Broadcasting

Implement broadcasting rules for tensor operations, allowing operations between tensors of different shapes.

Background

Broadcasting allows operations between arrays of different shapes by virtually expanding the smaller array. Rules:

1. Compare shapes from right to left
2. Dimensions are compatible if they are equal or one of them is 1
3. Missing dimensions are treated as 1

Functions to implement

1. broadcast_shape(shape_a, shape_b)

Compute the resulting shape when broadcasting two tensors.

• Return the broadcast shape or None if incompatible

2. broadcast_add(a, b)

Add two tensors with broadcasting.

3. broadcast_multiply(a, b)

Multiply two tensors element-wise with broadcasting.

Examples

broadcast_shape((3, 1), (1, 4))  # (3, 4)
broadcast_shape((2, 3), (3,))   # (2, 3)
broadcast_shape((2, 3), (4,))   # None (incompatible)

# [[1], [2], [3]] + [10, 20, 30, 40] with broadcasting:
# [[11, 21, 31, 41],
#  [12, 22, 32, 42],
#  [13, 23, 33, 43]]