Arranging numpy arrays in a block matrix

Question

I have 3 numpy arrays A, B and C. For simplicity, let\'s assume that they are all of shape [n, n]. I want to arrange them as

Answer 1

As of NumPy 1.13, there's np.block. This builds matrices out of nested lists of blocks, but it's also more general, handling higher-dimensional arrays and certain not-quite-grid cases. It also produces an ndarray, unlike bmat.

np.block([[A, B], [B.T, C]])

---

For previous versions, you can use the NumPy built-in np.bmat that's perfectly suited for such a task, like so -

np.bmat([[A, B], [B.T, C]])

As mentioned in the comments by @unutbu, please note that the output would be a NumPy matrix. If the intended output is an array instead, we need to convert it, like so -

np.asarray(np.bmat([[A, B], [B.T, C]]))

or

np.bmat([[A, B], [B.T, C]]).A

Answer 2

Stripped of some bells and whisles, np.bmat does this:

def foo(alist):
    rowlist=[]
    for row in alist:
        rowlist.append(np.concatenate(row,axis=1))
    return np.concatenate(rowlist, axis=0)

So for example:

In [1026]: A=np.arange(4).reshape(2,2);B=np.arange(2).reshape(2,1);C=np.array([0]).reshape(1,1)

In [1027]: foo([[A,B],[B.T,C]])
Out[1027]: 
array([[0, 1, 0],
       [2, 3, 1],
       [0, 1, 0]])

Making the inputs matrices simplifies the reshape preparation.