IDA 2: Introduction to Python (selected solutions)

gradient_descent.py

# Solution Exercise 2.2

def gradient_descent(gradient, eta, x0=0, max_iter=10000, tol=1e-7):
    # Your code
    
    x_k = x0
    i = 0
    diff = tol + 1
    
    while i < max_iter and diff >= tol:
        x_k1 = x_k - eta * gradient(x_k)
        diff = abs(x_k - x_k1)
        x_k = x_k1
        i += 1
        
    return x_k

f_1 = lambda x: x**2 - x - 3
gradient_1 = lambda x: 2*x - 1
print 'Function 1: x² - x - 3'
x_prime = gradient_descent(gradient_1, 0.01)
print 'Local min {} at {}.'.format(f_1(x_prime), x_prime)

ys = [f_1(0.01 * x) for x in range(-1000, 1001)]
print 'Global min (?): {}'.format(min(ys))

from math import sin, cos
from random import uniform

f_2 = lambda x: sin(x)**2 / (x**2 + 1)
gradient_2 = lambda x: (2 * sin(x) * ( (x**2 + 1) * cos(x) - x * sin(x))) / (x**2 + 1)**2

print 'Function 2: sin²(x) / (x² + 1)'
x_primes = []

for i in range(10):
    x0 = uniform(-6.0, 6.0)
    x_prime = gradient_descent(gradient_2, -0.001, x0)
    print 'Local max {} at {} with start value {}.'.format(f_2(x_prime), x_prime, x0)
    x_primes.append(x_prime)

ys = [f_2(0.01 * x) for x in range(-1000, 1001)]
print 'Global max (?): {}'.format(max(ys))

missclassification.py

# Solution Exercise 4.1
idx = (svc.predict(X_test) != y_test)
X_miss = X_test[idx, :]
y_miss = y_test[idx]
len(X_miss) # number of missclassifications

for i in range(min(10, len(X_miss))):
    plt.matshow(X_miss[i].reshape(8,8), cmap=plt.cm.Greys)
    plt.xlabel('Classified as ' + str(svc.predict(X_miss[i])[0]) + ' but is ' + str(y_miss[i]))

So here a compromise, I post some solutions (which I deem most helpful for you) and delete them after the semester.