# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
"""
General plotting utilities. These are used in tutorials and are designed for narrow uses.
"""
import matplotlib as mpl
import matplotlib.pyplot as plt
import numpy as np
import torch
import torch.nn as nn
from mpl_toolkits.mplot3d import Axes3D
[docs]def plot_2d_boundary(model, X, y, mesh, num_classes=2, figsize=(8,4), alpha=0.8):
"Plots decision boundary of a 2-dimensional task"
preds = torch.argmax(nn.Softmax(1)(model(mesh)), dim=1)
preds = preds.detach().cpu().reshape(mesh.size(0), mesh.size(1))
plt.figure(figsize=figsize)
plt.contourf(torch.linspace(0, mesh.size(0), mesh.size(0)), torch.linspace(0, mesh.size(1), mesh.size(1)),
preds, cmap='winter', alpha=alpha, levels=10)
for i in range(num_classes):
plt.scatter(X[y==i,0], X[y==i,1], alpha=alpha)
[docs]def plot_2d_flows(trajectory, num_flows=2, figsize=(8,4), alpha=0.8):
"Plots datasets flows learned by a neural differential equation."
plt.figure(figsize=figsize)
plt.subplot(121)
plt.title('Dimension: 0')
for i in range(num_flows):
plt.plot(trajectory[:,i,0], color='red', alpha=alpha)
plt.subplot(122)
plt.title('Dimension: 1')
for i in range(num_flows):
plt.plot(trajectory[:,i,1], color='blue', alpha=alpha)
defaults_1D = {'n_grid':100, 'n_levels':30, 'x_span':[-1,1],
'contour_alpha':0.7, 'cmap':'winter',
'traj_color':'orange', 'traj_alpha':0.1,
'device':'cuda:0'}
[docs]def plot_traj_vf_1D(model, s_span, traj, device, x_span, n_grid,
n_levels=30, contour_alpha=0.7, cmap='winter', traj_color='orange', traj_alpha=0.1):
"Plots 1D datasets flows."
ss = torch.linspace(s_span[0], s_span[-1], n_grid)
xx = torch.linspace(x_span[0], x_span[-1], n_grid)
S, X = torch.meshgrid(ss,xx)
if model.controlled:
ax = st['ax']
u_traj = traj[0,:,0].repeat(traj.shape[1],1)
e = torch.abs(st['y'].T - traj[:,:,0])
color = plt.cm.coolwarm(e)
for i in range(traj.shape[1]):
tr = ax.scatter(s_span, u_traj[:,i],traj[:,i,0],
c=color[:,i],alpha=1, cmap=color[:,i],zdir='z')
norm = mpl.colors.Normalize(e.min(),e.max())
plt.colorbar(mpl.cm.ScalarMappable(norm=norm, cmap='coolwarm'),
label='Approximation Error', orientation='horizontal')
ax.set_xlabel(r"$s$ [depth]")
ax.set_ylabel(r"$u$")
ax.set_zlabel(r"$h(s)$")
# make the panes transparent
ax.xaxis.set_pane_color((1.0, 1.0, 1.0, 0.0))
ax.yaxis.set_pane_color((1.0, 1.0, 1.0, 0.0))
ax.zaxis.set_pane_color((1.0, 1.0, 1.0, 0.0))
# make the grid lines transparent
ax.xaxis._axinfo["grid"]['color'] = (1,1,1,0)
ax.yaxis._axinfo["grid"]['color'] = (1,1,1,0)
ax.zaxis._axinfo["grid"]['color'] = (1,1,1,0)
else:
U, V = torch.ones(n_grid, n_grid), torch.zeros(n_grid, n_grid)
for i in range(n_grid):
for j in range(n_grid):
V[i,j] = model.vf(
S[i,j].reshape(1,-1).to(device),
X[i,j].reshape(1,-1).to(device)
).detach().cpu()
F = torch.sqrt(U**2 + V**2)
plt.contourf(S,X,F,n_levels,cmap=cmap,alpha=contour_alpha)
plt.streamplot(S.T.numpy(),X.T.numpy(),
U.T.numpy(),V.T.numpy(),
color='black',linewidth=1)
if not traj==None:
plt.plot(s_span, traj[:,:,0],
color=traj_color,alpha=traj_alpha)
plt.xlabel(r"$s$ [Depth]")
plt.ylabel(r"$h(s)$")
return (S, X, U, V)
[docs]def plot_2D_depth_trajectory(s_span, trajectory, yn, n_samples=128):
"Plots 2-dimensional trajectories of points."
color=['orange', 'blue']
fig = plt.figure(figsize=(8,2))
ax0 = fig.add_subplot(121)
ax1 = fig.add_subplot(122)
for i in range(n_samples):
ax0.plot(s_span, trajectory[:,i,0], color=color[int(yn[i])], alpha=.1)
ax1.plot(s_span, trajectory[:,i,1], color=color[int(yn[i])], alpha=.1)
ax0.set_xlabel(r"$s$ [Depth]")
ax0.set_ylabel(r"$h_0(s)$")
ax0.set_title("Dimension 0")
ax1.set_xlabel(r"$s$ [Depth]")
ax1.set_ylabel(r"$h_1(s)$")
ax1.set_title("Dimension 1")
[docs]def plot_2D_state_space(trajectory, yn, n_samples=128):
"Plots state-space trajectories."
color=['orange', 'blue']
fig = plt.figure(figsize=(3,3))
ax = fig.add_subplot(111)
for i in range(n_samples):
ax.plot(trajectory[:,i,0], trajectory[:,i,1], color=color[int(yn[i])], alpha=.1);
ax.set_xlabel(r"$h_0$")
ax.set_ylabel(r"$h_1$")
ax.set_title("Flows in the state-space")
[docs]def plot_2D_space_depth(s_span, trajectory, yn, n_lines):
"Plots 2D trajectories in a 3D space (2 dimensions of the system + time)."
colors = ['orange', 'blue']
fig = plt.figure(figsize=(6,3))
ax = Axes3D(fig, auto_add_to_figure=False)
fig.add_axes(ax)
for i in range(n_lines):
ax.plot(s_span, trajectory[:,i,0], trajectory[:,i,1], color=colors[yn[i].int()], alpha = .1)
ax.view_init(30, -110)
ax.set_xlabel(r"$s$ [Depth]")
ax.set_ylabel(r"$h_0$")
ax.set_zlabel(r"$h_1$")
ax.set_title("Flows in the space-depth")
ax.xaxis._axinfo["grid"]['color'] = (1,1,1,0)
ax.yaxis._axinfo["grid"]['color'] = (1,1,1,0)
ax.zaxis._axinfo["grid"]['color'] = (1,1,1,0)
[docs]def plot_static_vector_field(model, trajectory, t=0., N=50, device='cuda'):
"Plots vector field and trajectories on it."
x = torch.linspace(trajectory[:,:,0].min(), trajectory[:,:,0].max(), N)
y = torch.linspace(trajectory[:,:,1].min(), trajectory[:,:,1].max(), N)
X, Y = torch.meshgrid(x,y)
U, V = torch.zeros(N,N), torch.zeros(N,N)
for i in range(N):
for j in range(N):
p = torch.cat([X[i,j].reshape(1,1), Y[i,j].reshape(1,1)],1).to(device)
O = model.defunc(t,p).detach().cpu()
U[i,j], V[i,j] = O[0,0], O[0,1]
fig = plt.figure(figsize=(3,3))
ax = fig.add_subplot(111)
ax.contourf(X, Y, torch.sqrt(U**2 + V**2), cmap='RdYlBu')
ax.streamplot(X.T.numpy(),Y.T.numpy(),U.T.numpy(),V.T.numpy(), color='k')
ax.set_xlim([x.min(),x.max()])
ax.set_ylim([y.min(),y.max()])
ax.set_xlabel(r"$h_0$")
ax.set_ylabel(r"$h_1$")
ax.set_title("Learned Vector Field")
[docs]def plot_3D_dataset(X, yn):
"Plots set of points in 3D."
colors = ['orange', 'blue']
fig = plt.figure(figsize=(4,4))
ax = Axes3D(fig)
for i in range(len(X)):
ax.scatter(X[:,0],X[:,1],X[:,2], color=colors[yn[i].int()], alpha = .1)
ax.set_xlabel(r"$h_0$")
ax.set_ylabel(r"$h_1$")
ax.set_zlabel(r"$h_2$")
ax.set_title("Data Points")
ax.xaxis._axinfo["grid"]['color'] = (1,1,1,0)
ax.yaxis._axinfo["grid"]['color'] = (1,1,1,0)
ax.zaxis._axinfo["grid"]['color'] = (1,1,1,0)
