% This m-file draws mapping diagrams. Before running it, you need to enter,
% at the MatLab prompt, a "string" s which gives the function you want to
% study. This is very simple. Suppose you want to study x*x - sin(x). At
% the >> prompt in the command window you type in:
%                    
%                         s = 'x*x - sin(x)'
% 
% (Don't forget the single quotes!); then you run the program mapdiag. The
% whole transaction looks like:
%
% >> s = 'x*x - sin(x)'
% s =
% x*x - sin(x)
% >> mapdiag
%
% Once you have entered the function s = 'x*x-sin(x)' say, each time you
% run mapdiag it will plot this function. To change functions, simply
% enter a new "function string" at the main command prompt >>; for example:
% >> s = '3*x^3 - 2*x^2 -sqrt(x) + 10' (note that powers are entered using
% the "^" sign (above the 6 on the top keyboard row).
%
% Mapdiag draws the "axes" as the vertical lines at x=0 (input
% axis) and x=1 (output axis), and draws mapping lines connecting x (on
% input axis) with f(x) (on the output axis).
% Mapdiag allows a larger view of these lines. This is set by prompts for
% the left and right boundaries of the viewing "window". If these are set
% to 0 and 1 respectively, you get just the region between the axes. If you
% set them to, say, -1 and 2 respectively, then you'll see more of the
% mapping lines to the left and right of the vertical input and output
% axes.
%
% Next, you enter the starting value (x) on the input axis and ending
% value. The lines start and end at these x values. The next prompt asks
% for N, the number of lines to be drawn. Mapdiag actually takes this many
% SUBDIVISIONS of (end x) - (start x), so draws N + 1 lines.
%
% Finally, when the plot is on the screen, you can zoom in or out by left or 
% right clicking, or dragging a region.


disp(['Plotting: ', s])
ff=inline(s,'x'); % This creates the function from the string
LeftWin = input('Enter window left: ');
RightWin= input('Enter window right: ');
FirstX = input('Enter starting x: ');
LastX  = input('Enter ending x: ');
NumLines = input('Enter number of lines: ');
hold on
for LL = FirstX:(LastX - FirstX)/NumLines:LastX % Actually draws NumLines + 1
   x = [LeftWin,RightWin]; % Begin and end x coordinates
   y=(feval(ff,LL) - LL)*x + LL; % Begin and end y coordinates
   plot(x,y,'b')
end
% xlim=get(gca,'XLim');
ylim=get(gca,'YLim');
x=[0,1;0,1];
y=[ylim(1),ylim(2)];
plot(x,y,'r')
%linePQ(0,ylim(1),0,ylim(2),'r')
%linePQ(1,ylim(1),1,ylim(2),'r')
title(['Mapping Diagram for \it',s])
zoom on