def plots_weights_layer(mu_W,
sigma_W,
sigma_b,
mu_b,
ax1,
ax2,
legend_layer,
plot_pdf=1):
"""
Plot the given weights of the layer
"""
# For each of the weights we plot them !!
color = gl.get_color(None)
if (plot_pdf):
for i in range(sigma_W.size):
x_grid, y_val = bMA.gaussian1D_points(mean=mu_W[i],
std=sigma_W[i],
std_K=3)
gl.plot(
x_grid,
y_val,
ax=ax1,
fill=1,
alpha=0.15,
color=color,
labels=["Bayesian weights", "", "p(w)"],
alpha_line=0.15 # ,legend = ["W:%i"%(i+1)]
) ###legend = ["M: %.2e, std: %.2e"%(mu_W2[i], sigma_W2[i])])
gl.scatter(mu_W,
sigma_W,
ax=ax2,
labels=["", r"$\mu_w$", r"$\sigma_w$"],
color=color,
legend=legend_layer,
alpha=0.3)
if (plot_pdf):
for i in range(sigma_b.size):
x_grid, y_val = bMA.gaussian1D_points(mean=mu_b[i],
std=sigma_b[i],
std_K=3)
# color = gl.get_color(None)
gl.plot(
x_grid,
y_val,
ax=ax1,
color=color,
fill=1,
alpha=0.3,
alpha_line=0.15,
AxesStyle="Normal - No xaxis",
ls="--"
# ,legend = ["b:%i"%(i+1)]
) ###legend = ["M: %.2e, std: %.2e"%(mu_W2[i], sigma_W2[i])])
gl.scatter(mu_b, sigma_b, ax=ax2, color=color, marker="s", alpha=0.3)
def plots_weights_layer(mu_W, sigma_W,sigma_b, mu_b, ax1, ax2, legend_layer, plot_pdf = 1):
"""
Plot the given weights of the layer
"""
# For each of the weights we plot them !!
color = gl.get_color(None)
if (plot_pdf):
for i in range(sigma_W.size):
x_grid, y_val = bMA.gaussian1D_points(mean = mu_W[i], std = sigma_W[i], std_K = 3)
gl.plot(x_grid, y_val, ax = ax1, fill = 1, alpha = 0.15, color = color,
labels = ["Bayesian weights","","p(w)"],alpha_line = 0.15 # ,legend = ["W:%i"%(i+1)]
) ###legend = ["M: %.2e, std: %.2e"%(mu_W2[i], sigma_W2[i])])
gl.scatter( mu_W, sigma_W, ax = ax2, labels = ["",r"$\mu_w$",r"$\sigma_w$"],
color = color, legend = legend_layer, alpha = 0.3)
if (plot_pdf):
for i in range(sigma_b.size):
x_grid, y_val = bMA.gaussian1D_points(mean = mu_b[i], std = sigma_b[i], std_K = 3)
# color = gl.get_color(None)
gl.plot(x_grid, y_val, ax = ax1, color = color, fill = 1, alpha = 0.3, alpha_line = 0.15, AxesStyle = "Normal - No xaxis", ls = "--"
# ,legend = ["b:%i"%(i+1)]
) ###legend = ["M: %.2e, std: %.2e"%(mu_W2[i], sigma_W2[i])])
gl.scatter(mu_b, sigma_b, ax = ax2, color = color, marker = "s", alpha = 0.3)
labels = ["Convergence of LL with generated data","Iterations","LL"],
lw = 2)
gl.savefig(folder_images +'Likelihood_Evolution_' + clusters_relation+ "_"+str(periods[0])+ '.png',
dpi = 100, sizeInches = [12, 6])
if (final_clusters_graph):
gl.init_figure()
ax1 = gl.scatter(ret1, np.zeros(ret1.size), alpha = 0.2, color = "k",
legend = ["Data points %i"%(ret1.size)], labels = ["EM algorithm %i Gaussian fits"%(K),"Return",""])
for k in range(len(theta_list[-1])):
mu_k = theta_list[-1][k][0]
std_k = theta_list[-1][k][1]
model_theta_last = model_theta_list[-1]
x_grid, y_values = bMA.gaussian1D_points(mean = float( mu_k), std = float(np.sqrt(std_k)), std_K = 3.5)
color = gl.get_color()
if (len(model_theta_last) == 1):
pi = model_theta_last[0]
gl.plot(x_grid, y_values, color = color, fill = 1, alpha = 0.1,
legend = ["Kg(%i), pi:%.2f"%(k+1,pi[0,k])])
else:
pi = model_theta_last[0]
A = model_theta_last[1]
gl.plot(x_grid, y_values, color = color, fill = 1, alpha = 0.1,
legend = ["Kg(%i), pi:%.2f, A: %s"%(k+1,pi[0,k], str(A[k,:]))])
gl.set_fontSizes(ax = [ax1], title = 20, xlabel = 20, ylabel = 20,
legend = 12, xticks = 10, yticks = 10)
ymax = ymax + (ymax - ymin)*0.2
xymin, xymax = [np.min([xmin,ymin]),np.max([xmax,ymax])]
# Plot the marginalization of Y
x_1_list = np.linspace(-7,2,5)
i1 = 0;
i2= 1;
for x_1 in x_1_list:
# Compute the conditional mu_2 and std_2
L = (cov[i2,i1]/cov[i1,i1])
mu_2_cond = mu_2 + L*(x_1 - mu_1)
sigma_2_cond = np.sqrt(cov[i2,i2] - L*cov[i1,i2])
x_grid, y_val = bMA.gaussian1D_points(mean = mu_2_cond, std = sigma_2_cond, std_K = std_K)
y_val = y_val * (1/np.sqrt(2*np.pi*std_1*std_1))*np.exp(-np.power((x_1 - mu_1),2)/(2*std_1*std_1))
ax3D.plot(x_grid,y_val, xymin, zdir='x')
ax3D.add_collection3d(plt.fill_between(x_grid,y_val, 0, color='k', alpha=0.3),x_1, zdir='x')
# Set the visualization limits !
# ax3D.set_xlim(xmin, xmax)
# ax3D.set_ylim(ymin, ymax)
ax3D.set_xlim(xymin, xymax)
ax3D.set_ylim(xymin, xymax)
ax3D.set_zlim(zmin, zmax)
# ax1.pcolormesh(xx, yy, zz)
# ax1.imshow(zz, origin='lower', extent=[-3,3,-3,3], cmap="gray")
X = []
for i in range(Nx):
X_i = np.random.randn(Nsam,1)*stds[i] + mus[i]
X.append(X_i)
X = np.concatenate((X),axis = 1)
Nsim = 1000
x_grid = np.linspace(-6,8,Nsim)
if(distribution_graph):
## Plot the 3 distributions !
gl.init_figure()
for i in range(Nx):
X_i = X[:,[i]]
x_grid, y_values = bMA.gaussian1D_points(mean = mus[i], std = stds[i],
x_grid = x_grid)
color = gl.get_color()
gl.scatter(X_i, np.zeros(X_i.shape), alpha = 0.1, lw = 4, AxesStyle = "Normal",
color = color, labels = ["3 independent Gaussian distributions","x","pdf(x)"])
gl.plot(x_grid, y_values, color = color, fill = 1, alpha = 0.1,
legend = ["X%i: m:%.1f, std:%.1f"%(i+1,mus[i],stds[i])])
gl.savefig(folder_images +'Gaussians.png',
dpi = 100, sizeInches = [18, 10])
############################################################
################# PLOT DATA ###############################
############################################################
ax3D.set_ylim(xymin, xymax)
ax3D.set_zlim(zmin, zmax)
# Plot the marginalization of Y
x_1_list = np.linspace(-7,2,5)
i1 = 0;
i2= 1;
for x_1 in x_1_list:
# Compute the conditional mu_2 and std_2
L = (cov[i2,i1]/cov[i1,i1])
mu_2_cond = mu_2 + L*(x_1 - mu_1)
sigma_2_cond = np.sqrt(cov[i2,i2] - L*cov[i1,i2])
x_grid, y_val = bMA.gaussian1D_points(mean = mu_2_cond, std = sigma_2_cond, std_K = std_K)
y_val = y_val * (1/np.sqrt(2*np.pi*std_1*std_1))*np.exp(-np.power((x_1 - mu_1),2)/(2*std_1*std_1))
ax3D.plot(x_grid,y_val, xymin, zdir='x')
ax3D.add_collection3d(plt.fill_between(x_grid,y_val, 0, color='k', alpha=0.3),x_1, zdir='x')
# Set the visualization limits !
# ax3D.set_xlim(xmin, xmax)
# ax3D.set_ylim(ymin, ymax)
ax3D.set_xlim(xymin, xymax)
ax3D.set_ylim(xymin, xymax)
ax3D.set_zlim(zmin, zmax)
# ax1.pcolormesh(xx, yy, zz)
# ax1.imshow(zz, origin='lower', extent=[-3,3,-3,3], cmap="gray")
gl.scatter(ret1,ret2, alpha = 0.5, ax = ax1, lw = 4, AxesStyle = "Normal",
labels = ["",symbolIDs[0], symbolIDs[1]],
legend = ["%i points"%ret1.size])
## X distribution
ax2 = gl.subplot2grid((4,4), (0,0), rowspan=1, colspan=3, sharex = ax1)
gl.histogram(X = ret1, ax = ax2, AxesStyle = "Normal - No xaxis",
color = "k", alpha = 0.5)
x_grid = np.linspace(min(ret1),max(ret1),n_grids)
y_val = bMA.kde_sklearn(ret1, x_grid, bandwidth=np.std(ret1)/kde_K)
gl.plot(x_grid, y_val, color = "k",
labels = ["","",""], legend = ["M: %.2e, std: %.2e"%(mean[0], cov[0,0])])
x_grid, y_val = bMA.gaussian1D_points(X = ret1, std_K = 3)
gl.plot(x_grid, y_val, color = "b",
labels = ["","",""], legend = ["M: %.2e, std: %.2e"%(mean[0], cov[0,0])])
# Y distribution
ax3 = gl.subplot2grid((4,4), (1,3), rowspan=3, colspan=1,sharey = ax1,)
gl.histogram(X = ret2, ax = ax3, orientation = "horizontal",
AxesStyle = "Normal - No yaxis",
color = "k", alpha = 0.5)
x_grid = np.linspace(min(ret2),max(ret2),n_grids)
y_val = bMA.kde_sklearn(ret2, x_grid, bandwidth=np.std(ret2)/kde_K)
gl.plot(y_val, x_grid, color = "k",
labels = ["","",""], legend = ["M: %.2e, std: %.2e"%(mean[0], cov[1,1])])
gl.subplots_adjust(left=.09, bottom=.10, right=.90, top=.95, wspace=.01, hspace=0.01)
# V1_pr= []
# V2_pr= []
#
# for i in range(Y.shape[1]):
# V1_pr.append([Y[:,i],Y[:,i]- R[0,:].dot(Y[:,i]) * R[0,:]])
# V2_pr.append([Y[:,i],Y[:,i] - R[1,:].dot(Y[:,i]) * R[1,:]])
#
# gl.plot([V1_pr[i][0][0],V1_pr[i][1][0]],[V1_pr[i][0][1],V1_pr[i][1][1]], color = "y")
# gl.plot([V2_pr[i][0][0],V2_pr[i][1][0]],[V2_pr[i][0][1],V2_pr[i][1][1]], color = "r")
# gl.plot(V2_pr[i][0],V2_pr[i][1], color = "y")
# gl.plot([mu[0],n*R[0,0] + mu[0]],[mu[1],n*R[0,1]+ mu[1]],color = "y");
# gl.plot([mu[0],n*R[1,0] + mu[0]],[mu[1],n*R[1,1]+ mu[1]],color = "y");
## X distribution
ax2 = gl.subplot2grid((4,4), (0,0), rowspan=1, colspan=3, sharex = ax1)
x_grid, y_val = bMA.gaussian1D_points(mean = mu_Y[0], std = SigmaY[0,0], std_K = 3)
gl.plot(x_grid, y_val, color = "k",
labels = ["","",""], legend = ["M: %.2e, std: %.2e"%(mu_Y[0], SigmaY[0,0])])
x_grid, y_val = bMA.gaussian1D_points(mean = mu_Z[0], std = SigmaZ[0,0], std_K = 3)
gl.plot(x_grid, y_val, color = "g",
labels = ["","",""], legend = ["M: %.2e, std: %.2e"%(mu_Z[0], SigmaZ[0,0])])
# Y distribution
ax3 = gl.subplot2grid((4,4), (1,3), rowspan=3, colspan=1,sharey = ax1,)
x_grid, y_val = bMA.gaussian1D_points(mean = mu_Y[1], std = SigmaY[1,1], std_K = 3)
gl.plot(y_val, x_grid, color = "k",
labels = ["","",""], legend = ["M: %.2e, std: %.2e"%(mu_Y[1], SigmaY[1,1])])
x_grid, y_val = bMA.gaussian1D_points(mean = mu_Z[1], std = SigmaZ[1,1], std_K = 3)
gl.plot( y_val,x_grid , color = "g",
labels = ["","",""], legend = ["M: %.2e, std: %.2e"%(mu_Z[1], SigmaZ[1,1])])
alpha=0.5,
ax=ax1,
lw=4,
AxesStyle="Normal",
labels=["", symbolIDs[0], symbolIDs[1]],
legend=["%i points" % ret1.size])
## X distribution
ax2 = gl.subplot2grid((4, 4), (0, 0), rowspan=1, colspan=3, sharex=ax1)
gl.histogram(X=ret1,
ax=ax2,
AxesStyle="Normal - No xaxis",
color="k",
alpha=0.5)
x_grid, y_val = bMA.gaussian1D_points(X=ret1, std_K=3)
gl.plot(x_grid,
y_val,
color="k",
labels=["", "", ""],
legend=["M: %.2e, std: %.2e" % (mean[0], cov[0, 0])])
# Y distribution
ax3 = gl.subplot2grid(
(4, 4),
(1, 3),
rowspan=3,
colspan=1,
sharey=ax1,
)
gl.histogram(X=ret2,
for i in range(Nx):
X_i = np.random.randn(Nsam, 1) * stds[i] + mus[i]
X.append(X_i)
X = np.concatenate((X), axis=1)
Nsim = 1000
x_grid = np.linspace(-6, 8, Nsim)
if (distribution_graph):
## Plot the 3 distributions !
gl.init_figure()
for i in range(Nx):
X_i = X[:, [i]]
x_grid, y_values = bMA.gaussian1D_points(mean=mus[i],
std=stds[i],
x_grid=x_grid)
color = gl.get_color()
gl.scatter(
X_i,
np.zeros(X_i.shape),
alpha=0.1,
lw=4,
AxesStyle="Normal",
color=color,
labels=["3 independent Gaussian distributions", "x", "pdf(x)"])
gl.plot(x_grid,
y_values,
color=color,
ax1 = gl.scatter(ret1, np.zeros(ret1.shape), alpha = 0.5, lw = 4, AxesStyle = "Normal",
labels = ["",symbolIDs[0], ""],
legend = ["%i points"%ret1.size])
for i in range(int(ret1.size/26)):
gl.scatter(ret1[i*26:(i+1)*26], np.ones(ret1[i*26:(i+1)*26].shape)*(i+1), alpha = 0.5, lw = 4, AxesStyle = "Normal",
legend = ["Day %i"%(i+1)])
gl.set_zoom(ax = ax1, X = ret1,xlimPad = [0.1,0.8])
gl.savefig(folder_images +'InitPointsInferenceDays.png',
dpi = 100, sizeInches = [10, 4])
if (estimation_days_graph):
gl.init_figure()
x_grid, y_values = bMA.gaussian1D_points(X = ret1, num = 100, std_K = 2, x_grid = None)
ax1 = gl.plot(x_grid, y_values, alpha = 0.1, lw = 4, AxesStyle = "Normal",
labels = ["",symbolIDs[0], "Distribution"],
legend = ["%i points"%ret1.size] , color = "k")
for i in range(int(ret1.size/26)):
D = ret1[i*26:(i+1)*26]
x_grid, y_values = bMA.gaussian1D_points(X = D, num = 100, std_K = 2, x_grid = None)
color = gl.get_color()
gl.scatter(D, np.zeros(D.shape), alpha = 0.3, lw = 4, AxesStyle = "Normal",
legend = ["Day %i"%(i+1)],color = color)
gl.plot(x_grid, y_values, color = color, fill = 1, alpha = 0.1)
gl.init_figure()
ax1 = gl.scatter(
ret1,
np.zeros(ret1.size),
alpha=0.2,
color="k",
legend=["Data points %i" % (ret1.size)],
labels=["EM algorithm %i Gaussian fits" % (K), "Return", ""])
for k in range(len(theta_list[-1])):
mu_k = theta_list[-1][k][0]
std_k = theta_list[-1][k][1]
model_theta_last = model_theta_list[-1]
x_grid, y_values = bMA.gaussian1D_points(mean=float(mu_k),
std=float(np.sqrt(std_k)),
std_K=3.5)
color = gl.get_color()
if (len(model_theta_last) == 1):
pi = model_theta_last[0]
gl.plot(x_grid,
y_values,
color=color,
fill=1,
alpha=0.1,
legend=["Kg(%i), pi:%.2f" % (k + 1, pi[0, k])])
else:
pi = model_theta_last[0]
A = model_theta_last[1]
gl.plot(x_grid,