%% Mfile name
%        test_mydiff.m

%% Revised: 
%       October 2, 2007

%% Purpose
%       Testing the mydiff function to find the the first derivative of the
%       function at x within a prespecified percentage tolerance tol and a
%       starting step size of dx.  The function uses forward divided difference 
%       method. 

%% Usage
%       fp=mydiff(f,x,dx,tol)
% Input variables
%       f = function
%       x = point at which derivative of f is sought
%       dx = starting step size
%       tol = prespecified percentage tolerance
% Output variables
%       fp = approximate value of derivative of f at point x 

% Keyword
%       Differentiation
%       Forward Divided Difference

% Author
%       Autar Kaw
%       Section: All
%       Semester: Fall 2007

clc
disp('Name: Autar Kaw')
disp('Section: All')

%% Test 1
%Test#1 to see if the procedure works for prespecified tolerance being small 
% For a tolerance of 0.000005%, find the derivative of 2*exp(1.5*x) at
% x=2.5 with a starting step size of 0.2.  We should get results close to
% the exact value
disp ('Test#1')

tol=0.000005;
fprintf ('\nTolerance = %g\n', tol)

y=2.5;
fprintf ('Value at which derivative is to be found = %g\n', y)

dy=0.2;
fprintf ('Starting value of step size=%g\n', dy)

g=inline('2*exp(1.5*x)');
fun_string=['Function of which derivative is found is  f=' char(g)];
fprintf(fun_string)

% Value obtained using my own differentiation routine
fpvalue=mydiff(g,y,dy,tol);
fprintf ('\n\nApproximate value of derivative= %g\n', fpvalue)
% Value obtained using exact differentiation of matlab
syms x;
f=2*exp(1.5*x);
fpexact=subs(diff(f,x),y);
fprintf ('Exact value of derivative= %g\n', fpexact)
disp('_________________________________________________________')

%% Test 2
%Test#2 to see if the procedure works for prespecified tolerance being small 
% For a small tolerance of 0.5%, find the derivative of 2*exp(1.5*x) at
% x=2.5 with a starting step size of 0.2. 
% We should get results NOT close to exact value.
disp ('Test#2')

tol=0.5;
fprintf ('\nTolerance = %g\n', tol)

y=2.5;
fprintf ('Value at which derivative is to be found = %g\n', y)

dy=0.2;
fprintf ('Starting value of step size=%g\n', dy)

g=inline('2*exp(1.5*x)');
fun_string=['Function of which derivative is found is  f=' char(g)];
fprintf(fun_string)

% Value obtained using my own differentiation routine
fpvalue=mydiff(g,y,dy,tol);
fprintf ('\n\nApproximate value of derivative= %g\n', fpvalue)
% Value obtained using exact differentiation of matlab
syms x;
f=2*exp(1.5*x);
fpexact=subs(diff(f,x),y);
fprintf ('Exact value of derivative= %g\n', fpexact)
disp('_________________________________________________________')