How can I add a small matrix into a big one with numpy?

Question

I'm trying to figure out how to take a small matrix (Matrix B below) and add the values into a larger matrix (Matrix A below) at a certain index. It seems like numpy would be a good option for this scenario but I can't figure out how to do it.

Matrix A:

[[0, 0, 0, 0, 0, 0]
 [0, 0, 0, 0, 0, 0]
 [0, 0, 0, 0, 0, 0]
 [0, 0, 0, 0, 0, 0]
 [0, 0, 0, 0, 0, 0]]

Matrix B:

[[2, 3, 4]
 [5, 6, 7]
 [8, 9, 3]]

Desired end result:

[[0, 0, 0, 0, 0, 0]
 [0, 0, 2, 3, 4, 0]
 [0, 0, 5, 6, 7, 0]
 [0, 0, 8, 9, 3, 0]
 [0, 0, 0, 0, 0, 0]]

Answer 1

If you want to add B to A with the upper left-hand corner of B going to index (r, c) in A, you can do it using the index and the shape attribute of B:

A[r:r+B.shape[0], c:c+B.shape[1]] += B

If you want to just set the elements (overwrite instead of adding), replace += with =. In your particular example:

>>> A = np.zeros((5, 6), dtype=int)
>>> B = np.r_[np.arange(2, 10), 3].reshape(3, 3)

>>> r, c = 1, 2

>>> A[r:r+B.shape[0], c:c+B.shape[1]] += B
>>> A
array([[0, 0, 0, 0, 0, 0],
       [0, 0, 2, 3, 4, 0],
       [0, 0, 5, 6, 7, 0],
       [0, 0, 8, 9, 3, 0],
       [0, 0, 0, 0, 0, 0]])

The indexing operation produces a view into A since it is simple indexing, meaning that the data is not copied, which makes the operation fairly efficient for large arrays.