Gradient vector field not perpendicular to contour map

Question

Cole Butler 2017-10-10

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/360524-gradient-vector-field-not-perpendicular-to-contour-map

评论： Cole Butler 2017-10-16

I have the following code:

function [  ] = kermack( I0,r,p,c,N,numSteps )
I(1)=I0;
S(1)=N-I0;
for t = 1:numSteps % construct I and S vectors
    I(t+1) = I(t) + (p*c*I(t)*S(t) - r*I(t));
    S(t+1) = S(t) - p*c*I(t)*S(t);
end
% create contour
x = min(I):0.2:max(I);
y = min(S):0.2:max(S);
[xx,yy] = meshgrid(x,y);
zz = xx + yy - (r/(p*c))*log(yy); % f(I,S)
[DX,DY] = gradient(zz);
figure % new window
contour(xx,yy,zz)
hold on % superimpose graphs
scale=10; % to make the arrows visible
quiver(xx,yy,DX,DY,scale) % vector field of f(I,S)
xlim([0 60]); % set bounds on the window
ylim([0,80]);
xlabel('I(t) (infected/infectious population)');
ylabel('S(t) (susceptible population)');
hold off

Now, as made clear by the title of my question, the generated gradient vector field doesn't seem to be perpendicular with the superimposed contour mapping. How can this be? What am I doing wrong?

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KSSV 2017-10-12

Give the input directly.....how did you run code and what you expect?

Cole Butler 2017-10-16

In response to the previous comments, I have attached an example of the code. This is the output of kermack() for p=0.05, c=0.2, r=0.2, numSteps = 50, N=100, I0=10. Clearly, the solid blue lines are the contour lines. When you zoom in, you can see that the gradient field is not perpendicular to the contour lines.

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Answer 1

David Goodmanson 2017-10-16

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/360524-gradient-vector-field-not-perpendicular-to-contour-map#answer_286044

Hi Cole,

I believe this is an artifact of the zoom process. If you zoom in by drawing a rectangle, the axes get scaled differently and right angles no longer appear to be right angles. If you add

axis equal

at the end of the code and then zoom in simply by repeated clicking on a point on a contour line (which does 2x on each axis), the results appear to be good.