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

# ## numpy broadcasting is like "sharing" a smaller array for the bigger array
# - An array sharing a number
# - Regression paramters/weights sharing 1 intercept
# - Image data classification 2-D array of weights sharing 1-D array of intercept weights
# 
# 
# ### Remember: 
# 
# 
# 1. shape (3,) is treated as (1,3)
# 
# 2. shape column sizes must match in order to broadcast
# 
# 3. any ufunc can be broadcasted, not just +-

# In[1]:


import numpy as np


# <a id= 'back-to-top'></a>

# <a id= 'back-to-top'></a>
# ## [Broadcasting 1 number](#Broadcasting1Number)
# 
# ## [Broadcasting 1D array](#Broadcasting1D)
# 
# ## [Broadcast 2 ways](#two-way)
# 
# ## [Examples](#examples)
# 

# *** 
# <a id='Broadcasting1Number'></a>
# ## Broadcasting 1 number

# In[2]:


a = np.arange(10)
a


# In[3]:


a +10


# In[4]:


a = np.arange(15).reshape(3,5)


# In[5]:


a + 1000


# <a id='Broadcasting1D'></a>
# ## Broadcasting 1D array

# In[6]:


a = np.arange(3)
a


# In[7]:


b = np.eye(3)
b


# In[8]:


a + b


# In[9]:


b = np.ones((2,3), int)


# In[10]:


a + b


# <div class="alert alert-block alert-warning">
# <b>Won't work:</b> when column sizes don't match unless one of them has only 1 column!  Column sizes must match!  (3,) is treated as (1,3) when broadcasting.  (6,) is treated as (1,6)
# </div>

# In[11]:


b = np.arange(10)
b


# In[12]:


a + b


# In[ ]:


# even though 6 is divisable by 3, a refuses to be shared :(
b = np.arange(6)
a + b


# In[ ]:


# as soon as we reshape b to have the same column size as a, it works. 
a + b.reshape(2,3)


# <a id='two-way'></a>
# ## Broadcast two ways

# In[ ]:


a = np.arange(3)
a.shape


# In[ ]:


a


# In[ ]:


b = np.arange(3)[:, np.newaxis]
b.shape


# In[ ]:


b


# In[ ]:


# it is working because b has 1 column
a + b


# <a id='examples'></a>
# ## Examples

# ### Ex. 1 long - wide
# - long duplicates itself horizontally to match wide's width
# - wide duplicates itself vertically to match long's width

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X = np.ones((2,1), dtype=int)
X


# In[ ]:


Y = np.ones((1,2), dtype=int)
Y


# In[ ]:


X - Y


# ### Ex. 2 long - wide
# - long duplicates itself horizontally to match wide's width
# - wide duplicates itself vertically to match long's width

# In[ ]:


X = np.full((2,1),2)
X


# In[ ]:


Y = np.full((1,2),1)
Y


# In[ ]:


X - Y


# ### Ex. 3 long - wide
# - long duplicates itself horizontally to match wide's width
# - wide duplicates itself vertically to match long's width

# In[ ]:


X = np. array([[1],[2]])
X


# In[ ]:


Y = np.array([[2, 1]])
Y


# In[ ]:


X -Y


# ## Tricking it into doing something with evey row
# If we think of each row is a point on 2-D space (like a sheet of paper), if we want to get its distance from all other points, including itself,which we called X here,
# 
# then we reshape a copy of it into 3-D space, which we call Y.  So when we take the difference between them, X will be duplicated along the 3rd dimension.
# 
# The trick is that we do not reshape Y in (2,2,1).  Rather, we reshape Y in (2,1,2). 
# 
# In the first 2D space, X is (2,2) whereas Y is (2,1).  So Y has to duplicate itself to become (2,2). 
# 
# In the last dimension, X has to duplicate itself for Y.  

# In[ ]:


X = np.array([[1,0],
       [2,1]])
X


# In[ ]:


Y = X.reshape(2,1,2)
Y


# In[ ]:


#[[0,0] ,[-1,-1]] = [[1, 0]] - [[1, 0],[2, 1]]
#[[ 1,  1],[ 0,  0]]] = [[2, 1]] - [[1, 0],[2, 1]]
Y-X


# #### Let's check to see if we can replicate what numpy did

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np.array([[1, 0]]) - np.array([[1, 0],[2, 1]])


# In[ ]:


np.array([[2, 1]]) - np.array([[1, 0],[2, 1]])


# In[ ]:


np.hstack((np.array([[1, 0]]) - np.array([[1, 0],[2, 1]]), np.array([[2, 1]])) - np.array([[1, 0],[2, 1]])  )