def LandscapePnorm(ts,
p,
ts2=None,
dim=1,
maxrad=1,
t_min=None,
t_max=None,
n_points=100):
# compute L^p norm of all landscapes from multidimensional timeseries (or just set of points)
# input:
# ts - m x d numpy array, one timeseries (or just point coordinates) per column (d series), m samples per series
# p - integer (type of L^p norm to compute)
# ts2 - m x d numpy array, one timeseries (or just point coordinates) per column (d series), m samples per series
# if this is set, then the L^p distance will be returned
# dim - dimension of the persistence diagram from which to derive the landscape
# maxrad - max distance between pairwise points to consider for the Rips complex
# t_min, t_max (int or None) - same as inputs to dgm2landscape; if universal start/stop radii are desired for computing landscapes
# setting these to fixed values might reduce computation time a little bit
# n_points (int) - same as input to dgm2landscape; number of data points for landscape functions
# output:
# float32 - the L^p norm of the landscapes or difference
# need to go one dim up, above the one we want, as otherwise get free hom group at the top of the chains.
frips = d.fill_rips(np.array(ts, dtype='float32'), dim + 1, maxrad)
mrips = d.homology_persistence(frips)
dgms = d.init_diagrams(mrips, frips)
# acquire birth/death pairs
if len(dgms) <= dim:
# set the only birth/death pair to (0.0,0.0) if no gens found
bd = np.zeros((1, 2))
else:
bd = dgm2array(dgms[dim])
# acquire landscape functions
landscapes, rstart, rend = dgm2landscape(bd,
t_min=t_min,
t_max=t_max,
n_points=n_points)
if ts2 is not None:
frips2 = d.fill_rips(np.array(ts2, dtype='float32'), dim + 1, maxrad)
mrips2 = d.homology_persistence(frips2)
dgms2 = d.init_diagrams(mrips2, frips2)
if len(dgms2) <= dim:
# set the only birth/death pair to (0.0,0.0) if no gens found
bd2 = np.zeros((1, 2))
else:
bd2 = dgm2array(dgms2[dim])
landscapes2, rstart2, rend2 = dgm2landscape(bd2,
t_min=t_min,
t_max=t_max,
n_points=n_points)
# compute L^p distances
lpnorms = LpNorms(landscapes,
min(rstart, rstart2),
max(rend, rend2),
landscapes2=landscapes2,
p=p)
else:
# compute L^p norms
lpnorms = LpNorms(landscapes, rstart, rend, p=p)
normie = LandscapeLpNorm(lpnorms, p=p)
return (normie)
def get_upper_star(pcpds_obj):
f = d.fill_freudenthal(pcpds_obj.get_point_cloud().astype('f4'), False)
m = d.homology_persistence(f)
diagram = d.init_diagrams(m, f)
pcpds_obj.set_persistance_diagram(diagram)
pcpds_obj.set_filtration_used(Filtration.get_upper_star, "upper_star")
return pcpds_obj
def compare_diagrams(n=16, negate=False, n_threads=4, seed=1, top_dim=2):
# no wrap in Dionysus
wrap = False
# generate random grid data
np.random.seed(seed)
a = np.random.randn(n**3).reshape((n, n, n))
# compute diagrams with Oineus
oin_dgms = oin.compute_diagrams_ls(a, negate, wrap, top_dim, n_threads)
# compute diagrams with Dionysis
fil_us = dion.fill_freudenthal(a, reverse=negate)
p = dion.homology_persistence(fil_us)
dion_dgms = dion.init_diagrams(p, fil_us)
dist = 0.0
for dim in range(top_dim):
# convert Oineus diagram to Dionysus format
oin_dgm = dion.Diagram(oin_dgms[dim])
dion_dgm = dion_dgms[dim]
dist += dion.bottleneck_distance(oin_dgm, dion_dgm)
print("total dist: ", dist)
assert (dist < 0.001)
def compute_dgm_from_edges(
all_edges_for_diagrams, astuple: bool = True, negate: bool = True
):
_prepare_edges_for_diagram(all_edges_for_diagrams)
# Dionysus computations (persistent diagrams)
# logger.info(f"Before filtration")
#logger.info(f"len all_edges_for_diagrams = {len(all_edges_for_diagrams)}")
f = Filtration()
for vertices, weight in all_edges_for_diagrams:
if negate:
timing = -weight.round(3)
else:
timing = weight.round(3)
f.append(Simplex(vertices, timing))
f.sort()
#logger.info(f"{f}")
m = homology_persistence(f)
dgms = init_diagrams(m, f)
dgm = dgms[0]
if not astuple:
return dgm
else:
ret = list()
for pt in dgm:
# ret.append((pt.birth, pt.death if not np.isposinf(pt.death) else 2**64))
ret.append((round(pt.birth, 2), round(pt.death, 2)))
return ret
def create_sample_graph(f):
m = dion.homology_persistence(f)
dgms = dion.init_diagrams(m, f)
subgraphs = {}
for i, c in enumerate(m):
if len(c) == 2:
if f[c[0].index][0] in subgraphs:
subgraphs[f[c[0].index][0]].add_edge(f[c[0].index][0],
f[c[1].index][0],
weight=f[i].data)
else:
eaten = False
for k, v in subgraphs.items():
if v.has_node(f[c[0].index][0]):
v.add_edge(f[c[0].index][0],
f[c[1].index][0],
weight=f[i].data)
eaten = True
break
if not eaten:
g = nx.Graph()
g.add_edge(f[c[0].index][0],
f[c[1].index][0],
weight=f[i].data)
subgraphs[f[c[0].index][0]] = g
return subgraphs, dgms[0]
def test_homology(args, model, device, test_loader, epoch, res_df):
model.eval()
test_loss = 0
correct = 0
# capture a hidden state to use later, we don't care about its values though
hiddens = None
with torch.no_grad():
for data, target in test_loader:
data, target = data.to(device), target.to(device)
output, hiddens = model(data, hiddens=True)
test_loss += F.nll_loss(
output, target, reduction='sum').item() # sum up batch loss
pred = output.max(
1, keepdim=True)[1] # get the index of the max log-probability
correct += pred.eq(target.view_as(pred)).sum().item()
test_loss /= len(test_loader.dataset)
print(
'\nTest set: Average loss: {:.4f}, Accuracy: {}/{} ({:.0f}%)\n'.format(
test_loss, correct, len(test_loader.dataset),
100. * correct / len(test_loader.dataset)))
this_hiddens = [hiddens[0][0], hiddens[1][0], hiddens[2][0]]
f = model.compute_static_filtration(data[0, 0], this_hiddens)
m = dion.homology_persistence(f)
dgms = dion.init_diagrams(m, f)
row = {
'diagrams': dgms,
'loss': test_loss,
'epoch': epoch,
'accuracy': 100. * correct / len(test_loader.dataset)
}
res_df.append(row)
return res_df
def from_simplices(self, simplices):
if not isinstance(simplices, dionysus.Filtration):
simplices = dionysus.Filtration(simplices)
# import pdb; pdb.set_trace()
# Add cone point to force homology to finite length; Dionysus only gives out cycles of finite intervals
spxs = [dionysus.Simplex([-1])] + [c.join(-1) for c in simplices]
for spx in spxs:
spx.data = 1
simplices.append(spx)
# Compute persistence diagram
persistence = dionysus.homology_persistence(simplices)
diagrams = dionysus.init_diagrams(persistence, simplices)
# Set all the results
self._filtration = simplices
self._diagram = diagrams[self.order]
self._persistence = persistence
self.barcode = np.array([(d.birth, d.death) for d in self._diagram])
self._build_cycles()
def dionysus_test():
import dionysus as d
simplices = [([0, 6], 0.0035655512881059928),
([0, 5], 0.004388370816130452),
([0, 4], 0.024136039488717488),
([0, 3], 0.035381239705051776),
([3, 5], 0.035381239705051776),
([0, 1], 0.9824465164612051),
#([1, 1], 0.9824465164612051),
([1, 3], 0.9824465164612051),
([1, 4], 0.9824465164612051),
([1, 5], 0.9824465164612051),
([1, 6], 0.9824465164612051),
([0, 2], 0.9999999997257268),
([1, 2], 0.9999999997257268),
([2, 2], 0.9999999997257268),
([2, 3], 0.9999999997257268),
([2, 4], 0.9999999997257268),
([2, 5], 0.9999999997257268),
([2, 6], 0.9999999997257268),
([0], 0.0016456390560489196),
([6], 0.0035655512881059928),
([5], 0.004388370816130452),
([4], 0.024136039488717488),
([3], 0.035381239705051776),
([1], 0.9824465164612051),
([2], 0.9999999997257268)]
f = d.Filtration()
for vertices, time in simplices:
f.append(d.Simplex(vertices, time))
f.sort()
m = d.homology_persistence(f)
for i, c in enumerate(m):
print(i, c)
def compute_ph_boundary_using_graph_distance(gexfile, districtid, latstring,
lonstring):
""" Computes the persistent homology of an boundary outward march with graph distance
:param gexffile: location of input gexf
:param districtid: identifier for the district whose boundary we're examining
:param latstring: string ID for latitude field of centroid
:param lonstring: string ID for longitude field of centroid
:return:
"""
G = nx.read_gexf(gexfile)
get_dist_to_boundary(G, districtid)
nbr_list = gen_cclockwise_neighbors(G, lonstring, latstring)
faces = find_faces(G, nbr_list)
dims, idxs, time = get_dims_and_idx(G, G.edges(), faces)
filtration = build_filtered_complex(dims, idxs, time)
plot_simplexes_from_boundary(G, lonstring, latstring, time, dims)
m = d.homology_persistence(filtration)
dgms = d.init_diagrams(m, filtration)
d.plot.plot_bars(dgms[1], show=True)
def epd(self, g__, pd_flag=False, debug_flag=False):
w = -1
values = nx.get_node_attributes(g__, 'fv')
simplices = [[x[0], x[1]]
for x in list(g__.edges)] + [[x] for x in g__.nodes()]
up_simplices = [
d.Simplex(s, max(values[v] for v in s)) for s in simplices
]
down_simplices = [
d.Simplex(s + [w], min(values[v] for v in s)) for s in simplices
]
if pd_flag == True:
down_simplices = [] # mask the extended persistence here
up_simplices.sort(key=lambda s1: (s1.dimension(), s1.data))
down_simplices.sort(reverse=True,
key=lambda s: (s.dimension(), s.data))
f = d.Filtration([d.Simplex([w], -float('inf'))] + up_simplices +
down_simplices)
m = d.homology_persistence(f)
dgms = d.init_diagrams(m, f)
if debug_flag == True:
print(
'Calling compute_EPD here with success. Print first dgm in dgms'
)
print_dgm(dgms[0])
return dgms
def fit(self, data):
""" Generate Rips filtration and cycles for data.
"""
# Generate rips filtration
maxeps = np.max(data.std(axis=0)) # TODO: is this the best choice?
cpx = dionysus.fill_rips(data, self.order+1, maxeps)
# Add cone point to force homology to finite length; Dionysus only gives out cycles of finite intervals
spxs = [dionysus.Simplex([-1])] + [c.join(-1) for c in cpx]
for spx in spxs:
spx.data = 1
cpx.append(spx)
# Compute persistence diagram
persistence = dionysus.homology_persistence(cpx)
diagrams = dionysus.init_diagrams(persistence, cpx)
# Set all the results
self._filtration = cpx
self._diagram = diagrams[self.order]
self._persistence = persistence
self.barcode = np.array([(d.birth, d.death) for d in self._diagram])
self._build_cycles()
def generate_rv_complex(PointsArray, Dimension):
dists = pdist(PointsArray)
# adjacentDist = [norm(PointsArray[i,:] - PointsArray[i+1,:]) for i in range(len(PointsArray)-1)]
Alpha = max(dists)
rips = d.fill_rips(dists, Dimension, Alpha)
m = d.homology_persistence(rips)
dgms = d.init_diagrams(m, rips)
return rips, m, dgms
def computePD(i):
# print('Process %s' % i)
# np.random.seed(42)
f1 = d.fill_rips(np.random.random((i + 10, 2)), 2, 1)
m1 = d.homology_persistence(f1)
dgms1 = d.init_diagrams(m1, f1)
# return [(p.birth, p.death) for p in dgms1[1]] # advice from Dmitriy
return dgms1[1]
def get_rips_diagram(pcpds_obj):
f = d.fill_rips(pcpds_obj.get_point_cloud().astype('f4'),
pcpds_obj.get_skeleton(), pcpds_obj.get_distance())
m = d.homology_persistence(f)
diagram = d.init_diagrams(m, f)
pcpds_obj.set_persistance_diagram(diagram)
pcpds_obj.set_filtration_used(Filtration.get_rips_diagram, "rips")
return pcpds_obj
def PersistentDiagram(nparray,dim=1,skeletondim=2):
stime=timer()
DisM=distance.pdist(nparray,'euclidean')
M=DisM.max()
VRC=d.fill_rips(nparray,skeletondim,M)
ph=d.homology_persistence(VRC)
dgms=d.init_diagrams(ph,VRC)
timer(stime)
return dgms[dim]
def get_persistence(f):
"""
Args:
f: filtration
Returns:
m: reduced boundary matrix
"""
m = d.homology_persistence(f)
return m
def create_diagrams(args, model):
use_cuda = not args.no_cuda and torch.cuda.is_available()
device = torch.device("cuda" if use_cuda else "cpu")
kwargs = {'num_workers': 1, 'pin_memory': True}
test_loader = torch.utils.data.DataLoader(datasets.MNIST(
'../data',
train=False,
download=True,
transform=transforms.Compose([
transforms.ToTensor(),
transforms.Normalize((0.1307, ), (0.3081, ))
])),
batch_size=args.test_batch_size,
shuffle=False,
**kwargs)
df_filename = model.save_string()
df_filename = str(
args.up_to) + '_' + df_filename[:df_filename.find('.pt')] + '.pkl'
df_loc = os.path.join(args.diagram_directory, df_filename)
model.eval()
test_loss = 0
correct = 0
t = 0
res_df = []
with torch.no_grad():
for data, target in test_loader:
data, target = data.to(device), target.to(device)
output, hiddens = model(data, hiddens=True)
test_loss += F.nll_loss(
output, target, reduction='sum').item() # sum up batch loss
pred = output.max(
1, keepdim=True)[1] # get the index of the max log-probability
correct += pred.eq(target.view_as(pred)).sum().item()
for s in range(data.shape[0]):
# check if this makes sense
this_hiddens = [hiddens[0][s], hiddens[1][s], hiddens[2][s]]
print('Filtration: {}'.format(s + t))
f = model.compute_dynamic_filtration(data[s, 0], this_hiddens)
#
m = dion.homology_persistence(f)
dgms = dion.init_diagrams(m, f)
row = {
'diagrams': dgms,
'loss': output.cpu().numpy()[s][0],
'class': target.cpu().numpy()[s],
'prediction': pred.cpu().numpy()[s][0]
}
res_df.append(row)
t += args.test_batch_size
if t >= args.up_to:
break
res_df = pd.DataFrame(res_df)
res_df.to_pickle(df_loc)
def run_simple_example():
"""runs a simple illustrative example"""
Gspatial = nx.Graph()
Gspatial.add_nodes_from(range(9))
Gspatial.add_edges_from([(0, 1), (0, 2), (1, 3), (2, 3), (3, 4), (3, 6),
(3, 8), (4, 5), (5, 6), (5, 7), (6, 7), (7, 8)])
xcoord = {
0: 0.,
1: 1.,
2: 0.,
3: 1.,
4: 4.,
5: 3.,
6: 2.,
7: 2.,
8: 1.,
}
ycoord = {
0: 0.,
1: 0.,
2: -1.,
3: -1.,
4: -1.,
5: -2.,
6: -2.,
7: -3.,
8: -4.
}
pos = {k: np.array([xcoord[k], ycoord[k]]) for k in xcoord.keys()}
nx.set_node_attributes(Gspatial, xcoord, 'xcoord')
nx.set_node_attributes(Gspatial, ycoord, 'ycoord')
nx.set_node_attributes(Gspatial, pos, 'pos')
Gdem = nx.Graph()
Gdem.add_nodes_from(range(9))
Gdem.add_weighted_edges_from([(0, 1, .1), (0, 2, .1), (0, 3, .2),
(1, 3, .1), (2, 3, 0.1), (3, 4, .1),
(4, 8, 0.1), (3, 8, .1), (5, 6, .2),
(5, 7, .1), (6, 7, .1)])
nx.set_node_attributes(Gdem, xcoord, 'xcoord')
nx.set_node_attributes(Gdem, ycoord, 'ycoord')
nx.set_node_attributes(Gdem, pos, 'pos')
nbr_list = gen_cclockwise_neighbors(Gspatial, 'xcoord', 'ycoord')
nbr_list = {k: [int(i) for i in v] for k, v in nbr_list.items()}
faces_spatial = find_faces(Gspatial, nbr_list)
tris_spatial = triangulate_faces(faces_spatial)
dims, idxs, times = get_dims_and_idx_from_multiple(Gdem, tris_spatial, 1.,
20)
plot_simplexes_from_multiple(Gdem, dims, times)
filtration = build_filtered_complex(dims, idxs, times)
m = d.homology_persistence(filtration)
dgms = d.init_diagrams(m, filtration)
d.plot.plot_bars(dgms[1], show=True)
def compute_diagrams(data, k_filt=3, to_return=2):
diagrams = []
for i in range(len(data)):
# print("Processing data: " + str(i) + "\n")
filtration = dion.fill_rips(data[i], k_filt, 3.0)
homology = dion.homology_persistence(filtration)
diagram = dion.init_diagrams(homology, filtration)
diagrams.append(diagram[to_return])
return diagrams
def EPH_mask(vertex_values, simplices):
s2v_lst = [[
sorted(s),
sorted([[vertex_values[v], v] for v in s], key=lambda x: x[0])
] for s in simplices]
f_ord = [dionysus.Simplex(s[0], s[1][-1][0]) for s in s2v_lst] #takes max
f_ext = [dionysus.Simplex([-1] + s[0], s[1][0][0])
for s in s2v_lst] #takes min
ord_dict = {tuple(s[0]): s[1][-1][1] for s in s2v_lst}
ext_dict = {tuple([-1] + s[0]): s[1][0][1] for s in s2v_lst}
f_ord.sort(key=lambda s: (s.data, len(s)))
f_ext.sort(key=lambda s: (-s.data, len(s)))
#computes persistence
f = dionysus.Filtration([dionysus.Simplex([-1], -float('inf'))] + f_ord +
f_ext)
m = dionysus.homology_persistence(f)
dgms = [[[], []], [[], []], [[], []], [[],
[]]] #H0ord, H0ext, H1rel, H1ext
for i in range(len(m)):
dim = f[i].dimension()
if m.pair(i) < i:
continue # skip negative simplices to avoid double counting
if m.pair(
i
) != m.unpaired: #should be no unpaired apart from H0 from fictitious -1 vertex
pos, neg = f[i], f[m.pair(i)]
if pos.data != neg.data: #off diagonal
if -1 in pos and -1 in neg: #rel1
dgms[2][0].append(ext_dict[tuple(neg)])
dgms[2][1].append(ext_dict[tuple(pos)])
elif -1 not in pos and -1 not in neg: #ord0
dgms[1][0].append(ord_dict[tuple(pos)])
dgms[1][1].append(ord_dict[tuple(neg)])
else:
if dim == 0: #H0ext
dgms[0][0].append(ord_dict[tuple(pos)])
dgms[0][1].append(ext_dict[tuple(neg)])
if dim == 1: #H1ext
dgms[3][0].append(ext_dict[tuple(neg)])
dgms[3][1].append(ord_dict[tuple(pos)])
return dgms
def geomill(arr,dim=1,cutoff=2,elevation=45,azimuth=30):
#E3view(arr,elevation,azimuth)
#VR complex
stime=timer()
skeletondim=dim+1
filtration = d.fill_rips(arr, skeletondim, cutoff)
#persistent homology
ph = d.homology_persistence(filtration)
dgms = d.init_diagrams(ph, filtration)
d.plot.plot_bars(dgms[dim], show = True)
timer(stime)
return dgms
def create_sample_graphs(res_df, ids, wms):
sample_graphs = []
dgms = []
lifetimes = []
for s in range(res_df.shape[0]):
print(s)
wm = wms[s]
tnms = ids[s]
subgraphs = {}
f = res_df['filtration'].iloc[s]
m = dion.homology_persistence(f)
dgm = dion.init_diagrams(m, f)[0]
dgms.append(dgm)
for i, c in enumerate(m):
if len(c) == 2:
w = f[i].data
if (tnms[f[c[0].index][0]], tnms[f[c[1].index][0]]) in wm:
w = wm[(tnms[f[c[0].index][0]], tnms[f[c[1].index][0]])]
elif (tnms[f[c[1].index][0]], tnms[f[c[0].index][0]]) in wm:
w = wm[(tnms[f[c[1].index][0]], tnms[f[c[0].index][0]])]
# else:
# print((tnms[f[c[0].index][0]],tnms[f[c[1].index][0]]))
# raise Exception('NO WM!')
if False: #tnms[f[c[0].index][0]] in subgraphs:
subgraphs[tnms[f[c[0].index][0]]].add_edge(
tnms[f[c[0].index][0]],
tnms[f[c[1].index][0]],
weight=w)
else:
eaten = False
for k, v in subgraphs.items():
if v.has_node(tnms[f[c[0].index][0]]):
if tnms[f[c[1].index][0]] in subgraphs:
v.add_node(tnms[f[c[1].index][0]])
# subgraphs[k] = nx.union(v, subgraphs[tnms[f[c[1].index][0]]])
else:
v.add_edge(tnms[f[c[0].index][0]],
tnms[f[c[1].index][0]],
weight=w)
eaten = True
break
if not eaten:
g = nx.Graph()
g.add_edge(tnms[f[c[0].index][0]],
tnms[f[c[1].index][0]],
weight=w)
subgraphs[tnms[f[c[0].index][0]]] = g
sample_graphs.append(subgraphs)
lifetimes.append(create_lifetimes(f, subgraphs, dgm, ids[s]))
return sample_graphs, dgms, lifetimes
def compute_diagrams(data):
diagrams = []
for i in range(len(data)):
# print("Processing data: " + str(i))
filtration = dion.fill_rips(data[i], 2, 3.0)
homology = dion.homology_persistence(filtration)
diagram = dion.init_diagrams(homology, filtration)
diagrams.append(diagram[1])
# print()
return diagrams
def compute_PD(self, simplices, sub=True, inf_flag='False', zigzag = False):
def cmp(a, b):
return (a > b) - (a < b)
def compare(s1, s2, sub_flag=True):
if sub_flag == True:
if s1.dimension() > s2.dimension():
return 1
elif s1.dimension() < s2.dimension():
return -1
else:
return cmp(s1.data, s2.data)
elif sub_flag == False:
return -compare(s1, s2, sub_flag=True)
def zigzag_less(x, y):
# x, y are simplex
dimx, datax = x.dimension(), x.data
dimy, datay = y.dimension(), y.data
if dimx == dimy == 0:
return datax <= datay
elif dimx == dimy == 1:
return datax >= datay
else:
return dimx < dimy
f = d.Filtration()
for simplex, time in simplices:
f.append(d.Simplex(simplex, time))
if not zigzag:
f.sort() if sub else f.sort(reverse=True)
else:
f.sort(zigzag_less, reverse=True)
# print('After zigzag\n')
# print_f(f)
# simplices = [([2], 4), ([1, 2], 5), ([0, 2], 6),([0], 1), ([1], 2), ([0, 1], 3)]
# f = d.Filtration()
# for vertices, time in simplices:
# f.append(d.Simplex(vertices, time))
# f.append(d.Simplex(vertices, time))
# f.sort(cmp=zigzag_less,reverse=True)
# print_f(f)
m = d.homology_persistence(f)
dgms = d.init_diagrams(m, f)
if inf_flag == 'False':
dgms = self.del_inf(dgms)
# for some degenerate case, return dgm(0,0)
if (dgms == []) or (dgms == None):
return d.Diagram([[0,0]])
return dgms
def persistent(self):
"""
This method is used to create dionysus persistent homology
implementation of given vectors
:return: dionysus diagrams
"""
vectors = self._get_vectors()
f_lower_star = dn.fill_freudenthal(vectors)
p = dn.homology_persistence(f_lower_star)
dgms = dn.init_diagrams(p, f_lower_star)
return dgms
def persistent(self):
"""
This method is used to create dionysus persistent homology
implementation of given vectors
:return: dionysus diagrams
"""
vectors = self._get_vectors()
f_lower_star = dn.fill_freudenthal(vectors)
p = dn.homology_persistence(f_lower_star)
dgms = dn.init_diagrams(p, f_lower_star)
return dgms
def geomill(arr, skeletondim=2, elevation=45, azimuth=30):
#3D illustration
fig = pyplot.figure()
ax = Axes3D(fig)
ax.view_init(elev=elevation, azim=azimuth)
ax.scatter(arr[:, 0], arr[:, 1], arr[:, 2])
pyplot.show()
#VR complex
filtration = d.fill_rips(circ, skeletondim, 2)
#persistent homology
ph = d.homology_persistence(filtration)
dgms = d.init_diagrams(ph, filtration)
d.plot.plot_bars(dgms[1], show=True)
return ax, dgms
def random_choice_homology(self,
choice_size=1,
replace_bool=False,
root=None,
plot=None,
show=True):
colors = ['r', 'g', 'b', 'c', 'm', 'y', 'k']
if root == None:
choice_index = np.random.choice(len(self.dim2_fill_list),
size=choice_size,
replace=replace_bool)
dim2_fill_list = [self.dim2_fill_list[i] for i in choice_index]
dim2_fill_lens = np.array(
[len(dim2_fill) for dim2_fill in dim2_fill_list])
axes_depo = [
np.sum(dim2_fill_lens[:i])
for i in range(len(dim2_fill_lens) + 1)
]
dgms_lists = []
for count, dim2_fill in enumerate(dim2_fill_list):
print(f'loading dim2_fill {count}')
fig, axes = plt.subplots(4, 4, figsize=(12, 20))
one_dim_axes = axes.ravel()
dim2_fill_dgms = []
for i, fill in enumerate(dim2_fill):
p = d.homology_persistence(fill)
dgms = d.init_diagrams(p, fill)
dim2_fill_dgms.append(dgms)
for k, dgm in enumerate(dgms):
style = {'color': colors[k]}
if fill == dim2_fill[-1]:
style = {
'color': colors[k],
'label': 'dim = ' + str(k)
}
try:
d.plot.plot_diagram(dgm,
ax=one_dim_axes[i],
pt_style=style)
except ValueError:
continue
dgms_lists.append(dim2_fill_dgms)
fig.legend()
if show == True:
plt.show()
return dgms_lists
def EPH_fast(vertex_values, simplices):
N = len(vertex_values)
order2vertex = np.argsort(vertex_values)
vertex2order = np.empty(N, dtype=int)
vertex2order[order2vertex] = np.arange(N)
f_ord = [(s, max(vertex2order[v] for v in s))
for s in simplices] #takes max
f_ext = [([-1] + s, min(vertex2order[v] for v in s))
for s in simplices] #takes min
f_ord.sort(key=lambda s: (s[1], len(s[0])))
f_ext.sort(key=lambda s: (-s[1], len(s[0])))
full_filtration = [([-1], -float('inf'))] + f_ord + f_ext
f = dionysus.Filtration(full_filtration)
m = dionysus.homology_persistence(f)
dgms = dionysus.init_diagrams(m, f)
H0 = list(dgms[0])
H0.remove(max(H0, key=lambda x: x.death))
Dgm0b = [order2vertex[int(pt.birth)] for pt in H0]
Dgm0d = [order2vertex[int(pt.death)] for pt in H0]
H1 = list(dgms[1])
index_cutoff = len(f_ord) + 1
Dgm1extb = [
order2vertex[int(pt.birth)] for pt in H1 if pt.data < index_cutoff
]
Dgm1extd = [
order2vertex[int(pt.death)] for pt in H1 if pt.data < index_cutoff
]
Dgm0b += [
order2vertex[int(pt.birth)] for pt in H1 if pt.data >= index_cutoff
]
Dgm0d += [
order2vertex[int(pt.death)] for pt in H1 if pt.data >= index_cutoff
]
return [[Dgm0b, Dgm0d], [Dgm1extd, Dgm1extb]]
def compute_ph_spatial_edge_dem_face_from_percent(spatial_gexf,
dem_csv,
idstring,
xstring,
ystring,
attrstrings,
numfils=20):
"""runs persistent homology on the simplicial complex with edges from a spatial graph and faces from demographic distance. Requires
demographic data to be percentile
:param spatial_gexf: path to gexf of rook adjacency
:param dem_csv: path to csv with demographic data
:param idstring:
:param xstring:
:param ystring:
:param attrstrings: list of desired demographic attributes
:param numfils:
:return:
"""
Gspatial = nx.read_gexf(spatial_gexf)
Gdem = build_adj_matrix_percent(dem_csv, idstring, xstring, ystring,
attrstrings)
pos = nx.get_node_attributes(Gdem, 'pos')
xcoord = {k: u for k, (u, v) in pos.items()}
ycoord = {k: v for k, (u, v) in pos.items()}
nx.set_node_attributes(Gspatial, pos, 'pos')
nx.set_node_attributes(Gspatial, xcoord, 'xcoord')
nx.set_node_attributes(Gspatial, ycoord, 'ycoord')
build_spatial_graph_with_weights(Gspatial, 'xcoord', 'ycoord')
weights = nx.get_edge_attributes(Gspatial, 'weight')
maxfil = np.median([w for w in weights.values()]) / 10.
faces_dem = get_faces_from_distance(Gdem, maxfil)
dims, idxs, times = get_dims_and_idx_from_multiple(Gspatial, faces_dem,
maxfil, numfils)
plot_simplexes_from_multiple(Gdem, dims, times)
filtration = build_filtered_complex(dims, idxs, times)
m = d.homology_persistence(filtration)
dgms = d.init_diagrams(m, filtration)
d.plot.plot_bars(dgms[1], show=True)
def EPH_fast3(vertex_values, simplices):
N = len(vertex_values)
order2vertex = np.argsort(vertex_values)
vertex2order = np.empty(N, dtype=int)
vertex2order[order2vertex] = np.arange(N)
f_ord = [(s, max(vertex2order[v] for v in s))
for s in simplices] #takes max
f_ext = [([-1] + s, min(vertex2order[v] for v in s))
for s in simplices] #takes min
f_ord.sort(key=lambda s: (s[1], len(s[0])))
f_ext.sort(key=lambda s: (-s[1], len(s[0])))
full_filtration = [([-1], -float('inf'))] + f_ord + f_ext
f = dionysus.Filtration(full_filtration)
m = dionysus.homology_persistence(f)
dgms = dionysus.init_diagrams(m, f)
H0 = list(dgms[0])
H0.remove(max(H0, key=lambda x: x.death))
Dgm0, Dgm1 = [[], []], [[], []]
for pt in H0:
Dgm0[0].append(order2vertex[int(pt.birth)])
Dgm0[1].append(order2vertex[int(pt.death)])
H1 = list(dgms[1])
index_cutoff = len(f_ord) + 1
for pt in H1:
if pt.data < index_cutoff:
Dgm1[0].append(order2vertex[int(pt.death)])
Dgm1[1].append(order2vertex[int(pt.birth)])
else:
Dgm0[0].append(order2vertex[int(pt.death)])
Dgm0[1].append(order2vertex[int(pt.birth)])
return Dgm0, Dgm1
