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helper_plot.py
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helper_plot.py
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import numpy as np
import matplotlib as mpl
import matplotlib.pyplot as plt
import torch
from sklearn.mixture import GaussianMixture
import torch.distributions as distribution
from matplotlib.patches import Ellipse
def hdr_plot_style():
plt.style.use('dark_background')
mpl.rcParams.update({'font.size': 18, 'lines.linewidth': 3, 'lines.markersize': 15})
# avoid type 3 (i.e. bitmap) fonts in figures
mpl.rcParams['ps.useafm'] = True
mpl.rcParams['pdf.use14corefonts'] = True
mpl.rcParams['text.usetex'] = False
mpl.rcParams['font.family'] = 'sans-serif'
mpl.rcParams['font.sans-serif'] = 'Courier New'
#mpl.rcParams['text.hinting'] = False
# Set colors cycle
colors = mpl.cycler('color', ['#3388BB', '#EE6666', '#9988DD', '#EECC55', '#88BB44', '#FFBBBB'])
#plt.rc('figure', facecolor='#00000000', edgecolor='black')
#plt.rc('axes', facecolor='#FFFFFF88', edgecolor='white', axisbelow=True, grid=True, prop_cycle=colors)
plt.rc('legend', facecolor='#666666EE', edgecolor='white', fontsize=16)
plt.rc('grid', color='white', linestyle='solid')
plt.rc('text', color='white')
plt.rc('xtick', direction='out', color='white')
plt.rc('ytick', direction='out', color='white')
plt.rc('patch', edgecolor='#E6E6E6')
# define function that allows to generate a number of sub plots in a single line with the given titles
def prep_plots(titles, fig_size, fig_num=1):
"""
create a figure with the number of sub_plots given by the number of totles, and return all generated subplot axis
as a list
"""
# first close possibly existing old figures, if you dont' do this Juyter Lab will coplain after a while when it collects more than 20 existing ficgires for the same cell
# plt.close(fig_num)
# create a new figure
hdr_plot_style()
fig=plt.figure(fig_num, figsize=fig_size)
ax_list = []
for ind, title in enumerate(titles, start=1):
ax=fig.add_subplot(1, len(titles), ind)
ax.set_title(title)
ax_list.append(ax)
return ax_list
def finalize_plots(axes_list, legend=True, fig_title=None):
"""
adds grid and legend to all axes in the given list
"""
if fig_title:
fig = axes_list[0].figure
fig.suptitle(fig_title, y=1)
for ax in axes_list:
ax.grid(True)
if legend:
ax.legend()
def plot_patterns(P,D):
""" Plots the decision boundary of a single neuron with 2-dimensional inputs """
hdr_plot_style()
nPats = P.shape[1]
nUnits = D.shape[0]
if nUnits < 2:
D = np.concatenate(D, np.zeros(1,nPats))
# Create the figure
fig = plt.figure(figsize=(10, 8))
ax = plt.gca()
# Calculate the bounds for the plot and cause axes to be drawn.
xmin, xmax = np.min(P[0, :]), np.max(P[0, :])
xb = (xmax - xmin) * 0.2
ymin, ymax = np.min(P[1, :]), np.max(P[1, :])
yb = (ymax-ymin) * 0.2
ax.set(xlim=[xmin-xb, xmax+xb], ylim=[ymin-yb, ymax+yb])
plt.title('Input Classification')
plt.xlabel('x1'); plt.ylabel('x2')
# classVal = 1 + D[1,:] + 2 * D[2,:];
colors = [[0, 0.2, 0.9], [0, 0.9, 0.2], [0, 0, 1], [0, 1, 0]]
symbols = 'ooo*+x'; Dcopy = D[:]
#Dcopy[Dcopy == 0] = 1
for i in range(nPats):
c = Dcopy[i]
ax.scatter(P[0,i], P[1,i], marker=symbols[c], c=np.array(colors[c]).reshape(1,-1), s=50, linewidths=2, edgecolor='w')
#ax.legend()
ax.grid(True)
return fig
def plot_boundary(W,iVal,style,fig):
""" Plots (bi-dimensionnal) input patterns """
nUnits = W.shape[0]
colors = plt.cm.inferno_r.colors[1::3]
xLims = plt.gca().get_xlim()
for i in range(nUnits):
if len(style) == 1:
color = [1, 1, 1];
else:
color = colors[int((3 * iVal + 9) % len(colors))]
plt.plot(xLims,(-np.dot(W[i, 1], xLims) - W[i, 0]) / W[i, 2], linestyle=style, color=color, linewidth=1.5);
fig.canvas.draw()
def visualize_boundary_linear(X, y, model):
# VISUALIZEBOUNDARYLINEAR plots a linear decision boundary learned by the SVM
# VISUALIZEBOUNDARYLINEAR(X, y, model) plots a linear decision boundary
# learned by the SVM and overlays the data on it
hdr_plot_style()
w = model["w"]
b = model["b"]
xp = np.linspace(np.min(X[:, 0]), np.max(X[:, 0]), 100).transpose()
yp = - (w[0] * xp + b) / w[1]
plt.figure(figsize=(12, 8))
pos = (y == 1)[:, 0]
neg = (y == -1)[:, 0]
plt.scatter(X[pos, 0], X[pos, 1], marker='x', linewidths=2, s=23, c=[0, 0.5, 0])
plt.scatter(X[neg, 0], X[neg, 1], marker='o', linewidths=2, s=23, c=[1, 0, 0])
plt.plot(xp, yp, '-b')
plt.scatter(model["X"][:, 0], model["X"][:, 1], marker='o', linewidths=4, s=40, c=None, edgecolors=[0.1, 0.1, 0.1])
def plot_data(X, y):
#PLOTDATA Plots the data points X and y into a new figure
# PLOTDATA(x,y) plots the data points with + for the positive examples
# and o for the negative examples. X is assumed to be a Mx2 matrix.
#
# Note: This was slightly modified such that it expects y = 1 or y = 0
hdr_plot_style()
# Find Indices of Positive and Negative Examples
pos = (y == 1)[:, 0]
neg = (y == 0)[:, 0]
# Plot Examples
fig = plt.figure(figsize=(12, 8))
plt.scatter(X[pos, 0], X[pos, 1], marker='x', edgecolor='k', linewidths=2, s=50, c=[0, 0.5, 0])
plt.scatter(X[neg, 0], X[neg, 1], marker='o', edgecolor='k', linewidths=2, s=50, c=[1, 0, 0])
return fig
def visualize_boundary(X, y, model):
#VISUALIZEBOUNDARY plots a non-linear decision boundary learned by the SVM
# VISUALIZEBOUNDARYLINEAR(X, y, model) plots a non-linear decision
# boundary learned by the SVM and overlays the data on it
hdr_plot_style()
# Plot the training data on top of the boundary
plot_data(X, y)
# Make classification predictions over a grid of values
x1plot = np.linspace(np.min(X[:, 0]), np.max(X[:, 0]), 100).transpose()
x2plot = np.linspace(np.min(X[:, 1]), np.max(X[:, 1]), 100).transpose()
[X1, X2] = np.meshgrid(x1plot, x2plot)
vals = np.zeros(X1.shape)
for i in range(X1.shape[1]):
this_X = np.vstack((X1[:, i], X2[:, i]))
vals[:, i] = svmPredict(model, this_X)
# Plot the SVM boundary
plt.contour(X1, X2, vals, [1, 1], c='b')
# Plot the support vectors
plt.scatter(model["X"][:, 0], model["X"][:, 1], marker='o', linewidths=4, s=10, c=[0.1, 0.1, 0.1])
def plot_svc_decision_function(model, ax=None, plot_support=True):
"""Plot the decision function for a 2D SVC"""
if ax is None:
ax = plt.gca()
xlim = ax.get_xlim()
ylim = ax.get_ylim()
# create grid to evaluate model
x = np.linspace(xlim[0], xlim[1], 30)
y = np.linspace(ylim[0], ylim[1], 30)
Y, X = np.meshgrid(y, x)
xy = np.vstack([X.ravel(), Y.ravel()]).T
P = model.decision_function(xy).reshape(X.shape)
# plot decision boundary and margins
ax.contour(X, Y, P, colors='w',
levels=[-1, 0, 1], alpha=0.9,
linestyles=['--', '-', '--'])
# plot support vectors
if plot_support:
ax.scatter(model.support_vectors_[:, 0],
model.support_vectors_[:, 1],
s=300, linewidth=2, edgecolor='w', facecolors='none');
ax.set_xlim(xlim)
ax.set_ylim(ylim)
def plot_gaussian_ellipsoid(m, C, sdwidth=1, npts=None, axh=None, color='r'):
# PLOT_GAUSSIAN_ELLIPSOIDS plots 2-d and 3-d Gaussian distributions
#
# H = PLOT_GAUSSIAN_ELLIPSOIDS(M, C) plots the distribution specified by
# mean M and covariance C. The distribution is plotted as an ellipse (in
# 2-d) or an ellipsoid (in 3-d). By default, the distributions are
# plotted in the current axes.
# PLOT_GAUSSIAN_ELLIPSOIDS(M, C, SD) uses SD as the standard deviation
# along the major and minor axes (larger SD => larger ellipse). By
# default, SD = 1.
# PLOT_GAUSSIAN_ELLIPSOIDS(M, C, SD, NPTS) plots the ellipse or
# ellipsoid with a resolution of NPTS
#
# PLOT_GAUSSIAN_ELLIPSOIDS(M, C, SD, NPTS, AX) adds the plot to the
# axes specified by the axis handle AX.
#
# Examples:
# -------------------------------------------
# # Plot three 2-d Gaussians
# figure;
# h1 = plot_gaussian_ellipsoid([1 1], [1 0.5; 0.5 1]);
# h2 = plot_gaussian_ellipsoid([2 1.5], [1 -0.7; -0.7 1]);
# h3 = plot_gaussian_ellipsoid([0 0], [1 0; 0 1]);
# set(h2,'color','r');
# set(h3,'color','g');
#
# # "Contour map" of a 2-d Gaussian
# figure;
# for sd = [0.3:0.4:4],
# h = plot_gaussian_ellipsoid([0 0], [1 0.8; 0.8 1], sd);
# end
#
# # Plot three 3-d Gaussians
# figure;
# h1 = plot_gaussian_ellipsoid([1 1 0], [1 0.5 0.2; 0.5 1 0.4; 0.2 0.4 1]);
# h2 = plot_gaussian_ellipsoid([1.5 1 .5], [1 -0.7 0.6; -0.7 1 0; 0.6 0 1]);
# h3 = plot_gaussian_ellipsoid([1 2 2], [0.5 0 0; 0 0.5 0; 0 0 0.5]);
# set(h2,'facealpha',0.6);
# view(129,36); set(gca,'proj','perspective'); grid on;
# grid on; axis equal; axis tight;
# -------------------------------------------
#
# Gautam Vallabha, Sep-23-2007, [email protected]
# Revision 1.0, Sep-23-2007
# - File created
# Revision 1.1, 26-Sep-2007
# - NARGOUT==0 check added.
# - Help added on NPTS for ellipsoids
if axh is None:
axh = plt.gca()
if m.size != len(m):
raise Exception('M must be a vector');
if (m.size == 2):
h = show2d(m[:], C, sdwidth, npts, axh, color)
elif (m.size == 3):
h = show3d(m[:], C, sdwidth, npts, axh, color)
else:
raise Exception('Unsupported dimensionality');
return h
#-----------------------------
def show2d(means, C, sdwidth, npts=None, axh=None, color='r'):
if (npts is None):
npts = 50
# plot the gaussian fits
tt = np.linspace(0, 2 * np.pi, npts).transpose()
x = np.cos(tt);
y = np.sin(tt);
ap = np.vstack((x[:], y[:])).transpose()
v, d = np.linalg.eigvals(C)
d = sdwidth / np.sqrt(d) # convert variance to sdwidth*sd
bp = np.dot(v, np.dot(d, ap)) + means
h = axh.plot(bp[:, 0], bp[:, 1], ls='-', color=color)
return h
#-----------------------------
def show3d(means, C, sdwidth, npts=None, axh=None):
if (npts is None):
npts = 20
x, y, z = sphere(npts);
ap = np.concatenate((x[:], y[:], z[:])).transpose()
v, d = eigvals(C)
if any(d[:] < 0):
print('warning: negative eigenvalues')
d = np.max(d, 0)
d = sdwidth * np.sqrt(d); # convert variance to sdwidth*sd
bp = (v * d * ap) + repmat(means, 1, size(ap,2));
xp = reshape(bp[0,:], size(x));
yp = reshape(bp[1,:], size(y));
zp = reshape(bp[2,:], size(z));
h = axh.surf(xp, yp, zp);
return h
def fit_multivariate_gaussian(X_s):
gmm = GaussianMixture(n_components=1).fit(X_s)
labels = gmm.predict(X_s)
N = 50
X = np.linspace(-2, 10, N)
Y = np.linspace(-4, 4, N)
X, Y = np.meshgrid(X, Y)
# Pack X and Y into a single 3-dimensional array
pos = np.empty(X.shape + (2,))
pos[:, :, 0] = X
pos[:, :, 1] = Y
norm = distribution.MultivariateNormal(torch.Tensor(gmm.means_[0]), torch.Tensor(gmm.covariances_[0]))
Z = torch.exp(norm.log_prob(torch.Tensor(pos))).numpy()
plt.figure(figsize=(10, 8));
ax = plt.gca()
cset = ax.contourf(X, Y, Z, cmap='magma')
plt.scatter(X_s[:, 0], X_s[:, 1], c='b', s=60, edgecolor='w', zorder=2.5); plt.grid(True);
return labels
def fit_gaussian_mixture(X_s):
gmm = GaussianMixture(n_components=4).fit(X_s)
labels = gmm.predict(X_s)
N = 50
X = np.linspace(-2, 10, N)
Y = np.linspace(-4, 4, N)
X, Y = np.meshgrid(X, Y)
# Pack X and Y into a single 3-dimensional array
pos = np.empty(X.shape + (2,))
pos[:, :, 0] = X
pos[:, :, 1] = Y
Z = np.zeros((pos.shape[0], pos.shape[1]))
for i in range(4):
norm = distribution.MultivariateNormal(torch.Tensor(gmm.means_[i]), torch.Tensor(gmm.covariances_[i]))
Z += torch.exp(norm.log_prob(torch.Tensor(pos))).numpy()
plt.figure(figsize=(10, 8));
ax = plt.gca()
cset = ax.contourf(X, Y, Z, cmap='magma')
plt.scatter(X_s[:, 0], X_s[:, 1], c='b', s=60, edgecolor='w', zorder=2.5); plt.grid(True);
return labels
def draw_ellipse(position, covariance, ax=None, **kwargs):
"""Draw an ellipse with a given position and covariance"""
ax = ax or plt.gca()
# Convert covariance to principal axes
if covariance.shape == (2, 2):
U, s, Vt = np.linalg.svd(covariance)
angle = np.degrees(np.arctan2(U[1, 0], U[0, 0]))
width, height = 2 * np.sqrt(s)
else:
angle = 0
width, height = 2 * np.sqrt(covariance)
# Draw the Ellipse
for nsig in range(1, 4):
ax.add_patch(Ellipse(position, nsig * width, nsig * height,
angle, **kwargs))
def plot_gmm(gmm, X, label=True, ax=None):
plt.figure(figsize=(10,8))
ax = ax or plt.gca()
labels = gmm.fit(X).predict(X)
if label:
ax.scatter(X[:, 0], X[:, 1], c=labels, s=40, cmap='magma', edgecolor='gray', zorder=2)
else:
ax.scatter(X[:, 0], X[:, 1], s=40, zorder=2)
ax.axis('equal')
w_factor = 0.4 / gmm.weights_.max()
for pos, covar, w in zip(gmm.means_, gmm.covariances_, gmm.weights_):
draw_ellipse(pos, covar, alpha=w * w_factor)