numpy.r_ 中的字符串是什么意思？

Question

in numpy's documents :

>>> np.r_['0,2,0', [1,2,3], [4,5,6]]
array([[1],
       [2],
       [3],
       [4],
       [5],
       [6]])

what does the third number mean in the string '0,2,0'?

Answer 1

I haven't used the string parameter of r_ much; it's easier, for me, to work directly with concatanate and its variantes.

But looking at the docs:

A string with three comma-separated integers allows specification of the axis to concatenate along, the minimum number of dimensions to force the entries to, and which axis should contain the start of the arrays which are less than the specified number of dimensions.

'0.2.0'
 axis = 0
 make it 2d
 start with 0d

In [79]: np.r_['0,2,0', [1,2,3], [4,5,6]]
Out[79]: 
array([[1],
       [2],
       [3],
       [4],
       [5],
       [6]])

A concatenate equivalent

In [80]: np.concatenate(([1,2,3], [4,5,6]))
Out[80]: array([1, 2, 3, 4, 5, 6])
In [81]: np.concatenate(([1,2,3], [4,5,6]))[:,None]
Out[81]: 
array([[1],
       [2],
       [3],
       [4],
       [5],
       [6]])

Here I've concatenated on axis=0, and expanded to 2d after concatenate. But it sounds like r_ expands the dimensions of the elements first (but we can double check in the code).

In [83]: alist = ([1,2,3], [4,5,6]) 
In [86]: [np.expand_dims(a,1) for a in alist]
Out[86]: 
[array([[1],
        [2],
        [3]]), array([[4],
        [5],
        [6]])]
In [87]: np.concatenate(_, axis=0)
Out[87]: 
array([[1],
       [2],
       [3],
       [4],
       [5],
       [6]])

I'm using expand_dims to make the inputs 2 d, and to add the new dimension after the first. Having done that I can concatenate on axis 0.

Note that the inputs to r_ could already be 2d, as in:

np.r_['0,2,0',[1,2,3], [[4],[5],[6]]]
np.r_['0,2,0',[1,2,3], np.expand_dims([4,5,6],1)]
np.r_['0,2,0',[1,2,3], np.atleast_2d([4,5,6]).T]

The 3d number, if 1, turns the components into

In [105]: np.atleast_2d([4,5,6])
Out[105]: array([[4, 5, 6]])

In [103]: np.r_['0,2,1',[1,2,3],[4,5,6]]
Out[103]: 
array([[1, 2, 3],
       [4, 5, 6]])

Often if documentation is unclear I like to either dig into the code, or experiment with alternative inputs.

In [107]: np.r_['1,2,1',[1,2,3], [4,5,6]]
Out[107]: array([[1, 2, 3, 4, 5, 6]])
In [108]: np.r_['1,2,0',[1,2,3], [4,5,6]]
Out[108]: 
array([[1, 4],
       [2, 5],
       [3, 6]])

---

Looking at the code, I see it uses

array(newobj, copy=False, subok=True, ndmin=ndmin)

to expand the components to the desired ndmin . The 3d number is used to construct a transpose parameter. Details are messy, but the effect is something like:

In [111]: np.array([1,2,3], ndmin=2)
Out[111]: array([[1, 2, 3]])
In [112]: np.array([1,2,3], ndmin=2).transpose(1,0)
Out[112]: 
array([[1],
       [2],
       [3]])

Answer 2

Thank you for all the answers!!! Now, I think I have a better understanding of this problem. So, I drawed the mind map. Please correct me if I'm wrong. As a beginner of Python, I am trying my best to learn more and think more. Lastly, I have to apologize for my poor English.😋

Answer 3

'0,2,0' is a three comma-separated string. When used with numpy.r_ each element respectively specifies:

1. Which dimension to use as the axis of concatenation
2. What is the minimum number of dimensions that each array needs to have. If an array has less dimensions than the number specified here then numpy.r_ upgrades the shape tuple of that array by adding 1s to its shape tuple.
3. How the extra dimensions need to be added if an upgrade is needed

For the third element you have two choices:

1. 0 or a positive integer
2. A negative integer

If a 0 or a positive integer is used this specifies where in the dimension of the array's upgraded shape tuple should the original shape tuple begin. For example a 0 would indicate that the original shape tuple should begin at dimension 0 of the upgraded shape tuple.

If a negative number is used the integer following the negative sign specifies where in the dimension of the array's upgraded shape tuple should the original shape tuple end. For example -1 would indicate that the original shape tuple should end at the last dimension of the upgraded shape tuple. -2 would indicate the same but at the second last dimension.

Finally let's apply the above to your example.

np.r_['0,2,0', [1,2,3], [4,5,6]]

The above contains two arrays. Each has a dimension (3,) which means that both are one-dimensional arrays. The second element in the comma-separated integer string is a 2 which means that each array needs to have a dimension of at least 2 . Since both arrays are one-dimensional they both need to have one dimension added to their shape tuple. The third element in the comma-separated integer string is a 0 which means that the original shape tuples, which is (3,) for both arrays, need to start at dimension 0 of the shape tuple of the upgraded arrays. This is achieved by adding a 1 to the end of the original shape tuple. This upgrades both arrays to having a (3,1) shape tuple. Now since the first element of the comma-separated integer string is a 0 the upgraded arrays will be concatenated using dimension 0 as the axis of concatenation. This means that if dimension 0 is set aside for both upgraded arrays the remaining dimension(s) need to be identical. In this example if dimension 0 is set aside from both upgraded arrays only dimension 1 remains and for both upgraded arrays dimension 1 has a value of 1 . Therefore when concatenating the two upgraded arrays the result will have a shape tuple of (3+3,1) == (6,1) which is the shape of

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