2-D Max Pooling

Max pooling shrinks feature maps in CNNs by keeping the largest value in each window.

Implement max_pool2d(x, kernel, stride=None):

• x has shape (channels, height, width).
• kernel is the window size (square). stride defaults to kernel.
• No padding: only windows that fit entirely inside the input are used, so the output height is $\lfloor (H - k) / s \rfloor + 1$ (same for width).
• Return shape (channels, out_h, out_w). Pool each channel independently.

Example

max_pool2d(np.array([[[1, 2, 5, 6], [3, 4, 7, 8], [9, 1, 2, 3], [4, 5, 0, 1]]]), 2)
# array([[[4, 8], [9, 3]]])