% m18_prettynewton.m - Newton's method -- beautiful output, not beautiful program!

function m18_prettynewton()
close all
set(gcf,'doublebuffer','on');
clear all
global th
fs = 'fontsize'; ms = 'markersize';
x = (-.8:.001:1.2);
p = x.^5 -4*x.^4 + 5*x.^2 + x - 1;
hold off
plot(x,p,'b','linewidth',3), grid on
axis([-.6 1.1 -1.5 2.2])
hold on
plot([-2 2],[0 0],'-k','linewidth',2)
set(gca,fs,18)
x = .8;
plot(x,0,'.k',ms,25)
sh = text(-.442,1.7,'step 0',fs,22);
clear th
printroot(x,0);
pause

for step = 1:100
  y = x^5 -4*x^4 + 5*x^2 + x - 1;
  plot([x x],[0 y],'--k','linewidth',1.8)
  plot(x,y,'.r',ms,25);
  pause
  yp = 5*x^4 - 16*x^3 + 10*x + 1;
  xnew = x - y/yp;
  plot([xnew x],[0 y],'r','linewidth',2)
  x = xnew;
  plot(x,0,'.k',ms,25)
  delete(sh);
  sh = text(-.442,1.7,['step ' int2str(step)],fs,22);
  printroot(x,step);
  pause
end

% printroot - print root in color
  function printroot(x,n);
  exact = 0.37339086218684;
  fs = 'fontsize';
  len = 16;
  if abs(x-exact) > .01, s = num2str(x+1e-16,len);
  else
     s = num2str(x,len); end
  x = num2str(exact,len);
  col = 'black';
  if exist('th'), delete(th), end
  th = zeros(len,1);
  for i = 1:len
    if s(i) ~= x(i), col = 'red'; end
    if i>2, th(i) = text(-.525+.058*i,1.3,s(i),fs,22,'color',col);
    elseif i==1
        th(i) = text(-.5+.058*i,1.3,s(i),fs,22,'color',col);
    else
        th(i) = text(-.5+.058*i,1.3,s(i),fs,22,'color',col);
    end
  end
  end

end