Simple numeric gradients

simplegrad.jl

# Author: Lewin Bormann, 2021
# A simple finite difference algorithm for differentiating a function numerically with respect to multiple dimensions.

function mydiff(func, theta, releps=1e-3, reltol=1e-3)
	scale_eps = 1/2
	grad = zeros(size(theta))
	upper, lower = theta[:], theta[:]
	for (i, t) in enumerate(theta)
		count = 0
		flipflop = 0
		this_eps = releps * t
		last_diff = 0

		while true
			upper[i] += this_eps/2
			lower[i] -= this_eps/2
			diff = (func(upper...)-func(lower...))/this_eps
			println("$i $count: $this_eps -> $diff")
			if this_eps < 1e-6
				grad[i] = diff
				break
			end
			
			upper[i] -= this_eps/2
			lower[i] += this_eps/2
			
			ratio = last_diff / diff
			if ratio - 1 >= 0
				if abs(ratio-1) < reltol
					grad[i] = diff
					break
				else
					last_diff = diff
				end
			else
				flipflop += 1
				last_diff = diff
			end

			if count > 5
				grad[i] = diff
				break
			end

			this_eps *= scale_eps
			count += 1
		end
	end

	return grad
end