# L-24 MCS 471 Mon 17 October 2022 : difforward.jl

# Program to experiment with forward differentiation on exp(x),
# with plotting instructions for a log plot.

# using Plots

using Printf

# the forward difference formula :

fwdexp(x, h) = (exp(x+h) - exp(x))/h

"""
    Prompts the user for a value for x,
    the initial value for h, 
    the number of approximations, and then
    applies the forward difference formula,
    each time dividing h by 10.

    Suggested values for x, h, and the number
    of approximations are 1, 0.1, and 16.
"""
function main()
    print("Give a value for x : ")
    line = readline(stdin)
    xval = parse(Float64, line)
    print("Give an upper bound for h : ")
    line = readline(stdin)
    hval = parse(Float64, line)
    print("Give the number of approximations : ")
    line = readline(stdin)
    nbr = parse(Float64, line)
    exact = exp(xval)
    strexact = @sprintf("%.16e", exact)
    println("Approximating $strexact :")
    for i=1:nbr
        approx = fwdexp(xval, hval)
        err = abs(exact - approx)
        strhval = @sprintf("%.3e", hval)
        strapprox = @sprintf("%.16e", approx)
        strexact = @sprintf("%.16e", exact)
        strerr = @sprintf("%.3e", err)
        println("  $strhval   $strapprox   $strerr")
        hval = hval/10.0
    end
end

main()

# we make a logplot of the errors :

# aloghvals = [abs(log(10,10.0^(-p))) for p=1:16]
# alogerror = [log(10,abs(fwdexp(1.0, 10.0^(-p)) - exp(1.0))) for p=1:16]
# scatter(aloghvals, alogerror, marker=(:red), label="log(10, errors)")
# savefig("forwarderrors.png")