def test_barcode():
N = 200
N_s = 50
k = int(N/5)
w = .5
r = .6
vertices = get_image('C', 1, size=200, sample_size=N)[0]
tangents = hm.find_tangents(vertices, k)
curve = hm.get_curve(vertices, k = k, w = w)
sparse = sparse_sample(vertices, N_s)
v_s = vertices[sparse,:]
t_s = tangents[sparse]
c_s = curve[sparse]
edges = hm.get_rips_complex(v_s, tangents=t_s, k = k, w = w, r = r)
f, ax = plt.subplots(1,2)
plt_edges, plt_barcode = ax
plt_edges.scatter(v_s[:,0], v_s[:,1], marker = '.', c=c_s, s=200)
for edge in edges:
plt_edges.plot(v_s[edge, 0], v_s[edge, 1], lw = 1, c = 'blue')
plt_edges.invert_yaxis()
ordered_simplices, curve_lookup = hm.get_ordered_simplices(v_s, c_s, edges)
barcode = bc.get_barcode(ordered_simplices, degree_values=c_s[np.argsort(c_s)])
b0 = barcode[barcode[:,2] == 0, :]
bc.plot_barcode_gant(b0, plt=plt_barcode)
plt.show()
def test_edges():
N = 200
N_s = 50
k = int(N/5)
w = .5
r = .6
vertices = get_image('A', 2, size=200, sample_size=N)[0]
tangents = hm.find_tangents(vertices, k)
sparse = sparse_sample(vertices, N_s)
v_s = vertices[sparse,:]
t_s = tangents[sparse]
edges = hm.get_rips_complex(v_s, tangents=t_s, k = k, w = w, r = r)
plot_edges(v_s, edges, plt)
plt.gca().invert_yaxis()
plt.show()
def test_alpha_4d():
N = 200
N_s = 100
k = int(N/5)
w = .2
r = .15
vertices = get_image('B', 2, size=200, sample_size=N)[0]
tangents = hm.find_tangents(vertices, k)
edges, v_s, _ = hm.alpha_complex_4d(vertices, tangents, r = r, w=w, N_s = N_s)
plt.scatter(vertices[:,0], vertices[:,1], marker='.', c='gray')
plt.scatter(v_s[:,0], v_s[:,1], marker='+', c='red')
for edge in edges:
plt.plot(v_s[edge,0], v_s[edge,1], lw = 1, c = 'blue')
plt.gca().invert_yaxis()
plt.show()
def test_witness_complex_4d():
N = 200
N_s = 20
k = int(N/5)
w = .5
r = .6
vertices = get_image('V', 2, size=200, sample_size=N)[0]
tangents = hm.find_tangents(vertices, k)
edges, landmarks, sparse = hm.witness_complex_4d(vertices, tangents, w, N_s)
plt.scatter(vertices[:,0], vertices[:,1], marker='.', c='gray')
plt.scatter(landmarks[:,0], landmarks[:,1], marker='+', c='red')
for edge in edges:
plt.plot(landmarks[edge,0], landmarks[edge,1], lw = 1, c = 'blue')
plt.gca().invert_yaxis()
plt.show()
def test_edges_for_point():
N = 200
k = int(N/5)
w = .2
r = 0.2
vertices = get_image('P', 0, size=100, sample_size=N)[0]
# edges = hm.get_rips_complex(vertices, k, w, r)
tangents = hm.find_tangents(vertices, k)
tspace = hm.get_tspace(vertices, tangents, w)
kd_tree = spatial.KDTree(tspace)
edges = hm.rips_complex_for_point(0, tspace, kd_tree, r = r).T
print(edges)
plt.scatter(vertices[:,0], vertices[:,1], marker = '.', c='gray', s=4)
for edge in edges:
plt.plot(vertices[edge, 0], vertices[edge, 1], lw = 1, c = 'blue')
# if annotate:
# plt.annotate("{0}".format(edge[0]), (vertices[edge[0],0], vertices[edge[0],1]))
# plt.annotate("{0}".format(edge[1]), (vertices[edge[1],0], vertices[edge[1],1]))
plt.show()
def test_filtration():
N = 200
N_s = 50
k = int(N/5)
w = .5
r = .6
vertices = get_image('A', 2, size=200, sample_size=N)[0]
tangents = hm.find_tangents(vertices, k)
curve = hm.get_curve(vertices, k = k, w = w)
sparse = sparse_sample(vertices, N_s)
v_s = vertices[sparse,:]
t_s = tangents[sparse]
c_s = curve[sparse]
edges = hm.get_rips_complex(v_s, tangents=t_s, k = k, w = w, r = r)
simplices, curve_lookup = hm.get_ordered_simplices(v_s, c_s, edges)
max_degree = np.max(simplices[:,3])
degree_step = math.ceil(max_degree/16.0)
verts_degree = simplices[simplices[:,4] == 0,0:3]
f, ax = plt.subplots(4,4, sharex=True, sharey=True)
ax[0][0].invert_yaxis()
for i in range(4):
for j in range(4):
idx = i*4 + j
deg = min(idx * degree_step, max_degree)
plot_simplices(simplices, deg, v_s, ax[i][j])
ax[i][j].set_title("κ={0:1.4f}".format(curve[verts_degree[deg,0]]), fontsize=8)
ax[i][j].set_xticklabels([])
ax[i][j].set_yticklabels([])
plt.tight_layout()
plt.figure()
barcode = bc.get_barcode(simplices, degree_values=c_s[np.argsort(c_s)])
b0 = barcode[barcode[:,2] == 0, :]
bc.plot_barcode_gant(b0, plt=plt)
plt.show()