Stream: helpdesk (published)

Topic: forward finite differences

Dale Black (Sep 11 2021 at 23:47):

Is this the proper way of computing a simple forward difference algorithm in the x-direction in Julia, given h=1 on a 2D array/image?

image.png

function forward_diff_i(f)
    ∇ᵢ₊ = zeros(size(f))

    for j in 1:size(f, 2), i in 1:size(f, 1) - 1
        ∇ᵢ₊[i, j] = f[i + 1, j] - f[i, j]
    end

    # Compute backward diff for edge case
    for j in 1:size(f, 2)
        ∇ᵢ₊[end, j] = f[end, j] - f[end - 1, j]
    end

    return ∇ᵢ₊
end

If so, what's the recommended way to account for the edge?

Sundar R (Sep 12 2021 at 00:04):

have you looked at the difffunction in base Julia?

Dale Black (Sep 12 2021 at 00:09):

Oh no I hadn't actually. Looks like it's performing a similar operation and the results are similar on my end. Thanks

Dale Black (Sep 12 2021 at 00:26):

Here is what I have decided on, in case this is at all useful

function forward_diff_i(f)
    ∇ᵢ₊ = padarray(f, Pad(1, 1))

    for j in 1:size(f, 2), i in 1:size(f, 1)
        ∇ᵢ₊[i, j] = ∇ᵢ₊[i + 1, j] - ∇ᵢ₊[i, j]
    end

    return parent(∇ᵢ₊[1:end-1, 1:end-1])
end

Simon Christ (Sep 27 2021 at 09:43):

I'd consider renaming this topic to "forward differences" to not confuse it with forward mode automatic differentiation like implemented in ForwardDiff.jl

Mason Protter (Sep 27 2021 at 15:00):

Done

Last updated: Nov 06 2024 at 04:40 UTC