Concatenate two NumPy arrays vertically

Question

I tried the following:

>>> a = np.array([1,2,3])
>>> b = np.array([4,5,6])
>>> np.concatenate((a,b), axis=0)
array([1, 2, 3, 4, 5, 6])
>>> np.concatenate((a,b), axis=1)
array([1, 2, 3, 4, 5, 6])

However, I'd expect at least that one result looks like this

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

Why is it not concatenated vertically?

Solution 1

Because both a and b have only one axis, as their shape is (3), and the axis parameter specifically refers to the axis of the elements to concatenate.

this example should clarify what concatenate is doing with axis. Take two vectors with two axis, with shape (2,3):

a = np.array([[1,5,9], [2,6,10]])
b = np.array([[3,7,11], [4,8,12]])

concatenates along the 1st axis (rows of the 1st, then rows of the 2nd):

np.concatenate((a,b), axis=0)
array([[ 1,  5,  9],
       [ 2,  6, 10],
       [ 3,  7, 11],
       [ 4,  8, 12]])

concatenates along the 2nd axis (columns of the 1st, then columns of the 2nd):

np.concatenate((a, b), axis=1)
array([[ 1,  5,  9,  3,  7, 11],
       [ 2,  6, 10,  4,  8, 12]])

to obtain the output you presented, you can use vstack

a = np.array([1,2,3])
b = np.array([4,5,6])
np.vstack((a, b))
array([[1, 2, 3],
       [4, 5, 6]])

You can still do it with concatenate, but you need to reshape them first:

np.concatenate((a.reshape(1,3), b.reshape(1,3)))
array([[1, 2, 3],
       [4, 5, 6]])

Finally, as proposed in the comments, one way to reshape them is to use newaxis:

np.concatenate((a[np.newaxis,:], b[np.newaxis,:]))

Solution 2

If the actual problem at hand is to concatenate two 1-D arrays vertically, and we are not fixated on using concatenate to perform this operation, I would suggest the use of np.column_stack:

In []: a = np.array([1,2,3])
In []: b = np.array([4,5,6])
In []: np.column_stack((a, b))
array([[1, 4],
       [2, 5],
       [3, 6]])

Solution 3

A not well known feature of numpy is to use r_. This is a simple way to build up arrays quickly:

import numpy as np
a = np.array([1,2,3])
b = np.array([4,5,6])
c = np.r_[a[None,:],b[None,:]]
print(c)
#[[1 2 3]
# [4 5 6]]

The purpose of a[None,:] is to add an axis to array a.

Solution 4

a = np.array([1,2,3])
b = np.array([4,5,6])
np.array((a,b))

works just as well as

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

Regardless of whether it is a list of lists or a list of 1d arrays, np.array tries to create a 2d array.

But it's also a good idea to understand how np.concatenate and its family of stack functions work. In this context concatenate needs a list of 2d arrays (or any anything that np.array will turn into a 2d array) as inputs.

np.vstack first loops though the inputs making sure they are at least 2d, then does concatenate. Functionally it's the same as expanding the dimensions of the arrays yourself.

np.stack is a new function that joins the arrays on a new dimension. Default behaves just like np.array.

Look at the code for these functions. If written in Python you can learn quite a bit. For vstack:

return _nx.concatenate([atleast_2d(_m) for _m in tup], 0)

View more solutions

Comments

[Abid Rahman K]

weird !!! You can use np.vstack((a,b)) for this purpose (in case you don't know it)

[Dmitry Isakov]

Guys, sorry for the stupid comment, but why do you use brackets twice in case of vstack?

[Ian]

@DmitryIsakov Don't worry, it's not a stupid comment. numpy does this because the one required argument when using vstack is a tuple. In other words, np.vstack((a,b)) is the same as doing np.vstack(tup=(a,b)). See here: numpy.org/doc/stable/reference/generated/numpy.vstack.html

[Ian]

@DmitryIsakov assuming of course that you were asking about parentheses ( ) and not square brackets [ ]

[Abid Rahman K]

are you sure reshaping will work? It didn't work for me.

[wim]

Try np.concatenate([a[None,:],b[None,:]])

[gg349]

yes it does. Maybe you ran a.reshape(1,3) without assigning it, instead of a=a.reshape(1,3)?

[gg349]

strange. I suppose you then did d=b.reshape(1,3)? Still, concatenate((c,d)) works here.

[toom]

Actually this implementation is not particularly intutive. At some (suprisingly basic) points numpy does not make sense to me.

[Evgeni Sergeev]

So why doesn't Numpy raise an exception? It's clearly a contradiction in terms when we explicitly request axis=1, when it is non-existent.

[BallpointBen]

np.newaxis is None (quite literally) and makes its intent clearer than None -- a[np.newaxis, :].

[Employee]

Please edit the answer changing vstack((a,b)) to np.vstack((a,b))