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

# # Broadcasting operations

# ## General principle
# 
# If you have an $(m, n)$ matrix $A$ and apply operations like sub(-), add(+), mul(*) or div(/) by a vector $v$ the shape of $v$ will be grow vertically or horizontally like:
# 
# $(1,n)$ -> $(m,n)$
# 
# $(m,1)$ -> $(m,n)$

# ## Examples
# 
# 
# 1) First
# 
# $v = [1,2,3,4], x = 100$
# 
# $v + x = $ vector + escalar
# 
# Python turns the 100 into a vector with the same shape of $v$, like:
# 
# $v = [1,2,3,4] + [100, 100, 100, 100]$
# 
# $v = [101, 102, 103, 104]$
# 
# 
# 2) Second
# 
# $v_1 = [[1,2,3],[4,5,6]]$ + $v_2 = [100, 200, 300]$
# 
# $v_2$ will become like: $[[100, 200, 300], [100, 200, 300]]$
# 
# 3) Third
# 
# $v_1 = [[1,2,3],[4,5,6]]$ + $v2 = [[100],[200]]$
# 
# $v_2$ will become like: $[[100, 100, 100], [200, 200, 200]]$
# 

# ## In practice

# In[2]:


import numpy as np;


# In[43]:


A = np.array(
    [[56.0, 0.0, 4.4, 68.0],
    [1.2, 104.0, 52.0, 8.0],
    [1.8, 135.0, 99.0, 0.9]]
)
print(A)


# In[45]:


sum = A.sum(axis = 0)
sum


# In[47]:


A/sum