python - numpy array row major and column major

Question

I'm having trouble understanding how numpy stores its data. Consider the following:

>>> import numpy as np
>>> a = np.ndarray(shape=(2,3), order='F')
>>> for i in xrange(6): a.itemset(i, i+1)
... 
>>> a
array([[ 1.,  2.,  3.],
       [ 4.,  5.,  6.]])
>>> a.flags
  C_CONTIGUOUS : False
  F_CONTIGUOUS : True
  OWNDATA : True
  WRITEABLE : True
  ALIGNED : True
  UPDATEIFCOPY : False

This says that a is column major (F_CONTIGUOUS) thus, internally, a should look like the following:

[1, 4, 2, 5, 3, 6]

This is just what it is stated in in this glossary. What is confusing me is that if I try to to access the data of a in a linear fashion instead I get:

>>> for i in xrange(6): print a.item(i)
... 
1.0
2.0
3.0
4.0
5.0
6.0

At this point I'm not sure what the F_CONTIGUOUS flag tells us since it does not honor the ordering. Apparently everything in python is row major and when we want to iterate in a linear fashion we can use the iterator flat.

The question is the following: given that we have a list of numbers, say: 1, 2, 3, 4, 5, 6, how can we create a numpy array of shape (2, 3) in column major order? That is how can I get a matrix that looks like this

array([[ 1.,  3.,  5.],
       [ 2.,  4.,  6.]])

I would really like to be able to iterate linearly over the list and place them into the newly created ndarray. The reason for this is because I will be reading files of multidimensional arrays set in column major order.

Answer 1

The numpy stores data in row major order.

>>> a = np.array([[1,2,3,4], [5,6,7,8]])
>>> a.shape
(2, 4)
>>> a.shape = 4,2
>>> a
array([[1, 2],
       [3, 4],
       [5, 6],
       [7, 8]])

If you change the shape, the order of data do not change.

If you add a 'F', you can get what you want.

>>> b
array([1, 2, 3, 4, 5, 6])
>>> c = b.reshape(2,3,order='F')
>>> c
array([[1, 3, 5],
       [2, 4, 6]])