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"""
lab_utils_uni.py
routines used in Course 1, Week2, labs1-3 dealing with single variables (univariate)
"""
import numpy as np
import matplotlib.pyplot as plt
from matplotlib.ticker import MaxNLocator
from matplotlib.gridspec import GridSpec
from matplotlib.colors import LinearSegmentedColormap
from ipywidgets import interact
from lab_utils_common import compute_cost
from lab_utils_common import dlblue, dlorange, dldarkred, dlmagenta, dlpurple, dlcolors
plt.style.use('deeplearning.mplstyle')
n_bin = 5
dlcm = LinearSegmentedColormap.from_list(
'dl_map', dlcolors, N=n_bin)
##########################################################
# Plotting Routines
##########################################################
def plt_house_x(X, y,f_wb=None, ax=None):
''' plot house with aXis '''
if not ax:
fig, ax = plt.subplots(1,1)
ax.scatter(X, y, marker='x', c='r', label="Actual Value")
ax.set_title("Housing Prices")
ax.set_ylabel('Price (in 1000s of dollars)')
ax.set_xlabel(f'Size (1000 sqft)')
if f_wb is not None:
ax.plot(X, f_wb, c=dlblue, label="Our Prediction")
ax.legend()
def mk_cost_lines(x,y,w,b, ax):
''' makes vertical cost lines'''
cstr = "cost = (1/m)*("
ctot = 0
label = 'cost for point'
addedbreak = False
for p in zip(x,y):
f_wb_p = w*p[0]+b
c_p = ((f_wb_p - p[1])**2)/2
c_p_txt = c_p
ax.vlines(p[0], p[1],f_wb_p, lw=3, color=dlpurple, ls='dotted', label=label)
label='' #just one
cxy = [p[0], p[1] + (f_wb_p-p[1])/2]
ax.annotate(f'{c_p_txt:0.0f}', xy=cxy, xycoords='data',color=dlpurple,
xytext=(5, 0), textcoords='offset points')
cstr += f"{c_p_txt:0.0f} +"
if len(cstr) > 38 and addedbreak is False:
cstr += "\n"
addedbreak = True
ctot += c_p
ctot = ctot/(len(x))
cstr = cstr[:-1] + f") = {ctot:0.0f}"
ax.text(0.15,0.02,cstr, transform=ax.transAxes, color=dlpurple)
##########
# Cost lab
##########
def plt_intuition(x_train, y_train):
w_range = np.array([200-200,200+200])
tmp_b = 100
w_array = np.arange(*w_range, 5)
cost = np.zeros_like(w_array)
for i in range(len(w_array)):
tmp_w = w_array[i]
cost[i] = compute_cost(x_train, y_train, tmp_w, tmp_b)
@interact(w=(*w_range,10),continuous_update=False)
def func( w=150):
f_wb = np.dot(x_train, w) + tmp_b
fig, ax = plt.subplots(1, 2, constrained_layout=True, figsize=(8,4))
fig.canvas.toolbar_position = 'bottom'
mk_cost_lines(x_train, y_train, w, tmp_b, ax[0])
plt_house_x(x_train, y_train, f_wb=f_wb, ax=ax[0])
ax[1].plot(w_array, cost)
cur_cost = compute_cost(x_train, y_train, w, tmp_b)
ax[1].scatter(w,cur_cost, s=100, color=dldarkred, zorder= 10, label= f"cost at w={w}")
ax[1].hlines(cur_cost, ax[1].get_xlim()[0],w, lw=4, color=dlpurple, ls='dotted')
ax[1].vlines(w, ax[1].get_ylim()[0],cur_cost, lw=4, color=dlpurple, ls='dotted')
ax[1].set_title("Cost vs. w, (b fixed at 100)")
ax[1].set_ylabel('Cost')
ax[1].set_xlabel('w')
ax[1].legend(loc='upper center')
fig.suptitle(f"Minimize Cost: Current Cost = {cur_cost:0.0f}", fontsize=12)
plt.show()
# this is the 2D cost curve with interactive slider
def plt_stationary(x_train, y_train):
# setup figure
fig = plt.figure( figsize=(9,8))
#fig = plt.figure(constrained_layout=True, figsize=(12,10))
fig.set_facecolor('#ffffff') #white
fig.canvas.toolbar_position = 'top'
#gs = GridSpec(2, 2, figure=fig, wspace = 0.01)
gs = GridSpec(2, 2, figure=fig)
ax0 = fig.add_subplot(gs[0, 0])
ax1 = fig.add_subplot(gs[0, 1])
ax2 = fig.add_subplot(gs[1, :], projection='3d')
ax = np.array([ax0,ax1,ax2])
#setup useful ranges and common linspaces
w_range = np.array([200-300.,200+300])
b_range = np.array([50-300., 50+300])
b_space = np.linspace(*b_range, 100)
w_space = np.linspace(*w_range, 100)
# get cost for w,b ranges for contour and 3D
tmp_b,tmp_w = np.meshgrid(b_space,w_space)
z=np.zeros_like(tmp_b)
for i in range(tmp_w.shape[0]):
for j in range(tmp_w.shape[1]):
z[i,j] = compute_cost(x_train, y_train, tmp_w[i][j], tmp_b[i][j] )
if z[i,j] == 0: z[i,j] = 1e-6
w0=200;b=-100 #initial point
### plot model w cost ###
f_wb = np.dot(x_train,w0) + b
mk_cost_lines(x_train,y_train,w0,b,ax[0])
plt_house_x(x_train, y_train, f_wb=f_wb, ax=ax[0])
### plot contour ###
CS = ax[1].contour(tmp_w, tmp_b, np.log(z),levels=12, linewidths=2, alpha=0.7,colors=dlcolors)
ax[1].set_title('Cost(w,b)')
ax[1].set_xlabel('w', fontsize=10)
ax[1].set_ylabel('b', fontsize=10)
ax[1].set_xlim(w_range) ; ax[1].set_ylim(b_range)
cscat = ax[1].scatter(w0,b, s=100, color=dlblue, zorder= 10, label="cost with \ncurrent w,b")
chline = ax[1].hlines(b, ax[1].get_xlim()[0],w0, lw=4, color=dlpurple, ls='dotted')
cvline = ax[1].vlines(w0, ax[1].get_ylim()[0],b, lw=4, color=dlpurple, ls='dotted')
ax[1].text(0.5,0.95,"Click to choose w,b", bbox=dict(facecolor='white', ec = 'black'), fontsize = 10,
transform=ax[1].transAxes, verticalalignment = 'center', horizontalalignment= 'center')
#Surface plot of the cost function J(w,b)
ax[2].plot_surface(tmp_w, tmp_b, z, cmap = dlcm, alpha=0.3, antialiased=True)
ax[2].plot_wireframe(tmp_w, tmp_b, z, color='k', alpha=0.1)
plt.xlabel("$w$")
plt.ylabel("$b$")
ax[2].zaxis.set_rotate_label(False)
ax[2].xaxis.set_pane_color((1.0, 1.0, 1.0, 0.0))
ax[2].yaxis.set_pane_color((1.0, 1.0, 1.0, 0.0))
ax[2].zaxis.set_pane_color((1.0, 1.0, 1.0, 0.0))
ax[2].set_zlabel("J(w, b)\n\n", rotation=90)
plt.title("Cost(w,b) \n [You can rotate this figure]", size=12)
ax[2].view_init(30, -120)
return fig,ax, [cscat, chline, cvline]
#https://matplotlib.org/stable/users/event_handling.html
class plt_update_onclick:
def __init__(self, fig, ax, x_train,y_train, dyn_items):
self.fig = fig
self.ax = ax
self.x_train = x_train
self.y_train = y_train
self.dyn_items = dyn_items
self.cid = fig.canvas.mpl_connect('button_press_event', self)
def __call__(self, event):
if event.inaxes == self.ax[1]:
ws = event.xdata
bs = event.ydata
cst = compute_cost(self.x_train, self.y_train, ws, bs)
# clear and redraw line plot
self.ax[0].clear()
f_wb = np.dot(self.x_train,ws) + bs
mk_cost_lines(self.x_train,self.y_train,ws,bs,self.ax[0])
plt_house_x(self.x_train, self.y_train, f_wb=f_wb, ax=self.ax[0])
# remove lines and re-add on countour plot and 3d plot
for artist in self.dyn_items:
artist.remove()
a = self.ax[1].scatter(ws,bs, s=100, color=dlblue, zorder= 10, label="cost with \ncurrent w,b")
b = self.ax[1].hlines(bs, self.ax[1].get_xlim()[0],ws, lw=4, color=dlpurple, ls='dotted')
c = self.ax[1].vlines(ws, self.ax[1].get_ylim()[0],bs, lw=4, color=dlpurple, ls='dotted')
d = self.ax[1].annotate(f"Cost: {cst:.0f}", xy= (ws, bs), xytext = (4,4), textcoords = 'offset points',
bbox=dict(facecolor='white'), size = 10)
#Add point in 3D surface plot
e = self.ax[2].scatter3D(ws, bs,cst , marker='X', s=100)
self.dyn_items = [a,b,c,d,e]
self.fig.canvas.draw()
def soup_bowl():
""" Create figure and plot with a 3D projection"""
fig = plt.figure(figsize=(8,8))
#Plot configuration
ax = fig.add_subplot(111, projection='3d')
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))
ax.zaxis.set_rotate_label(False)
ax.view_init(45, -120)
#Useful linearspaces to give values to the parameters w and b
w = np.linspace(-20, 20, 100)
b = np.linspace(-20, 20, 100)
#Get the z value for a bowl-shaped cost function
z=np.zeros((len(w), len(b)))
j=0
for x in w:
i=0
for y in b:
z[i,j] = x**2 + y**2
i+=1
j+=1
#Meshgrid used for plotting 3D functions
W, B = np.meshgrid(w, b)
#Create the 3D surface plot of the bowl-shaped cost function
ax.plot_surface(W, B, z, cmap = "Spectral_r", alpha=0.7, antialiased=False)
ax.plot_wireframe(W, B, z, color='k', alpha=0.1)
ax.set_xlabel("$w$")
ax.set_ylabel("$b$")
ax.set_zlabel("$J(w,b)$", rotation=90)
ax.set_title("$J(w,b)$\n [You can rotate this figure]", size=15)
plt.show()
def inbounds(a,b,xlim,ylim):
xlow,xhigh = xlim
ylow,yhigh = ylim
ax, ay = a
bx, by = b
if (ax > xlow and ax < xhigh) and (bx > xlow and bx < xhigh) \
and (ay > ylow and ay < yhigh) and (by > ylow and by < yhigh):
return True
return False
def plt_contour_wgrad(x, y, hist, ax, w_range=[-100, 500, 5], b_range=[-500, 500, 5],
contours = [0.1,50,1000,5000,10000,25000,50000],
resolution=5, w_final=200, b_final=100,step=10 ):
b0,w0 = np.meshgrid(np.arange(*b_range),np.arange(*w_range))
z=np.zeros_like(b0)
for i in range(w0.shape[0]):
for j in range(w0.shape[1]):
z[i][j] = compute_cost(x, y, w0[i][j], b0[i][j] )
CS = ax.contour(w0, b0, z, contours, linewidths=2,
colors=[dlblue, dlorange, dldarkred, dlmagenta, dlpurple])
ax.clabel(CS, inline=1, fmt='%1.0f', fontsize=10)
ax.set_xlabel("w"); ax.set_ylabel("b")
ax.set_title('Contour plot of cost J(w,b), vs b,w with path of gradient descent')
w = w_final; b=b_final
ax.hlines(b, ax.get_xlim()[0],w, lw=2, color=dlpurple, ls='dotted')
ax.vlines(w, ax.get_ylim()[0],b, lw=2, color=dlpurple, ls='dotted')
base = hist[0]
for point in hist[0::step]:
edist = np.sqrt((base[0] - point[0])**2 + (base[1] - point[1])**2)
if(edist > resolution or point==hist[-1]):
if inbounds(point,base, ax.get_xlim(),ax.get_ylim()):
plt.annotate('', xy=point, xytext=base,xycoords='data',
arrowprops={'arrowstyle': '->', 'color': 'r', 'lw': 3},
va='center', ha='center')
base=point
return
def plt_divergence(p_hist, J_hist, x_train,y_train):
x=np.zeros(len(p_hist))
y=np.zeros(len(p_hist))
v=np.zeros(len(p_hist))
for i in range(len(p_hist)):
x[i] = p_hist[i][0]
y[i] = p_hist[i][1]
v[i] = J_hist[i]
fig = plt.figure(figsize=(12,5))
plt.subplots_adjust( wspace=0 )
gs = fig.add_gridspec(1, 5)
fig.suptitle(f"Cost escalates when learning rate is too large")
#===============
# First subplot
#===============
ax = fig.add_subplot(gs[:2], )
# Print w vs cost to see minimum
fix_b = 100
w_array = np.arange(-70000, 70000, 1000)
cost = np.zeros_like(w_array)
for i in range(len(w_array)):
tmp_w = w_array[i]
cost[i] = compute_cost(x_train, y_train, tmp_w, fix_b)
ax.plot(w_array, cost)
ax.plot(x,v, c=dlmagenta)
ax.set_title("Cost vs w, b set to 100")
ax.set_ylabel('Cost')
ax.set_xlabel('w')
ax.xaxis.set_major_locator(MaxNLocator(2))
#===============
# Second Subplot
#===============
tmp_b,tmp_w = np.meshgrid(np.arange(-35000, 35000, 500),np.arange(-70000, 70000, 500))
z=np.zeros_like(tmp_b)
for i in range(tmp_w.shape[0]):
for j in range(tmp_w.shape[1]):
z[i][j] = compute_cost(x_train, y_train, tmp_w[i][j], tmp_b[i][j] )
ax = fig.add_subplot(gs[2:], projection='3d')
ax.plot_surface(tmp_w, tmp_b, z, alpha=0.3, color=dlblue)
ax.xaxis.set_major_locator(MaxNLocator(2))
ax.yaxis.set_major_locator(MaxNLocator(2))
ax.set_xlabel('w', fontsize=16)
ax.set_ylabel('b', fontsize=16)
ax.set_zlabel('\ncost', fontsize=16)
plt.title('Cost vs (b, w)')
# Customize the view angle
ax.view_init(elev=20., azim=-65)
ax.plot(x, y, v,c=dlmagenta)
return
# draw derivative line
# y = m*(x - x1) + y1
def add_line(dj_dx, x1, y1, d, ax):
x = np.linspace(x1-d, x1+d,50)
y = dj_dx*(x - x1) + y1
ax.scatter(x1, y1, color=dlblue, s=50)
ax.plot(x, y, '--', c=dldarkred,zorder=10, linewidth = 1)
xoff = 30 if x1 == 200 else 10
ax.annotate(r"$\frac{\partial J}{\partial w}$ =%d" % dj_dx, fontsize=14,
xy=(x1, y1), xycoords='data',
xytext=(xoff, 10), textcoords='offset points',
arrowprops=dict(arrowstyle="->"),
horizontalalignment='left', verticalalignment='top')
def plt_gradients(x_train,y_train, f_compute_cost, f_compute_gradient):
#===============
# First subplot
#===============
fig,ax = plt.subplots(1,2,figsize=(12,4))
# Print w vs cost to see minimum
fix_b = 100
w_array = np.linspace(-100, 500, 50)
w_array = np.linspace(0, 400, 50)
cost = np.zeros_like(w_array)
for i in range(len(w_array)):
tmp_w = w_array[i]
cost[i] = f_compute_cost(x_train, y_train, tmp_w, fix_b)
ax[0].plot(w_array, cost,linewidth=1)
ax[0].set_title("Cost vs w, with gradient; b set to 100")
ax[0].set_ylabel('Cost')
ax[0].set_xlabel('w')
# plot lines for fixed b=100
for tmp_w in [100,200,300]:
fix_b = 100
dj_dw,dj_db = f_compute_gradient(x_train, y_train, tmp_w, fix_b )
j = f_compute_cost(x_train, y_train, tmp_w, fix_b)
add_line(dj_dw, tmp_w, j, 30, ax[0])
#===============
# Second Subplot
#===============
tmp_b,tmp_w = np.meshgrid(np.linspace(-200, 200, 10), np.linspace(-100, 600, 10))
U = np.zeros_like(tmp_w)
V = np.zeros_like(tmp_b)
for i in range(tmp_w.shape[0]):
for j in range(tmp_w.shape[1]):
U[i][j], V[i][j] = f_compute_gradient(x_train, y_train, tmp_w[i][j], tmp_b[i][j] )
X = tmp_w
Y = tmp_b
n=-2
color_array = np.sqrt(((V-n)/2)**2 + ((U-n)/2)**2)
ax[1].set_title('Gradient shown in quiver plot')
Q = ax[1].quiver(X, Y, U, V, color_array, units='width', )
ax[1].quiverkey(Q, 0.9, 0.9, 2, r'$2 \frac{m}{s}$', labelpos='E',coordinates='figure')
ax[1].set_xlabel("w"); ax[1].set_ylabel("b")