Resources for PS 2 and 3

[keertanavc]

I received a few questions for the coding part of the assignment and I felt it would be useful to share a few functions that might help you with PS 2 and 3. Good luck!

# Converting a symbolic function to a regular python function that takes arguments
import sympy as sy

x = sy.symbols('x')
f = (2 * sy.pi * sy.cos(x)) 
# Note: when you use functions like cosine/sine or constants like pi, not using the
# sympy version of the function / constant can lead to errors
print('function:', f)

# Method 1: lamdifying the function
g = sy.lambdify(x, f)
# g is a regular python function that takes x and correspondingly
# evaluates f(x)
print('lamdified evaluation:', g(10)) # = 2 * pi * cos(10)

# Method 2: substitution
print('substitution evaluation:', f.subs({x:10}).evalf())

# Keeping track of time to run a code
import time

# Record start time
start_time = time.clock()
count = 0
for i in range(100000):
    count += i
end_time = time.clock()
print('Running time for code = ', end_time-start_time, ' seconds')

# Drawing values from distribution
import scipy.stats as ss
import numpy as np
x, mu, sigma = (0, 0, 1)
# Normal distribution
# Cummulative probability
print(ss.norm.cdf(x, mu, sigma))
# Probability density function
print(ss.norm.pdf(x, mu, sigma))

# Lognormal distribution
# Cummulative probability
x = 1
print(ss.lognorm.cdf(x, sigma, mu, np.exp(mu)))
# Probability density function
print(ss.lognorm.pdf(x, sigma, mu, np.exp(mu)))

# Random draws from a uniform distribution
np.random.seed = 25
x_lb, x_ub, N = 0, 1, 10
# Setting the seed allows you to get the same random draws everytime
print(np.random.uniform(x_lb, x_ub, N))
# This code draws 10 random samples uniformly 
# distributed between 0 and 1

# Some standard numpy arrays
print(np.zeros((3, 5))) # Creates a matrix of size 3x5 filled with zeros
print(np.eye(4)) # Creates an identity matrix of size 4x4