% draws vector/direction field for system dx/dt = u(x,y)
%                                         dy/dt = v(x,y)
%
% you may change values only for:
%      xmin, xmax, dx,
%      ymin, ymax, dy,
%      v2d, scale
%
% you may also change definition of functions u and v


clear;
clf;

% parameters for problem definition
xmin =  0;  xmax =  3;  dx = 0.25;
ymin =  0;  ymax =  3;  dy = 0.25;
v2d = 1;
scale = 0.4;

xx = [xmin : dx : xmax];
yy = [ymin : dy : ymax];

axis([xmin xmax ymin ymax]);

nx = length(xx);
ny = length(yy);

for i = 1:nx                        
        for j = 1:ny
                x = xx(i);
                y = yy(j);

                % definition of functions u and v
                u(j,i) = cos(x * y);
                v(j,i) = sin(y^2);

                if v2d == 1
                        L = sqrt(u(j,i)^2 + v(j,i)^2);
                        u(j,i) = u(j,i) / L;
                        v(j,i) = v(j,i) / L;
                end
        end
end

quiver(xx, yy, u, v, scale);
xlabel('\it{x}');
ylabel('\it{y}');