%----------------------------------------------
%     Example Commands for Lab 2
%----------------------------------------------

%---------------------------------------------------------
%Now Lets look at Scalar and Vector fields
%---------------------------------------------------------
clear;		%Its a good idea to always clear variables at the beginning
x=[1:0.2:5]; y=[1:0.2:5];	%two vectors defining positions to be used in meshgrid

[X,Y]=meshgrid(x,y);	%X is a 10 x 10 matrix of x coordinates.  Each
			%column is a different x-coordinate.
			%Y is a 10 x 10 matrix of y coordinates.  Each
			%row is a different y-coordinate
			
R=sqrt(X.^2 + Y.^2);	%R is a 10 x 10 matrix of distance from origin
			%This just illustrates that you can do arithmetic
			%on matrices just like vectors

Vx=ones(size(X));	%X component of vector set to an arbitray function
			% In this case it is a matrix of 1's of the same
			% size/shape as X 
Vy=0.2.*Y;		%Y component of vector increases with Y

figure(2);
clf;				%clear the figure
C=contourf(X,Y,Vy); hold on;	%Contour horizontal component of V
				%which is a scalar field
clabel(C);

alscale=1;			%arrow length scale
quiver(X,Y,Vx,Vy,alscale,'k'); hold on;	%plot vectors V=<Vx,Vy>
colormap hot
axis([1 4 1 4]);
axis('equal');
colorbar('horiz')