conv1d-valid — Intel case

Intel-inspired edge inference prototype is validating a small one-dimensional convolution before mapping it to an optimized kernel. You need to compute the valid convolution output for a single channel with stride 1. The operation is cross-correlation (the kernel is not flipped): out[i] = sum_j x[i+j]*k[j] over valid positions only.

Compute the 'valid' one-dimensional convolution of the signal x with the kernel k, without flipping the kernel (cross-correlation): $\text{out}[i]={\sum }_{j}x[i+j]k[j]\backslash text\{out\}[i]=\backslash sum\_jx[i+j]\backslash ,k[j]$ for every position where the kernel fits entirely inside the signal.

Implement solve(x,k).

Returns. Return a float NumPy array of length len(x) - len(k) + 1 (empty if the kernel is longer than the signal).

Examples

Example 1

Input:

solve([1, 2, 3, 4], [1, 0, -1])

Output:

[-2.0, -2.0]

Example 2

Input:

solve([1.0, 1.0, 1.0], [2.0])

Output:

[2.0, 2.0, 2.0]