Exploiting Symmetry in Large Numpy Array

Question

Want to make large array, B, that is made up of a smaller numpy array, A, flipped in different ways:

B[0,:,:,:,:]   = A
B[1,:,:,:,:]   = B[0,:,::-1,:,:]
B[2:4,:,:,:,:] = B[0:2,:,:,::-1,:]
B[4:8,:,:,:,:] = B[0:4,:,:,:,::-1]

Is there a way to only store A in memory, but keep some of the functionality of a numpy array for B? I was primarily interested in two things:

• Be able to scale B[m,n,...] (i.e. B[m,n,...] *= C where B.shape[2:] == C.shape)
• Be able sum down to the second dimension (i.e. np.sum(B, axis=(2,3,4)))

Answer 1

What I ended up doing was creating a class to return a view of an arbitrarily reflected portion of A. I was doing scaling by C, as well as sums, after returning this view, which seemed quick enough for now. This is it without error checking:

class SymmetricArray:
    '''
    Attributes:
        A (np.ndarray): an [m, (a,b,c...)] array.
        idx (np.ndarray): an [n,] array where idx[n] points to A[idx[n], ...]
            to be used.
        reflect (np.ndarray): an [n, d] array where every entry is 1 or -1 and
            reflect[n, i] indicates whether or not the ith dimension of
            A[idx[n], ...] should be reflected, and d = len(A.shape - 1).
    '''
    def __init__(self, A, idx, reflect):
        self.A = np.asarray(A)
        self.idx = np.asarray(idx, dtype=int)
        self.reflect = np.asarray(reflect, dtype=int)

    def __getitem__(self, ii):
        '''
        Returns:
            np.ndarray: appropriately reflected A[idx[ii], ...]
        '''
        a_mask = [slice(None, None, a) for a in self.reflect[ii, :]]
        return self.A[self.idx[ii], ...][a_mask]