Successfully implement harmonic oscillator phase plot

I'm trying to implement this first order ODE:

This is the current code I have written:

%set up the requirements

xval = linspace(-5, 5, 20);

vval = linspace(-5, 5, 20);

[x, v] = meshgrid(xval, vval);

dotx = NaN(size(x));

dotv = NaN(size(v));

%phase map

for i = 1:numel(x)

dotx(i) = v(i);

dotv(i) = -x(i); %<--- not sure about this!

end

close all;

figure;

quiver(x, v, dotx, dotv, 'red');

axis equal manual;

xlabel('x(t)');

ylabel('v(t)');

title('Harmonic Oscillator');

However, I'm not sure if the phase map part is correct. Comments / suggestions?

Thanks