Row major and Column major Explained, using Python against Matlab

In both cases, a 2d array of 2 rows, 4 columns is created.
Then, it is reshaped to 1 row, 8 columns.
This clearly demonstrates how Matlab stores the array data column-wise, and Python stores the array data row-wise after it is flattened out to 1d.

Matlab (Column Major)

Screen Shot 2017-06-04 at 10.51.20 AM

>> a = = [1 2 3 4 ; 5 6 7 8]

a = 
 1 2 3 4
 5 6 7 8

a = a(:)

a =

1 
5 
2 
6 
3 
7 
4 
8

Python (Row-major)

Screen Shot 2017-06-04 at 10.51.13 AM

>> import numpy as np
>> a = np.array([[1, 2, 3, 4], [5, 6, 7, 8]])
>> a
Out[]: 
array([[1, 2, 3, 4], 
        5, 6, 7, 8]])

>> a = a.tostring() # shows the memory arrangement, in a string

Out[] : b'\x01\x00\x00\x00\x02\x00\x00\x00\x03\x00\x00\x00\x04\x00\x00\x00\x05\x00\x00\x00\x06\x00\x00\x00\x07\x00\x00\x00\x08\x00\x00\x00'

If you look at the string printed, it shows that the elements are arranged in the fashion 1, 2, 3, 4, 5, 6, 7, 8.

Why is this important to know, you ask?

For optimization, it is important. In Python, C/C++, the elements will be laid out contiguously row-wise in memory. So you should strive to process the elements row-wise. The entire row could be copied to cache and worked on from there by the OS. If you processed the elements column wise, contrary to how it is laid out in memory, you would incur expensive context switching as the OS copies in the elements you require into cache for processing for every column-wise element you process!

 

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