I have two arrays A,B and want to take the outer product on their last dimension,
e.g.
result[:,i,j]=A[:,i]*B[:,j]
when A,B are 2-dimensional.
How can I do this if I don't know whether they will be 2 or 3 dimensional?
In my specific problem A,B are slices out of a bigger 3-dimensional array Z,
Sometimes this may be called with integer indices A=Z[:,1,:], B=Z[:,2,:] and other times
with slices A=Z[:,1:3,:],B=Z[:,4:6,:].
Since scipy "squeezes" singleton dimensions, I won't know what dimensions my inputs
will be.
The array-outer-product I'm trying to define should satisfy
array_outer_product( Y[a,b,:], Z[i,j,:] ) == scipy.outer( Y[a,b,:], Z[i,j,:] )
array_outer_product( Y[a:a+N,b,:], Z[i:i+N,j,:])[n,:,:] == scipy.outer( Y[a+n,b,:], Z[i+n,j,:] )
array_outer_product( Y[a:a+N,b:b+M,:], Z[i:i+N, j:j+M,:] )[n,m,:,:]==scipy.outer( Y[a+n,b+m,:] , Z[i+n,j+m,:] )
for any rank-3 arrays Y,Z and integers a,b,...i,j,k...n,N,...
The kind of problem I'm dealing with involves a 2-D spatial grid, with a vector-valued function at each grid point. I want to be able to calculate the covariance matrix (outer product) of these vectors, over regions defined by slices in the first two axes.