CODEWITHSUNDEEP
pythonnumpymultidimensional-arrayindexingslice
user2303141
user2303141

Reputation: 107

numpy: slicing and vectorized looping with 1d and 2d arrays

I want to vectorize the following loops for efficiency:

A = np.array([[0., 1., 0., 2.],
              [1., 0., 3., 0.],
              [0., 0., 0., 4.],
              [2., 0., 4., 0.]]) # quadratic, not symmetric Matrix, shape (i, i)
B = np.array([2., 4., 2., 1.]) # vector shape (i)
C = np.zeros(A.shape) # Result Matrix 
# classical Loop:
for i in range(len(B)):
    for j in range(len(B)):
        C[i, j] = A[i, j]*(B[i]-B[j])

My first attempt, that uses vectorisation like in Mathcad, does not what I want:

i = np.arange(len(B))
j = np.arange(len(B))
C[i,j] = A[i,j]*(B[i]-B[j]) # this fails to do what I want

Is my second attempt the best way t do it, or is there an easier more natural "numpy way"?

idx = np.indices(A.shape)
C[idx] = A[idx]*(B[idx[0]]-B[idx[1]])

Upvotes: 2

Views: 816

Answers (1)

Francesco Montesano
Francesco Montesano

Reputation: 8658

The following does what you want:

A = np.array([[0., 1., 0., 2.],
             [1., 0., 3., 0.],
             [0., 0., 0., 4.],
             [2., 0., 4., 0.]]) # quadratic, not symmetric Matrix, shape (i, i)
B = np.array([2., 4., 2., 1.]) # vector shape (i)

C = A*(B[:,None]-B)

C is 

array([[ 0., -2.,  0.,  2.],
       [ 2.,  0.,  6.,  0.],
       [ 0., -0.,  0.,  4.],
       [-2., -0., -4.,  0.]])

A little explanation:
B[:,None] converts B to a column vector of shape [4,1]. B[:,None]-B automatically broadcast the result to a 4x4 matrix that you can simply multiply by A

Upvotes: 2

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