import numpy as np
import matplotlib.pyplot as plt


# Exercise 1

# Function definition 
def myfunc( x ):
   out = np.cos(x) * np.exp(x)
   return out


# Exercise 2

# a) plot function

# create vector for x
x = np.linspace(-2*np.pi, 2*np.pi, 100, endpoint=True);
print x

# call the function
y = myfunc(x);

# plot the data
plt.plot(x, y)
plt.grid()
plt.ylabel('cos(x) * exp(x)')
plt.xlabel('x')

# b) store image
plt.savefig('myfunc.png')
plt.show()

# Exercise 3

# e) fix random seed
np.random.seed(123)

# a) normal distrubution
mu, sigma = 5.0, 2.0
normal_vector = np.random.normal(mu, sigma, 100000)

# b) uniform distribution
uniform_vector = np.random.uniform(0, 10, 100000)

# c) print mean and std. dev.
print np.mean(normal_vector), np.std(normal_vector)
print np.mean(uniform_vector), np.std(uniform_vector)

# d) plot
plt.figure()
count, bins, ignored = plt.hist(uniform_vector, 100, normed=True)
plt.plot(bins, np.ones_like(bins)*0.1, linewidth=2, color='r')

plt.figure()
count, bins, ignored = plt.hist(normal_vector, 100, normed=True)
plt.plot(bins, 1/(sigma * np.sqrt(2 * np.pi)) *
                np.exp( - (bins - mu)**2 / (2 * sigma**2) ),
         linewidth=2, color='r')

plt.show()

