#!/usr/bin/env python
-import math
+# Any copyright is dedicated to the Public Domain.
+# https://creativecommons.org/publicdomain/zero/1.0/
-import torch, torchvision
+# Written by Francois Fleuret <francois@fleuret.org>
+import math
+import matplotlib.pyplot as plt
+
+import torch
from torch import nn
-from torch.nn import functional as F
-model = nn.Sequential(
- nn.Linear(2, 100),
- nn.ReLU(),
- nn.Linear(100, 2)
-)
+######################################################################
+
+
+def data_rectangle(nb):
+ x = torch.rand(nb, 1) - 0.5
+ y = torch.rand(nb, 1) * 2 - 1
+ data = torch.cat((y, x), 1)
+ alpha = math.pi / 8
+ data = data @ torch.tensor(
+ [[math.cos(alpha), math.sin(alpha)], [-math.sin(alpha), math.cos(alpha)]]
+ )
+ return data, "rectangle"
-############################################################
def data_zigzag(nb):
a = torch.empty(nb).uniform_(0, 1).view(-1, 1)
# zigzag
- x = 0.4 * ((a-0.5) * 5 * math.pi).cos()
+ x = 0.4 * ((a - 0.5) * 5 * math.pi).cos()
y = a * 2.5 - 1.25
data = torch.cat((y, x), 1)
- data = data @ torch.tensor([[1., -1.], [1., 1.]])
- return data
+ data = data @ torch.tensor([[1.0, -1.0], [1.0, 1.0]])
+ return data, "zigzag"
+
def data_spiral(nb):
a = torch.empty(nb).uniform_(0, 1).view(-1, 1)
x = (a * 2.25 * math.pi).cos() * (a * 0.8 + 0.5)
y = (a * 2.25 * math.pi).sin() * (a * 0.8 + 0.5)
data = torch.cat((y, x), 1)
- return data
+ return data, "spiral"
+
+
+def data_penta(nb):
+ a = (torch.randint(5, (nb,)).float() / 5 * 2 * math.pi).view(-1, 1)
+ x = a.cos()
+ y = a.sin()
+ data = torch.cat((y, x), 1)
+ data = data + data.new(data.size()).normal_(0, 0.05)
+ return data, "penta"
+
######################################################################
-# data = data_spiral(1000)
-data = data_zigzag(1000)
-data = data - data.mean(0)
+def train_model(data):
+ model = nn.Sequential(nn.Linear(2, 100), nn.ReLU(), nn.Linear(100, 2))
+
+ batch_size, nb_epochs = 100, 1000
+ optimizer = torch.optim.Adam(model.parameters(), lr=1e-3)
+ criterion = nn.MSELoss()
-batch_size, nb_epochs = 100, 1000
-optimizer = torch.optim.Adam(model.parameters(), lr = 1e-3)
-criterion = nn.MSELoss()
+ for e in range(nb_epochs):
+ acc_loss = 0
+ for input in data.split(batch_size):
+ noise = input.new(input.size()).normal_(0, 0.1)
+ output = model(input + noise)
+ loss = criterion(output, input)
+ acc_loss += loss.item()
+ optimizer.zero_grad()
+ loss.backward()
+ optimizer.step()
+ if (e + 1) % 100 == 0:
+ print(e + 1, acc_loss)
+
+ return model
-for e in range(nb_epochs):
- acc_loss = 0
- for input in data.split(batch_size):
- noise = input.new(input.size()).normal_(0, 0.1)
- output = model(input + noise)
- loss = criterion(output, input)
- acc_loss += loss.item()
- optimizer.zero_grad()
- loss.backward()
- optimizer.step()
- if (e+1)%10 == 0: print(e+1, acc_loss)
######################################################################
-a = torch.linspace(-1.5, 1.5, 30)
-x = a.view( 1, -1, 1).expand(a.size(0), a.size(0), 1)
-y = a.view(-1, 1, 1).expand(a.size(0), a.size(0), 1)
-grid = torch.cat((y, x), 2).view(-1, 2)
-# Take the origins of the arrows on the part of grid closer than 0.1
-# from the data points
-dist = (grid.view(-1, 1, 2) - data.view(1, -1, 2)).pow(2).sum(2).min(1)[0]
-origins = grid[torch.arange(grid.size(0)).masked_select(dist < 0.1)]
+def save_image(data_name, model, data):
+ a = torch.linspace(-1.5, 1.5, 30)
+ x = a.view(1, -1, 1).expand(a.size(0), a.size(0), 1)
+ y = a.view(-1, 1, 1).expand(a.size(0), a.size(0), 1)
+ grid = torch.cat((y, x), 2).view(-1, 2)
-field = model(origins).detach() - origins
+ # Take the origins of the arrows on the part of the grid closer than
+ # sqrt(0.1) to the data points
+ dist = (grid.view(-1, 1, 2) - data.view(1, -1, 2)).pow(2).sum(2).min(1)[0]
+ origins = grid[torch.arange(grid.size(0)).masked_select(dist < 0.1)]
-######################################################################
+ field = model(origins).detach() - origins
-import matplotlib.pyplot as plt
+ fig = plt.figure()
+ ax = fig.add_subplot(1, 1, 1)
-fig = plt.figure()
-ax = fig.add_subplot(1, 1, 1)
+ ax.axis("off")
+ ax.set_xlim(-1.6, 1.6)
+ ax.set_ylim(-1.6, 1.6)
+ ax.set_aspect(1)
-ax.axis('off')
-ax.set_xlim(-1.6, 1.6)
-ax.set_ylim(-1.6, 1.6)
-ax.set_aspect(1)
+ plot_field = ax.quiver(
+ origins[:, 0].numpy(),
+ origins[:, 1].numpy(),
+ field[:, 0].numpy(),
+ field[:, 1].numpy(),
+ units="xy",
+ scale=1,
+ width=3e-3,
+ headwidth=25,
+ headlength=25,
+ )
-plot_field = ax.quiver(origins[:, 0].numpy(), origins[:, 1].numpy(),
- field[:, 0].numpy(), field[:, 1].numpy(),
- units = 'xy', scale = 1,
- width = 3e-3, headwidth = 25, headlength = 25)
+ plot_data = ax.scatter(
+ data[:, 0].numpy(), data[:, 1].numpy(), s=1, color="tab:blue"
+ )
-plot_data = ax.scatter(data[:, 0].numpy(), data[:, 1].numpy(), s = 1, color = 'tab:blue')
+ filename = f"denoising_field_{data_name}.pdf"
+ print(f"Saving {filename}")
+ fig.savefig(filename, bbox_inches="tight")
-fig.savefig('denoising_field.pdf', bbox_inches='tight')
######################################################################
+
+for data_source in [data_rectangle, data_zigzag, data_spiral, data_penta]:
+ data, data_name = data_source(1000)
+ data = data - data.mean(0)
+ model = train_model(data)
+ save_image(data_name, model, data)
projects / pytorch.git / blobdiff