# L-6 MCS 471 Fri 2 Sep 2022 : secantmethod.jl
# A basic implementation of the secant method.

using Printf
"""
Applies the secant method to a function.

ON ENTRY :

    f        a function in one variable
    x1,x2    two start points
    dxtol    tolerance on the forward error
    fxtol    tolerance on the backward error
    N        maximum number of iterations

ON RETURN : (x, absdx, absfx, nbrit, fail)

    x        approximation for the root
    absdx    estimated forward error
    absfx    estimated backward error
    nbrit    number of iterations
    fail     true if tolerances not reached,
             false otherwise.

EXAMPLE:

   (root, err, res, nit, fail) = secant(cos,pi/4,2*pi/3)
"""
function secant(f::Function,x1::Float64,x2::Float64,
                dxtol::Float64=1.0e-8,fxtol::Float64=1.0e-8,N::Int64=10)
    dx = 1
    println("running the secant method...")
    title = "         root             |dx|     |f(x)|"
    println("step : $title")
    fx1 = f(x1)
    fx2 = f(x2)
    for i = 1:N 
        dx =  fx2*(x2 - x1)/(fx2 - fx1)
        x1 = x2 # store x2 for next step
        x2 = x2 - dx
        fx1 = fx2
        fx2 = f(x2)
        stri = @sprintf("%3d", i)
        strx = @sprintf("%.16e", x2)
        strdx = @sprintf("%.2e", abs(dx))
        strfx = @sprintf("%.2e", abs(fx2))
        println("$stri  : $strx  $strdx  $strfx")
        if((abs(fx2) < dxtol) | (abs(dx) < fxtol))
            stri = string(i)
            println("succeeded after $stri steps")
            return (x2, abs(dx), abs(fx2), i, false)
        end
    end
    strN = string(N)
    println("failed requirements after $strN steps")
    return (x2, abs(dx), abs(fx2), N, true)
end
# result = secant(cos,pi/4,2*pi/3)