How to create a numpy array of lists?

If you really need a 1-d array of lists you will have to wrap your lists in your own class as numpy will always try to convert your lists to arrays inside of an array (which is more efficient but obviously requires constant size-elements), for example through

class mylist:

    def __init__(self, l):
        self.l=l

    def __repr__(self): 
        return repr(self.l)

    def append(self, x):
        self.l.append(x)

and then you can change any element without changing the dimension of others

>>> x = mylist([1,2,3])
>>> y = mylist([1,2,3])
>>> import numpy as np
>>> data = np.array([x,y])
>>> data
array([[1,2,3], [1,2,3]], dtype=object)
>>> data[0].append(2)
>>> data
array([[1,2,3,2], [1,2,3]], dtype=object)

Update

As suggested by ali_m there is actually a way to force numpy to simply create a 1-d array for references and then feed them with actual lists

>>> data = np.empty(2, dtype=np.object)
>>> data[:] = [1, 2, 3], [1, 2, 3]
>>> data
array([[1, 2, 3], [1, 2, 3]], dtype=object)
>>> data[0].append(4)
>>> data
array([[1, 2, 3, 4], [1, 2, 3]], dtype=object)

As you discovered, np.array tries to create a 2d array when given something like

 A = np.array([[1,2],[3,4]],dtype=object)

You have apply some tricks to get around this default behavior.

One is to make the sublists variable in length. It can't make a 2d array from these, so it resorts to the object array:

In [43]: A=np.array([[1,2],[],[1,2,3,4]])
In [44]: A
Out[44]: array([[1, 2], [], [1, 2, 3, 4]], dtype=object)

And you can then append values to each of those lists:

In [45]: for i in A: i.append(34)
In [46]: A
Out[46]: array([[1, 2, 34], [34], [1, 2, 3, 4, 34]], dtype=object)

np.empty also creates an object array:

In [47]: A=np.empty((3,),dtype=object)
In [48]: A
Out[48]: array([None, None, None], dtype=object)

But you then have to be careful how you change the elements to lists. np.fill is tempting, but has problems:

In [49]: A.fill([])
In [50]: A
Out[50]: array([[], [], []], dtype=object)
In [51]: for i in A: i.append(34)
In [52]: A
Out[52]: array([[34, 34, 34], [34, 34, 34], [34, 34, 34]], dtype=object)

It turns out that fill puts the same list in all slots, so modifying one modifies all the others. You can get the same problem with a list of lists:

In [53]: B=[[]]*3
In [54]: B
Out[54]: [[], [], []]
In [55]: for i in B: i.append(34)
In [56]: B
Out[56]: [[34, 34, 34], [34, 34, 34], [34, 34, 34]]

The proper way to initial the empty A is with an iteration, e.g.

In [65]: A=np.empty((3,),dtype=object)
In [66]: for i,v in enumerate(A): A[i]=[v,i]
In [67]: A
Out[67]: array([[None, 0], [None, 1], [None, 2]], dtype=object)
In [68]: for v in A: v.append(34)
In [69]: A
Out[69]: array([[None, 0, 34], [None, 1, 34], [None, 2, 34]], dtype=object)

It's a little unclear from the question and comments whether you want to append to the lists, or append lists to the array. I've just demonstrated appending to the lists.

There is an np.append function, which new users often misuse. It isn't a substitute for list append. It is a front end to np.concatenate. It is not an in-place operation; it returns a new array.

Also defining a list to add with it can be tricky:

In [72]: np.append(A,[[1,23]])
Out[72]: array([[None, 0, 34], [None, 1, 34], [None, 2, 34], 1, 23],     dtype=object)

You need to construct another object array to concatenate to the original, e.g.

In [76]: np.append(A,np.empty((1,),dtype=object))
Out[76]: array([[None, 0, 34], [None, 1, 34], [None, 2, 34], None], dtype=object)

In all of this, an array of lists is harder to construct than a list of lists, and no easier, or faster, to manipulate. You have to make it a 2d array of lists to derive some benefit.

In [78]: A[:,None]
Out[78]: 
array([[[None, 0, 34]],
       [[None, 1, 34]],
       [[None, 2, 34]]], dtype=object)

You can reshape, transpose, etc an object array, where as creating and manipulating a list of lists of lists gets more complicated.

In [79]: A[:,None].tolist()
Out[79]: [[[None, 0, 34]], [[None, 1, 34]], [[None, 2, 34]]]

===

As shown in https://stackoverflow.com/a/57364472/901925, np.frompyfunc is a good tool for creating an array of objects.

np.frompyfunc(list, 0, 1)(np.empty((3,2), dtype=object))