phi_col, n_jobs=1, verbose=0) assert epsilon_diff(emds1, emds2, 10**-12) ev1 = np.random.rand(10, 1 + gdim) * 4 * np.pi ev2 = np.random.rand(20, 1 + gdim) * 4 * np.pi thetaw = np.zeros((len(ev1), len(ev2))) thetar = np.zeros((len(ev1), len(ev2))) for i, p1 in enumerate(ev1): for j, p2 in enumerate(ev2): dw, dr = 0., 0. for m, (k1, k2) in enumerate(zip(p1, p2)): if m == 0: continue elif m == phi_col: dw += (k1 - k2)**2 dr += np.min([ abs(k1 - (k2 + 2 * np.pi * n)) for n in range(-3, 3) ])**2 else: dw += (k1 - k2)**2 dr += (k1 - k2)**2 thetaw[i, j] = np.sqrt(dw) thetar[i, j] = np.sqrt(dr) zs1 = np.ascontiguousarray(ev1[:, 0] / np.sum(ev1[:, 0])) zs2 = np.ascontiguousarray(ev2[:, 0] / np.sum(ev2[:, 0])) ot_w, ot_r = ot.emd2(zs1, zs2, thetaw), ot.emd2(zs1, zs2, thetar) ef_w = emd.emd_pot(ev1, ev2, norm=True, gdim=gdim, periodic_phi=False, phi_col=phi_col) ef_r = emd.emd_pot(ev1, ev2, norm=True, gdim=gdim, periodic_phi=True, phi_col=phi_col) assert epsilon_diff(ot_w, ef_w, 10**-14) assert epsilon_diff(ot_r, ef_r, 10**-14)
def test_measure_list_input(measure, event, check_input): meas = ef.Measure(measure, check_input=check_input) list_event = event.tolist() nd0, nd1 = meas.evaluate(event) try: list0, list1 = meas.evaluate(list_event) except: assert not check_input else: assert check_input assert epsilon_diff(nd0, list0, 10**-14) assert epsilon_diff(nd1, list1, 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_measure_hadr_ptyphi(pts, ys, phis, beta, kappa, normed): M = len(pts) # compute using the energyflow package hmeas = ef.Measure('hadr', beta, kappa, normed, 'ptyphim', True) hzs, hthetas = hmeas.evaluate(np.vstack((pts,ys,phis)).T) # compute naively norm = 1 if not normed else np.sum(pts**kappa) 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)
def test_measure_ee(event, beta, theta_eps, kappa, normed, kappa_normed_behavior): if kappa == 'pf' and normed: pytest.skip() Es = event[:,0] emeas = ef.Measure('ee', beta, kappa, normed, 'epxpypz', True, kappa_normed_behavior) ezs, ethetas = emeas.evaluate(event) # compute naively norm = 1 if not normed else (np.sum(Es**kappa) if kappa_normed_behavior == 'orig' else np.sum(Es)**kappa) zs = (Es**kappa)/norm if kappa != 'pf' else np.ones(len(Es)) phats = np.asarray([p/(E if kappa != 'pf' else 1) for p,E in zip(event,Es)]) thetas = np.asarray([[2*abs(phti[0]*phtj[0]-np.dot(phti[1:],phtj[1:])) for phti in phats] for phtj in phats])**(beta/2) assert epsilon_diff(ezs, zs, 10**-13) assert epsilon_diff(ethetas, thetas, 10**-theta_eps)
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([[(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**-12) assert epsilon_diff(hthetas, thetas, 10**-12)
def test_n_jobs(n_jobs, M, norm, R): events = np.random.rand(nev, M, 3) emds1 = np.zeros((nev, nev)) for i, ev1 in enumerate(events): for j in range(i): emds1[i, j] = emd.emd(ev1, events[j], R=R, norm=norm) emds1 += emds1.T emds2 = emd.emds(events, R=R, norm=norm, verbose=0, n_jobs=n_jobs) assert epsilon_diff(emds1, emds2, 10**-12)
def test_measure_hadrdot_p4s(event, beta, theta_eps, kappa, normed): if normed and kappa == 'pf': pytest.skip() pTs = np.sqrt(event[:,1]**2 + event[:,2]**2) ps = event # compute using the energyflow package hmeas = ef.Measure('hadrdot', 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 if kappa != 'pf' else np.ones(len(pTs)) phats = np.asarray([p/(pT if kappa != 'pf' else 1) for p,pT in zip(ps,pTs)]) thetas = np.asarray([[2*abs(phti[0]*phtj[0]-np.dot(phti[1:],phtj[1:])) for phti in phats] for phtj in phats])**(beta/2) assert epsilon_diff(hzs, zs, 10**-13) assert epsilon_diff(hthetas, thetas, 10**-theta_eps)
def test_gdim(gdim, evdim, M, norm, R): if R < np.sqrt(gdim) / 2: pytest.skip('R too small') events = np.random.rand(nev, M, 1 + evdim) emds1 = emd.emds(events, gdim=gdim, norm=norm, R=R, n_jobs=1, verbose=0) emds2 = emd.emds(events[:, :, :1 + gdim], gdim=100, norm=norm, R=R, n_jobs=1, verbose=0) assert epsilon_diff(emds1, emds2, 10**-13)
def test_PFN_masking(mask_val): n, m1, m2 = (50, 10, 20) input_dim = 3 X_train = np.random.rand(n, m1, input_dim) y_train = np.random.rand(n, 2) pfn = archs.PFN(input_dim=input_dim, Phi_sizes=[10], F_sizes=[10], mask_val=mask_val) pfn.fit(X_train, y_train, epochs=1) X_test = np.random.rand(n, m2, input_dim) X_test_mask = np.concatenate((X_test, mask_val * np.ones( (n, 5, input_dim))), axis=1) assert epsilon_diff(pfn.predict(X_test), pfn.predict(X_test_mask), 10**-15) kf = K.function(inputs=pfn.inputs, outputs=pfn.latent) pure_mask = kf([0 * X_test + mask_val])[0] assert epsilon_diff(pure_mask, 0, 10**-15)
def test_measure_ee(event, beta, theta_eps, kappa, normed): if kappa == 'pf' and normed: pytest.skip() Es = event[:,0] emeas = ef.Measure('ee', beta, kappa, normed, 'epxpypz', True) ezs, ethetas = emeas.evaluate(event) # compute naively if kappa == 'pf': zs = np.ones(len(Es)) phats = event else: if normed: zs = Es**kappa/np.sum(Es**kappa) else: zs = Es**kappa phats = event/Es[:,np.newaxis] thetas = np.asarray([[2*abs(phti[0]*phtj[0]-np.dot(phti[1:],phtj[1:])) for phti in phats] for phtj in phats])**(beta/2) assert epsilon_diff(ezs, zs, 10**-13) assert epsilon_diff(ethetas, thetas, 10**-theta_eps)
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)