echo off;
% NUMERICAL METHODS: MATLAB Programs, (c) John H. Mathews 1994
% To accompany the text:
% NUMERICAL METHODS for Mathematics, Science and Engineering, 2nd Ed, 1992
% Prentice Hall, Englewood Cliffs, New Jersey, 07632, U.S.A.
% This free software is complements of the author.

% Algorithm 2.2 (Bisection Method).
% Section 2.2, Bracketing Methods for Locating a Root, Page 61
echo on; clc; format long; hold off; clear

% This program implements the bisection method.

% Define and store f(x) in the M-file f.m
% function y = f(x)
% y = x.*sin(x) - 1;

delete f.m
diary f.m; disp('function y = f(x)');...
disp('y = x.*sin(x) - 1;');...
diary off;

% Remark. f.m and bisect.m are used for Algorithm 2.2
f(0); % Test for file f.m
pause % Press any key to see the graph y = f(x).

clc; clg;
a = 0;
b = 2;
c = -1;
d = 1;
h = (b-a)/150;
X = a:h:b;
Y = f(X);
axis([a b c d]);...
plot(X,Y,'-g');...
hold on;...
plot([a b],[0 0],'b',[0 0],[c d],'b');...
xlabel('x');...
ylabel('y');...
title('Graph of y = f(x).');...
grid;...
axis;...
hold off;...
shg; pause % Press any key to continue.

clc;
% Place the starting endpoints for [a,b] in a and b

% Place the tolerance in delta

a = 0;
b = 2;
delta = 1e-6;

[p,yp,err,P] = bisect('f',a,b,delta);

pause % Press any key for the list of iterations.

clc; clg;
[m1 m2] = size(P);
n0 = min(7,m1);
Xc = (P(1:n0,1)+P(1:n0,2))'/2;
X0 = [a,Xc,b];
Z0 = zeros(1,n0+2);
axis([a b c d]);...
plot(X,Y,'-g',X0,Z0,'or');...
hold on;...
plot([a b],[0 0],'b',[0 0],[c d],'b');...
xlabel('x');...
ylabel('y');...
title('Graphical analysis for the bisection method.');...
grid;...
axis;
hold off;...
shg; pause % Press any key to continue.

Mx1 = 'Iterations for the bisection method.';
Mx2 = ' a b';
Mx3 = 'The approximate root is:';
Mx4 = 'The error estimate for p is ± ';
clc,echo off, diary output,...
disp(''),disp(Mx1),disp(''),disp(Mx2),disp(P),...
disp(''),disp(Mx3),disp(''),disp('p = '),disp(p),...
disp('f(p) = '),disp(yp),disp(''),...
disp([Mx4,num2str(err)]),diary off, echo on