Perform a series of outer products using tracedot in scipy

To perform an outer product between two vectors in Python (scipy/numpy) you can use the outer function, or you can simply use dot 开发者_运维百科like this:

In [76]: dot(rand(2,1), rand(1,2))
Out[76]: 
array([[ 0.43427387,  0.5700558 ],
       [ 0.19121408,  0.2509999 ]])

Now the question is, suppose I have a list of vectors (or two lists...) and I want to calculate all the outer products, creating a list of square matrices. How do I do that easily? I believe tensordot is able to do that, but how?

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The third (and easiest to generalize) way to compute outer products is via broadcasting.

Some 3-vectors (vectors on rows):

import numpy as np
x = np.random.randn(100, 3)
y = np.random.randn(100, 3)

Outer product:

from numpy import newaxis
xy = x[:,:,newaxis] * y[:,newaxis,:]

# 10th matrix
print xy[10]
print np.outer(x[10,:], y[10,:])

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Actually the answer provided by pv. is not correct, as the resulting xy array would have shape (100,3,3). The correct broadcasting is the following:

import numpy as np
from numpy import newaxis
x = np.random.randn(100, 3)
y = np.random.randn(100, 3)

xy =  x[:,newaxis, :,newaxis] * y[newaxis,:,newaxis,:] 

The resulting xy array is now of shape (100,100,3,3) and contains cross products of all couples of 3-vectors in x and y:

for i,a in enumerate(x):
    for j,b in enumerate(y):
        if not np.alltrue(np.outer(a,b) == xy[i,j]): print("The code is wrong")

gives no output :)