Broadcasting a 1D array to a particular dimension of a varying nD array via .reshape(generator)

问题

I have a large matrix of the shape (2,2,2,...n) of nD dimensions, which often varies.

However I am also receiving incoming data which is always a 1D array of shape (2,).

Now I want to multiply my former matrix of nD dimensions with my 1D array via reshape... and I also have an 'index' of which dimensions I want to broadcast and modify in particular.

Thus I'm doing the following (within a loop):

matrix_nd *= array_1d.reshape(1 if i!=index else dimension for i, dimension in enumerate(matrix_nd.shape))

However this generator as input does not seem to be valid. Note that the dimension would always equal to 2 and only be placed once within our sequence.

For example, if we have a 5D matrix of shape (2,2,2,2,2) and an index of 3; we would want to reshape the 1D array to a (1,1,1,2,1).

Any ideas?

Thanks in advance.

EDIT:

So it turns out my entire approach is wrong: Getting the tuple that I was after still seems to broadcast the (2,) 1D array to all dimensions.

For example: I have numpy array test_nd.shape of (2,2,2) and which looks like this:

array([[[1, 1],
  [1, 1]],
 [[1, 1],
  [1, 1]]])

I then reshape a (2,) 1D array to be broadcasted to the 3rd dimensions only:

toBroadcast = numpy.asarray([0,0]).reshape(1,1,2)

Where toBroadcast has the form array([[[0, 0]]])

However... test_nd*toBroadcast returns the following result:

array([[[0, 0],
      [0, 0]],
     [[0, 0],
      [0, 0]]])

It seems to have been broadcasting to all the dimensions. Any ideas?

回答1:

You can define a function like

def broadcast_axis(data, ndims, axis):
    newshape = [1] * ndims
    newshape[axis] = -1
    return data.reshape(*newshape)

and use it like

vector = broadcast_axis(vector, matrix.ndim, 3)

回答2:

One way would be to permute axes. So, we could push the relevant axis from matrix_nd to the last, let it be multiplied with the 1D array and finally permute back the axes. Hence, with given axis along which in matrix_nd, we need to multiply 1D array, it would be -

np.moveaxis(np.moveaxis(matrix_nd,axis,-1)*array_1d,-1,axis)

Again, we don't need to reshape the 1D array to (1,1,1,2,1). We can reshape it to just the relevant axis, i.e. (2,1) and broadcasting would still work, as the leading axes are broadcasted automatically. Hence, another way would be -

matrix_nd*array_1d.reshape((-1,)+(1,)*(matrix_nd.ndim-axis-1))

来源：https://stackoverflow.com/questions/58979588/broadcasting-a-1d-array-to-a-particular-dimension-of-a-varying-nd-array-via-res