Why the output here
array = np.arange(3)
array.shape
is
(3,)
and not
(1,3)
What does the missing dimension means or equals?
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1@NaN the reshape will change it to (1, 3), but why the original array is not (1,3)?Thomas Lee– Thomas Lee2018-07-14 00:45:54 +00:00Commented Jul 14, 2018 at 0:45
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1That is covered in the docsNaN– NaN2018-07-14 00:49:05 +00:00Commented Jul 14, 2018 at 0:49
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1You are creating a vector which by definition is only one dimension, not two.David– David2018-07-14 00:59:21 +00:00Commented Jul 14, 2018 at 0:59
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1Or, is simply tautological, equivalent to "your array is one dimensional because you created a one dimensional array" which wouldn't be wrongjuanpa.arrivillaga– juanpa.arrivillaga2018-07-14 01:34:07 +00:00Commented Jul 14, 2018 at 1:34
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1@juanpa.arrivillaga yes, it is tautological as what they are asking boils down to "why does the one dimensional array that I have created only have one dimension?"David– David2018-07-14 03:21:55 +00:00Commented Jul 14, 2018 at 3:21
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1 Answer
In case there's confusion, (3,) doesn't mean there's a missing dimension. The comma is part of the standard Python notation for a single element tuple. Shapes (1,3), (3,), and (3,1) are distinct,
While they can contain the same 3 elements, their use in calculations (broadcasting) is different, their print format is different, and their list equivalent is different:
In [21]: np.array([1,2,3])
Out[21]: array([1, 2, 3])
In [22]: np.array([1,2,3]).tolist()
Out[22]: [1, 2, 3]
In [23]: np.array([1,2,3]).reshape(1,3).tolist()
Out[23]: [[1, 2, 3]]
In [24]: np.array([1,2,3]).reshape(3,1).tolist()
Out[24]: [[1], [2], [3]]
And we don't have to stop at adding just one singleton dimension:
In [25]: np.array([1,2,3]).reshape(1,3,1).tolist()
Out[25]: [[[1], [2], [3]]]
In [26]: np.array([1,2,3]).reshape(1,3,1,1).tolist()
Out[26]: [[[[1]], [[2]], [[3]]]]
In numpy an array can have 0, 1, 2 or more dimensions. 1 dimension is just as logical as 2.
In MATLAB a matrix always has 2 dim (or more), but it doesn't have to be that way. Strictly speaking MATLAB doesn't even have scalars. An array with shape (3,) is missing a dimension only if MATLAB is taken as the standard.
numpy is built on Python which as scalars, and lists (which can nest). How many dimensions does a Python list have?
If you want to get into history, MATLAB was developed as a front end to a set of Fortran linear algebra routines. Given the problems those routines solved the concept of matrix with 2 dimensions, and row vs column vectors made sense. It wasn't until version 3.something that MATLAB was generalized to allow more than 2 dimensions (in the late 1990s).
numpy is based on several attempts to provide arrays to Python (e.g. numeric). Those developers took a more general approach to arrays, one where 2d was an artificial constraint. That has precedence in computer languages and mathematics (and physics). APL was developed in the 1960s, first as a mathematical notation, and then as a computer language. Like numpy its arrays can be 0d or higher. (Since I used APL before I used MATLAB, the numpy approach feels quite natural.)
In APL there aren't separate lists or tuples. So the shape of an array, rho A is itself an array, and rho rho A is the number of dimensions of A, also called the rank.
4 Comments
juanpa.arrivillaga
I would say Python has various containers, and the concept of scalars doesn't really apply. And lists don't have dimensions :)
David
This answer really isn't an answer to what they are saying and would be better served being a comment.
hpaulj
@David, I started to write a comment, and then decided it was too long for that. This issue has been hashed out many times, and probably should be closed as a duplicate, or may be a matter of opinion.
juanpa.arrivillaga
@David this answers the question, insofar as I can make sense of the OPs question