def pbc_sep(p1, p2):
arrow = sep(p1, p2)
rem = np.mod(arrow, 18) # The image in the first cube
mic_separation_vector = np.mod(rem+18/2, 18)-18/2
return np.array(mic_separation_vector)
def updatePlot(self, time, data):
'''
Adds data to the plot.
time is a list,
data is a list of lists, each list corresponding to a line on the plot
'''
if self.init == True: # Initialize the plot the first time routine is called
for i in range(len(data)):
# Instantiate line object and add it to the axes
self.line.append(
Line2D(time,
data[i],
color=self.colors[np.mod(i,
len(self.colors) - 1)],
ls=self.line_styles[np.mod(
i,
len(self.line_styles) - 1)],
label=self.legend if self.legend != None else None))
self.ax.add_line(self.line[i])
self.init = False
# add legend if one is specified
if self.legend != None:
plt.legend(handles=self.line)
else: # Add new data to the plot
# Updates the x and y data of each line.
for i in range(len(self.line)):
self.line[i].set_xdata(time)
self.line[i].set_ydata(data[i])
# Adjusts the axis to fit all of the data
self.ax.relim()
self.ax.autoscale()
def animate(k):
# clear panels
ax.cla()
ax2.cla()
# print rendering update
if np.mod(k+1,25) == 0:
print ('rendering animation frame ' + str(k+1) + ' of ' + str(num_frames))
if k == num_frames - 1:
print ('animation rendering complete!')
time.sleep(1.5)
clear_output()
####### plot total model on original dataset #######
ax.scatter(self.x_train,self.y_train,color = 'k',s = 60,edgecolor = self.colors[1] ,linewidth = 1.5)
ax.scatter(self.x_valid,self.y_valid,color = 'k',s = 60,edgecolor = self.colors[0] ,linewidth = 1.5)
# plot fit
if k > 0:
# plot current fit
a = inds[k-1]
steps = runner.best_steps[:a+1]
self.draw_fit(ax,steps,a)
# plot train / valid errors up to this point
self.plot_train_valid_errors(ax2,k-1,train_errors,valid_errors,inds)
# make panel size
ax.set_xlim([xmin,xmax])
ax.set_ylim([ymin,ymax])
return artist,
def animate(k):
# clear panels
ax.cla()
ax1.cla()
# print rendering update
if np.mod(k + 1, 25) == 0:
print('rendering animation frame ' + str(k + 1) + ' of ' +
str(num_frames))
if k == num_frames - 1:
print('animation rendering complete!')
time.sleep(1.5)
clear_output()
# get current run for cost function history plot
a = inds[k]
run = runs[a]
# pluck out current weights
self.draw_fit_trainval(ax, runs, a)
# show cost function history
if show_history == True:
ax1.cla()
self.plot_train_valid_errors(ax1, k, train_errors,
valid_errors, labels)
return artist,
def animate(k):
# clear panels
ax1.cla()
ax2.cla()
ax3.cla()
ax4.cla()
# print rendering update
if np.mod(k+1,25) == 0:
print ('rendering animation frame ' + str(k+1) + ' of ' + str(num_frames))
if k == num_frames - 1:
print ('animation rendering complete!')
time.sleep(1.5)
clear_output()
#### plot training, testing, and full data ####
# pluck out current weights
a = inds[k]
steps = runner.best_steps[:a+1]
# produce static img
self.draw_boundary(ax1,steps,a)
self.static_N2_simple(ax1,train_valid = 'original')
self.draw_boundary(ax2,steps,a)
self.static_N2_simple(ax2,train_valid = 'train')
self.draw_boundary(ax3,steps,a)
self.static_N2_simple(ax3,train_valid = 'validate')
#### plot training / validation errors ####
self.plot_train_valid_errors(ax4,a,train_errors,valid_errors,inds)
return artist,
def animate(k):
# clear current plots for next frame of animation
ax1.cla()
ax2.cla()
# print rendering update
if np.mod(k + 1, 25) == 0:
print('rendering animation frame ' + str(k + 1) + ' of ' +
str(num_frames))
if k == len(lam_range) - 1:
print('animation rendering complete!')
time.sleep(1.5)
clear_output()
# choose current regularization parameter
self.lam = lam_range[k]
# run gradient descent with two user-chosen initial values and chosen regularization value
w_hist_1 = self.gradient_descent(w=w_init_1,
alpha=alpha,
max_its=max_its)
w_hist_2 = self.gradient_descent(w=w_init_2,
alpha=alpha,
max_its=max_its)
# plot data points in panel 1, and cost function in panel 2
self.show_data_and_fit(ax1, w_hist_1[-1], color='lime')
self.show_data_and_fit(ax1, w_hist_2[-1], color='magenta')
# plot logistic surface, as well as gradient descent paths, in panel 2
self.plot_logistic_surface(ax2)
self.show_descent_path(ax2, w_hist_1, color='lime')
self.show_descent_path(ax2, w_hist_2, color='magenta')
return artist,
def animate(t):
# clear panels for next slide
ax1.cla()
ax2.cla()
ax3.cla()
# print rendering update
if np.mod(t+1,25) == 0:
print ('rendering animation frame ' + str(t+1) + ' of ' + str(num_frames))
if t == num_frames - 1:
print ('animation rendering complete!')
time.sleep(1.5)
clear_output()
# plot function 1
ax1.plot_surface(w1_vals,w2_vals,g1_vals,alpha = 0.1,color = 'w',rstride=10, cstride=10,linewidth=2,edgecolor = 'k')
ax1.set_title("$g_1$",fontsize = 15)
ax1.view_init(view[0],view[1])
ax1.axis(set_axis)
# plot function 2
ax2.plot_surface(w1_vals,w2_vals,g2_vals,alpha = 0.1,color = 'w',rstride=10, cstride=10,linewidth=2,edgecolor = 'k')
ax2.set_title("$g_2$",fontsize = 15)
ax2.view_init(view[0],view[1])
ax2.axis(set_axis)
# plot combination of both
alpha = alpha_vals[t]
g_combo = alpha*g1_vals + (1 - alpha)*g2_vals
ax3.plot_surface(w1_vals,w2_vals,g_combo,alpha = 0.1,color = 'k',rstride=10, cstride=10,linewidth=2,edgecolor = 'k')
ax3.set_title('$\\alpha\,g_1 + (1 - \\alpha)\,g_2$',fontsize = 15)
ax3.view_init(view[0],view[1])
ax3.axis(set_axis)
return artist,
def animate(k):
# clear panels
ax1.cla()
# current color
color = self.colorspec[k]
# print rendering update
if np.mod(k+1,25) == 0:
print ('rendering animation frame ' + str(k+1) + ' of ' + str(num_frames))
if k == num_frames - 1:
print ('animation rendering complete!')
time.sleep(1.5)
clear_output()
###### make left panel - plot data and fit ######
# initialize fit
w = self.w_hist[k]
y_fit = w[0] + x_fit*w[1]
# scatter data
self.scatter_pts(ax1)
# plot fit to data
ax1.plot(x_fit,y_fit,color = color,linewidth = 3)
return artist,
def animate(k):
ax.cla()
# print rendering update
if np.mod(k+1,25) == 0:
print ('rendering animation frame ' + str(k+1) + ' of ' + str(num_slides))
if k == num_slides - 1:
print ('animation rendering complete!')
time.sleep(1.5)
clear_output()
# define beta
special_size = size_range[k]
special_weight = weight_range[k]
beta = np.ones((1,self.y.size))
beta[:,ind1] = special_weight
# run optimizer
w_hist,g_hist = bits.newtons_method(g,w,self.x,self.y,beta,max_its)
w_best = w_hist[-1]
self.model = lambda data: bits.model(data,w_best)
# scatter plot all data
self.plot_data(ax,special_class,special_size)
# draw decision boundary
self.draw_decision_boundary(ax)
return artist,
def animate(k):
# clear panels
ax.cla()
ax1.cla()
# print rendering update
if np.mod(k+1,25) == 0:
print ('rendering animation frame ' + str(k+1) + ' of ' + str(num_frames))
if k == num_frames - 1:
print ('animation rendering complete!')
time.sleep(1.5)
clear_output()
# get current run for cost function history plot
a = inds[k]
run = runs[a]
# pluck out current weights
self.draw_fit(ax,ax1,runs,a)
# show cost function history
if show_history == True:
ax1.cla()
ax1.scatter(current_ind,cost_history[current_ind],s = 60,color = 'r',edgecolor = 'k',zorder = 3)
self.plot_cost_history(ax1,cost_history,start)
return artist,
def animate(k):
# clear panels
ax.cla()
ax1.cla()
ax2.cla()
ax3.cla()
# print rendering update
if np.mod(k + 1, 25) == 0:
print('rendering animation frame ' + str(k + 1) + ' of ' +
str(num_frames))
if k == num_frames - 1:
print('animation rendering complete!')
time.sleep(1.5)
clear_output()
#### plot training, testing, and full data ####
# pluck out current weights
w_best = weight_history[k]
# produce static img
self.static_N2_simple(ax, w_best, run, train_valid='original')
self.draw_boundary(ax, run, w_best, train_valid='train')
self.static_N2_simple(ax1, w_best, run, train_valid='train')
self.draw_boundary(ax1, run, w_best, train_valid='train')
self.static_N2_simple(ax2, w_best, run, train_valid='validate')
self.draw_boundary(ax2, run, w_best, train_valid='validate')
#### plot training / validation errors ####
self.plot_train_valid_errors(ax3, k, train_errors, valid_errors,
num_units)
return artist,
def animate(k):
# clear panels
ax1.cla()
# current color
color = self.colorspec[k]
# print rendering update
if np.mod(k+1,25) == 0:
print ('rendering animation frame ' + str(k+1) + ' of ' + str(num_frames))
if k == num_frames - 1:
print ('animation rendering complete!')
time.sleep(1.5)
clear_output()
###### make left panel - plot data and fit ######
# initialize fit
w = self.w_hist[k]
y_fit = self.sigmoid(w[0] + x_fit*w[1])
# scatter data
self.scatter_pts(ax1)
# plot fit to data
ax1.plot(x_fit,y_fit,color = color,linewidth = 2)
###### make right panel - plot contour and steps ######
if k == 0:
ax2.scatter(w[0],w[1],s = 90,facecolor = color,edgecolor = 'k',linewidth = 0.5, zorder = 3)
if k > 0 and k < num_frames:
self.plot_pts_on_contour(ax2,k,color)
if k == num_frames -1:
ax2.scatter(w[0],w[1],s = 90,facecolor = color,edgecolor = 'k',linewidth = 0.5, zorder = 3)
return artist,
def animate(k):
# clear panels
ax1.cla()
ax2.cla()
# print rendering update
if np.mod(k + 1, 25) == 0:
print('rendering animation frame ' + str(k + 1) + ' of ' +
str(num_frames))
if k == num_frames - 1:
print('animation rendering complete!')
time.sleep(1.5)
clear_output()
# scatter original data
ax1.scatter(self.x.flatten(),
self.y.flatten(),
color='k',
s=40,
edgecolor='w',
linewidth=0.9)
if k > 0:
# get current run for cost function history plot
a = inds[k - 1]
run = runs[a]
# pluck out current weights
self.draw_fit(ax1, run, a)
# cost function history plot
self.cost_history_plot(ax2, cost_evals, a)
return artist,
def animate(k):
# clear panels
ax.cla()
# print rendering update
if np.mod(k + 1, 25) == 0:
print('rendering animation frame ' + str(k + 1) + ' of ' +
str(num_frames))
if k == num_frames - 1:
print('animation rendering complete!')
time.sleep(1.5)
clear_output()
# scatter original data
ax.scatter(self.x.flatten(),
self.y.flatten(),
color='k',
s=40,
edgecolor='w',
linewidth=0.9)
if k > 0:
# get current run for cost function history plot
a = inds[k - 1]
model = run.models[a]
steps = run.best_steps[:a + 1]
# pluck out current weights
self.draw_boosting_fit(ax, steps, a)
return artist,
def angle_diff(theta1, theta2):
''' An angle subtraction method.
'''
if isinstance(theta1, tf.Tensor) or isinstance(theta2, tf.Tensor):
delta = tf.mod(theta1 - theta2 - pi, 2 * pi) - pi
else:
delta = np.mod(theta1 - theta2 - pi, 2 * pi) - pi
return delta
def animate(k):
# clear panels
ax.cla()
lam = lams[k]
# print rendering update
if np.mod(k + 1, 25) == 0:
print('rendering animation frame ' + str(k + 1) + ' of ' +
str(num_frames))
if k == num_frames - 1:
print('animation rendering complete!')
time.sleep(1.5)
clear_output()
# run optimization
if algo == 'gradient_descent':
weight_history, cost_history = self.gradient_descent(
g, w, self.x, self.y, lam, alpha_choice, max_its,
batch_size)
if algo == 'RMSprop':
weight_history, cost_history = self.RMSprop(
g, w, self.x, self.y, lam, alpha_choice, max_its,
batch_size)
# choose set of weights to plot based on lowest cost val
ind = np.argmin(cost_history)
# classification? then base on accuracy
if 'counter' in kwargs:
# create counting cost history as well
counts = [
counter(v, self.x, self.y, lam) for v in weight_history
]
if k == 0:
ind = np.argmin(counts)
count = counts[ind]
acc = 1 - count / self.y.size
acc = np.round(acc, 2)
# save lowest misclass weights
w_best = weight_history[ind][1:]
# plot
ax.axhline(c='k', zorder=2)
# make bar plot
ax.bar(np.arange(0, len(w_best)), w_best, color='k', alpha=0.5)
# dress panel
title1 = r'$\lambda = ' + str(np.round(lam, 2)) + '$'
costval = cost_history[ind][0]
title2 = ', cost val = ' + str(np.round(costval, 2))
if 'counter' in kwargs:
title2 = ', accuracy = ' + str(acc)
title = title1 + title2
ax.set_title(title)
ax.set_xlabel('learned weights')
return artist,
def animate(k):
# clear panels
ax1.cla()
# set axis in left panel
self.move_axis_left(ax1)
# current color
color = self.colorspec[k]
# print rendering update
if np.mod(k+1,25) == 0:
print ('rendering animation frame ' + str(k+1) + ' of ' + str(num_frames))
if k == num_frames - 1:
print ('animation rendering complete!')
time.sleep(1.5)
clear_output()
###### make left panel - plot data and fit ######
# initialize fit
w = self.w_hist[k]
# reshape and plot the surface, as well as where the zero-plane is
y_fit = w[0] + w[1]*x1_vals + w[2]*x2_vals
# plot cost surface
ax1.plot_surface(x1_vals,x2_vals,y_fit,alpha = 0.1,color = color,rstride=25, cstride=25,linewidth=0.25,edgecolor = 'k',zorder = 2)
# scatter data
self.scatter_pts(ax1)
#ax1.view_init(view[0],view[1])
# plot connector between points for visualization purposes
if k == 0:
w_new = self.w_hist[k]
g_new = self.least_squares(w_new)[0]
ax2.scatter(k,g_new,s = 0.1,color = 'w',linewidth = 2.5,alpha = 0,zorder = 1) # plot approx
if k > 0:
w_old = self.w_hist[k-1]
w_new = self.w_hist[k]
g_old = self.least_squares(w_old)[0]
g_new = self.least_squares(w_new)[0]
ax2.plot([k-1,k],[g_old,g_new],color = color,linewidth = 2.5,alpha = 1,zorder = 2) # plot approx
ax2.plot([k-1,k],[g_old,g_new],color = 'k',linewidth = 3.5,alpha = 1,zorder = 1) # plot approx
# set viewing limits for second panel
ax2.axhline(y=0, color='k',zorder = 0,linewidth = 0.5)
ax2.set_xlabel('iteration',fontsize = 12)
ax2.set_ylabel(r'$g(\mathbf{w})$',fontsize = 12,rotation = 0,labelpad = 25)
ax2.set_xlim([-0.5,len(self.w_hist)])
# set axis in left panel
self.move_axis_left(ax1)
return artist,
def animate(k):
# clear panels
ax1.cla()
ax2.cla()
ax3.cla()
# print rendering update
if np.mod(k+1,25) == 0:
print ('rendering animation frame ' + str(k+1) + ' of ' + str(num_frames))
if k == num_frames - 1:
print ('animation rendering complete!')
time.sleep(1.5)
clear_output()
# scatter data
ind0 = np.argwhere(self.y == +1)
ind0 = [e[1] for e in ind0]
ind1 = np.argwhere(self.y == -1)
ind1 = [e[1] for e in ind1]
for ax in [ax1,ax2,ax3]:
ax.scatter(self.x[0,ind0],self.x[1,ind0],s = pt_size, color = self.colors[0], edgecolor = 'k',antialiased=True)
ax.scatter(self.x[0,ind1],self.x[1,ind1],s = pt_size, color = self.colors[1], edgecolor = 'k',antialiased=True)
if k == 0:
ax1.set_title(str(0) + ' units fit to data',fontsize = 14,color = 'w')
ax1.set_title(str(0) + ' units fit to data',fontsize = 14,color = 'w')
ax1.set_title(str(0) + ' units fit to data',fontsize = 14,color = 'w')
ax1.set_xlim([xmin1,xmax1])
ax1.set_ylim([xmin2,xmax2])
ax2.set_xlim([xmin1,xmax1])
ax2.set_ylim([xmin2,xmax2])
ax3.set_xlim([xmin1,xmax1])
ax3.set_ylim([xmin2,xmax2])
# plot fit
if k > 0:
# get current run
a1 = inds1[k-1]
a2 = inds2[k-1]
a3 = inds3[k-1]
run1 = runs1[a1]
a1 = len(run1.w_init) - 1
run2 = runs2[a2]
model3 = runs3.models[a3]
steps = runs3.best_steps[:a3+1]
# plot models to data
self.draw_fit(ax1,run1,a1)
self.draw_fit(ax2,run2,a2 + 1)
self.draw_boosting_fit(ax3,steps,a3)
return artist,
def animate(k):
# clear panels
ax1.cla()
# print rendering update
if np.mod(k + 1, 25) == 0:
print('rendering animation frame ' + str(k + 1) + ' of ' +
str(num_frames))
if k == num_frames - 1:
print('animation rendering complete!')
time.sleep(1.5)
clear_output()
# plot x
ax1.plot(np.arange(1, x.size + 1),
x,
alpha=1,
c='k',
linewidth=1,
zorder=2)
# plot moving average - initial conditions
if k == 1:
ax1.plot(np.arange(1, T + 1),
y[:T],
alpha=0.75,
c='fuchsia',
linewidth=3,
zorder=3)
# make vertical visual guides
ax1.axvline(x=1)
ax1.axvline(x=T)
# plot moving average - everything after and including initial conditions
if k > 1:
j = k - 1
# plot
ax1.plot(np.arange(1, T + j + 1),
y[:T + j],
alpha=0.7,
c='fuchsia',
linewidth=3,
zorder=3)
# make vertical visual guides
ax1.axvline(x=j)
ax1.axvline(x=j + T - 1)
# label axes
ax1.set_xlim([xmin, xmax])
ax1.set_ylim([ymin, ymax])
return artist,
def advect(f, vx, vy):
"""Instead of moving the cell centers forward in time using the velocity fields,
we look for the particles which end up exactly at the cell centers by tracing
backwards in time from the cell centers. See 'implicit Euler integration.'"""
rows, cols = f.shape
cell_xs, cell_ys = np.meshgrid(np.arange(cols), np.arange(rows))
center_xs = (cell_xs - vx).ravel() # look backwards one timestep
center_ys = (cell_ys - vy).ravel()
left_ix = np.floor(center_ys).astype(int) # get locations of source cells.
top_ix = np.floor(center_xs).astype(int)
rw = center_ys - left_ix # relative weight of cells on the right
bw = center_xs - top_ix # same for cells on the bottom
left_ix = np.mod(left_ix, rows) # wrap around edges of simulation.
right_ix = np.mod(left_ix + 1, rows)
top_ix = np.mod(top_ix, cols)
bot_ix = np.mod(top_ix + 1, cols)
# a linearly-weighted sum of the 4 cells closest to the source of the cell center.
flat_f = (1 - rw) * ((1 - bw)*f[left_ix, top_ix] + bw*f[left_ix, bot_ix]) \
+ rw * ((1 - bw)*f[right_ix, top_ix] + bw*f[right_ix, bot_ix])
return np.reshape(flat_f, (rows, cols))
def advect(f, vx, vy):
"""Move field f according to x and y velocities (u and v)
using an implicit Euler integrator."""
rows, cols = f.shape
cell_ys, cell_xs = np.meshgrid(np.arange(rows), np.arange(cols))
center_xs = (cell_xs - vx).ravel()
center_ys = (cell_ys - vy).ravel()
# Compute indices of source cells.
left_ix = np.floor(center_xs).astype(np.int)
top_ix = np.floor(center_ys).astype(np.int)
rw = center_xs - left_ix # Relative weight of right-hand cells.
bw = center_ys - top_ix # Relative weight of bottom cells.
left_ix = np.mod(left_ix, rows) # Wrap around edges of simulation.
right_ix = np.mod(left_ix + 1, rows)
top_ix = np.mod(top_ix, cols)
bot_ix = np.mod(top_ix + 1, cols)
# A linearly-weighted sum of the 4 surrounding cells.
flat_f = (1 - rw) * ((1 - bw)*f[left_ix, top_ix] + bw*f[left_ix, bot_ix]) \
+ rw * ((1 - bw)*f[right_ix, top_ix] + bw*f[right_ix, bot_ix])
return np.reshape(flat_f, (rows, cols))
def advect(f, vx, vy):
"""Move field f according to x and y velocities (u and v)
using an implicit Euler integrator."""
rows, cols = f.shape
cell_ys, cell_xs = np.meshgrid(np.arange(rows), np.arange(cols))
center_xs = (cell_xs - vx).ravel()
center_ys = (cell_ys - vy).ravel()
# Compute indices of source cells.
left_ix = np.floor(center_xs).astype(np.int)
top_ix = np.floor(center_ys).astype(np.int)
rw = center_xs - left_ix # Relative weight of right-hand cells.
bw = center_ys - top_ix # Relative weight of bottom cells.
left_ix = np.mod(left_ix, rows) # Wrap around edges of simulation.
right_ix = np.mod(left_ix + 1, rows)
top_ix = np.mod(top_ix, cols)
bot_ix = np.mod(top_ix + 1, cols)
# A linearly-weighted sum of the 4 surrounding cells.
flat_f = (1 - rw) * ((1 - bw)*f[left_ix, top_ix] + bw*f[left_ix, bot_ix]) \
+ rw * ((1 - bw)*f[right_ix, top_ix] + bw*f[right_ix, bot_ix])
return np.reshape(flat_f, (rows, cols))
def _sim_step(self, a):
pos = self._qsoc.snd_rcv(a)
# Transform the relative cart position to [-0.4, +0.4]
if self._calibrated:
pos[0] = (pos[0] - self._norm_x_lim[0]
) - 1. / 2. * (self._norm_x_lim[1] - self._norm_x_lim[0])
x_dot = self._vel_filt_x(pos[0:1])
th_dot = self._vel_filt_th(pos[1:2])
# Normalize the angle from 0. to 2.*pi
pos[1] = np.mod(pos[1], 2. * np.pi) - np.pi
return np.concatenate([pos, x_dot, th_dot])
def animate(k):
# clear panels
ax.cla()
# print rendering update
if np.mod(k + 1, 25) == 0:
print('rendering animation frame ' + str(k + 1) + ' of ' +
str(num_frames))
if k == num_frames - 1:
print('animation rendering complete!')
time.sleep(1.5)
clear_output()
#### scatter data ####
# plot points in 2d and 3d
ind0 = np.argwhere(self.y == +1)
ind0 = [e[1] for e in ind0]
ax.scatter(self.x[0, ind0],
self.x[1, ind0],
s=55,
color=self.colors[0],
edgecolor='k')
ind1 = np.argwhere(self.y == -1)
ind1 = [e[1] for e in ind1]
ax.scatter(self.x[0, ind1],
self.x[1, ind1],
s=55,
color=self.colors[1],
edgecolor='k')
# plot boundary
if k > 0:
# get current run for cost function history plot
a = inds[k - 1]
model = run.models[a]
steps = run.best_steps[:a + 1]
# pluck out current weights
self.draw_boosting_fit(ax, steps, a)
# cleanup panel
ax.set_yticklabels([])
ax.set_xticklabels([])
ax.set_xticks([])
ax.set_yticks([])
ax.set_xlabel(r'$x_1$', fontsize=15)
ax.set_ylabel(r'$x_2$', fontsize=15, rotation=0, labelpad=20)
return artist,
def animate(k):
# clear panels
ax1.cla()
ax2.cla()
# print rendering update
if np.mod(k+1,25) == 0:
print ('rendering animation frame ' + str(k+1) + ' of ' + str(num_frames))
if k == num_frames - 1:
print ('animation rendering complete!')
time.sleep(1.5)
clear_output()
#### scatter data ####
# plot points in 2d and 3d
ind0 = np.argwhere(self.y == +1)
ind0 = [e[1] for e in ind0]
ax1.scatter(self.x[0,ind0],self.x[1,ind0],s = 55, color = self.colors[0], edgecolor = 'k')
ind1 = np.argwhere(self.y == -1)
ind1 = [e[1] for e in ind1]
ax1.scatter(self.x[0,ind1],self.x[1,ind1],s = 55, color = self.colors[1], edgecolor = 'k')
# plot boundary
if k > 0:
# get current run for cost function history plot
a = inds[k-1]
run = runs[a]
# pluck out current weights
self.draw_fit(ax1,run,a)
# cost function value
ax2.plot(np.arange(1,num_elements + 1),cost_evals,color = 'k',linewidth = 2.5,zorder = 1)
ax2.scatter(a + 1,cost_evals[a],color = self.colors[0],s = 70,edgecolor = 'w',linewidth = 1.5,zorder = 3)
# cleanup panels
ax1.set_yticklabels([])
ax1.set_xticklabels([])
ax1.set_xticks([])
ax1.set_yticks([])
ax1.set_xlabel(r'$x_1$',fontsize = 15)
ax1.set_ylabel(r'$x_2$',fontsize = 15,rotation = 0,labelpad = 20)
ax2.set_xlabel('number of units',fontsize = 12)
ax2.set_title('cost function plot',fontsize = 14)
ax2.set_xlim([minxc,maxxc])
ax2.set_ylim([ymin,ymax])
return artist,
def gradient_descent(g, w_unflat, alpha_choice, max_its, version, **kwargs):
verbose = False
if 'verbose' in kwargs:
verbose = kwargs['verbose']
# flatten the input function, create gradient based on flat function
g_flat, unflatten, w = flatten_func(g, w_unflat)
grad = compute_grad(g)
# record history
w_hist = []
w_hist.append(w_unflat)
# over the line
for k in range(max_its):
if verbose == True:
if np.mod(k, 5) == 0:
print('started iteration ' + str(k) + ' of ' + str(max_its))
# check if diminishing steplength rule used
if alpha_choice == 'diminishing':
alpha = 1 / float(k)
else:
alpha = alpha_choice
# plug in value into func and derivative
grad_eval = grad(w_unflat)
grad_eval, _ = flatten(grad_eval)
### normalized or unnormalized descent step? ###
if version == 'normalized':
grad_norm = np.linalg.norm(grad_eval)
if grad_norm == 0:
grad_norm += 10**-6 * np.sign(2 * np.random.rand(1) - 1)
grad_eval /= grad_norm
# take descent step
w = w - alpha * grad_eval
# record weight update
w_unflat = unflatten(w)
w_hist.append(w_unflat)
if verbose == True:
print('finished all ' + str(max_its) + ' iterations')
return w_hist
def animate(k):
# clear panels for next slide
ax1.cla()
ax2.cla()
ax3.cla()
# print rendering update
if np.mod(k + 1, 25) == 0:
print('rendering animation frame ' + str(k + 1) + ' of ' +
str(num_frames))
if k == num_frames - 1:
print('animation rendering complete!')
time.sleep(1.5)
clear_output()
# plot function 1
ax1.plot(w_plot, g1_plot, color='k', zorder=1)
ax1.set_title(title1, fontsize=15)
# plot function 2
ax2.plot(w_plot, g2_plot, color='k', zorder=1)
ax2.set_title(title2, fontsize=15)
# plot combination of both
alpha = alpha_vals[k]
if mode == 'regularization':
g_combo = g1_plot + alpha * g2_plot
else:
g_combo = (1 - alpha) * g1_plot + alpha * g2_plot
ax3.plot(w_plot, g_combo, color='k', zorder=1)
ax3.set_title(title3, fontsize=15)
# set vertical limits
ax1.set_ylim([g1_min, g1_max])
ax2.set_ylim([g2_min, g2_max])
# set vertical limit markers
gmin = np.amin(g_combo)
gmax = np.amax(g_combo)
g_gap = 0.2 * (gmax - gmin)
gmin = gmin - g_gap
gmax = gmax + g_gap
ax3.set_ylim([gmin, gmax])
return artist,
def animate(k):
# clear the panel
ax.cla()
# print rendering update
if np.mod(k + 1, 5) == 0:
print('rendering animation frame ' + str(k + 1) + ' of ' +
str(self.num_elements))
if k == self.num_elements - 1:
print('animation rendering complete!')
time.sleep(1)
clear_output()
####### plot a stump ######
# pick a stump
w = np.zeros((self.num_elements, 1))
w[k] = 1
# produce learned predictor
s = np.linspace(xmin, xmax, 400)
t = [self.tree_predict(np.asarray([v]), w) for v in s]
# plot approximation and data in panel
ax.scatter(self.x, self.y, c='k', edgecolor='w', s=50, zorder=2)
ax.plot(s, t, linewidth=2.5, color=self.colors[0], zorder=3)
# plot horizontal axis and dashed line to split point
ax.axhline(c='k', linewidth=1, zorder=0)
mid = (self.levels[k][0] + self.levels[k][1]) / float(2)
o = np.linspace(0, ymax, 100)
e = np.ones((100, 1))
sp = self.splits[k]
ax.plot(sp * e,
o,
linewidth=1.5,
color=self.colors[1],
linestyle='--',
zorder=1)
# cleanup panel
ax.set_xlim([xmin, xmax])
ax.set_ylim([ymin, ymax])
ax.set_xlabel(r'$x$', fontsize=14, labelpad=10)
ax.set_ylabel(r'$y$', rotation=0, fontsize=14, labelpad=10)
ax.set_xticks(np.arange(round(xmin), round(xmax) + 1, 1.0))
ax.set_yticks(np.arange(round(ymin), round(ymax) + 1, 1.0))
def animate(k):
# clear panels
ax1.cla()
# print rendering update
if np.mod(k + 1, 25) == 0:
print('rendering animation frame ' + str(k + 1) + ' of ' +
str(num_frames))
if k == num_frames - 1:
print('animation rendering complete!')
time.sleep(1.5)
clear_output()
# plot x
ax1.plot(np.arange(1, x.size + 1),
x,
alpha=1,
c='k',
linewidth=1,
zorder=2)
# plot running average - everything after and including initial conditions
if k >= 1:
j = k - 1
# plot
a = np.arange(1, j + 2)
b = y[:j + 1]
#print (a.shape,b.shape)
ax1.plot(np.arange(1, j + 2),
y[:j + 1],
alpha=0.7,
c='fuchsia',
linewidth=3,
zorder=3)
ax1.scatter(1,
y[0],
alpha=0.7,
c='fuchsia',
linewidth=3,
zorder=3)
# label axes
ax1.set_xlim([xmin, xmax])
ax1.set_ylim([ymin, ymax])
return artist,
def animate(k):
# clear panels
ax1.cla()
# print rendering update
if np.mod(k + 1, 25) == 0:
print('rendering animation frame ' + str(k + 1) + ' of ' +
str(num_frames))
if k == num_frames - 1:
print('animation rendering complete!')
time.sleep(1.5)
clear_output()
# plot x
ax1.plot(np.arange(1, x.size + 1),
x,
alpha=1,
c='k',
linewidth=1,
zorder=2)
# create y
if k == 0:
alpha = params[0]
y = func(x, alpha)
#ax1.plot(np.arange(1,y.size + 1),y,alpha = 1,c = 'fuchsia',linewidth = 3,zorder = 3);
ax1.set_title(r'Original data')
if k > 0:
alpha = params[k - 1]
y = func(x, alpha)
ax1.plot(np.arange(1, y.size + 1),
y,
alpha=0.9,
c='fuchsia',
linewidth=3,
zorder=3)
ax1.set_title(r'$\alpha = $ ' + str(np.round(alpha, 2)))
# label axes
ax1.set_xlabel(r'$t$', fontsize=13)
ax1.set_xlim([xmin, xmax])
ax1.set_ylim([ymin, ymax])
return artist,
def animate(k):
# clear the panels
ax1.cla()
ax2.cla()
# print rendering update
if np.mod(k + 1, 25) == 0:
print('rendering animation frame ' + str(k + 1) + ' of ' +
str(num_frames))
if k == num_frames - 1:
print('animation rendering complete!')
time.sleep(1.5)
clear_output()
if k > 0:
# pull current tracer
tracer = tracer_range[k - 1]
tracer = np.array([float(tracer[0]), float(tracer[1])])
tracer.shape = (2, 1)
g_tracer = func(tracer)
### draw 3d version ###
for ax in [ax1, ax2]:
# plot function
plot_func(func, view, ax)
if k > 0:
# scatter anchor point
ax.scatter(anchor[0],
anchor[1],
g_anchor,
s=50,
c='lime',
edgecolor='k',
linewidth=1)
# plot hyperplane connecting the anchor to tracer
secant(func, anchor, tracer, ax)
# reset tracer
tracer = np.flipud(tracer)
return artist,
def test_mod_arg1():
fun = lambda x, y : np.mod(x, y)
d_fun = grad(fun, 1)
check_grads(fun, npr.rand(), npr.rand())
check_grads(d_fun, npr.rand(), npr.rand())
def test_mod_arg1():
fun = lambda x, y : np.mod(x, y)
check_grads(fun)(npr.rand(), npr.rand())
