Subtract each row of matrix A from every row of matrix B without loops

It's possible to do it efficiently (without using any loops) by leveraging broadcasting like:

In [28]: (A[:, np.newaxis] - B).reshape(-1, A.shape[1])
Out[28]: 
array([[   -9,   -18,   -27],
       [ -999, -1998, -2997],
       [   11,    22,     5],
       [   90,   180,   270],
       [ -900, -1800, -2700],
       [  110,   220,   302]])

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Or, for a little faster solution than broadcasting, we would have to use numexpr like:

In [31]: A_3D = A[:, np.newaxis]
In [32]: import numexpr as ne

# pass the expression for subtraction as a string to `evaluate` function
In [33]: ne.evaluate('A_3D - B').reshape(-1, A.shape[1])
Out[33]: 
array([[   -9,   -18,   -27],
       [ -999, -1998, -2997],
       [   11,    22,     5],
       [   90,   180,   270],
       [ -900, -1800, -2700],
       [  110,   220,   302]], dtype=int64)

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One more least efficient approach would be by using np.repeat and np.tile to match the shapes of both arrays. But, note that this is the least efficient option because it makes copies when trying to match the shapes.

In [27]: np.repeat(A, B.shape[0], 0) - np.tile(B, (A.shape[0], 1))
Out[27]: 
array([[   -9,   -18,   -27],
       [ -999, -1998, -2997],
       [   11,    22,     5],
       [   90,   180,   270],
       [ -900, -1800, -2700],
       [  110,   220,   302]])