% Sample session with MATLAB

% (1) GETTING STARTED:

% First log into a unity machine with your id and password.
% Start an xterm.
% Type "add matlab7" at the prompt to ensure that you
% will use MATLAB 7 hereafter. This has only to be done once.
% Type "matlab" at the prompt
% A MATLAB desktop should now appear.
% Download the programs "bisect.m" and "myfunc.m"
% from the course webpage into your home directory.


% (2) A SAMPLE SESSION WITH BISECTION method in MATLAB

% I assume you now have the MATLAB desktop running
% You should type the following lines
% in your MATLAB desktop in the following order:
% I have interspaced my comments in the discussion .
% These comments appear on a line that starts with a % sign.
% You need not type these comment lines in your MATLAB desktop.

% Kartik's MATLAB session: 17th August 2007

% Consider Example 1 in Chapter 2 on pages 48-49 of Burden and Faires

% We will solve the nonlinear equation f(x) = x^3+4x^2-10=0
% using the bisection method
% The file 'myfunc.m' contains the function f(x)
% The intial interval is [a,b] = [1,2] since f(1) =-5 and f(2) = 14

help bisect
 
%    function [a, b, x, ithist, iflag] = bisect( f, a, b, tol, maxit )
%  
%    use the bisection method to compute an approximate root of f.
%   Compare with Algorithm 2.1 on page 47 of Burden and Faires
%  
%    Input parameters:
%      func    name of a matlab file containing a function
%      for example
%      f = myfunc(x)
%      f = x^3 + 4*x^2 -10
%      a, b    real numbers satisfying f(a)*f(b) < 0
%      tol    stopping tolerance (optional. Default tolx = 1e-7)
%              the bisection method stops if  b-a < tol
%      maxit   maximum number of iterations (optional. Default maxit = 100)
%  
%  
%    Output parameters:
%      a, b    real numbers satisfying f(a)*f(b) < 0; a root of f is
%              located between a and b
%      x       approximation of the solution. x = a + 0.5*(b-a)
%      ithist  array with the iteration history
%              The i-th row of ithist contains  [it, a, b, c, fc]
%      ifag    return flag
%              iflag = -1  error in input data, f(a)*f(b) > 0
%              iflag =  0  |b-a| < tol and |x-x*| < 0.5*tol, where x*
%                          is a root of f
%              iflag =  1  iteration terminated because maximum number of 
%                          iterations was reached. |b-a| >= tol
%  
%  
%    Kartik Sivaramakrishnan
%    Department of Mathematics
%    North Carolina State University
%    August 17, 2007



[a,b,x,ithist,flag] = bisect(@myfunc,1,2,1e-7,100);
% x
% 
% x =
% 
%     1.3652

format long
x

% x =
% 
%    1.36522999405861

ithist

% ithist =
% 
%                   0   1.00000000000000   2.00000000000000   1.50000000000000   2.37500000000000
%    1.00000000000000   1.00000000000000   1.50000000000000   1.25000000000000  -1.79687500000000
%    2.00000000000000   1.25000000000000   1.50000000000000   1.37500000000000   0.16210937500000
%    3.00000000000000   1.25000000000000   1.37500000000000   1.31250000000000  -0.84838867187500
%    4.00000000000000   1.31250000000000   1.37500000000000   1.34375000000000  -0.35098266601562
%    5.00000000000000   1.34375000000000   1.37500000000000   1.35937500000000  -0.09640884399414
%    6.00000000000000   1.35937500000000   1.37500000000000   1.36718750000000   0.03235578536987
%    7.00000000000000   1.35937500000000   1.36718750000000   1.36328125000000  -0.03214997053146
%    8.00000000000000   1.36328125000000   1.36718750000000   1.36523437500000   0.00007202476263
%    9.00000000000000   1.36328125000000   1.36523437500000   1.36425781250000  -0.01604669075459
%   10.00000000000000   1.36425781250000   1.36523437500000   1.36474609375000  -0.00798926281277
%   11.00000000000000   1.36474609375000   1.36523437500000   1.36499023437500  -0.00395910152292
%   12.00000000000000   1.36499023437500   1.36523437500000   1.36511230468750  -0.00194365901007
%   13.00000000000000   1.36511230468750   1.36523437500000   1.36517333984375  -0.00093584728188
%   14.00000000000000   1.36517333984375   1.36523437500000   1.36520385742188  -0.00043191879925
%   15.00000000000000   1.36520385742188   1.36523437500000   1.36521911621094  -0.00017994890323
%   16.00000000000000   1.36521911621094   1.36523437500000   1.36522674560547  -0.00005396254153
%   17.00000000000000   1.36522674560547   1.36523437500000   1.36523056030273   0.00000903099274
%   18.00000000000000   1.36522674560547   1.36523056030273   1.36522865295410  -0.00002246580384
%   19.00000000000000   1.36522865295410   1.36523056030273   1.36522960662842  -0.00000671741291
%   20.00000000000000   1.36522960662842   1.36523056030273   1.36523008346558   0.00000115678807
%   21.00000000000000   1.36522960662842   1.36523008346558   1.36522984504700  -0.00000278031288
%   22.00000000000000   1.36522984504700   1.36523008346558   1.36522996425629  -0.00000081176252
%   23.00000000000000   1.36522996425629   1.36523008346558   1.36523002386093   0.00000017251275

flag

% flag =
% 
%      0

a

% a =
% 
%    1.36522996425629

b

% b =
% 
%    1.36523002386093

exit