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utils.py
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utils.py
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from random import sample
import numpy as np
import torch
import matplotlib.pyplot as plt
import os
from scipy import sparse
from typing import Tuple, List
import argparse
import gril.gril as gril
import torch
import torch.nn as nn
from scipy.spatial import Delaunay
def delaunay_complex(x):
edge_dict = {}
edges = []
tri_converted = []
tri = Delaunay(x)
triangles = tri.simplices
for t in triangles:
s = sorted(t)
tri_boundary = []
for i in range(len(s)):
edge_key = tuple(sorted(s[:i] + s[i + 1:]))
if edge_key not in edge_dict:
edge_dict[edge_key] = len(edge_dict)
edges.append(list(edge_key))
tri_boundary.append(edge_dict[edge_key])
tri_converted.append(tri_boundary)
edges_t = torch.tensor(edges, dtype=torch.long)
tri_t = torch.tensor(triangles, dtype=torch.long)
tri_converted_t = torch.tensor(tri_converted, dtype=torch.long)
return edges_t, tri_t, tri_converted_t
def pre_process_edges(edge_index):
e = edge_index.permute(1, 0)
e = e.sort(1)
e = e[0].tolist()
e = set([tuple(ee) for ee in e])
return torch.tensor([ee for ee in e], dtype=torch.long, device=edge_index.device)
def get_simplices(num_vertices, edges, triangles=None):
simp = [[i] for i in range(num_vertices)]
for e in edges:
e_ = sorted([e[0].item(), e[1].item()])
simp.append(e_)
if triangles is not None:
for f in triangles:
f_ = sorted([f[0].item(), f[1].item(), f[2].item()])
simp.append(f_)
return simp
def get_filtration(x, edges, tri, tri_converted, nn_k=6):
# edges = pre_process_edges(edge_index)
d_xx = torch.cdist(x, x)
nn_k = min([nn_k, x.shape[0]])
d_xx = d_xx.topk(nn_k, 1, largest=False).values
# d_xy = -(d_xx * d_xx)
d_xx = -d_xx[:, 1:]
d_xx = torch.exp(d_xx).sum(1) / nn_k
d_xx = 1 - d_xx
# d_xx = d_xx * 3.;
# d_xx = d_xx / d_xx.max()
e_val = d_xx.unsqueeze(0).expand((edges.size(0), -1))
e_val = e_val.gather(1, edges)
e_val = e_val.max(1)[0]
tri_val = d_xx.unsqueeze(0).expand((tri.size(0), -1))
tri_val = tri_val.gather(1, tri)
tri_val = tri_val.max(1)[0]
e_val_x = x[edges[:, 0]]
e_val_y = x[edges[:, 1]]
e_val_y = torch.norm(e_val_x - e_val_y, dim=1)
e_val_y = 1 - torch.exp(-e_val_y)
tri_val_2 = e_val_y.unsqueeze(0).expand((tri_converted.size(0), -1))
tri_val_2 = tri_val_2.gather(1, tri_converted)
tri_val_2 = tri_val_2.max(1)[0]
f_v = torch.cat([d_xx.view((-1, 1)), torch.zeros((d_xx.size(0), 1))], dim=1)
e_val = torch.cat([e_val.view((-1, 1)), e_val_y.view((-1, 1))], dim=1) + 0.01
tri_val = torch.cat([tri_val.view((-1, 1)), tri_val_2.view((-1, 1))], dim=1) + 0.02
filt = torch.cat([f_v, e_val, tri_val], dim=0)
# filt = torch.cat([f_v, e_val], dim=0)
return filt, edges
def create_circle(center, radius, w_noise=False, num_points=100):
np.random.seed(0)
theta = np.random.uniform(size=(num_points,)) * np.pi * 2
data_x = radius * np.cos(theta) + center[0]
data_y = radius * np.sin(theta) + center[1]
data = np.column_stack((data_x, data_y))
if w_noise:
np.random.seed(0)
U1 = np.random.uniform(size=10)
np.random.seed(42)
U2 = np.random.uniform(size=10)
# np.random.seed(0)
# U3 = np.random.uniform(0, 1, (10, 2))
data_noise_x = 0.1 * np.sqrt(U2) * np.cos(2 * np.pi * U1) + center[0]
data_noise_y = 0.1 * np.sqrt(U2) * np.sin(2 * np.pi * U1) + center[1]
data_noise = np.column_stack([data_noise_x, data_noise_y])
data = np.row_stack([data, data_noise])
return data
def create_disk(center, radius, num_points=100):
np.random.seed(0)
U1 = np.random.uniform(size=num_points)
np.random.seed(42)
U2 = np.random.uniform(size=num_points)
data_x = radius * np.sqrt(U2) * np.cos(2 * np.pi * U1) + center[0]
data_y = radius * np.sqrt(U2) * np.sin(2 * np.pi * U1) + center[1]
data = np.column_stack((data_x, data_y))
return data
def create_circles(n_circles=2, w_noise=False):
circles = []
# centers = [[0.15 + (i * 0.80), (0.35 + i * 0.15)] for i in range(n_circles)]
centers = [[0.15, 0.2], [0.75, 0.9], [0.2, 0.7]]
radius = [0.15, 0.17, 0.2]
centers = np.array(centers)
for i in range(n_circles):
np.random.seed(0)
theta = np.random.uniform(size=(100,)) * np.pi * 2
data_x = radius[i] * np.cos(theta).reshape((theta.shape[0], 1)) + centers[i][0]
data_y = radius[i] * np.sin(theta).reshape((theta.shape[0], 1)) + centers[i][1]
data = np.concatenate([data_x, data_y], axis=1)
if w_noise:
np.random.seed(0)
U1 = np.random.uniform(size=10)
np.random.seed(42)
U2 = np.random.uniform(size=10)
r = 0.1
data_noise_x = r * np.sqrt(U2) * np.cos(2 * np.pi * U1) + centers[i][0]
data_noise_y = r * np.sqrt(U2) * np.sin(2 * np.pi * U1) + centers[i][1]
data_noise = np.column_stack([data_noise_x, data_noise_y])
data = np.row_stack([data, data_noise])
# data = data + np.random.normal(scale=0.015, size=data.shape)
circles.append(data)
circles = np.concatenate(circles, axis=0)
return circles
def create_disks(n_disks=1, num_pts=100):
disks = []
centers = [[0.15, 0.2], [0.75, 0.7], [0.2, .65]]
for i in range(n_disks):
# ind = start_from
np.random.seed(0)
U1 = np.random.uniform(size=num_pts)
np.random.seed(42)
U2 = np.random.uniform(size=num_pts)
r = 0.2
data_x = r * np.sqrt(U2) * np.cos(2 * np.pi * U1) + centers[i][0]
data_y = r * np.sqrt(U2) * np.sin(2 * np.pi * U1) + centers[i][1]
data = np.column_stack((data_x, data_y))
disks.append(data)
disks = np.row_stack(disks)
return disks
def create_sparse_circles(n_circles=3):
circles = []
centers = [[0.8, 0.8], [1.0, 1.0], [0.25, 0.85], [0.6, 0.45]]
centers = np.array(centers)
num_points = [50, 90, 35, 20]
r = [0.15, 0.1, 0.17, 0.3]
for i in range(n_circles):
np.random.seed(0)
theta = np.random.uniform(size=(num_points[i],)) * np.pi * 2
data_x = r[i] * np.cos(theta).reshape((theta.shape[0], 1)) + centers[i][0]
data_y = r[i] * np.sin(theta).reshape((theta.shape[0], 1)) + centers[i][1]
# U1 = np.random.uniform(size=10)
# U2 = np.random.uniform(size=10)
# r = 0.1
# data_noise_x = r * np.sqrt(U2) * np.cos(2 * np.pi * U1) + centers[i][0]
# data_noise_y = r * np.sqrt(U2) * np.sin(2 * np.pi * U1) + centers[i][1]
# data_noise = np.column_stack([data_noise_x, data_noise_y])
data_ = np.concatenate([data_x, data_y], axis=1)
# data = data + np.random.normal(scale=0.015, size=data.shape)
# data = np.row_stack([data, data_noise])
circles.append(data_)
circles = np.concatenate(circles, axis=0)
return circles
def create_sparse_disks(n_disks=3):
disks = []
centers = [[0.3, 0.2], [0.6, 0.45], [0.25, 0.85], [1.0, 1.0]]
centers = np.array(centers)
num_points = [200, 100, 70, 50]
for i in range(n_disks):
np.random.seed(0)
U1 = np.random.uniform(size=num_points[i])
np.random.seed(0)
U2 = np.random.uniform(size=num_points[i])
r = 0.15
data_x = r * np.sqrt(U2) * np.cos(2 * np.pi * U1) + centers[i][0]
data_y = r * np.sqrt(U2) * np.sin(2 * np.pi * U1) + centers[i][1]
data_ = np.column_stack((data_x, data_y))
disks.append(data_)
disks = np.row_stack(disks)
return disks
def create_circles_and_disks(num_circles, num_disks, w_noise=False):
centers = [[0.3, 0.2], [0.8, 0.8], [0.25, 0.85], [1.0, 0.45]]
centers = np.array(centers)
data_pts = []
num_points = [100, 90, 100, 100]
r = [0.2, 0.15, 0.17, 0.1]
for i in range(num_circles):
if i %2 == 0:
circle = create_circle(centers[i, :], r[i], w_noise, num_points[i])
else:
circle = create_sparse_circles(1)
data_pts.append(circle)
for i in range(num_circles, num_circles + num_disks):
disk = create_disk(centers[i, :], r[i], num_points[i])
data_pts.append(disk)
data_ = np.row_stack(data_pts)
return data_