Vectorize numpy code [duplicate]

Question

So I am trying to vectorize this code in numpy and im having trouble Heres is my for loop version which works as desired:

B is a 3x3 Matrix

 for i in range(b.shape[0]):  
    for j in range(b.shape[0]):
       Z[i,j] = np.sqrt(np.dot((b[i,:].T - b[j,:].T).T  ,  b[i,:].T - b[j,:].T))

Now I am trying to vectorized this code so I dont have to use a double for loop. Here what I have gotten so far which does not work:

i = 0, j = 0
np.sqrt( np.dot ( (p[i,:].T - p[j:,:].T).T  , p[i,:].T - p[j,:].T ))

Ideally it should perform this if you break down to what a for loop would do.

np.sqrt( np.dot ( (p[0,:].T - p[0,:].T).T  ,  p[0,:].T - p[0,:].T  ))
np.sqrt( np.dot ( (p[0,:].T - p[1,:].T).T  ,  p[0,:].T - p[1,:].T  )) 
np.sqrt( np.dot ( (p[1,:].T - p[0,:].T).T  ,  p[1,:].T - p[0,:].T  ))
np.sqrt( np.dot ( (p[1,:].T - p[1,:].T).T  ,  p[1,:].T - p[1,:].T  ))

Can someone kindly provide some insight. I would prefer not to use any built in functions and stick to using things like np.dot. Btw this is to compute the Eucledean distance matrix.

for starter you can simplify to Z[i,j] = np.linalg.norm(b[:,i]-b[:,j]) — Julien
– Julien, Commented Oct 4, 2017 at 0:42

akuiper · Accepted Answer · 2017-10-04 00:45:12Z

You can vectorize it as:

b = np.asarray(b)                      # in case you have a matrix, convert it to an array
np.linalg.norm(b - b[:,None], axis=2)

b - b[:,None] does a row wise outer subtraction of b, and np.sqrt(np.dot(...,...)) can be calculated with np.linalg.norm.

Example:

a = np.arange(9).reshape(3,3)
b = np.matrix(a)

Z = np.zeros_like(b, dtype=np.float32)


for i in range(b.shape[0]):  
    for j in range(b.shape[0]):
        Z[i,j] = np.sqrt(np.dot((b[i,:].T - b[j,:].T).T  ,  b[i,:].T - b[j,:].T))

Z
#array([[  0.        ,   5.19615221,  10.39230442],
#       [  5.19615221,   0.        ,   5.19615221],
#       [ 10.39230442,   5.19615221,   0.        ]], dtype=float32)

b = np.asarray(b) 
np.linalg.norm(b - b[:,None], axis=2)
#array([[  0.        ,   5.19615242,  10.39230485],
#       [  5.19615242,   0.        ,   5.19615242],
#       [ 10.39230485,   5.19615242,   0.        ]])

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