X is an n by d matrix, W is an m by d matrix, for every row in X I want to compute the squared Euclidean distance with every row in W, so the results will be an n by m matrix.
If there's only one row in W, this is easy
x = tensor.TensorType("float64", [False, False])()
w = tensor.TensorType("float64", [False])()
z = tensor.sum((x-w)**2, axis=1)
fn = theano.function([x, w], z)
print fn([[1,2,3], [2,2,2]], [2,2,2])
# [ 2. 0.]
What do I do when W is a matrix (in Theano)?
Short answer, use scipy.spatial.distance.cdist
Long answer, if you don't have scipy, is to broadcast subtract and then norm by axis 0.
np.linalg.norm(X[:,:,None]-W[:,None,:], axis=0)
Really long answer, of you have an ancient version of numpy without a vecorizable linalg.norm (i.e. you're using Abaqus) is
np.sum((X[:,:,None]-W[:,None,:])**2, axis=0).__pow__(0.5)
Edit by OP
In Theano we can make X and W both 3d matrices and make the corresponding axes broadcastable like
x = tensor.TensorType("float64", [False, True, False])()
w = tensor.TensorType("float64", [True, False, False])()
z = tensor.sum((x-w)**2, axis=2)
fn = theano.function([x, w], z)
print fn([[[0,1,2]], [[1,2,3]]], [[[1,1,1], [2,2,2]]])
# [[ 2. 5.]
# [ 5. 2.]]