% hw2: compare dfdx_exact dfdx_CDS
%      f= exp(-xexact).*cos(5*xexact);

clear all;
close all;

%determine exact derivative
xexact=[0:0.001:3];

dfexact = -5.0*exp(-xexact).*sin(5*xexact)-cos(5*xexact).*exp(-xexact);
fexact  = exp(-xexact).*cos(5*xexact);

plot(xexact,dfexact,'r-',xexact,fexact,'k-');
hold on;


% determine approximated derivative on separte grids
dxtest=[1 0.3 0.003 0.0003];
error=[];

for i=1:length(dxtest)
  dx   = dxtest(i);
  x    = [-dx:dx:3+dx];
  xloc = x(2:length(x)-1);

  f    = exp(-x).*cos(5*x);
  dfdx(1:length(f)-2)=(-f(1:length(f)-2) + f(3:length(f)))/(2*dx);

  dfdx_exact = -5.0*exp(-xloc).*sin(5*xloc) - cos(5*xloc).*exp(-xloc);
  error= [error sum(abs(dfdx - dfdx_exact))/(length(f)-2)];
  
  plot(x(2:length(f)-1), dfdx(1:length(f)-2),'k+')
  hold on;
end

figure;
loglog(dxtest, error)