Julia's numerical derivative following Numpy gradient

gistfile1.txt

function numerical_derivative(y, x)
    """
    Compute the derivative of the function y(x) which has been sampled in discrete steps. The implementation here has
    been adapted from Numpy's gradient function (centered finite differences). Boundaries have just forward differences.
    It works only for 1D functions, but should be possible to easily extend to other things.
    """

    #Create target vector
    n = length(x)
    derivs = Vector{Float64}(undef, n)

    #Take care of the boundary conditions
    derivs[1] = (y[2] - y[1]) / (x[2] - x[1]) 
    derivs[end] = (y[end] - y[end-1]) / (x[end] - x[end-1]) 

    #dx for non-equally spaced points
    xdiff = @views x[2:end] - x[1:end-1]
    dx1 = xdiff[1:end-1]
    dx2 = xdiff[2:end]

    #Constants for left, centered and right steps
    a = @. -(dx2)/(dx1 * (dx1 + dx2))
    b = @. (dx2 - dx1) / (dx1 * dx2)
    c = @. dx1 / (dx2 * (dx1 + dx2))

    #Slices 
    slice1 = 2:n-1
    slice2 = 1:n-2
    slice3 = 2:n-1
    slice4 = 3:n
    
    #Finish computation and return values
    @. derivs[slice1] = @views a*y[slice2] + b*y[slice3] + c*y[slice4]  

    return derivs
end