# coding: utf-8

# # How are numpy arrays stored?

# In[1]:

import numpy as np


# Numpy presents an n-dimensional abstraction that has to be fit into 1-dimensional computer memory.
# 
# Even for 2 dimensions (matrices), this leads to confusion: row-major, column-major.

# In[4]:

A = np.arange(9).reshape(3, 3)
print(A)


# ## Strides and in-memory representation

# How is this represented in memory?

# In[6]:

A.strides


# * `strides` stores for each axis by how many bytes one needs to jump to get from one entry to the next (in that axis)
# * So how is the array above stored?
# * This captures row-major ("C" order) and column-major ("Fortran" order), but is actually much more general.

# We can also ask for Fortran order:

# In[10]:

A2 = np.arange(9).reshape(3, 3, order="F")
A2


# `numpy` defaults to row-major order.

# In[11]:

A2.strides


# ## Strides and Contiguity

# How is the stride model more general than just saying "row major" or "column major"?

# In[15]:

A = np.arange(16).reshape(4, 4)
A


# In[18]:

A.strides


# In[14]:

Asub = A[:3, :3]
Asub


# Recall that `Asub` constitutes a *view* of the original data in `A`.

# In[19]:

Asub.strides


# Now `Asub` is no longer a *contiguous* array!
# 
# From the linear-memory representation (as show by the increasing numbers in `A`) 3, 7, 11 are missing.
# 
# This is easy to check by a flag:

# In[20]:

Asub.flags