Numpy repeating a row or column

Question

Suppose we have the matrix A:

A = [1,2,3
     4,5,6
     7,8,9]

I want to know if there is a way to obtain:

B = [1,2,3
     4,5,6
     7,8,9
     7,8,9]

As well as:

B = [1,2,3,3
     4,5,6,6
     7,8,9,9]

This is because the function I want to implement is the following:

U(i,j) = min(A(i+1,j)^2, A(i,j)^2)
V(i,j) = min(A(i,j+1)^2, A(i,j)^2)

And the numpy.minimum seems to need two arrays with equal shapes.

My idea is the following:

np.minimum(np.square(A[1:]), np.square(A[:]))

but it will fail.

Answer 1

For your particular example you could use numpy.hstack and numpy.vstack:

In [11]: np.vstack((A, A[-1]))
Out[11]: 
array([[1, 2, 3],
       [4, 5, 6],
       [7, 8, 9],
       [7, 8, 9]])

In [12]: np.hstack((A, A[:, [-1]]))
Out[12]: 
array([[1, 2, 3, 3],
       [4, 5, 6, 6],
       [7, 8, 9, 9]])

An alternative to the last one is np.hstack((A, np.atleast_2d(A[:,-1]).T)) or np.vstack((A.T, A.T[-1])).T): you can't hstack a (3,) array to a (3,3) one without putting the elements in the rows of a (3,1) array.