# I am drawing a plot in order to review work done by a student. I'm a TA.

using Plots
pyplot()

function cbweb(g::Function,x0::Float64,maxit::Int,tol::Float64,
                a::Float64,b::Float64,figname::String)

# EXAMPLE :
#   g(x) = 1-x^2
#   (x, numit, fail) = fixedpoint(g,0.5,10,1.0e-4)
#
   r = a:0.01:b
   plot(g, r, label="g")
   ylims!((a, b))
   diagonal(x) = x
   plot!(diagonal, r, label="")
   println("running a fixed-point iteration ...")
   strit = @sprintf("%3d", 0)
   strx0 = @sprintf("%.4e", x0)
   println("$strit : $strx0")
   xprevious = x0
   xnext = xprevious
   for i=1:maxit
       xnext = g(xprevious)
       if i == 1
           plot!([xprevious], [xnext], line=(:sticks, :black), label="")
       else
           if xprevious < xnext
              plot!([xprevious], xprevious:0.01:xnext, line=(:black), label="")
           else
              plot!([xprevious], xnext:0.01:xprevious, line=(:black), label="")
           end
       end
       if xprevious < xnext
           plot!(xprevious:0.01:xnext, [xnext], line=(:black), label="")
       else
           plot!(xnext:0.01:xprevious, [xnext], line=(:black), label="")
       end
       strit = @sprintf("%3d", i)
       strxi = @sprintf("%.4e", xnext)
       error = abs(xnext - xprevious)
       strerr = @sprintf("%.2e", error)
       println("$strit : $strxi : $strerr" )
       if error < tol
           savefig(figname)
           return (xnext, i, false)
       end
       xprevious = xnext
   end
   savefig(figname)
   return (xnext, maxit, true)
end

function main()
# Calls the fixed point iteration.
    x0 = 0.5
    maxit = 15
    tol = 1.0e-8
    g(x) = 2*sin(x)
    (endpt, numit, fail) = cbweb(g, x0, maxit, tol, 0.0, 2.1, "cobweb4")
end

main()

gui()