In Python 3, convert np.array object type to float type, with variable number of object element

Question

I have a np.array with dtype as object. Each element here is a np.array with dtype as float and shape as (2,2) --- in maths, it is a 2-by-2 matrix. My aim is to obtain one 2-dimenional matrix by converting all the object-type element into float-type element. This can be better presented by the following example.

dA = 2  # dA is the dimension of the following A, here use 2 as example only
A = np.empty((dA,dA), dtype=object)  # A is a np.array with dtype as object
A[0,0] = np.array([[1,1],[1,1]])   # each element in A is a 2-by-2 matrix
A[0,1] = A[0,0]*2
A[1,0] = A[0,0]*3
A[1,1] = A[0,0]*4

My aim is to have one matrix B (the dimension of B is 2*dA-by-2*dA). The form of B in maths should be

If dA is fixed at 2, then things can be easier, because I can hard-code

a00 = A[0,0]
a01 = A[0,1]
a10 = A[1,0]
a11 = A[1,1]
B0 = np.hstack((a00,a01))
B1 = np.hstack((a10,a11))
B = np.vstack((B0,B1))

But in reality, dA is a variable, it can be 2 or any other integer. Then I don't know how to do it. I think nested for loops can help but maybe you have brilliant ideas. It would be great if there is something like cell2mat function in MATLAB. Because here you can see A[i,j] as a cell in MATLAB.

Thanks in advance.

Why are you using a numpy object array for A? From what I can see, a list of lists, or even just a list with length 4, would work just as well. — Warren Weckesser
– Warren Weckesser, Commented Aug 24, 2016 at 18:58
@WarrenWeckesser, the reason is: in my program, "A" is a characteristic matrix of a system of 2 copper wires. See "A" as matrix, so its main diagonal blocks "A[0,0]" and "A[1,1]" are characteristics of wire 0 and wire 1, respectively; while the off-diagonal blocks are mutual impacts on those two wires, "A[0,1]" and "A[1,0]". These 4 blocks are calculated individually. After obtained them all, I want to assemble them in to one matrix "A". Using the matrix index-style "[i,j]" is easier to program the whole computational process and easier to read for people with technical background. — aura
– aura, Commented Aug 26, 2016 at 12:51
OK, that makes sense. In that case, instead of a 2-d object array, I would use a 4-d array: A = np.empty((dA, dA, 2, 2)). I try to avoid object arrays as much as possible. Many numpy and scipy functions don't work well with them. — Warren Weckesser
– Warren Weckesser, Commented Aug 26, 2016 at 13:20

Warren Weckesser · Accepted Answer · 2016-08-24 16:46:15Z

Here's a quick way.

Your A:

In [137]: A
Out[137]: 
array([[array([[1, 1],
       [1, 1]]), array([[2, 2],
       [2, 2]])],
       [array([[3, 3],
       [3, 3]]), array([[4, 4],
       [4, 4]])]], dtype=object)

Use numpy.bmat, but convert A to a python list first, so bmat does what we want:

In [138]: B = np.bmat(A.tolist())

In [139]: B
Out[139]: 
matrix([[1, 1, 2, 2],
        [1, 1, 2, 2],
        [3, 3, 4, 4],
        [3, 3, 4, 4]])

The result is actually a numpy.matrix. If you need a regular numpy array, use the .A attribute of the matrix object:

In [140]: B = np.bmat(A.tolist()).A

In [141]: B
Out[141]: 
array([[1, 1, 2, 2],
       [1, 1, 2, 2],
       [3, 3, 4, 4],
       [3, 3, 4, 4]])

Here's an alternative. (It still uses A.tolist().)

In [164]: np.swapaxes(A.tolist(), 1, 2).reshape(4, 4)
Out[164]: 
array([[1, 1, 2, 2],
       [1, 1, 2, 2],
       [3, 3, 4, 4],
       [3, 3, 4, 4]])

In the general case, you would need something like:

In [165]: np.swapaxes(A.tolist(), 1, 2).reshape(A.shape[0]*dA, A.shape[1]*dA)
Out[165]: 
array([[1, 1, 2, 2],
       [1, 1, 2, 2],
       [3, 3, 4, 4],
       [3, 3, 4, 4]])

hpaulj · Accepted Answer · 2016-08-24 16:53:32Z

2

Your vstack/hstack could be written more compactly, and generally as

In [132]: np.vstack((np.hstack(a) for a in A))
Out[132]: 
array([[1, 1, 2, 2],
       [1, 1, 2, 2],
       [3, 3, 4, 4],
       [3, 3, 4, 4]])

since for a in A iterates on the rows of A.

Warren suggests np.bmat, which is fine. But if you look at the bmat code, you'll see that it just doing this kind of nested concatenate (expressed a row loop with arr_rows.append(np.concatenate...)).

answered Aug 24, 2016 at 16:53

hpaulj

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