#!/usr/bin/env python
# coding: utf-8

# # Foundations of Computational Economics #5
# 
# by Fedor Iskhakov, ANU
# 
# <img src="_static/img/dag3logo.png" style="width:256px;">

# ## Python essentials: control flow and functions
# 
# <img src="_static/img/lecture.png" style="width:64px;">

# <img src="_static/img/youtube.png" style="width:65px;">
# 
# [https://youtu.be/KDOH2R-Ambk](https://youtu.be/KDOH2R-Ambk)
# 
# Description: Flow control, user defined functions. Sieve of Eratosthenes example.

# ### Plan for the lecture
# 
# 1. Flow control  
# 1. User defined functions  
# 
# 
# 📖 Kevin Sheppard “Introduction to Python for Econometrics, Statistics
# and Data Analysis.” *Chapters: 3, 5, 10, 11, 13, 18, 22*

# ### Flow control: conditional expression and loops
# 
# Branch the program depending on a condition
# 
# - if  
# - if .. else  
# - if .. elif  
# - if .. elif .. else  
# 
# 
# **Remember about indentation!**- Should be 4 spaces according to PEP8 - Better not use Tab

# #### Examples of if-then-else

# In[1]:


x = 2
y = 2.0
z = [1, 2.1, 3.0, 0.0]

if y==2 and z[-1] >= 0.0:
    print("Condition 1")
elif y<2:
    print("Condition 2")
else:
    print("Condition 3")


# In[2]:


x = True
y = False

if x and y:
    print("Condition 1")
elif x and not y:
    print("Condition 2")
elif not x and y:
    print("Condition 3")
elif not x and not y:
    print("Condition 4")
else:
    print("Condition 5")


# #### Pass statement
# 
# Do nothing, but have correct indent

# In[3]:


if True:
    pass
else:
    print("check")
print("done")


# #### Ternary conditional operator

# In[4]:


a, b, condition = 1, 3, True

a if condition else b      # expression, not a statement

c = a if condition else b  # therefore this is possible


# #### Flow control: loops
# 
# - for  
# - while  
# - break  
# - continue  
# - for .. else, while .. else  
# 
# 
# **Remember about indent**- Should be 4 spaces according to PEP8 - Better not use Tab

# #### Examples of for

# In[5]:


for i in [0,1,2,3,4,5]:
    print("A iteration %d" % i)
print()

for i in range(5):
    print("B iteration %d" % i)


# #### List comprehensions

# In[6]:


x = []
for i in range(15):
    if i%3==0:
        x.append("item %d"%i)
x


# In[7]:


x = ["item %d"%i for i in range(15) if i%3==0]
x


# #### Multiple indexes in list comprehensions

# In[8]:


for i,j in zip(range(4),["a","b","c","d"]):
    print("i=%d j=%s"%(i,j))


# In[9]:


p= [x**y for x in  (2,3,5) for y in range(5)] #three power series
p


# #### For .. else
# 
# Very useful to check if for loop did not **break**

# In[10]:


k=0
for i in range(100):
    if k>15:
        break
    if i%5==0:
        k+=1
else:
    print("i went all the way up to %d"%i) #only runs if loop completed
print("loop complete with k=%d i=%d"%(k,i))


# #### While .. break .. continue example
# 
# **Sieve of Eratosthenes** to find prime numbers up to a certain value
# 
# Algorithm:
# - initialize the list of primes with all integers
# - go through a list of divisors (have to be in the list of primes)
# - cross all candidates divisible by the considered divisor
# - stop when all divisors up to the boundary are considered
# 
# Exercise: how can the algorithm be improved?

# In[11]:


upper = 23
primes = list(range(1,upper+1))  # all numbers between 1 and upper
divisor = 1  # initial divisor
while True:
    divisor+=1  # next divisor
    if divisor>upper:  # checked all divisors (?)
        break
    if not divisor in primes:
        continue  # skip divisor which is not itself prime
    i=0
    while i<len(primes):
        if primes[i]!=divisor and primes[i]%divisor==0:
            primes.remove(primes[i])  # remove, next is with the same index
        else:
            i+=1 # skip to go to next
    print("divisor %d:"%divisor,primes)
print("Primes up to %d are:" % upper,primes)


# ### User defined functions
# 
# - particular function in the code  
# - inputs and outputs  
# - can occur in the same file as the main program  
# - docstrings **!!!**  

# #### Defining a custom function

# In[12]:


def my_function():
    '''This is docstring for my function which explains what the function does:
       This function simply returns zero
    '''
    return 0.0

# call from the main program
x=my_function()
print(x)

# see docs
help(my_function)


# #### Input arguments
# 
# Python supports **named arguments** as well as **positional arguments**
# 
# Functions can have default values for optional arguments

# In[13]:


def my_function(a,b,c = 5):
    '''Build a list from three input arguments'''
    return [a,b,c]

# call from the main program
x=my_function(0,"test")
print(x)
y=my_function(a="one", c=3, b="two")
print(y)


# #### Variable scope

# In[14]:


def my_function(a, b):

    def my_nested_function(c, d):
        print("my_nested_function variables:")    # printing all variables in the scope of the function
        for symbol, value in locals().items():    # printing all variables in the scope of the function
            print ("    %s=%r "%(symbol,value))   # printing all variables in the scope of the function
        return c + d

    print("my_function variables are:")           # printing all variables in the scope of the function
    for symbol, value in locals().items():        # printing all variables in the scope of the function
        print ("    %s=%r "%(symbol,value))       # printing all variables in the scope of the function

    x = a * b * my_nested_function(a,b)
    return x

# call from the main program
x=10
y=2
print('The output from my function is ',my_function(x,y))


# #### Lambda functions (inline functions)
# 
# Short way to define simple functions, useful in bigger language constructs

# In[15]:


def f(x):
    return x**3

y = lambda x: x**3

print("f(5)=%f"%f(5))
print("y(3)=%f"%y(3))


# #### Example of user defined function: memory usage
# 
# First, plotting function

# In[3]:


def my_plot(d):
    '''Makes a nice plot using passed data'''
    import matplotlib.pyplot as plt
    plt.plot(d["x"],d["y"])
    plt.axis([min(d["x"]),max(d["x"]),0,max(d["y"])+1])
    plt.ylabel('size in memory, bytes')
    plt.xlabel('steps of variable update')
    plt.show()


# In[4]:


import sys
def memory_usage(var,grow,steps=10):
    '''Returns data on memory usage when var is grown using supplied function for given number of steps'''
    d={"x":[],"y":[],"v":[]} # dictionary for x, y data, and values
    for i in range(steps):
        var=grow(var) # next value
        d["v"].append(var)
        d["x"].append(i+1) # start with step 1 rather than 0
        d["y"].append(sys.getsizeof(var))
    return d


# In[5]:


d=memory_usage(var='*',grow=lambda x: x+"*",steps=10)
# d=memory_usage(var='*',grow=lambda x: x*2,steps=10)
# d=memory_usage(var=1,grow=lambda x: x*2,steps=200)
# d=memory_usage(var=1e249,grow=lambda x: x*2,steps=200)
print("Last value: %r"%d["v"][-5:])
my_plot(d)


# ### Further learning resources
# 
# - Python book: Kevin Sheppard “Introduction to Python for Econometrics,
#   Statistics and Data Analysis.” 3rd Edition University of Oxford
#   Thursday 1st February, 2018  
# - Coding style
#   [https://docs.python-guide.org/writing/style/#idioms](https://docs.python-guide.org/writing/style/#idioms)  
# - Formatting output
#   [https://pyformat.info/](https://pyformat.info/)  
# - Python inbuilt functions
#   [https://docs.python.org/3/library/functions.html](https://docs.python.org/3/library/functions.html)