Transposed Convolution without using Python built-in functions

Amateur here: How can we write a 2D transposed convolution (aka deconvolution) using the steepest descent method given the following restrictions:

• cannot use any Python built-in functions

• cannot explicitly transpose the matrix

• cannot explicitly perform matrix-vector multiplications

I have already written a forward 2D convolution method, and would like to reuse it to perform the backward process. I am not sure how this can be done with the given restrictions.

Zero-padding the filters did not seem to work…

I don’t have a specific background in data science so any help is appreciated, thanks!