1-D Convolution Forward Pass

Implement the forward pass of a 1-D convolution layer (strictly speaking a cross-correlation, like every deep-learning framework uses).

conv1d(x, w, b, stride=1, padding=0)

x: input of shape (C_in, L)
w: kernels of shape (C_out, C_in, K)
b: bias of shape (C_out,)
Pad both ends of x with padding zeros, then slide each kernel with the given stride.

Output shape is (C_out, L_out) with

L_{out} = \left\lfloor \frac{L + 2\cdot\text{padding} - K}{\text{stride}} \right\rfloor + 1

Example

conv1d(np.array([[1., 2., 3., 4.]]), np.array([[[1., 0., -1.]]]), np.array([0.]))
# array([[-2., -2.]])